- Email: [email protected]
Electromagnetic methods in conductive terranes
Geoexploration, 12(1974)121-183 0 Elsevier Scientific Publishing
ELECTROMAGNETIC
Company,
Amsterdam
-
Printed
METHODS IN CONDUCTIVE
S.H. WARD’,
J. RYU’ , W.E. GLENN”,
’ department
of Geology
G.W. HOHMANN2,
and Geophysics,
University
for publication
November
TERRANES
A. DEY3
and B.D.
of Utah, Salt Lake city,
(U.S.A.) 2Kennecott Exploration Inc., Salt Lake City, Utah (U.S.A.) “Engineering Geoscience, University of California, Berkeley, (Accepted
in The Netherlands
SMITH’
Utah
Calif. (U.S.A.)
29, 1973)
ABSTRACT Ward, S.H., Ryu, Electromagnetic
J., Glenn, W.E., Hohmann, G.W., Dey, A. and Smith, B.D., 1974. methods in conductive terranes. Geoexploration, 12: 121-183.
Measurement of a natural or artificial electromagnetic field yields information on the distribution of electrical parameters in the earth’s subsurface. Frequencies in the range 100 Hz to 5,000 Hz and transmitter-receiver separations in the range 30 m to 1 km are most commonly used for electromagnetic probing of the earth’s shallow crust. Two fundamentally different objectives may be served by electromagnetic probing. The first objective is the search for local regions of exceptionally high electrical conductivity such as arise in metallic ore deposits or faults. To meet this objective, electromagnetic profiling is executed, i.e., one or more descriptors of the electromagnetic field are measured along a profile over the area of interest and local anomalies in the measured descriptor are sought. These anomalies are then interpreted in terms of a range of expected geologic occurrences, Mathematical and scaled physical models are used to produce catalogues of anomaly profiles with which we compare the field observations. The second objective is the detection and delineation of horizontal interfaces marking changes in electrical conductivity. To meet this objective, electromagnetic sounding is executed. Electromagnetic sounding is effected in two ways, parametric sounding and geometric sounding. In the former, frequency is varied with the transmitter-receiver separation held constant, while in the latter, separation is varied with frequency held constant. Mathematical models are most commonly used to produce catalogues of field component versus frequency or versus separation, with which we compare the field observations, The use of eatalogues of curves with which we may interpret field observations, the forward method, is limited by the huge volume of curves required for generalized interpretation, and by the subjective comparisons made by the interpreter. Recent advances in application of the generalized linear inverse method of interpretation to the electromagnetic method, indicate that the use of catalogues of model curves may soon not be required. The inverse method avoids human bias in matching field curves to model curves, it provides estimates of the reliability of the model or models selected to match the field data, and it permits the design of field surveys which optimize the information density of the observed data. Scaled physical and mathematical modeling has revealed that conductive ouerburden rotates the phase and decreases the amplitude of anomalies due to buried inhomogeneities for several electromagnetic systems. Modeling also has revealed that conductive host rock can lead to an increase in amplitude and a rotation of the phase of an anomaly. These
122
latter effects are dependent upon the dip and depth of the inhomogeneity, upon the conductivity of the host medium, and upon the particular electromagnetic system used. In general, present methods of interpretation of electromagnetic data are invalidated by conductive overburden or conductive host rock. Conductive in this sense extends from 1 mho/m to 10 ~3 mho/m and hence encompasses host rock and overburden conductivities encountered routinely throughout the world. The finite element numerical method has been used herein to calculate electromagnetic scattering from some simple two-dimensional earth models. By these models, the effects of surface topography, buried topography, overburden, and faults are investigated singly and collectively. The model calculations readily demonstrate that interpretation of electromagnetic profiling data can be accomplished more completely while simultaneously interpreting electromagnetic sounding data or vice versa. This observation leads to the conclusion that dual-mode broad-band continuous sounding-profiling is highly desirable if one is to deduce geologic structure from electromagnetic survey data. The deductions presented are drawn from plane wave analysis and they pertain to the AMT and AFMAG methods. They may readily be extended by inference to the VLF method. Numerous field techniques and system configurations are used in application of the electromagnetic method. Despite nearly 50 years of application of the electromagnetic method in mining exploration, no optimum technique has been developed for application to all environments, We believe that this results because all currently used techniques are too simple. Accordingly we have developed a more generalized system and are investigating its advantages and limitations. A description is given of a 14-frequency electromagnetic system with which sounding, profiling or continuous sounding-profiling may be achieved. The tilt of the major axis and the ratio of minor to major axis, of the ellipse of magnetic field polarization, are measured at 14 frequencies over the range 10 Hz to 86 kHz. The system is a generalization of the Beiler-Watson method used in Australia as early as 1928. The transmitting loop may be oriented in either the vertical or the horizontal plane and sufficient moment is available to permit measurements at distances of one or two kilometers from the transmitting loop. Preliminary field results illustrate the application of the method in sounding and continuous sounding-profiling. These preliminary results indicate that the frequency range 10 Hz to 10’ Hz and the transmitter-receiver separation range of 80 m to 1 km are required for generalized electromagnetic exploration. A greater sophistication in equipment, field techniques, and interpretation techniques is required if the electromagnetic method is to be successful in conductive terrsnes. The cost effectiveness of this degree of sophistication is yet to be established, although a still greater degree of sophistication may ultimately be required.
INTRODUCTION
The problems From the geometrical and/or frequency variation of one or more magnetic or electric field components, one usually attempts to estimate the depth, thickness, width, length, and the electrical conductivity of each subsurface scatterer when utilizing the electromagnetic method for sounding or profiling. Catalogues of reference curves are used to guide the forward method of interpretation, Practical application of the inverse method of interpretation now seems possible and hence it is expected to replace the forward method at some time in the future. For a generally inhomogeneous earth with topographic relief the interpretation problem is a difficult one and the only hope, in the general case, is to vary frequency and the location of a receiver relative
123
to a transmitter over wide ranges. Often the transmitter location is also varied and several field components are measured in order to reduce ambig~~ity in interpretation. In some simple cases where the earth cooperates, such as when the earth may be modeled by horizontal, homogeneous, isotropic layers, interpretation is relatively simple. In many instances, however, we suspect that we are deluding ourselves that the earth is simple. In this paper we explore the effects of surface and buried topography, conductivity and thickness of overburden, conductivity of host rock, and the presence of faults, and of the source type and mode of excitation on the electromagnetic profiling anomalies due to buried sulphide deposits which may be simulated by thin sheets or slabs. Next we explore the forward method of interpretation of electromagnetic sounding over horizontally layered terranes. With this basis, we then illustrate theoretical predictions for the advantages of dual-mode broad-band continuous sounding-profili~lg to electromagnetic exploration of a generally inhomogeneous earth. The latter results are applicable to field investigations of layered media in which inhomogeneities and surface topographic relief are unwanted contaminants (as in groundwater studies), and to inhomogeneous media in which overburden, host rock, and surface or buried topographic relief are present as unwanted contaminants (as in massive sulphide.ore search). The results are intended primarily to emphasize the ambiguities which may arise in typical real-world application of electromagnetic methods in those instances where dual-mode, broad-band, continuous sounding-profiling is not contemplated. However, we postulate that an optimum electromagnetic method for use in conductive terranes may well involve use of several frequencies in the lo---10’ I-Iz range and of transmitter-receiver separations in the 30-m to l-km range, Preliminary results with a system exhibiting these capabilities are encouraging although the costeffectiveness of this approach has yet to be established.
Pro filing
A loop of wire, erected in a vertical or horizontal plane at the earth’s surface and energized with alternating current, may serve as a transmitter in an active system of profiling for the purpose of detecting lateral conductivity inhomogeneities near the surface. The transmitting loop may be fixed in location and measurements made of alternating magnetic field components in its proximity. Alternatively both the transmitter and the receiver are moved in tandem. The magnetic field may be described by its orthogonal Cartesian components H,, Hy , and HZ or by its ellipse descriptors CYand E, the tilt angle and ellipticity, respectively. Fig.l‘illustrates these descriptors; the tilt angle is the ’ Note added in proof: E-llipticity as here used should be designated as “modulus of ellipticity”. For a complete discussion of ellipticity refer to: Smith, B.D. and Ward, S.H., 1974. Short note: On the computation of polarization ellipse parameters. Geophysics, in press.
124
EI
I+~
;Pe (Ht) * REAL tt
tH,)=
* /
[tWOSOL-HrSINal
I
HzSIN~+H,COSO.
PART
IMAGINARY
OF TdTAL
MAGNETIC
PART OF TOTAL
MAGNETIC
FIELD FIELD
Fig.1. Ellipse of magnetic field polarization; HZ and H,. are complex vertical and horizontal components of total field, respectively; @t- and & are phases of vertical and horizontal components of total field, respectively.
inclination from the horizontal of the major axis of the ellipse of magnetic field polarization while the ellipticity is the ratio of the minor to the major axes of the ellipse. Any of the above five quantities will vary systematically in the vicinity of a subsurface conductive inhomogeneity. Measurements of Q and E, as functions of the frequency of the current in the transmitting loop and as functions of the horizontal x and y coordinates are used to deduce the depth, depth extent, length, and other pertinent parameters of the subsurface inhomogeneity. The major and minor axes of the ellipse of magnetic field pol~ization may assume any orientation or ratio in the vicinity of an inhomogeneity. However, the projections of Q and E on the vertical plane passing through either a vertical or a horizontal transmitting loop are most commonly measured; the vertical plane of a vertical transmitting loop is oriented to contain the point of observation when profiling. In the vertical loop electromagnetic method (Ward, 1967b), the VLF method, the AFMAG method, and the Crone Shootback method, tilt angle is measured. With some VLF methods, a quantity related to 4lipticity is also measured. In the horizontal loop method (Ward, 196’713) of electromagnetic profiling the real and imaginary parts of the vertical magnetic field, Re(H,) and Im (H,), are measured. In the Turam method, the measured quantities are the ratio Re(&, )/Re(Hz2 ) of the real parts and the ratio Im (Hz, )/1m (N,, ) of the imaginary parts of the vertical magnetic field, observed at locations 1 and 2 at a distance of the order of 30 m apart. Alternatively the ratio of the amplitudes A, (H,, )/A2 (Hz2 ) and the phase difference #(Hz1 ) - @(Hzz) are measured.
125
Sounding A loop of wire laid out horizontally on the surface of the earth or a loop of wire erected in a vertical plane, energized with alternating current, may serve as a transmitter in an active system for sounding the thicknesses and conductivities of the layers of a horizontally layered earth. If the frequency of the source current is a variable, then parametric sounding is permissible while if the transmitter-receiver separation is a variable then geometric sounding is permissible. The total electric field, for a horizontal current loop, is confined to the horizontal everywhere and hence is represented totally by the tangential electric field component Ee . The quantity EO is complex, i.e., phase-shifted, when referred to the loop current. Both its amplitude and phase are functions of the angular frequency w , the transmitter-receiver separation r, and the conductivities and thicknesses of the layers. Obviously the electric field does not cross formation boundaries in a horizontally layered earth. For this reason a horizontal loop electromagnetic sounding method is sensitive to conductive horizons but relatively insensitive to resistive horizons; the induced currents will tend to be concentrated in the conductive horizons. The magnetic field from a horizontal loop is fully described by the two complex components H, and Hz whose amplitudes and phases are governed by the same earth parameters governing EO . Insofar as H,. and Hz are characteristically of different phase at any distance r, the magnetic field is elliptically polarized. The major axis of the ellipse of magnetic field polarization on the surface of a conductive earth, of,isotropic and homogeneous layers, tilts away from a horizontal loop transmitter but is confined to the vertical plane containing the center of the loop and the observation point. The total electric field is confined to a vertical plane parallel to the plane of a vertical loop situated over a horizontally layered earth. It consists of E, and E, components and hence it both crosses and parallels formation boundaries in the subsurface. For this reason, the vertical loop electromagnetic sounding method is sensitive to both resistive layers and conductive layers. The magnetic field components H,. and H, are measured at locations along the axis of a vertical transmitting loop for electromagnetic sounding. Alternatively, the tilt angle CKand the ellipticity E may be measured in that vertical plane which contains the axis of the loop. To obtain a satisfactory electromagnetic sounding, it is necessary to trace out the variation of Hz, H,., a, or E with induction number B = (apw )” r from a low asymptote to a high asymptote. (The quantity u is here the apparent conductivity of the geoelectric section.) In parametric sounding, the frequency w must be varied over four decades to achieve this. In geometric sounding the transmitter-receiver separation r must be varied over two decades to assure that both high and low response asymptotes are achieved. Descriptions of field techniques Grant and West (1965) and Ward (1967b)
describe the numerous
electro-
125
magnetic profiling techniques, Vanyan (1967) describes component sounding techniques, while Dey and Ward (1970) and Ryu, Morrison, and Ward (1970) describe tilt angle and ellipticity sounding techniques. Keller and Frischknecht (1966) provide a good overview of both sounding and profiling. Continuous sounding-profiling The conventional Turam method, utilizing a large horizontal rectangular transmitting loop, may be used for geometric sounding of a layered earth. If Turam is generalized, to allow for frequency variable over four decades, then it may be used for parametric sounding of a layered earth. If a generalized Turam system is utilized, in both parametric and geometric modes simultaneously, over a laterally inhomogeneous earth, then we might state that we were conducting continuous sounding-profiling. Similarly a generalized vertical loop system may be utilized for continuous sounding-profiling. The quantity HO could be measured in the plane of the loop, or the quantities H,, Hz, a, or E could be measured along the axis of the loop for this purpose. In a later section of this paper we explore the theoretical responses for dual-mode, broad-band, plane wave, continuous sounding-profiling over terranes which are two-dimensionally heterogeneous. We shall discover that the responses are critically dependent upon the orientation of the exciting magnetic field vector. Sounding complements profiling and vice versa, so that it is self-evident, a priori, that continuous-sounding profiling is idealistically better than either profiling or sounding, regardless of the objective of the electromagnetic survey. Justification for the time and expense involved in continuous sounding-profiling must be established, however, for each exploration problem. The theory of the forward problem The customary method of interpretation of electromagnetic sounding or profiling data involves us in matching observed data with predicted data obtained by mathematical or scaled physical modeling. Plots are made, for both observed and predicted data, of the real and imaginary parts of field components (or of tilt angle and ellipticity) versus induction number, frequency, or separation between transmitter and receiver. This curve-matching technique relies upon the forward solution of an electromagnetic boundary value problem. Extensive catalogues of curves pertaining to typical earth models are required for the forward solution. For example, the theoretical tilt angle and ellipticity profiles near a horizontal loop source situated upon a two-layered half-space are illustrated as smooth curves in Fig.2. Field observational data are shown as crosses and circles in the diagram. Agreement between experiment and theory, as judged by the experienced eye of the experimenter, is taken as satisfactory establishment of the validity of the model upon which the theoretical predictions are
127
0 2
3
4
3
6
7
9910
Fig.2. Observed tilt angle (0) and ellipticity two-layered earth. Horizontal transmitting distance of 900 ft from center.
(E) versus f ‘12r, and theoretical curves for a loop of 200 ft diameter with receiver at a
f4 r Fig.3. Observed tilt angle ((L) and magnitude of frequency f and distance r, near a vertical medium.
of e$lipticity (e) profiles observed as functions loop, over an assumed horizontally-layered
128
based. No attempt has been made, in the example presented, to compute the theoretical curves for a model which best fits the data, as judged by the eye. Rather, available model curves (Ryu et al., 1970) are used for comparison with observational data. However, a model earth described by the parameters u, = 0.04 mhos/m, uZ = 0.4 mhos/m, and d = 270 m would fit the observed data to a first approximation. Fig.3 contains tilt angle and ellipticity versus frequency for several distances from a vertical loop source situated over an ostensibly horizontally layered earth of two strata. A logical progression of the ellipticity and tilt angle versus f” r is observed for various values of r, the transmitter-receiver separation. In each of the above cases, one would normally seek the best fit of observed to theoretical data for a multiple-layered earth rather than a two-layered earth. When interpretation of profiling data is carried out, a similar comparison of theory and experiment is made (Ward, 1967b). The theory of the inverse problem A direct interpretation of electromagnetic sounding or profiling data may be achieved by using the method of generalized linear inversion developed by Backus and Gilbert (1967,1968 and 1970) and reviewed by Wiggins (1972) and Jackson (1972). The essence of the generalized linear inversion scheme is outlined below, and a numerical illustration with horizontal loop sounding data over a conductive region is given in section 3.4. The generalized linear inversion requires an expression to calculate a theoretical output Yj for a given input set, Xi, of rz earth model parameters, as written by:
where the operator Lj is a non-linear function for most geoelectromagnetic systems. Upon expanding eq.1 in a Taylor’s series and neglecting second and higher order terms, we linearize the non-linear function of eq.1 as: (Oj _ yj, =
5 j=l
aLj
axi
(Xj -Xl!),
j = 1,m
Xi=Xy
or: AY=AAX
(2)
where Oj is the jth measurement and X0 is an initially guessed point in the unknown parameter space. The inverse problem requires finding the model parameters, Xi, that minimize the data difference vector AY in a least squares sense. In general, the number of measurements, m, is not equal to the number of
129
model parameters, IZ. Using eigenvalue decomposition, system matrix A and its natural inverse H as (Lanczos,
one can write the 1961):
A=UAVT
(3)
and: H = VA-’ UT
(4)
The matrix U consists of p eigenvectors of length m and V consists of p eigenvectors of length n. The matrix A is a diagonal matrix consisting of p eigenvalues, and p is the rank of the matrix A. Then the solution to eq.2 is AX = HAY
(5)
As mentioned above, the functional relationship of eq.1 is non-linear, therefore several iterations are required to obtain the best estimates of the actual earth model parameters. The hat (-) in eq.5 indicates the new set of parameter corrections being sought after each iteration toward the global minimum of the data difference vector AY in the unknown parameter space. From eq.2 and 5, one can construct: AX = HAAX
= RAX
(6)
= SAY
(7)
and: A%
=
AHAY
where we have used the resolution matrix R = V VT. The deltaness of R is considered to be a measure of the resolution of the parameters while the deltaness of S shows information distribution among data points for resolving the model parameters. Table I shows three types of systems which may arise in practice. S is called the information-density matrix. An overdetermined case occurs for most geoelectromagnetic systems and the above analysis results in a mathematically unique solution, relative to an initial guess. From a practical viewpoint there will be noise in the data and linear dependencies between the parameters so that a geophysically unique TABLE
I
Underdetermined, System
critical, Rank
and overdetermined R
systems S
Remarks
Underdetermined
p
R=I
S=I
no unique solution
Critical
p=m=n
R=I
S=I
unique solution possible mathematically
Overdetermined
p
R=I
S=I
unique solution not possible mathematically
I is the identity
matrix
130
solution will probably never be identified. If p < n < m, the generalized inverse method yields a natural inverse of reduced rank, and the resolution matrix is no longer the identity matrix. In those unfortunate and infrequent instances where the system is underdetermined, no unique solution, mathematically or geophysically, can occur. In summary, the principle advantages of the generalized inverse method are: (1) It avoids human bias in judging a “best fit”. (2) It avoids the logistical problem of compiling and using an infinite number of type curves. (3) It provides estimates of the resolution, and hence reliability, of the theoretical model used to fit the observed data. (4) It estimates the information density contained in the observed data and hence it permits the design of an experiment to optimize the information density. The application of the method of the generalized linear inverse to electromagnetic sounding and/or profiling is new so that illustration of its methodology requires detailed study. Hence we refer the reader to the articles by Glenn et al. (1973), by Ward et al. (1973), and an additional article by Inman et al. (1973). Scaled model
experiments
Under the scaling transformation (o(lw)ms
:
= (cr‘ p’ ,‘)li2$.
a model subsurface conductivity, a’, transforms to a field scale subsurface conductivity, u, depending upon the size scaling factor, S/S’, and the frequency scaling factor, w/o’. In the above relation, S is a linear dimension, u is a conductivity, w is angular frequency, and p is magnetic permeability. The unprimed quantities refer to the full-scale system, while the primed quantities refer to the model system. Usually, as here, p and p”’are each set equal to the free space permeability. Scaled model experiments, until recently, provided the principle basis upon which interpretation of electromagnetic profiling data was based. A wide range of two-dimensional theoretical models serving as a basis for interpretation of profiling data has recently been presented by Swift (1971), Vozoff (1971), Parry and Ward (1971), Hohmann (1971) and others. Extension of these numerical theoretical solutions to three-dimensional objects is now in progress. However, the scaled physical model experiments by Sarma and Maru (1971) and by Verma (1972) provide a current understanding of the electromagnetic response of complex three-dimensional geologic models.
131
PROFILING
Horizontal
loop
Insulated and bare wires immersed in solution Sarma and Maru (1971) have provided some very meaningful results from scaled physical modeling of the horizontal loop method. Fig.4 contains profiles of in-phase (IP) and quadrature (OP) parts of the anomalous field measured on traverse over an insulated (Fig.4a) and a bare (Fig.4b) copper wire immersed in a salt solution of 11.0 mho/m conductivity. The insulated wire was in electrical contact with the solution at its ends. The model characteristics are portrayed in the insets to Fig.4. The insulated wire yields approximately 1% anomaly in quadrature; the bare wire yields a 9% quadrature PERCENT
-Ia\
&____n-*-
x
‘P
ANOMALY
1
+=p~-o--Q“___~_____~
PERCENT
ANOMALY t
P
s-._Q
-_
--_Q
Fig.4. Horizontal loop in-phase (IP) and quadrature (OP) anomalies (a) Due to a long thin insulated wire in electrical contact, at its ends, with a salt solution of 11 mho/m. (b) Due to a long thin bare wire in total electrical contact with a salt solution of 11 mho/m. (After Sarma and Maru, 1971.)
132
anomaly and a 6.5% in-phase anomaly. The size of the anomaly seems to be dependent upon the contact impedance between the wire and the salt solution. The wire gave no anomaly when suspended in air. Sarma and Maru (1971) interpret these results as a short-circuiting, by the wire, of the currents induced in the salt solution. We shall call this phenomenon electric flux collection, by analogy with magnetic flux collection by a magnetic wire or bar, in order to facilitate discussion. Bare thin sheet
Fig.5 portrays the Sarma and Maru (1971) horizontal loop in-phase and quadrature profiles over a bare aluminum sheet immersed in salt water and suspended in air. The salt water enhances the in-phase anomaly by a factor of 1.4 and increases the quadrature anomaly by a factor of 50. Electric flux collection has amplified the anomaly and rotated its phase. We can conclude from this simple example that a conductive host medium increases the detectability of a buried inhomogeneity; other factors may change this conclusion as we shall see subsequently. PERCENT
ANOMALY
Fig.5. Horizontal loop in-phase (IP) and quadrature aluminum plate immersed in salt solution.
(OP) anomalies
due to a thin
The model host medium of 10.1 mhos/m conductivity scales to a full scale host medium conductivity of about lo-* mhos/m. This latter conductivity characterizes many of the areas of the world in which exploration is carried out. Hence the flux collection phenomenon must be common. It will be even more pronounced in terranes of conductivity greater than 10e2 mhos/m. The effects
of overburden
and host rock
Lowrie and West (1965) demonstrated
that conductive
overburden
rotated
133
the phase and reduced the amplitude of an anomaly due to a buried conductor. Sarma and Maru (1971) have illustrated that conductive host rock rotated the phase and increased the amplitude of an anomaly due to a buried conductor. When conductive overburden and conductive host rock are both present, the result is not readily predicted. Clearly, present quantitative interpretation of horizontal loop data, depending upon the ratio of in-phase to quadrature anomalies, is readily invalidated in conductive terranes. This result is not new to experienced geophysicists, yet quantitative interpretation of field data commonly is pursued on the assumption that the overburden or host rock do not exist. A comparison of four airborne electromagnetic coil systems: Rotary Horizontal Coplanar, Vertical Coplanar, and Vertical Coaxial
Field,
Introduction In a recent, careful, use of scaled physical models, Verma (1972) illustrated the anomalies obtained with a simulated rotary field airborne electromagnetic system over a graphite slab immersed in dilute hydrochloric acid. Verma also modeled a vertical coaxial, a vertical coplanar, and a horizontal coplanar coil system of the same 280-m coil separation as the rotary field system. While these latter configurations, because of the large separation, do not simulate any current operating airborne electromagnetic system, a comparative study of results from them and from the simulated rotary field system is enlightening One should bear in mind that the rotary field system is comprised of a horizontal coplanar coil pair and a vertical coplanar coil pair and that the output of the horizontal coplanar pair dominates an anomaly obtained with the rotary field system. The model parameters used by Verma to obtain the results to be presented here, and their full scale equivalents, are listed in Table II. Comparison of systems Fig.6 illustrates the anomaly profiles over the graphite slab when in air and when immersed in dilute hydrochloric acid. The dip of the slab is vertical. The quadrature anomaly is very small, for all four systems, when the slab is in air, but the quadrature becomes substantial when the slab is immersed in acid. The multiplication of the quadrature is approximately 15 for the horizontal coplanar and the rotary field systems, while it is approximately 8 for the coaxial system and probably less than 4 for the vertical coplanar system. The in-phase anomaly is largest for the horizontal coplanar and rotary field systems and least for the vertical coplanar system when the slab is in air. The in-phase anomalies multiply by 3.5, 3.25, 2.6, and 1.6 for rotary field, horizontal coplanar, vertical coaxial, and vertical coplanar systems, respectively, when the host medium is added. The above observations lead to the conclusion that a host medium of uniform conductivity increases detectability of a buried conductor for all four systems, but that increased detectability is most pronounced for the
134
TABLE
II
Model parameters
used by Verma (1972) --.
-
Parameter
Model
Field scale
Frequency Coil separation System height Depth to top of slab Slab length Slab width Slab thickness Slab conductivity Acid conductivity
100 kHz 0.5 m 0.17 m 0.05 m 0.505 m 0.088 m 0.02 m 26.3 *lo3 mho/m 18 mholm
400 Hz 250 m 85 m 25 m 253 m 44 m 10 m 26.3 mho/m 1.8 *lo-* mho/m
X INPHASE
-
X OUAORATURE
ANOMALY
(bl
VERTICAL
($1 VERTICAL (d)
ROTARY
COAXIAL COPLANAR FIELD
COIL
COIL
SYSTEM
COIL
SYSTEM
SYSTEM
ANOMALY
-4 * COIL
SYSTEM
e
*
SO’
D
*
0.051~
F
-
O.l?m
Qn =
Fig.6. In-phase (IP) and quadrature (OP) anomalies, due to a vertical hydrochloric acid solution, for four different coil systems.
graphite
26.3
VARIABLE
X I0?nllhI
slab in
rotary field and horizontal coplanar systems and least pronounced for the vertical coplanar system. The distortion of the ratio of in-phase to quadrature brought about by the presence of the host medium follows the same order. Quantitative interpretation of slab parameters is degenerated most for the
135
rotary field and horizontal coplanar systems and degenerated least for the vertical coplanar system when the slab is immersed in a conductive host medium. This simple illustration serves to demonstrate that different systems are affected to different degrees by the presence of a conductive host medium. Criteria for dip
Fig.7 illustrates the anomaly profiles over the same slab, in air and in acid, but the dip has been changed to 45”. X
INPHASE
ANOMALY
X OUADRATURE
I”’
-24
COPLANAR
-*I(
Us = OUN AIR1
(al
HORIZONTAL
(b)
VERTICAL
(cl (d)
VERTICAL COPLANAR COIL SYSTEM ROTARY FIELD COIL SYSTEM
COAXIAL
ANOMALY -24
COIL SYSTEM
COIL SYSTEM
Fig.7. In-phase and quadrature anomalies, immersed in a hydrochloric acid solution,
a; = O(IN AIR1
COIL SYSTEM VARIABLE 8= 45’ D- O.OSm F. 0.17 m cr. * 263 a IO’mhc,,,,
due to a graphite for four different
slab dipping at 45” and coil systems.
136
The slab in air produces asymmetrical profiles for all four systems. These profiles become almost symmetrical and hence almost identical to the profiles over a vertically dipping slab immersed in a conductive host medium. This latter result confirms earlier findings by Gaur (1959, 1963), who simulated the Hunting quadrature airborne electromagnetic system, and concluded that a conductive host medium transforms the shape of an anomaly profile so as to make all buried slabs appear to be vertical. Turam modeling Introduction The main objective of the scaled physical modeling reported in this section is a qualitative study of the effects of conductive host rock on Turam anomalies observed over dipping veins of finite extent. This work therefore represents a logical extension of Bosschart’s (1964) excellent pioneering study of the Turam method. For a vein of finite length, the departure of the dip of the vein from vertical produces dramatic changes in the shapes, phases, and amplitudes of anomalies, as we shall subsequently demonstrate. To test whether or not these changes occur for veins of infinite length, theoretical numerical modeling was performed. A subsidiary objective of the scaled physical modeling is a study of the effect of conductive host rock on the Turam anomaly observed over a horizontal circular cylinder. Interpretation of Turam data typically is based upon two critical assumptions (1) The normal magnetic field over a homogeneous earth is the magnetic field due to the transmitting loop situated in free space (Bosschart, 1964). (2) The effect, on anomalies due to buried inhomogeneities, of conductive overburden or conductive host rock is negligible (Bosschart, 1964). Hohmann (1971) has examined the effect on Turam interpretation of an overburden of limited width, constant thin depth, and infinite strike length. Swift (1971) generalized this study by allowing the overburden depth to be variable and to occur over an inhomogeneity. Both Swift and Hohmann have examined the effect of conductive host rock on the Turam anomalies due to veins of infinite strike length. The studies of Swift and Hohmann were based on theoretical formulation and clearly demonstrated that neglect of conductive overburden or of conductive host rock cannot, in general, be tolerated in interpretation of data resulting from a Turam survey. The Turam anomaly due to a buried inhomogeneity was obscured by an overburden of irregular depth in Swift’s study, while the Turam anomaly due to an inhomogeneity was shifted in phase and decreased in amplitude on account of the conductive host rock, according to Hohmann. Both Swift and Hohmann demonstrated that a free space normal magnetic field is incorrect and that a normal magnetic field that includes the effect of the conductive earth is necessary. However, Turam amplitudes and phase differences due to a conductive homogeneous half-space are approximately constant with distance. Therefore, the use of
137
the free space normal field is not too bad inasmuch as one is looking for deviations from this constant value. Swift and Hohmann have clearly advanced our basic understanding of the Turam method over that developed by Bosschart (1964). Models of infinite strike length do not conform to real occurrences. Hence, in our scaled physical modeling, an aluminum sheet, immersed in a tank of NaCl solution, was used to simulate a “perfect” conductor of finite strike length buried in a conductive half-space. The results for a vein of finite length differ markedly from those of a vein of infinite length, as a comparison of our physical and theoretical modeling demonstrates. Model measurements of the real (r, inphase) and the imaginary (i, quadrature) values of both the horizontal and the vertical components of magnetic field were made over a sheet of finite length for which the dip was discretely varied and for which the strike was parallel to one side of the loop source. Mathematical modeling over a vein of the same depth extent as the aluminum sheet, infinite length, and of similar thickness was also made. A horizontal cylinder, of axis parallel to one side of the transmitting loop, was also immersed in solution to facilitate study of a short body of revolution.
Description
of physical
models
Characteristics of inhomogeneities and host media. The scaled physical models used in these studies are summarized in Table III. The aluminum sheet, used to simulate a thin vein, and the hollow brass cylinder, used to simulate a manto, were each immersed in a tank of water in which three different salinities (1.74 * 10m2, 5.2, and 10.6 mhos/m) were used. The water simulated conductive host rock. We selected the aluminum sheet and the brass cylinder to represent “perfect” conductors at the 15 kHz frequency employed in these studies. In free space, the inhomogeneities produced no measurable quadrature magnetic field. When immersed in conducting solution, these conductors produced large quadrature magnetic fields, proof of which was one of the expectations of the study. We have not placed a horizontal linear scale on the anomaly curves because the carriage speed was only approximately constant, with the result that the precise conversion from model horizontal distance to full-scale horizontal distance may vary slightly from profile to profile. In Fig.9, 10, 11, 12, 15, 16, 17, 19, 20, 21, and 23, the left-hand ordinate corresponds to the location of the word START on Fig.8. The dot on each of the former set of figures corresponds to the vertical projection of the top of the sheet shown in Fig.8 or to the vertical projection of the axis of the cylinder. The aluminum or brass full-scale resistivities shown in Table III are lower than most massive sulphides in situ (Bosschart, 1961). The full-scale resistivities of the host media, listed in Table III, are well within the range of those normally encountered, provided the tapwater is excluded.
--
------.
N
D
;,
7
h
6
a
d
Symbol
~..~___ 4.69 *lo-* 1.004~10-’ 1.325~10~ 2.10 *lo3 8.09 .105 1.88*10-3 4.01 *1o-3 5.28+103 1.08+104 3.24m106
1,000
_._~.
_.._
9
4.5*1o-2 2.5*10-* 2.5.10-2 0.21 1.03 4.0*10-” 0.10 15 kHz 6.0 0.67
400 366 114 0.406
2.0 1.83 0.57 2.03*10-3
1,200 134 -.
5 5 42 206 0.80 20 --
200
line source to center of anomaly aluminum sheet, length aluminum sheet, depth extent aluminum sheet, thickness height of measurement above water surface depth below water surface to top of vertical aluminum sheet receiving coil, dia. brass cylinder, dia. brass cylinder, length brass cylinder, wall thickness integration distance model frequency vinyl pool, dia. solution, depth
1.88*10-4 4.01 *lo+ 5.28.10* 1.08.10’ 3.24*105
200
.
3,000 335 _____._.
12.5 12.5 105 515 2.0 50 -
22.5
1,000 916 285 1.02
500
6,000 670
25 25 ‘210 1,030 4.0 100 -
45
2,000 1,830 570 2.03
1,000
1.172.10-3 2.51 *lo-’ 3.31 *lo3 6.76 *lo’ 2.01 *IOh
500
scale factor for f = 880 Hz
Full scale dimensions, m (p, am)
o’t’ aluminum sheet = 6.09*104 mhos
7.49 ‘lo+ 1.605.10-4 2.13 -10’ 4.33 *loa 1.292.10“
200 500 .._.~~~.____ _..._
Full-scale resistivities p (nm) --scale factor for f = 220 Hz
Model dimensions (m)
3.0*107 l.4*107 10.6 5.2 I.74.1o-2
-~
Model conductivity u’ (mhos/m)
Parameter description
Aluminum sheet Brass hollow cyl. NaCl solution NaCl solution Tapwater
--
Model material
Model parameters for Turam scaled physical modeling reported here
TABLE III
4.69 *lo--’ 1.004 *lo-” 1.325.10’ 2.70 *lo4 8.09 *lo”
1,000 --.-.._
139
DIP Fig.8.
Geometry
150°
130a
of dipping
IlOo
aluminum
SO’
70’
50”
30’
sheets.
When aluminum or brass is placed in a solution, the chemical reaction between the two media produces a surface layer on the metal whose electrical impedance is unknown. Very likely this impedance is not a scaled representative of the surface impedance of a sulphide body immersed in the watersaturated host rock. This feature may then render scaled physical models of uncertain value for quantitative study of electromagnetic methods. Because the surface impedance is expected to be dominated by capacitive coupling across the double layer of charge at the surface (Marshall and Madden, 1959), the higher the frequency the less important is the surface impedance. At 15 kHz we doubt that surface impedance is important, although we have no conclusive means for proving this point. In any event, it is not important for demonstration of the principles learned from this study. Orientations of inhomogeneities Aluminum sheet: Fig.8 illustrates the nomenclature used for a dipping sheet, chosen to correspond to that selected by Bosschart (1964). The receiver traverse starts at a position 2.87 m from, and ends approximately 1.0 m from, the line source. The axis of the aluminum sheet was maintained parallel to the line source. The depth to the top of the aluminum sheet beneath the water surface was 2.5 - lo-’ m for the vertical sheet. The choice existed to orient the sheet around the top edge or around its central axis. The latter scheme was selected primarily for convenience in handling the sheet. Therefore, the depth to the top of the sheet varied considerably as did the distance from the line source to the top edge of the sheet. Brass horizontal cylinder: The horizontal axis of the brass cylinder was situated 2.0 m laterally from, 0.23 m below, and parallel to, the line source. As a cylinder is a body of revolution, dip is not a variable. The cylinder length was approximately half that of the aluminum sheet. Clearly evident in the
140
results of experiments using this model is the effect of a conductive finite length, of a geometry in which dip is of no significance. Results from physical
body of
modeling
Dipping aluminum sheet in tapwater. The first experiment designed to elucidate the nature of the response of an inhomogeneity of finite length in a conductive medium involved the aluminum sheet in tapwater. Fig.9-12 portray the real and imaginary parts of the vertical and horizontal magnetic field components. The following observations are made:
-ANOMALOUS CURVE --NORMAL CURYE *
SENSlTlVlTY
REOUCEO 81 5
-ASSUMED F’VAE BRANCH
Fig.9.
H,,
versus
distance
x for seven values
of dip of aluminum
-ANOMALOUS
Fig.10.
H,i
versus
distance
E
CURVE
sheet
in tapwater.
CURVE
x for seven values of dip of aluminum
sheet
in tapwater.
141
.
YERTlCAL OF TOP
-ANOMALOUS
OF
PROJECTION SHEET CURVE
Fig.12. Hzi versus distance x for seven values of dip of aluminum sheet in tapwater.
(1) The H,, anomaly of Fig.9 appears to be a superposition of two anomaly components, one of which is small, positive (labeled E branch in Fig.9) and dominated by relatively long spatial wavelengths, and the other of which (labeled H branch in Fig.9) is dominated by relatively short spatial wavelengths. The latter anomaly component is positive at dips of 110” or greater and negative at dips of 110” or less. Destinction between these two anomalies is not clear for dips greater than 70”. (2) The sign of the horizontal real magnetic field (H,,) reverses at a dip between 90” and llO”(Fig.9). The HX, anomaly amplitude ranges from 62% (dip = 150”) of primary field at x ? 2.0 m to -53% (dip = 30”) of primary field at x = 2.0 m. (3) The horizontal imaginary magnetic field (HXi) anomaly amplitude is very small, never exceeding 5.5% of the primary field at x = 2.0 m (Fig.10).
142
It increases in amplitude monotonically from the value of zero at a dip of 150” to a peak value of 5.5% at a dip of 30”. (4) The real part of the vertical magnetic field (Hi.,) anomaly inverts at some angle between 90” and 110” (Fig.11). The peak-to-peak amplitude, relative to background, ranges from +73% of primary field at a dip of 150” to -62% at a dip of 30”. The smallest extreme peak-to-peak anomaly occurs when the top of the sheet is nearest the line source. Distance of the top of the sheet to the line source may be more important than dip in explaining this asymmetry. (5) The quadrature part of the vertical magnetic field anomaly varies systematically from a value of zero at a dip of 150”, through 6% at a dip of 50”, to a value of 5.5% at a dip of 30” (Fig.12). (6) Fig.13 contains a summary of the peak amplitudes of HZ,. and H,i and the ratio Q of H,, to H,i plotted according to the legend of Bosschart (1964). -Where Bosschart found that Q was independent of dip, we find that Q is a function of dip even for a “perfect” conductor. The “angle of extinction” predicted by Fig.11 of Bosschart (1964) is 100” + l”, whereas we observe an extinction angle of 102”. The effect on Q of distance from the line source and of depth to the top of the sheet has not been determined. cq = 1.74
Fig.13.
X 10-2tnhor/m
Hzr, Hzi, and Q = H,,/Hzi
r
versus dip for aluminum
sheet
in tapwater.
(7) One may make a similar plot for the horizontal components as in Fig.14, where an extinction angle of 97” is now found. Once again, Q is a marked function of dip. The extraordinary agreement of our results with those of Bosschart, in terms of extinction angle, is taken as validating both sets of results. The peak amplitudes of the anomalies recorded herein are generally consistent with those found by Bosschart, even though the time constant of our circuitry integrated fields over a significant lateral distance and hence tended to smooth the curves. The conductivity contrast (1.72 * 109) between the model and the host medium is much larger than that observed in practice but much less than that employed when models are suspended in air.
143
60-
CT, = 1.74 x IO-*
mhoc
0,
mhor/
m 3.0
x IO’
/m m
40 s E
-5
20 -
-6O-
Fig.14.
Hx,r, H,i and Q = Hx,/Hxi
versus
dip for aluminum
sheet
in tapwater.
Dipping aluminum sheet in NaCl solution of conductivity, 5.2 mhos/m. If the model host medium conductivity is increased to 5.2 mhos/m the following are observed: of two (1) Again the HX ,. anomaly of Fig.15 appears to be a superposition anomalies, one of which is positive (E branch) and dominated by long spatial wavelengths, and the other of which (H branch) is positive at dips greater than 90”, negative at dips less than 90”, and is dominated by short spatial wavelengths. The E branch anomaly is much larger for a conductivity of 5.2 mhos/m than for one of 1.74 *lo-’ mhos/m. (2) In Fig.16 we have labeled an E branch and an H branch of H,,. corresponding to these quantities identified in Fig.15. An extinction angle corresponding to zero of the H branch is thus defined, but a true extinction of anomaly does not occur. (3) The “extinction angle” changes from 97” to 85” when the host conductivity is changed from 1.74 * lo-* to 5.2 mhos/m, although this angle becomes difficult to define insofar as it involves only the H branch for a conductivity of 5.2 mhos/m (compare Fig.14 and 16). (4) The positive peak H, ,. anomaly changes from +62% to +63%, while the negative peak H,, anomaly changes from -53% to -44% as the conductivity changes from 1.74 * lo-* to 5.2 mhos/m. (Compare Fig.9 and 15.) The effect of integration time could easily account for these differences. (5) The negative trough in the H,, anomaly at a dip of 150” is reduced by nearly a factor of 2 when the host conductivity changes from 1.74 * 10m2 to 5.2 mhos/m (compare Fig.9 and 15). (6) The positive peak in the H,, anomaly at a dip of 30” is increased by a factor of 3 as the host conductivity is increased from 1.74 * lo-* to 5.2 mhos/m (compare Fig.9 and 15).
HxR f
iiN
PHASE
)
= I5 ithr
Q, = 5.2mhoslm .Y~ = 3.0
X lO?mhos
Im
p = 2.0m h = 4.5
x IO-‘rn
d = 2.5
X IO-‘m
I
= 183m
b = 0.57m l
VERTICAL PROJECTION OF TOP OF SHEET
-ANOMALOUS --NORMAL ....
CURVE CURVE
ASSUMED BRANCH
PURE CURVE
E
Fig.15. tf,,. versus distance x for seven values of dip of aluminum sheet in NaCl solution ofn, = 5.2 mhos/m.
60-
rr, = 5.2 mhos/m trz
= 3.0
)I IO’
mhor
40-
/m - IO
4 w -5
-BO-
Fig.16. Hxr, Hxi, and Q a (I, = 5.2 mhos/m.
Hxr/H_xi versus dip for aluminum sheet in NaCl solution of
145
(7) The quadrature part of the horizontal changes shape as the dip is varied.
magnetic
v
Ii x,
70”
f
//
distance
( QUADRATURE
)
= 15 khr
q
=
cz
= 3.0
5.2
mhos
/m
x lO’mhos/m
p = 2.0m h = 4.5
x 10-2m
d = 2.5
X IO-*
I
=
m
1.83m
b = 0.57m
-27x
Fig.17. Hxi versus O, = 5.2 mhos/m.
field, shown in Fig.17,
.
VERTICAL OF TOP
-ANOMALOUS --NORMAL
x for seven values
of dip of aluminum
sheet
OF
PROJECTION SHEET CURVE
CURVE
in NaCl solution
of
(8) The change in amplitude of H,i is small as dip is changed from 30” to 150” (see Fig.17). (9) Q varies with dip but is, in general, small (see Fig.16). (10) HX i changes sign and increases substantially in amplitude as the conductivity of the host medium was raised from 1.74 * lo-* to 5.2 mhos/m (compare Fig.10 and 17). (11) The H,, component appears to reach true extinction at 90” (see Fig.18). Dipping aluminum sheet in NaCl solution of conductivity, 10.6 mhoslm. Exaggeration of all effects noted for the aluminum sheet in a host medium of conductivity 5.2 mhos/m is evident in Fig.19-21 pertaining to a host medium conductivity of 10.6 mhos/m. The following relative features are noted: (1) The relative contributions of the anomaly components, of short and long spatial wavelength, change as host medium conductivity is changed (compare Fig.15 and 19). (2) The H branch “extinction angle” for H,, is changed from 85” for a host of 5.2 mhos/m (Fig.16) to 71” for a host of 10.6 mhos/m (Fig.22), but a strong HXT anomaly exists for any angle when the host medium is of conductivity 10.6 mhos/m.
146
H,,
(IN
f
PHASE)
= 15 khz
Q,
= 5.2
mhosf
cr2 = 3.0
m
X lO?mhas
Im
p = 2.0m h = 4.5
X 10v2m
d = 2.5
x 16’m
I =
1.83m
b
= 0.57m
*
VERTICAL OF TOP
PROJECTION OF SHEET
-ANOMALOUS
CURVE
--NORMAL
Fig.18. LY+~versus distance of (J, = 5.2 mhos/m.
x for seven values of dip of aluminum
76%
CURVE
sheet in NaCl solution
68%
150"
1
l1O0
1
130”
40%
90"
& i-
~
--
_
~
,
-_
/
--.
Ii,,
1
50”
30” 21%
(IN
PHASE)
.
f
= 15khz
ot
= to.6
mhosfm
me = 3.0
X 107mhor/m
p = 2.0m
- - _
‘._
.-
h = 4.5
X ld2m
d = 2.5
x IO-“m
I
= 1.83m
b
= 0.57111
l
~
Fig.19. H,, versus distance o, = 10.6 mhos/m.
-26%
for seven values of dip of aluminum
-
VERTICAL PROJECTION OF TOP OF SHEET ANOMALOUS
CURVE
--NORMAL
CURVE
...- ASSUMED BRANCH
PURE CURVE
E
sheet in NaCl solution
of
/ -Id 147
go*
-37%
H,, ( OUADRATURE 1 f = 15 khz QI = 10.6mhos /m q = 3.0 x IO’mhor /m p h d I
= = = =
2.0m 4.5 X id* m 2.5 X Idem 1.83m
b = 0.57m . VERTICAL PROJECTION OF TOP OF SHEET -ANOMALOUS CURVE --NORMAL CURVE
Fig.20. H,i versus o1 = 10.6 mhos/m.
distance
x for seven values of dip of aluminum
I
sheet
in NaCl solution
H,, .( IN PHASE 1 f = I5 khz * 10.6 mhos /m = 3.0 I IO’mhos /m
d I b .
= 2.5 X IO-*m = I.63m = 0.57m VERTICAL PROJECTION OF TOP OF SHEET -ANOMALOUS CURVE --NORMAL CURVE
Fig.21. Hz, versus distance of o1 = 10.6 mhos/m.
x for seven values of dip of aluminum
sheet
in NaCl solution
of
-60L
I
Fig.22. H,,, H,i, and Q = Hx,./H,i versus dip for aluminum 0, = 10.6 mhos/m.
sheet in NaCl solution
of
(3) The amplitude of the positive peak of HX, at all dips is increased for a host of 10.6 mhos/m relative to that observed for a host of 5.2 mhos/m. The accompanying negative peak is reduced as the conductivity of the host increases from 5.2 to 10.6 mhos/m (compare Fig.15 and 19). (4) Both the H,i, and its change of amplitude with dip, increase as the host conductivity changes from 5.2 to 10.6 mhos/m (compare Fig.17 and 20). The Q, meanwhile, becomes slightly more negative and it is a slightly more pronounced function of dip. (Compare Fig.16 and 22.) (5) The amplitude of the peak-to-peak Hz, anomaly is increased for all dips, as the host conductivity is raised from 1.74 - lo-* to 5.2 mhos/m to 10.6 mhos/m. (Compare Fig.11, 18 and 21.) An illustration of the orientation of the ellipse of pol~ization at the surface of the host medium, relative to the dip of the aluminum sheet at which H branch extinction occurs, is contained in Fig.23. No quantitative relationship between ellipse parameters and H branch extinction angle is evident, but qualitatively the “extinction” angle rotates counter-clockwise when the major axis of the ellipse rotates clockwise. Horizontal
cylinder. Fig.24 portrays the anomalies in H,,., Hxi, Hz,., and H,i for three values of host conductivity. From this single figure we observe that: (1) The negative peak of H,, decreases as conductivity increases. (2) The anomaly in HXi first changes sign, then increases as host conductivity increases. increases, while the (3) The positive peak of Hz, increases as conductivity negative peak remains virtually unchanged.
149
-
SOURCE
MEASURING
SURFACE
Fig.23. Theoretical polarization ellipses, at a height earth, in relation to dipping aluminum sheet.
of 4.5~10.* m above a two-layered
BACKGROUND CONDUCTIVITY mhos /m
0.0174
i-- L!!! LIIT!Li / _ q -_ I, c/ii J’
ILL..,..,,..
Hxn UN
PHASE1
Fig.24. H,,, a horizontal
Hxi, Hz,,
cylinder.
and Hz; versus distance
I HORIZONTAL BRASS CYLlNDER AXIS PARALLEL TO WRE A - t.03m 6 = o.etm
,-
,/’
,-!; I
/’
5.2
.
/
i’
I’
/I
IO 6
T - 4xto‘Jm Q, * A3 INDICATED 4 - 1.4llo’mho~/s
p = 2.Om h = 4.3 “IO% 6 * 4 5 x Id% f = ekhr l “2RTlCAt PROJECTiON OF AXIS OF CYLINDER - ANWALOUS CURYE --NORMAL CURVE
I/
/’
.
x, for three values of conductivity
o,, over
150
(4) The increases. (5) The increasing (6) The increasing
anomaly
in Hzi first changes sign, then increases as host conductivity
normal or background host conductivity. normal or background host conductivity.
gradient
in H,i and H,i both increase with
gradient
in H,,
and Hz, both decrease
with
interpretation of results A line source situated on or over a conductive half-space, when energized with alternating current, will induce eddy currents in the half-space. If, then, an inhomogeneity of much greater conductivity than the half-space is immersed in the half-space, eddy current induction in the inhomogeneity may be conceived as originating in two mechanisms. First, for half-space of very low conductivity, currents in the half-space may be neglected and eddy currents are induced in the highly conducting inhomogeneity by magnetic field induction in the inhomogeneity. Second, for an inhomogeneity of finite length situated in a fairly conductive half-space, one may view the inhomogeneity as an electric flux collector, i.e., the currents are locally diverted from the half-space and concentrated in the more conductive inhomogeneity. Current density is increased in the inhomogeneity and decreased adjacent to it. For an inhomogeneity of infinite strike length, parallel to the inducing electric field, this flux collection mechanism does not seem to be operative as subsequent discussion will illustrate. In this framework, the dominant part of the “E branch anomaly”, if such can be considered to exist separately, would seem to arise in electric flux collection and to be represented, therefore, by a -line of poles. The “H branch anomaly”, again in this debatable framework, would seem to arise in magnetic induction and to be represented, therefore, by a line of dipoles. An alternate explanation for the phenomenon of anomaly enhancement, for bodies of finite length, is that the surfa%e electromagnetic fields arise in a suEerpositizn of induced electric sources JE and induced magnetic sources JM, the JE contribution being negligible when the host medium is free space. Results from computer modeling The integral equation formulation for electromagnetic scattering, as established by Hohmann (1971) for the Turam method, has been used to calculate the real and imaginary parts of the vertical and horizontal magnetic field components near a thin slab of infinite strike length located near an infinite line source of current. Fig.25 displays the Re (H,) anomaly profiles so calculated. The model parameters are listed in Table IV. These parameters are very close to those used in the scaled physical modeling of the Turam system. The slab thickness was, by computational limi~tions, selected as 0.04 m rather than the 0.002 m used for the physical models. This extra thickness is not expected to change the basic conclusions since the results found here are consistent with those found by Hohmann (1971) for a slab of quite different cross-section.
151
Fig.25. Turam anomaly 45”, when host medium
TABLE
profiles of Re(H,) is of (a) 1.74.10.’
observed over an aluminum sheet dipping at mhoslm and (b) 1.06-10’ mhos/m.
IV
Model parameters
for Turam mathematical
modeling Thick dike
Thin dike Parameters
model
full scale (scaling factor 200)
model
full-scale
Conductor length Conductor thickness Conductor depth eitent Depth to top of conductor Height of observation Frequency Conductivity of half-space
infinite 0.04 m 0.56 m 0.025 m 0.045 m 1.5.10’ Hz as quoted
infinite 8m 112 m 5m 9m -
infinite -
infinite 15 m 150 m _25, 50,100,150 0 500 Hz 2*10-’ mhos/m
-
m
152
The real in-phase anomaly is decreased substantially, regardless of dip, as a result of raising the host rock conductivity from 1.74 - lo-’ to 10.6 mhos/m in the model system. This effect clearly must be due to attenuation of the downgoing primary wave and of the upgoing secondary wave. Electric flux collection, as we have phrased it, does not seem to be present, when all media are of infinite strike length. In other words, current lines for a two-dimensional model are everywhere parallel to the infinite direction for a line source parallel to that direction such that current diversion is not present. We are now faced with an observation that a conductive host medium increases the anomaly for a thin slab or sheet of finite length while it seems to decrease the anomaly for a thin slab or sheet of infinite length. A study of the effect of length of a conductor buried in a conductive host medium clearly is in order, but so far has not been reported for any method. The importance of the impedance between buried conductor and host medium, noted earlier, is of fundamental importance to this issue. Fig.26 indicates that the imaginary part of H, increases as the conductivity of the host medium increases; hence a phase rotation arises due to the high conductivity of the host medium.
x
= 8
____----
0
- 1.0 ,LlNE
- 2.0
I I.0
SOURCE
I
I I5
I
I 20
I
I 2.5
I
I 3.0
I
I 3.5
I
I 4.0
I
I 45
I
I 5.0
METERS
Fig.26. Turam anomaly 45”, when host medium
profiles of Zm(H,) observed over an aluminum sheet dipping at is of conductivity (a) 1.74-10-2 mhos/m, and (b) 1.06*10’ mhos/m.
Fig.27 indicates that the anomaly of the real part of Hz decreases while the anomaly of the imaginary part of Hz increases with increasing conductivity of the host medium. Conclusions Clearly, conductive host rock can have a profound effect on Turam anomalies. It is evident that a conductive host medium can: (1) cause the ratio of real to imaginary magnetic field components due to
153
METERS r-7
Fig.27. Turam anomaly profiles of Re (Hz ) and Im (Hz ) observed over an aluminum sheet dipping at 45”, when host medium is of conductivity (a) 1.74*10~’ mhos/m, and (b) 1.06~ 10’ mhos/m.
an inhomogeneity to be a function of dip of inhomogeneity, conductivity of host medium, position in space relative to the inhomogeneity, plus strike of the inhomogeneity. (2) invalidate the quantitative interpretation of Turam data in terms of depth of burial and conductivity-thickness product. The range of host medium conductivities which produce the results noted is well within the range of conductivities encountered throughout the world. The dramatic difference of the effect of host medium conductivity upon the anomaly due to a slab of infinite as opposed to one of finite extent is indicated in the foregoing results. Thus we tentatively conclude that the use of models of infinite strike length can be misleading in this respect. Further study of this observation is required, however. Tilt angle and ellipticity
near a line source
Rather than measure the amplitude and phase of a magnetic field component, one might measure the tilt angle and ellipticity of the magnetic field in order to ‘locate subsurface conductors in the vicinity of a large loop or a line source. Such measurements using a large horizontal rectangular loop, operating
154
at a single frequency, have been made by Paterson et al. (1973), and multifrequency measurements will be made using the 14-frequency EM system described subsequently. Fig.28 and 29 show theoretical results for a two-dimensional conductor energized by a line source. The former figure is for a poor conductor (3 mhos), while the latter figure pertains to a good conductor (30 mhos). These curves were computed using the numerical modeling program described by Hohmann (1971). A frequency of 500 Hz and a background resistivity of 500 L?m were used for the calculations. Results are shown for the following depths of burial: 25, 50,100, and 150 m. The three important points to note in Fig.28 and 29 are: (1) The inflection point for the left side of the tilt angle anomaly occurs directly over the inhomogeneity. (2) The ellipticity curves for a good conductor are quite different from
too -
-80
L
Y
k
z
Z60 D
w
d z 4o 4 IJ
+
-
20
-
0.4
-
f
0
100
200
300
DISTANCE
400
(METERS)
500
-500
hz
600
Fig.28. Theoretical tilt angle (CX) and ellipticity (e) profiles a homogeneous half-space; conductivity contrast is 10”.
700
over a two-dimensional
slab in
155
04
= u
03
I= a.
702
HOMOGENEOUS
EARTH
ii 01
0
0
100
200
300
DISTANCE
Fig.29. Theoretical conductor buried
400
500
600
700
(METERS)
tilt angle (a) and ellipticity in a homogeneous half-space;
(E) profiles over a two-dimensional conductivity contrast is 10’.
slab
those for a poor conductor, thus providing a means of discrimination. (3) A large ellipticity anomaly occurs for a good conductor even at a depth of burial of 150 m. Tilt angle and ellipticity measurements would appear to be quite useful for detecting and evaluating subsurface inhomogeneities with this particular prospecting system. The dramatic change of ellipticity anomaly with change of host rock conductivity is clear evidence of the sensitivity of this magnetic field descriptor to changes in the geological model. The tilt angle is not nearly as sensitive a descriptor. SOUNDING
Vertical Loop data Fig.3 depicts the curves of tilt angle and ellipticity as functions of frequency of an observed electromagnetic field. One attempts to deduce,
via
156
forward or inverse methods, the conductivity and the thickness of each layer in an assumed horizontally stratified earth from such curves. Lateral variation in layer conductivity or thickness are ignored or treated lightly. As noted earlier, Fig.3a, b, c, d, and e depict the tilt angle and ellipticity versus frequency curves at distances of 300, 450, 900, 1,500, and 2,400 ft. from the center of a vertical loop of 30 ft. diameter. The curves illustrate (a) systematic translation along the frequency axis as the transmitter-receiver separation varies, and (b) broadening of the (Yand E curves as r increases. whether the transition in curve shape with Z-is due to horizontal layering or to vertical inhomogeneities is, of course, unknown at this stage. Quantitative study of these data is in progress. For each set of tilt angle and ellipticity curves of Fig.3, corresponding to a given transmitter-receiver separation, a layered model may be found, via forward or inverse methods, which will provide theoretical curves fitting the observational ones. The five models so obtained may then be “patched together”, as is standard practice in resistivity sounding, to obtain an approximate geoelectric section. Insofar as the parametric sounding curves of Fig.3 vary from site to site, rather than merely translate along the frequency axis, one might conclude that the earth is inhomogeneous laterally. Models of a laterally and vertically inhomogeneous earth are then required to fit all observational data. The combined parametric and geometric sounding was required to permit recognition of the heterogeneity of the true earth. Vertical Loop
uersus Horizontal
Loop
in sounding
As noted earlier, a horizontal loop will induce horizontal current flow in a horizontally layered earth. The conductivity of conductive horizontal layers may be deduced from the resulting data. A vertical loop will induce currents both within horizontal layers and across the layer boundaries. The resistivity-thickness product of a resistive layer, and the conductivity of a conductive layer presumably may be deduced from the resulting data. Systematic study of the relative virtues of vertical loop and horizontal loop electromagnetic systems in sounding, and comparison of them with resistivity sounding, are now in progress at the University of Utah. Madden (1971) provides useful guidelines for analysis of the problem. App~ica~i~~s of sounding
The data of Fig.2 and 3 were obtained while mapping water-bearing strata in Curlew Valley, Utah. The exploration problem under study was a hydrological one. Keller (1970) has reported on application of electromagnetic sounding to geothermal resource detection, while Frischknecht (1967) reported on application of the method to detection of the top of liquid lava at Kilauea Iki crater and on measurement of the electrical conductivity of the molten basalt. References to application of electromagnetic sounding to mining
157
problems are scarce. Hohmann et al. (1970) describe an attempt to measure the induced electrical polarization phenomenon inductively. However, systematic application of the electromagnetic sounding method to determine the depth and conductivity of overburden covering a lateral conductivity anomaly in the bedrock is seldom attempted, evidently. In view of the fact that conductive overburden shifts the phase, changes the amplitude, and changes the shape of anomalies due to buried conductors detected by electromagnetic profiling (Roy, 1970), and thereby markedly degrades quantitative interpretation of the profiling data, this seems unusual. On the other side of the coin, the resistiuity method is used occasionally to determine conductivity and thickness of overburden covering a buried electromagnetic profiling anomaly. To us it seems logical that the electromagnetic method should be used for sounding the depth and the conductivity of overburden in areas in which electromagnetic profiling is performed to search for buried inhomogeneities such as massive sulphide deposits. Inversion of Horizontal Loop sounding data To illustrate the features of the inverse method described during our discussion earlier of the theory of the inverse problem (p.128) we have chosen a particular two-layered earth model (conductive overburden case) shown in Fig.30. We have elected, arbitrarily, to use parametric, horizontal loop sounding. The transmitter-receiver separation is fixed at 200 m and eight transmitter frequencies are used: 21,42,84,168, 336,672, 1,344, and 2,688 Hz. The analysis is strictly theoretical in the sense that the “observed data” (Oj of equation (2)) are theoretically generated for the model in Fig.30.
Fig.30. Configuration coplanar loop system,
for parametric
sounding
of a two-layered
earth
with a horizontal
An initial parameter guess, Xi of p, = 10 Qm, p2 = 100 52m, and d = 20 m was made and the percent parameter change as a function of iteration is shown in Fig.31 for the vertical magnetic field component. Note that convergence to the correct parameter values has occurred after seven iterations. A similar result for the horizontal magnetic component, not shown, can be obtained only if the initial guess is within 10% for each parameter and the incremental change in parameter value after each iteration is severely controlled (Glenn et
158
0
2
1
4
6
6
10
ITERATIONS Fig.31.
Percent
parameter
change
versus iteration
of inversion.
al., 1972). The problem of resolution that arises here can be discerned readily from an examination of the theoretical model curves shown in Fig.32 and Fig.33. The theoretical curves for the vertical magnetic field component (Fig.32) have more individual character than do the curves for the horizontal magnetic field component (Fig.33) over the typical induction number range considered appropriate for geoexploration problems. To describe the problem one need only to look at curve 3 of Fig.32 and Fig.33 which corresponds to the model in Fig.30 (that is, d/r = 0.125). Curve 3 for the horizontal magnetic field component could be shifted either to the right or to the left and would become nearly coincident with curves 2 or 4 because of similarity in shape of curves 2, 3, and 4. This fact would preclude using the horizontal magnetic field component in a parametric sounding mode in conductive overburden regions. In contrast curve 3 for the vertical magnetic field component, parametric sounding (Fig.32), would not coincide with either curve 2 or curve 4 if shifted to the right or to the left because, now, all three curves are of similar shape. For geometric sounding the reverse argument is true. Lateral separation between curves, on the induction number axis, may be used in addition to curve shape in order to minimize ambiguity in either forward or inverse interpretation. Thus one need only alter the d/r ratio by varying r, measure the offset on the induction number axis, and determine the correct curve. Therefore, for direct curve-matching or inversion interpretations to be successful one should have a general knowledge of the character of the magnetic field variations over a variety of terranes before the experiment is performed. One way to approach this problem is through the inversion scheme (Glenn et al., 1973). The S matrix obtained by using the inversion scheme provides a means to assess the relative information contained in each observed data point in terms
d UT’
INDUCTION NUMBER (w+)‘4
Fig.32.
Fig.33
2
5
10
2
5
‘7’
INOUCTION NUMBER (+)4
Fig.32. Normalized /HZ1versus induction number B for parametric sounding over a twolayered earth with a horizontal loop system. The loop radius is 10 m; the ratio K’ of first layer to second layer conductivity is 0.1. Fig.33. Normalized lH,I versus induction number B for parametric sounding over a twolayered earth with a horizontal loop system. The loop radius is 10 m; the ratio K of first layer to second layer conductivity is 0.1
FREQUENCY thz)
Fig.34.
Information
density matrix resulting from inversion of data pertinent to Fig.30.
of its contribution to the resolution of the particular model under study. As an illustration, the S matrix for the model in Fig.30 is shown in Fig.34. For this model the resolution matrix R is the identity matrix and is not shown but the information density matrix is not an identity matrix since m = 8 and
160
p = it = 3 (see Table I). The structure of the S matrix should approach that of an identity matrix; that is, the optimum S matrix for uniform information distribution would have rows approaching delta functions which are centered on the diagonals (Glenn et al., 19’73). From Fig.34 we observe that little information is contributed to the resolution of the model for the two lowest frequencies. This result may be observed from the theoretical curves of Fig.32. For the model studied here these two low frequencies, 21 and 42 Hz, would correspond to induction numbers less than one, a region where there is little individual character difference between the model curves. The inherent power of the inversion method lies not only in its application to interpretation but also to experimental design as illustrated by the preceding discussion.
Introduction In the last few years, several methods have been developed for numerical evaluation of electromagnetic scattering from two-dimensional earth structures, i.e., earth structures which are infinitely extended in the horizontal y direction. A suitable set of references appears in Geophysics, 36(l). We have used one of these methods, the finite element method, to compute the scattering from the model earth structures used in this section. The long axis of a two-dimensional inhomogeneity is taken to be the y axis; the x axis is horizontal and normal to y while the z axis is vertical as in Fig.35. The electromagnetic wave equations are decoupled if two modes are assumed. The TE mode pertains to a wave in which the electric vector is in the y direction, i.e., parallel to the long axis of the inhomogeneity. The TM mode pertains
TE
mode g
TM mode
= jEy
i = 3Hy
Fig.35. Illustrations of TE and TM modes relative to two-dimensional
inhomogeneities.
161
to a wave in which the magnetic vector is parallel to the long axis of the inhomogeneity. The cross-section of a twodimensional inhomogeneity can be arbitrary. A horizontally layered structure is a trivial case. Conductive
dike model
Description
of model
Fig.36 portrays a vertical dike model of infinite depth and strike length in an otherwise homogeneous bedrock, overlain by soil overburden. The resistivities selected are typical of the Canadian Precambrian Shield, provided the dike model is used to simulate a fault zone. The depth of overburden is 30 m and the width of the fault zone is either 30 or 60 m. We shall study the effect of the fault zone on electromagnetic sounding-profiling with AMT and the effect of the overburden on lateral profiling with both AMT and AFMAG. A frequency of 1,000 Hz is chosen for the profiling while the range of frequencies l-l,000 Hz is chosen for the AMT sounding-profiling. 20-
a:
2
TE
15-
I.d
IO-
2.
Dg
5 I-
=30m d f
I
w i 7
mods
=60m = IOOOhz
5-
600
I 900
500
I 900
0 -5-
-930
- 600
-300
-6M)
-300
OISTANCE
0
300
-IO-15-20
t
-
0.1 -
? i
0.05 0 -900
p, *
DISTANCE
lo3n-nl
‘t
METER?,’
0
t\
GROUND
30m SCALE
Fig.36. AFMAG TE mode tilt angle and ellipticity of conductive fault with overburden.
profiles
across
two-dimensional
model
162
AFMAG profiling Fig.36 also contains plots of tilt angle and ellipticity versus horizontal distance normal to the fault zone for the TE mode, when the overburden is present. Fig.37 contains the same information when the overburden is absent but the top of the fault zone remains at, 30 m. The tilt angle is virtually unchanged in shape or amplitude, over a fault zone of 30 m thickness, when the selected overburden is added. On the other hand, the elliptic&y changes significantly from the overburden to the non-overburden case. The rise in TE
mods
f
:
d
= 30m
1000
hz
3
F
a
r: w
ao50 -900
-600
0
-300
OtSTANCE
300 (METERS)
600
/ 900
AIR GROUND
/j * I04&rn SCALE 0
METERS
300
Fig.37. AFMAG TE mode tilt angle and ellipticity of conductive fault without overburden.
profiles
across two-dimensional
model
ellipticity beyond 400 m from the axis of the fault zone in Fig.36, presumably arises in phase shift of the fields scattered from the fault zone; when the overburden is absent, this phase shift is not large. It is difficult to visualize any physical explanation for the increase in flank ellipticity with increase in thickness of the fault zone, but it may be due to coupling between the induced currents within the overburden and within the fault zone. We have not computed the tilt angle and ellipticity profiles beyond 1,200 m from the axis of the fault zone because of four factors: (1) The tilt angle and ellipticity are slowly varying functions of distance beyond 1,200 m and we anticipate decreases to zero beyond 1,800 m from the axis of the fault zone.
163
(2) The model boundaries are 1,800 m on either side of the axis of the fault zone and boundary effects are expected within a few hundred meters of the boundaries. (3) It is impractical, because of finite computer storage, to extend the model to a size that will ensure that the tilt angle and ellipticity go to zero as distance from the fault zone increases. (4) From a practical viewpoint, field profiles would seldom extend more than 1,200 m from the axis of an inhomogeneity. Customarily one attempts, in interpretation of electromagnetic survey data, to obtain the conductivity-thickness (ot) product, the dip, the length, the depth, and the depth extent of an inhomogeneity. Ward et al. (1968) describe an interpretation scheme for AFMAG, based on the use of two frequencies over disc models in fr.ee space. One could develop a similar interpretation scheme based on tilt angle and ellipticity at a single frequency rather than tilt angle at two frequencies. However, if realistic overburden, and bedrock resistivities are substituted for free space values, used in presently available interpretation schemes, the interpretation is materially altered. The central zero values of tilt angle and ellipticity are clear markers of the axis of the buried fault zone.
a;
6-
L %
4
3
% 2-
d * 30m
-
TE
----
TM f
d. -900
I - 800
1 300
I -300
d DISTANCE
W&w&N mode mode
‘1000hz 1 600
900
(METERS) 0
X
AIR 30J
/!
Fig.38. AMT of conductive
GROUND
* IO’P-In
apparent resistivity (pa) versus traverse distance across two-dimensional fault with and without overburden for TE and TM modes.
model
164
As is well known, TM mode excitation produces no tilt of the major axis of the ellipse of magnetic field polarization and the field is linearly polarized. AMT profiling
Fig.38 portrays the AMT apparent resistivity plotted versus horizontal distance for both TE and TM modes. An overburden of lo3 Qrn resistivity and 30 m thickness is present for one set of calculations and is absent for another. The fault width is selected both as 30 and 60 m for the submodels which include an overburden. The TE mode, for each model, produces the anomaly of largest amplitude and half-width. The TM mode anomaly extends only over a lateral distance of 300 m for each model and the apparent resistivity beyond 150 m on either side of the fault zone is that of an appropriate one- or two-layered half-space. In this instance, then, the TM mode is best for detection of vertical structures provided amplitude of anomaly, and not resolution, of adjacent structures, is taken as the main criterion for detectability. The 30 m overburden markedly attenuates the TM mode anomaly from the 30 m fault zone, but the TE mode fault zone anomaly is affected only slightly. Increasing the thickness of the fault zone from 30 m to 60 m increases the TE and TM mode anomalies appreciably. The apparent resistivity for a two-layered earth, without an inhomogeneity, is shown for comparison in Fig.38. AMT sounding-profiling
Fig.39a is a plot, in frequency-distance space, of contours of TE mode AMT apparent resistivity. A broad inhomogeneity is suggested by the contours which are not clear evidence for either a narrow vertical fault zone nor a horizontally layered structure. The induced currents flow parallel to the fault zone in the overburden and along the fault zone itself. Fig.39b is a plot, in frequency-distance space, of contours of TM mode AMT apparent resistivity. Both the vertical fault zone and the horizontal layering are clearly evident in the contoured data. The induced currents flow normal to the fault zone in the overburden and transversely through the fault zone itself. The TM mode produces the larger fault zone anomaly at 1 Hz, but the smaller fault anomaly at 100 Hz and above. Conclusions
Vozoff (1971) previously studied a similar model for the TE mode and drew the following conclusions: (1) The frequency at which peak response occurs is, to first order, independent of bedrock resistivity for bedrock as resistive as lo3 Rm. (2) The peak Hz/H, ratio (approximately equal to tilt angle) depends on overburden thickness, overburden resistivity, and bedrock resistivity.
165
DISTANCE
( METERS)
DISTANCE
3” /
_-600
-3 00
(METERS) 0
600
300
900
’ Onnn
(bl 0
TM
mode AIR
I
Fig.39. Contours in frequency-distance resistivities across a buried fault.
space
of TE and TM mode
AMT apparent
(3) The overburden attenuates the peak Hz/H, anomaly according to the induction number B = (0~ w ) ‘12d where d is the depth of overburden. To these conclusions we add the following: (1) The apparent resistivity may be decreased in the vicinity of a conductive fault zone for both modes, but the apparent resistivity contours, in frequencydistance space, are quite different for the two modes. (2) Both TE and TM mode AMT depth sounding in an inhomogeneous terrane would lead to errors in estimates of overburden depth and resistivity within several hundred meters of the fault zone, but the TM mode fault zone anomaly is least extended laterally. (3) Since a fault zone alters sounding interpretation and overburden alters profiling interpretation, then continuous sounding-profiling is required for maximum interpretability of either sounding or profiling data in areas where both layering and inhomogeneities are expected. (4) A wide range of frequencies, preferably covering several decades, is required for maximum interpretability of sounding-profiling data.
166
Effect
of surface topography
Description
of model
Parry and Ward (1971) used an integral equation formulation to compute the 1,000 Hz TE mode scattering from a ridge. Their calculations pertain to measurements well above the ridge. For AMT and ground AFMAG purposes, it is necessary to calculate the scattered field components on the surface topography. Fig.40 describes a ridge 90 m high superimposed upon a 30-m deep layer of overburden under which lies resistive bedrock. A gravel ridge and gravel overburden such as a glacial esker and a layer of glacial gravel might be represented by the dimensions and resistivities selected. The bedrock is highly resistive as might be expected in the Precambrian Shield of Canada.
TE
mode
f = IOOOhr
-900
-600
-300 DISTANCE
600 ‘t
SOM
AIR
Gf7CUND
IOU--l
Fig.40. profile
Two-dimensional across it.
AFMAG
900
METEf%”
model
of surface
topography
and AFMAG
TE mode
tilt angle
profiling
The 1,000 Hz AFMAG TE mode tilt angle and ellipticity profiles over the ridge are illustrated in Fig.40. The peak-to-peak tilt angle anomaly is 20”, a value consistent with the lesser vertical field peak-to-peak anomaly obtained by Parry and Ward (1971) at an elevation of 150 m above the ridge.
167
The TE mode ellipticity varies systematically across the ridge. It is zero at the axis of the ridge and reaches peak values of 0.14 at 300 m on either side of the ridge. The TE mode ellipticity anomaly is larger and the TE mode tilt angle anomaly is smaller, for the ridge represented, compared to the fault zone and overburden combined (compare Fig.40 with Fig.36).
AMT profiling The apparent resistivity deduced from AMT continuous sounding-profiling at 1,000 Hz is drawn above the sketch of the ridge in Fig.41. A small central resistivity low, flanked by slight high values, is evident in the TE mode data. The central low and flanking highs are much larger for the TM mode than for the TE mode.
AIR
P,=103n-ml &=
GROUND
104n-m SCALE 0
METERS
300
f.looohz Fig.41. Two-dimensional model apparent resistitities across it.
of surface
topography
and AMT TE mode
and TM mode
Buried topography Depression
in bedrock surface
Faults frequently offset the bedrock topographic surface to produce a local thickening of the overburden, but otherwise do not affect the geoelectric section. Fig.42 portrays the TE mode 1,000 Hz tilt angle and ellipticity profiles across such a feature. Note the peak-to-peak tilt angle anomaly of +7 to -8” and the peak ellipticity anomaly in excess of 0.07. Both anomalies
I5
TE
z
mode
f=iooohz
-900
Fig.42. it.
-600
-300 DISTANCE
Two”di~ensional
600
900
’ (MET&i0
model
of buried
topography
and AFMAG
tilt angle profile
across
might be erroneously interpreted to indicate a vertical conductor located about 175 m to the left of the fault (compare Fig.37 and 42 for example).
Depression
in bedrock
surface plus conductive
fault zone
causing the bedrock depression is conductive by virtue of increased porosity associated with shattered rock, the model of Fig.43 might pertain. In comparison with the responses over a fault zone buried beneath overburden as in Fig.36, we note that the depressed bedrock makes the following disturbances in TE mode, 1,000 Hz responses: (1) the peak tilt angle at the left of the fault zone is shifted about 200 m to the left, (2) the peak-to-peak tilt angle increases, comparable with that over a fault zone of 60 m width buried beneath a uniform layer of overburden and (3) the peak ellipticity at the left of the fault zone is decreased, but is increased slightly at the right of the fault. The tilt angle profile could readily be interpreted as arising in a fault zone alone, but the ellipticity profile warns that the geoelectric section is complex. Evidently, both tilt angle and ellipticity should be recorded in an AFMAG survey. If the
fault
169
TE
mode
qi 1
-900
-390
- 600
0 DISTANCE
300
Fig.43. Two-dimensional model of buried and ellipticity profiles across it.
Conductive topography
,
600
topography
fault zone with overburden,
Description
--do
(METERS)
with fault and AFMAG
surface topography
tilt angle
and buried
of model
Fig.44 illustrates a simplified version of a rather common geological crosssection. A fault zone of resistivity 10’ Rm separates two blocks of the same country rock, the left-hand block being rotated and downdropped at the fault. A general layer of overburden, thickening to a ridge at the fault, hides the subsurface structure. This model represents the superposition of the previous several models. Whether one was attempting to find the thickness of overburden via sounding or the location of the fault zone via profiling, all elements of the geologic section would need to be taken into account. Dual-mode broad-band continuous sounding-profiling becomes highly desirable in such situations. Let us draw this conclusion, however, by studying finite element computations over this complex structure. AFMAG
profiling
Fig.44 also contains
TE mode tilt angle and ellipticity
profiles over the
170
02 = a15
u
F 5
d
O’ 0.05 0
-900
-600
-300D16TANCE0
wrE3F%
Fig.&. Two-dimensional model ellipticity profiles across it.
600
900
of inhomogeneous
earth,
and AFMAG
tilt angle and
structure with the fault zone width 0, 30, and 60 m. With no fault zone present, d = 0, the tilt angle profile is dominated by the combination of surface and subsurface topography (compare Fig.40 and 42 with 44). The tilt angle anomaly increases and the el1ipticit.y anomaly decreases in magnitude as the thickness d or induction number B = (opw )li2d of the fault zone increases.
Fig.45 contains the TE and TM mode AMT apparent resistivity profiles across the same structure. The TE mode anomaly increases with thickness of the fault zone; but surface and subsurface topography contribute modestly to it. Compare duplicates of the curves of Fig.41 with the other curves of Fig.45. The TM mode anomaly increases only slightly with thickness of the fault zone, it is dominated by the effect of surface topo~aphy and made asymmetrical by the effect of buried topography. AMT sounding-~rofi~~rzg
Fig46a,
b are plots, in frequency-distance
space, of contours
of TE mode
171
‘+m
0-
TOP0
l-d 2-d
ONLY = =
/
Om 30m
GROUND
v
SCALE METERS
Fig.45. earth.
AMT apparent
resistivity
profiles
across
two-dimensional
model
of an inhomogeneous
and TM mode, respectively, AMT apparent resistivity computed for the geometrical model shown in Fig.46c. Note that the resistivities of the media of this model were selected to be ten times lower than those of Fig.45b. The model now would simulate a sulphide deposit buried beneath a clay overburden and a clay ridge. However, if the values of frequency shown in Fig.46a or Fig.46b were multiplied by 10, the resistivities of Fig.46 could be multiplied by 10 and the model would again simulate a fault zone beneath gravel. Frequencies as high or higher than lo4 Hz, are required to reveal the shallow structure of Fig.45b, whereas frequencies of lo3 Hz are adequate to reveal the shallow structure of Fig.46c. The TE mode apparent resistivity plot of Fig.46a still suggests a broad inhomogeneity as for the simpler model producing the results of Fig.39a. Comparing Fig.46a with Fig.39a we observe asymmetry in the contours of the former figure, which may indicate a structural complexity. There are, however, no diagnostic criteria permitting Fig.46a to be interpreted in terms of a vertical fault zone, a horizontally layered structure, surface topography nor buried topography, as separate entities. The TM mode apparent resistivity plot of Fig.46a clearly reveals the complexity of the structure. A narrow central zone of the apparent resistivities,
172
DISTANCE
IMETERS)
((1)
DISTANCE
103n-In
mode
IMETERS)
(b)
Pz =
TE
u-
Pa-lo’n-m
TM mode
SCALE OF=-=METERS
‘O”
Fig.46. Contours in frequency-distance space of TE and TM mode AMT resistivities across two-dimensional model of an inhomogeneous earth.
apparent
less than 70 am, due to the buried fault zone, appears to be shifted to the left by the buried topography, and is flanked on either side by zones of slightly higher apparent resistivities. Beyond these latter zones, the resistivities rise again. The surface topography presumably produces the slightly higher resistivities near the center of Fig.46b, and also adds to the low at the left and contributes a slight low at the right. Frequencies in excess of 10’ Hz clearly reveal a horizontally layered structure of overburden and bedrock at distances in excess of 500 m on either side of the fault. Frequencies less than 10’ Hz do not appear to detect the horizontal stratification at such distances. If the resistivities of the media of Fig.46c were multiplied by 10 to comply with Fig.45b, horizontal stratification would be detected only if frequencies well in excess of lo3 Hz were employed.
173
Conclusions For two-dimensional complex geologic cross-sections, we can draw the following conclusions: (1) The amplitude and the shape of the AFMAG TE mode tilt angle and ellipticity anomalies are governed not. only by a buried fault zone but also by surface and buried topography adjacent to it and by the mode of excitation. (2) The amplitude and the shape of the TE mode AMT apparent resistivity anomaly is much more affected by a fault zone than by surface or buried topography adjacent to it. (3) The amplitude and the shape of the TM mode AMT apparent resistivity profile is dominated by the surface topography. (4) Provided the fault zone exhibits a larger induction number than the irregular overburden above it, the effect of the fault zone can be emphasized and the overburden de-emphasized by using lower frequencies. (5) The effect of the overburden can be emphasized relative to the fault zone by using higher frequencies. (6) The surface topography, the buried topography, and the fault zone will all affect the interpretation of overburden sounding data. According to our calculations these effects carry laterally for several hundreds of meters. (7) As frequency is varied for a sounding, the relative contributions of the surface topography, buried topography, and fault zone will each vary in the vicinity of the structure. (8) Dual-mode broad-band continuous sounding-profiling, provides the maximum amount of data for interpretation. The degree to which this amount of data can be exploited, and the economics of attempting to acquire this amount of information, require field study for evaluation. This field study is in progress. (9) Measurement of both tilt angle and ellipticity is to be preferred to measurement of tilt angle alone in an AFMAG survey, because, as a minimum, ellipticity seems to be a more sensitive indicator of complexity than tilt angle, while tilt angle is more readily interpretable. It is axiomatic that ambiguity of interpretation is made more apparent, and sometimes may be reduced, by measurement of two parameters rather than one. The anatomy
of an anomaly
The examples presented indicate that interpretation of AFMAG and AMT electromagnetic profiling data is ambiguous unless evaluation can be made of the effects of surface topography, buried topography, overburden resistivity, and bedrock resistivity. Further the examples indicate that interpretation of AMT electromagnetic sounding data is ambiguous unless surface topography and buried inhomogeneities, such as fault zones, are evaluated. The maximum information is provided when dual-mode, broad-band, continuous soundingprofiling is carried out. Whether or not all of this acquired information can be assimilated and will lead to improved interpretation remains to be established
174
by field studies. However, it can be said that a warning signal on the complexity of a geologic structure is provided when this full information is provided, but is usually lacking if both modes, broad band, or continuous sounding-profiling are not utilized. SUMMARY
OF LIMITATIONS
OF ELECTROMAGNETIC
EXPLORATION
Introduction The data presented so far permit us to make a summary of the limitations of electromagnetic sounding and profiling introduced by a complex geoelectric section. This summary appears below first under profiling and then under sounding.
Profiling Table V contains a summary of the deleterious effects introduced by overburden, host rock, and topography on interpretation of electromagnetic profiling data. This table is based on observations by Hedstrom and Parasnis (1958), Gaur (1959,1963), Lowrie and West (1965), Roy (1970), Hohmann (1971), Sarma and Mar-u (1971), Swift (1971), Vozoff (1971), Verma (1972), and on data presented in this paper.
Sounding Lateral inhomogeneities such as faults, surface topography, and buried topography all invalidate deduction of layer thicknesses and conductivities results in this paper illustrate. A 14-FREQUENCY
SOUNDING-PROFILING
as
SYSTEM
Introduction The authors have been studying the theory for tilt angle and ellipticity sounding and profiling for several years (Ward, 1967b; Dey and Ward, 1970; Ryu et al., 1970). We have published one case history of application of tilt angle and ellipticity sounding (Ryu et al., 1972). Fig.2 and 3 of this paper were obtained with a new 14-frequency tilt angle and ellipticity electromagnetic system suited to sounding, profiling, or continuous sounding-profiling and it is this system which we shall next describe.
Transmitting
system
The transmitter is capable of supplying up to 20 A, to either one of two transmitting coils at frequencies of 10.5, 21, 42, 84, 168, 336, 672, 1344,
175
TABLE
V
Summary of effects of overburden, host rock, surface topography and buried topography problem
Methods for which effect has been observed ~~___
Ingredient
Effect
Interpretation
Overburden
rotates phase
depth estimates invalid
horizontal loop
decreases amplitude
ot estimates invalid
TURAM AFMAG AMT VLF rotary field airborne
Host rock
rotates phase increases amplitude for shallow conductors
depth estimates invalid
horizontal loop
ot estimates invalid
TURAM
dip estimates invalid
AFMAG
expected to decrease amplitude for deep conductors
AMT VLF rotary field airborne
changes shape of profiles Surface and buried topography
hunting airborne
fall-off laws changed introduces geologic noise
depth estimates invalid
TURAM
ot estimates invalid
AFMAG
distorts or obscures anomalies
dip estimates invalid
AMT
anomalies not recognized
2688, 5376, 10752,21504,43008, and 86016 Hz. These frequencies are in geometric progression with a common ratio of 2 and are chosen to avoid 60 Hz and its harmonics. One transmitting coil is 200 ft in diameter when used as a circular horizontal loop while it is roughly 280 ft long by 33 ft high when erected on masts as a fixed vertical loop. The number of turns used on the loop range up to 10. A maximum magnetic moment of 2.92 *10’ A - turns * m2 is available with this loop, but the actual turns, current, and hence moment vary with frequency. A second loop may be used as a 30-ft diameter circular loop for orientation in either the horizontal or vertical planes. The maximum number of turns which may be connected in this loop is 38 while the maximum current is 20 A; a maximum moment of 2.81. lo4 A +turns - mz results. Fig.47 depicts this latter loop when erected in a vertical plane; it may be rotated about the vertical diameter when in this orientation. Table VI illustrates the several configurations possible with this transmitting system
VI
I, 0 = cylindrical f = frequency
Sounding
--
loop
coordinates
vertical loop
horizontal
vertical
___~
vertical _-- _~_I_-
horizontal
rotatable
vertical loop
._~
horizontal
.._ _____
“TURAM”
..-“__
._~
Profiling
-
--
1Cfrequency
Orientation of transmitting loop
for generalized
Technique
techniques
Function
_.-
Operational
TABLE
__
large or small
large or small
small
large or small
~___.
on axis of loop
on any radius
plane of loop
on any radius
~_
Location of point observation
system
-._. -
Transmitting loop size
.._~
electromagnetic
r,e,f
plane of vertical loop
r, f __~-
r,e,f
vertical plane through axis of loop ~__ _.._._^___~
r,e,f
plane normal to plane of loop
-
Variable parameters geometric
vertical radial
~-~--.
Plane of measurement
Fig.47. system.
Pictorial
description
of small loop
in vertical
plane,
of 14-frequency
elect] romagnel tic
178
Receiving
system
Two orthogonal receiving coils operating into a phase-sensitive detector permit measurement of tilt angle to a precision of 0.1” and of ellipticity to 2%. Accuracies are estimated as 0.5” and 5% for tilt angle and ellipticity, respectively. One such receiving coil system is used for the frequency range 10.5~2,688 Hz while another such system is used for the frequency range 5,376~86,016 Hz. Fig.48 depicts one receiving coil system. Table VI notes the manner of measurement of tilt angle and ellipticity for the several possible transmitter configurations. The operating principle of the orthogonal receiving coil system is quite similar to the principle of an AFMAG receiver as described by Ward (1967b). Ellipticity is not normally measured in an AFMAG survey nor in any other electromagnetic prospecting tilt angle system. Its measurement was, however, included in the Bieler-Watson method employed in Australia as early as 1928 (Broughton-Edge and Laby, 1931). Referring to Fig.49, the output of one coil, the reference coil, gates the output of the other, the signal coil, via a phase-sensitive detector. Thus for a linearly polarized field, the instantaneous detector output will be positive, zero, or negative according to the signal coil orientation relative t,o the field vector as illustrated in Fig.49. Because a phasesensitive detector is employed, an output will be recorded only for that part of the signal voltage which is in phase with the reference voltage. In a field which is elliptically polarized, the phase of the component along the axis of the reference coil governs the output of the phase sensitive detector. When the reference coil is oriented along the major axis of the ellipse, the output of the detector is zero, but it is positive or negative when the reference coil assumes another orientation. Thus by rotating the coil system about its axis, the signal coil is readily aligned along the minor axis and the reference coil along the major axis. Measurement of the signal coil and reference coil outputs then yields a voltage ratio proportional to the ellipticity. Preliminary
results obtained
with 14-frequency
system
Fig.2 and 3 illustrate preliminary results obtained ostensibly horizontally layered medium. Future use of the lo-frequency
with the system over an
system
Quantitative interpretation of the data obtained with the system has yet to be made. The amount of information collected for Fig.3 is comparable to the amount of information we normally expect to obtain in a combined resistivity-induced polarization survey. In the latter instance we commonly use two frequencies, five separations, and a large number of transmitter locations. With the 16frequency electromagnetic system we expect to use up to three transmitter locations, five to fifteen transmitter-receiver
Fig.48. system.
Pictorial
description
of one receiving
coil unit for 14-frequency
electromagnetic
180
REFAWCE COIL NET NEGATIVE METER
READING
NET POSITNE
METER
READING
0
I
+ ---INET ZERO METER READING
Fig.49.
Principle
of orthogonal
coil,
phase sensitive
detector,
receiving
unit
‘oo’“oo* 10,000-
i
z
IOOO-
!i
& IL
100
“0
12
4I
DISTANCE
Fig.50.
Contours,
61
FROM
6I
10 I
I2 I
14
16
16
20
TRANSMITTER-HUNDREDS
in frequency-distance
22
24
OF
space,
26 I
FEET
of tilt angle observed
near a vertical
loop,
separations and, of course, fourteen frequencies. The selection of precise values for number of transmitter locations, number of transmitter-receiver separations, and number of frequencies will depend upon optimization studies using the inverse method of interpretation to identify the density of informa-
181
tion and upon economic and logistical studies. The intent is to seek to make the electromagnetic method more cost-effective than the combined resistivityinduced polarization method when used in the same application. One possible data presentation scheme is contained in Fig.48 where tilt angle is contoured in frequency-distance space. Such diagrams for observed tilt angle and ellipticity would be used for comparison with similar diagrams obtained by forward problem solution. However, this would be intended only as a guide for initial guesses for the primary interpretation via inversion. Either the TE mode or the TM mode, or both, can be induced in a subsurface inhomogeneity depending upon the location and orientation of the transmitting coil relative to the inhomogeneity. It is entirely possible that with the generalized approach we have initiated in instrumentation, field technique, and interpretation we can significantly improve the application of the electromagnetic method in conductive terranes. ACKNOWLEDGEMENTS
Results presented here have been obtained in research sponsored by the National Science Foundation under grants GA 24421 and GA 31021, and by the National Aeronautics and Space Administration under contracts NASB5078, NAS9-11475, and NAS9-12168. O.P. Verma generously permitted use of unpublished data from scaled physical modeling. Mrs Kay Suiter typed the manuscript, Falko Friemann supervised drafting of the figures, Dennis Buzzell assisted with the field observations and S.A. Ward assisted with the Turam modeling; we are indebted to all of them. We are grateful to McPhar Geophysics Limited for designing and producing the 14-frequency electromagnetic system and for sharing in its cost. REFERENCES Backus, G.E. and Gilbert, J.T., 1967. Numerical applications of a formalism for geophysical inverse problem. Geophys. J. R. Astron. Sot. B, 15: 247-276. Backus, G.E. and Gilbert, J.T., 1968. The resolving power of gross earth data. Geophys. J. R. Astron. Sot., 16: 169-205. Backus, G.E. and Gilbert, J.T., 1970. Uniqueness in the inversion of inaccurate gross earth data. Philos. Trans. R. Sot. Lond., A, 266: 123-192. Bosschart, R.A., 1961. On the occurrence of low resistivity geological conductors. Geophys. Prospect., 9: 203-212. Bosschart, R.A., 1964. Analytical Interpretation of Fixed Source Electromagnetic Prospecting Data. Thesis, Technische Hogeschool, Delft, The Netherlands, 103 pp. Broughton-Edge, A.B. and Laby, T.H., 1931. Geophysical Prospecting, The Report of the Imperial Geophysical Experimental Survey of Australia. Cambridge University Press, Cambridge, England, 372 pp. Dey, A. and Ward, S.H., 1970. Inductive sounding of a layered earth with a horizontal magnetic dipole. Geophysics, 35: 660--703.
182
Frischknecht, F.C., 1967. Fields about an oscillating magnetic dipole over a two-layer earth, and application to ground and airborne electromagnetic surveys. Q., Colo. School Mines, 62(l): l-326. Gaur, V.K., 1959. Model Experiments Simulating Conditions Encountered in Airborne Electromagnetic Prospecting. Thesis, University of London, London, England. Gaur, V.K., 1963. Electromagnetic model experiments simulating an airborne method of prospecting. Bull. Natl. Geophys. Res. Inst., 1: 167-174. Glenn, W.E., Ryu, J., Ward, S.H., Peeples, W.J. and Phillips, R.J., 1973. Inversion of vertical magnetic dipole data over a layered structure, 3. Geophysics, 38(6): 1109-1129. Grant, F.S. and West, G.F., 1965. Interpretation Theory in Applied Geophysics. McGraw Hill, New York, 583 pp. Hedstrom, E.H. and Parasnis, D.S., 1958. Some model experiments relating to electromagnetic prospecting with special reference to airborne work. Geophys. Prospect., 4: 322-341. Hohmann, G.W., 1971. Electromagnetic scattering by conductors in the earth near a line source of current. Geophysics, 36(l): 101-131. Hohmann, G.W., Kintzinger, P.R., Van Voorhis, G.D. and Ward, SW., 1970. Evaluation of the measurement of induced electrical polarization with an inductive system. Geophysics, 35: 901-915. Inman Jr., J.R., Ryu, J. and Ward, S.H., 1973. Resistivity inversion. Geophysics, 38(6): 1088-1108. Jackson, D.D., 1972. Interpretation of inaccurate, insufficient and inconsistent data. Geophys. J. R. Astron. Sot., 28: 97-109. Keller, G.V., 1970. Induction methods in prospecting for hot water. Geothermics, Spec. Issue 2, 2(l): 318-332. Keller, G.V. and Frischknecht, F.C., 1966. Electrical Methods in Geophysical Prospecting. Pergamon, New York, N.Y., 517 pp. Lanczos, C., 1961. Linear Differential Operators. Van Nostrand, London, England, 539 pp. Lowrie, W. and West, G.F., 1965. The effect of conducting overburden on electromagnetic prospecting measurements. Geophysics, 30: 624-632. Madden, T.R., 1971. The resolving power of geoelectric measurements for delineating resistive zones within the crust. In: J.G. Heacock (Editor), The Structure and Physical Properties of the Earth’s Crust. American Geophysical Union, Washington, D.C., pp. 95-105. Marshall, D.J. and Madden, T.R., 1959. Induced polarization: a study of its causes. Geophysics, 24: 790-816. Parry, J.R. and Ward, S.H., 1971, Electromagnetic scattering from cylinders of arbitrary cross-section in a conductive half-space. Geophysics, 36(l): 67-100. Paterson, N.R., Hewitt, R.P. and Dockery, B., 1973. Extra low frequency (ELF) EM surveys with the EM-25 in Western Australia. In: B.D. Johnson, D.S. Parasnis and K. Vozoff (Editors), Geophysics of the Earth and the Oceans, Part III. Geoexploration, 12( 2/3): 226 (abstract). Roy, A., 1970. On the effect of overburden on EM anomalies, a review. Geophysics, 35(4): 646-659. Ryu, J., Morrison, H.F. and Ward, S.H., 1970. Electromagnetic fields about a loop source of current. Geophysics, 35: 862-896. Ryu, J., Morrison, H.F. and Ward, S.H., 1972. Electromagnetic depth sounding across Santa Clara Valley. Geophysics, 37(2): 351-374. Sarma, D.G. and Maru, V.M., 1971. A study of some effects of a conducting host rock with a new modeling apparatus. Geophysics, 36(l): 166-183. Swift Jr., C.M., 1971. Theoretical magnetotelluric and Turam response from twodimensional inhomogeneities. Geophysics, 36(l): 38-52. Vanyan, L.L., 1967. Electromagnetic depth sounding. Selected and translated by G.V. Keller, Consultants Bureau, New York, N.Y., 312 pp.
183
Verma, O.P., 1972. Electromagnetic Model Experiments Simulating Conditions Encountered in Geophysical Prospecting. Thesis, University of Roorkee, Roorkee, India, 143 pp. Vozoff, K., 1971. The effect of overburden on vertical component anomalies in AFMAG and VLF exploration: a computer model study. Geophysics, 36(l): 53-57. Ward, S.H., 1967a. Electromagnetic theory for geophysical applications. In: Mining Geophysics, II. Society of Exploration Geophysicists, Tulsa, Okla., pp.lO-196. Ward, S.H., 1967b. The electromagnetic method. In: Mining Geophysics, II. Society of Exploration Geophysicists, Tulsa, Okla., pp.224-372. Ward, S.H., O’Brien, D.P., Parry, J.R. and McKnight, B.K., 1968. AFMAG --. Interpretation. Geophysics, 33(4): 621-644. Ward, S.H., Peeples, W.J. and Ryu, J., 1973. Analysis of geoelectromagnetic data. In: Methods in Computational Physics, 13. Geophysics, 38(5): 1109-1129. Wiggins, R.A., 1972. The generalized inverse problem. In: Reviews of Geophysics and Snace Physics, 10: 251-286.
ELECTROMAGNETIC
Company,
Amsterdam
-
Printed
METHODS IN CONDUCTIVE
S.H. WARD’,
J. RYU’ , W.E. GLENN”,
’ department
of Geology
G.W. HOHMANN2,
and Geophysics,
University
for publication
November
TERRANES
A. DEY3
and B.D.
of Utah, Salt Lake city,
(U.S.A.) 2Kennecott Exploration Inc., Salt Lake City, Utah (U.S.A.) “Engineering Geoscience, University of California, Berkeley, (Accepted
in The Netherlands
SMITH’
Utah
Calif. (U.S.A.)
29, 1973)
ABSTRACT Ward, S.H., Ryu, Electromagnetic
J., Glenn, W.E., Hohmann, G.W., Dey, A. and Smith, B.D., 1974. methods in conductive terranes. Geoexploration, 12: 121-183.
Measurement of a natural or artificial electromagnetic field yields information on the distribution of electrical parameters in the earth’s subsurface. Frequencies in the range 100 Hz to 5,000 Hz and transmitter-receiver separations in the range 30 m to 1 km are most commonly used for electromagnetic probing of the earth’s shallow crust. Two fundamentally different objectives may be served by electromagnetic probing. The first objective is the search for local regions of exceptionally high electrical conductivity such as arise in metallic ore deposits or faults. To meet this objective, electromagnetic profiling is executed, i.e., one or more descriptors of the electromagnetic field are measured along a profile over the area of interest and local anomalies in the measured descriptor are sought. These anomalies are then interpreted in terms of a range of expected geologic occurrences, Mathematical and scaled physical models are used to produce catalogues of anomaly profiles with which we compare the field observations. The second objective is the detection and delineation of horizontal interfaces marking changes in electrical conductivity. To meet this objective, electromagnetic sounding is executed. Electromagnetic sounding is effected in two ways, parametric sounding and geometric sounding. In the former, frequency is varied with the transmitter-receiver separation held constant, while in the latter, separation is varied with frequency held constant. Mathematical models are most commonly used to produce catalogues of field component versus frequency or versus separation, with which we compare the field observations, The use of eatalogues of curves with which we may interpret field observations, the forward method, is limited by the huge volume of curves required for generalized interpretation, and by the subjective comparisons made by the interpreter. Recent advances in application of the generalized linear inverse method of interpretation to the electromagnetic method, indicate that the use of catalogues of model curves may soon not be required. The inverse method avoids human bias in matching field curves to model curves, it provides estimates of the reliability of the model or models selected to match the field data, and it permits the design of field surveys which optimize the information density of the observed data. Scaled physical and mathematical modeling has revealed that conductive ouerburden rotates the phase and decreases the amplitude of anomalies due to buried inhomogeneities for several electromagnetic systems. Modeling also has revealed that conductive host rock can lead to an increase in amplitude and a rotation of the phase of an anomaly. These
122
latter effects are dependent upon the dip and depth of the inhomogeneity, upon the conductivity of the host medium, and upon the particular electromagnetic system used. In general, present methods of interpretation of electromagnetic data are invalidated by conductive overburden or conductive host rock. Conductive in this sense extends from 1 mho/m to 10 ~3 mho/m and hence encompasses host rock and overburden conductivities encountered routinely throughout the world. The finite element numerical method has been used herein to calculate electromagnetic scattering from some simple two-dimensional earth models. By these models, the effects of surface topography, buried topography, overburden, and faults are investigated singly and collectively. The model calculations readily demonstrate that interpretation of electromagnetic profiling data can be accomplished more completely while simultaneously interpreting electromagnetic sounding data or vice versa. This observation leads to the conclusion that dual-mode broad-band continuous sounding-profiling is highly desirable if one is to deduce geologic structure from electromagnetic survey data. The deductions presented are drawn from plane wave analysis and they pertain to the AMT and AFMAG methods. They may readily be extended by inference to the VLF method. Numerous field techniques and system configurations are used in application of the electromagnetic method. Despite nearly 50 years of application of the electromagnetic method in mining exploration, no optimum technique has been developed for application to all environments, We believe that this results because all currently used techniques are too simple. Accordingly we have developed a more generalized system and are investigating its advantages and limitations. A description is given of a 14-frequency electromagnetic system with which sounding, profiling or continuous sounding-profiling may be achieved. The tilt of the major axis and the ratio of minor to major axis, of the ellipse of magnetic field polarization, are measured at 14 frequencies over the range 10 Hz to 86 kHz. The system is a generalization of the Beiler-Watson method used in Australia as early as 1928. The transmitting loop may be oriented in either the vertical or the horizontal plane and sufficient moment is available to permit measurements at distances of one or two kilometers from the transmitting loop. Preliminary field results illustrate the application of the method in sounding and continuous sounding-profiling. These preliminary results indicate that the frequency range 10 Hz to 10’ Hz and the transmitter-receiver separation range of 80 m to 1 km are required for generalized electromagnetic exploration. A greater sophistication in equipment, field techniques, and interpretation techniques is required if the electromagnetic method is to be successful in conductive terrsnes. The cost effectiveness of this degree of sophistication is yet to be established, although a still greater degree of sophistication may ultimately be required.
INTRODUCTION
The problems From the geometrical and/or frequency variation of one or more magnetic or electric field components, one usually attempts to estimate the depth, thickness, width, length, and the electrical conductivity of each subsurface scatterer when utilizing the electromagnetic method for sounding or profiling. Catalogues of reference curves are used to guide the forward method of interpretation, Practical application of the inverse method of interpretation now seems possible and hence it is expected to replace the forward method at some time in the future. For a generally inhomogeneous earth with topographic relief the interpretation problem is a difficult one and the only hope, in the general case, is to vary frequency and the location of a receiver relative
123
to a transmitter over wide ranges. Often the transmitter location is also varied and several field components are measured in order to reduce ambig~~ity in interpretation. In some simple cases where the earth cooperates, such as when the earth may be modeled by horizontal, homogeneous, isotropic layers, interpretation is relatively simple. In many instances, however, we suspect that we are deluding ourselves that the earth is simple. In this paper we explore the effects of surface and buried topography, conductivity and thickness of overburden, conductivity of host rock, and the presence of faults, and of the source type and mode of excitation on the electromagnetic profiling anomalies due to buried sulphide deposits which may be simulated by thin sheets or slabs. Next we explore the forward method of interpretation of electromagnetic sounding over horizontally layered terranes. With this basis, we then illustrate theoretical predictions for the advantages of dual-mode broad-band continuous sounding-profili~lg to electromagnetic exploration of a generally inhomogeneous earth. The latter results are applicable to field investigations of layered media in which inhomogeneities and surface topographic relief are unwanted contaminants (as in groundwater studies), and to inhomogeneous media in which overburden, host rock, and surface or buried topographic relief are present as unwanted contaminants (as in massive sulphide.ore search). The results are intended primarily to emphasize the ambiguities which may arise in typical real-world application of electromagnetic methods in those instances where dual-mode, broad-band, continuous sounding-profiling is not contemplated. However, we postulate that an optimum electromagnetic method for use in conductive terranes may well involve use of several frequencies in the lo---10’ I-Iz range and of transmitter-receiver separations in the 30-m to l-km range, Preliminary results with a system exhibiting these capabilities are encouraging although the costeffectiveness of this approach has yet to be established.
Pro filing
A loop of wire, erected in a vertical or horizontal plane at the earth’s surface and energized with alternating current, may serve as a transmitter in an active system of profiling for the purpose of detecting lateral conductivity inhomogeneities near the surface. The transmitting loop may be fixed in location and measurements made of alternating magnetic field components in its proximity. Alternatively both the transmitter and the receiver are moved in tandem. The magnetic field may be described by its orthogonal Cartesian components H,, Hy , and HZ or by its ellipse descriptors CYand E, the tilt angle and ellipticity, respectively. Fig.l‘illustrates these descriptors; the tilt angle is the ’ Note added in proof: E-llipticity as here used should be designated as “modulus of ellipticity”. For a complete discussion of ellipticity refer to: Smith, B.D. and Ward, S.H., 1974. Short note: On the computation of polarization ellipse parameters. Geophysics, in press.
124
EI
I+~
;Pe (Ht) * REAL tt
tH,)=
* /
[tWOSOL-HrSINal
I
HzSIN~+H,COSO.
PART
IMAGINARY
OF TdTAL
MAGNETIC
PART OF TOTAL
MAGNETIC
FIELD FIELD
Fig.1. Ellipse of magnetic field polarization; HZ and H,. are complex vertical and horizontal components of total field, respectively; @t- and & are phases of vertical and horizontal components of total field, respectively.
inclination from the horizontal of the major axis of the ellipse of magnetic field polarization while the ellipticity is the ratio of the minor to the major axes of the ellipse. Any of the above five quantities will vary systematically in the vicinity of a subsurface conductive inhomogeneity. Measurements of Q and E, as functions of the frequency of the current in the transmitting loop and as functions of the horizontal x and y coordinates are used to deduce the depth, depth extent, length, and other pertinent parameters of the subsurface inhomogeneity. The major and minor axes of the ellipse of magnetic field pol~ization may assume any orientation or ratio in the vicinity of an inhomogeneity. However, the projections of Q and E on the vertical plane passing through either a vertical or a horizontal transmitting loop are most commonly measured; the vertical plane of a vertical transmitting loop is oriented to contain the point of observation when profiling. In the vertical loop electromagnetic method (Ward, 1967b), the VLF method, the AFMAG method, and the Crone Shootback method, tilt angle is measured. With some VLF methods, a quantity related to 4lipticity is also measured. In the horizontal loop method (Ward, 196’713) of electromagnetic profiling the real and imaginary parts of the vertical magnetic field, Re(H,) and Im (H,), are measured. In the Turam method, the measured quantities are the ratio Re(&, )/Re(Hz2 ) of the real parts and the ratio Im (Hz, )/1m (N,, ) of the imaginary parts of the vertical magnetic field, observed at locations 1 and 2 at a distance of the order of 30 m apart. Alternatively the ratio of the amplitudes A, (H,, )/A2 (Hz2 ) and the phase difference #(Hz1 ) - @(Hzz) are measured.
125
Sounding A loop of wire laid out horizontally on the surface of the earth or a loop of wire erected in a vertical plane, energized with alternating current, may serve as a transmitter in an active system for sounding the thicknesses and conductivities of the layers of a horizontally layered earth. If the frequency of the source current is a variable, then parametric sounding is permissible while if the transmitter-receiver separation is a variable then geometric sounding is permissible. The total electric field, for a horizontal current loop, is confined to the horizontal everywhere and hence is represented totally by the tangential electric field component Ee . The quantity EO is complex, i.e., phase-shifted, when referred to the loop current. Both its amplitude and phase are functions of the angular frequency w , the transmitter-receiver separation r, and the conductivities and thicknesses of the layers. Obviously the electric field does not cross formation boundaries in a horizontally layered earth. For this reason a horizontal loop electromagnetic sounding method is sensitive to conductive horizons but relatively insensitive to resistive horizons; the induced currents will tend to be concentrated in the conductive horizons. The magnetic field from a horizontal loop is fully described by the two complex components H, and Hz whose amplitudes and phases are governed by the same earth parameters governing EO . Insofar as H,. and Hz are characteristically of different phase at any distance r, the magnetic field is elliptically polarized. The major axis of the ellipse of magnetic field polarization on the surface of a conductive earth, of,isotropic and homogeneous layers, tilts away from a horizontal loop transmitter but is confined to the vertical plane containing the center of the loop and the observation point. The total electric field is confined to a vertical plane parallel to the plane of a vertical loop situated over a horizontally layered earth. It consists of E, and E, components and hence it both crosses and parallels formation boundaries in the subsurface. For this reason, the vertical loop electromagnetic sounding method is sensitive to both resistive layers and conductive layers. The magnetic field components H,. and H, are measured at locations along the axis of a vertical transmitting loop for electromagnetic sounding. Alternatively, the tilt angle CKand the ellipticity E may be measured in that vertical plane which contains the axis of the loop. To obtain a satisfactory electromagnetic sounding, it is necessary to trace out the variation of Hz, H,., a, or E with induction number B = (apw )” r from a low asymptote to a high asymptote. (The quantity u is here the apparent conductivity of the geoelectric section.) In parametric sounding, the frequency w must be varied over four decades to achieve this. In geometric sounding the transmitter-receiver separation r must be varied over two decades to assure that both high and low response asymptotes are achieved. Descriptions of field techniques Grant and West (1965) and Ward (1967b)
describe the numerous
electro-
125
magnetic profiling techniques, Vanyan (1967) describes component sounding techniques, while Dey and Ward (1970) and Ryu, Morrison, and Ward (1970) describe tilt angle and ellipticity sounding techniques. Keller and Frischknecht (1966) provide a good overview of both sounding and profiling. Continuous sounding-profiling The conventional Turam method, utilizing a large horizontal rectangular transmitting loop, may be used for geometric sounding of a layered earth. If Turam is generalized, to allow for frequency variable over four decades, then it may be used for parametric sounding of a layered earth. If a generalized Turam system is utilized, in both parametric and geometric modes simultaneously, over a laterally inhomogeneous earth, then we might state that we were conducting continuous sounding-profiling. Similarly a generalized vertical loop system may be utilized for continuous sounding-profiling. The quantity HO could be measured in the plane of the loop, or the quantities H,, Hz, a, or E could be measured along the axis of the loop for this purpose. In a later section of this paper we explore the theoretical responses for dual-mode, broad-band, plane wave, continuous sounding-profiling over terranes which are two-dimensionally heterogeneous. We shall discover that the responses are critically dependent upon the orientation of the exciting magnetic field vector. Sounding complements profiling and vice versa, so that it is self-evident, a priori, that continuous-sounding profiling is idealistically better than either profiling or sounding, regardless of the objective of the electromagnetic survey. Justification for the time and expense involved in continuous sounding-profiling must be established, however, for each exploration problem. The theory of the forward problem The customary method of interpretation of electromagnetic sounding or profiling data involves us in matching observed data with predicted data obtained by mathematical or scaled physical modeling. Plots are made, for both observed and predicted data, of the real and imaginary parts of field components (or of tilt angle and ellipticity) versus induction number, frequency, or separation between transmitter and receiver. This curve-matching technique relies upon the forward solution of an electromagnetic boundary value problem. Extensive catalogues of curves pertaining to typical earth models are required for the forward solution. For example, the theoretical tilt angle and ellipticity profiles near a horizontal loop source situated upon a two-layered half-space are illustrated as smooth curves in Fig.2. Field observational data are shown as crosses and circles in the diagram. Agreement between experiment and theory, as judged by the experienced eye of the experimenter, is taken as satisfactory establishment of the validity of the model upon which the theoretical predictions are
127
0 2
3
4
3
6
7
9910
Fig.2. Observed tilt angle (0) and ellipticity two-layered earth. Horizontal transmitting distance of 900 ft from center.
(E) versus f ‘12r, and theoretical curves for a loop of 200 ft diameter with receiver at a
f4 r Fig.3. Observed tilt angle ((L) and magnitude of frequency f and distance r, near a vertical medium.
of e$lipticity (e) profiles observed as functions loop, over an assumed horizontally-layered
128
based. No attempt has been made, in the example presented, to compute the theoretical curves for a model which best fits the data, as judged by the eye. Rather, available model curves (Ryu et al., 1970) are used for comparison with observational data. However, a model earth described by the parameters u, = 0.04 mhos/m, uZ = 0.4 mhos/m, and d = 270 m would fit the observed data to a first approximation. Fig.3 contains tilt angle and ellipticity versus frequency for several distances from a vertical loop source situated over an ostensibly horizontally layered earth of two strata. A logical progression of the ellipticity and tilt angle versus f” r is observed for various values of r, the transmitter-receiver separation. In each of the above cases, one would normally seek the best fit of observed to theoretical data for a multiple-layered earth rather than a two-layered earth. When interpretation of profiling data is carried out, a similar comparison of theory and experiment is made (Ward, 1967b). The theory of the inverse problem A direct interpretation of electromagnetic sounding or profiling data may be achieved by using the method of generalized linear inversion developed by Backus and Gilbert (1967,1968 and 1970) and reviewed by Wiggins (1972) and Jackson (1972). The essence of the generalized linear inversion scheme is outlined below, and a numerical illustration with horizontal loop sounding data over a conductive region is given in section 3.4. The generalized linear inversion requires an expression to calculate a theoretical output Yj for a given input set, Xi, of rz earth model parameters, as written by:
where the operator Lj is a non-linear function for most geoelectromagnetic systems. Upon expanding eq.1 in a Taylor’s series and neglecting second and higher order terms, we linearize the non-linear function of eq.1 as: (Oj _ yj, =
5 j=l
aLj
axi
(Xj -Xl!),
j = 1,m
Xi=Xy
or: AY=AAX
(2)
where Oj is the jth measurement and X0 is an initially guessed point in the unknown parameter space. The inverse problem requires finding the model parameters, Xi, that minimize the data difference vector AY in a least squares sense. In general, the number of measurements, m, is not equal to the number of
129
model parameters, IZ. Using eigenvalue decomposition, system matrix A and its natural inverse H as (Lanczos,
one can write the 1961):
A=UAVT
(3)
and: H = VA-’ UT
(4)
The matrix U consists of p eigenvectors of length m and V consists of p eigenvectors of length n. The matrix A is a diagonal matrix consisting of p eigenvalues, and p is the rank of the matrix A. Then the solution to eq.2 is AX = HAY
(5)
As mentioned above, the functional relationship of eq.1 is non-linear, therefore several iterations are required to obtain the best estimates of the actual earth model parameters. The hat (-) in eq.5 indicates the new set of parameter corrections being sought after each iteration toward the global minimum of the data difference vector AY in the unknown parameter space. From eq.2 and 5, one can construct: AX = HAAX
= RAX
(6)
= SAY
(7)
and: A%
=
AHAY
where we have used the resolution matrix R = V VT. The deltaness of R is considered to be a measure of the resolution of the parameters while the deltaness of S shows information distribution among data points for resolving the model parameters. Table I shows three types of systems which may arise in practice. S is called the information-density matrix. An overdetermined case occurs for most geoelectromagnetic systems and the above analysis results in a mathematically unique solution, relative to an initial guess. From a practical viewpoint there will be noise in the data and linear dependencies between the parameters so that a geophysically unique TABLE
I
Underdetermined, System
critical, Rank
and overdetermined R
systems S
Remarks
Underdetermined
p
R=I
S=I
no unique solution
Critical
p=m=n
R=I
S=I
unique solution possible mathematically
Overdetermined
p
R=I
S=I
unique solution not possible mathematically
I is the identity
matrix
130
solution will probably never be identified. If p < n < m, the generalized inverse method yields a natural inverse of reduced rank, and the resolution matrix is no longer the identity matrix. In those unfortunate and infrequent instances where the system is underdetermined, no unique solution, mathematically or geophysically, can occur. In summary, the principle advantages of the generalized inverse method are: (1) It avoids human bias in judging a “best fit”. (2) It avoids the logistical problem of compiling and using an infinite number of type curves. (3) It provides estimates of the resolution, and hence reliability, of the theoretical model used to fit the observed data. (4) It estimates the information density contained in the observed data and hence it permits the design of an experiment to optimize the information density. The application of the method of the generalized linear inverse to electromagnetic sounding and/or profiling is new so that illustration of its methodology requires detailed study. Hence we refer the reader to the articles by Glenn et al. (1973), by Ward et al. (1973), and an additional article by Inman et al. (1973). Scaled model
experiments
Under the scaling transformation (o(lw)ms
:
= (cr‘ p’ ,‘)li2$.
a model subsurface conductivity, a’, transforms to a field scale subsurface conductivity, u, depending upon the size scaling factor, S/S’, and the frequency scaling factor, w/o’. In the above relation, S is a linear dimension, u is a conductivity, w is angular frequency, and p is magnetic permeability. The unprimed quantities refer to the full-scale system, while the primed quantities refer to the model system. Usually, as here, p and p”’are each set equal to the free space permeability. Scaled model experiments, until recently, provided the principle basis upon which interpretation of electromagnetic profiling data was based. A wide range of two-dimensional theoretical models serving as a basis for interpretation of profiling data has recently been presented by Swift (1971), Vozoff (1971), Parry and Ward (1971), Hohmann (1971) and others. Extension of these numerical theoretical solutions to three-dimensional objects is now in progress. However, the scaled physical model experiments by Sarma and Maru (1971) and by Verma (1972) provide a current understanding of the electromagnetic response of complex three-dimensional geologic models.
131
PROFILING
Horizontal
loop
Insulated and bare wires immersed in solution Sarma and Maru (1971) have provided some very meaningful results from scaled physical modeling of the horizontal loop method. Fig.4 contains profiles of in-phase (IP) and quadrature (OP) parts of the anomalous field measured on traverse over an insulated (Fig.4a) and a bare (Fig.4b) copper wire immersed in a salt solution of 11.0 mho/m conductivity. The insulated wire was in electrical contact with the solution at its ends. The model characteristics are portrayed in the insets to Fig.4. The insulated wire yields approximately 1% anomaly in quadrature; the bare wire yields a 9% quadrature PERCENT
-Ia\
&____n-*-
x
‘P
ANOMALY
1
+=p~-o--Q“___~_____~
PERCENT
ANOMALY t
P
s-._Q
-_
--_Q
Fig.4. Horizontal loop in-phase (IP) and quadrature (OP) anomalies (a) Due to a long thin insulated wire in electrical contact, at its ends, with a salt solution of 11 mho/m. (b) Due to a long thin bare wire in total electrical contact with a salt solution of 11 mho/m. (After Sarma and Maru, 1971.)
132
anomaly and a 6.5% in-phase anomaly. The size of the anomaly seems to be dependent upon the contact impedance between the wire and the salt solution. The wire gave no anomaly when suspended in air. Sarma and Maru (1971) interpret these results as a short-circuiting, by the wire, of the currents induced in the salt solution. We shall call this phenomenon electric flux collection, by analogy with magnetic flux collection by a magnetic wire or bar, in order to facilitate discussion. Bare thin sheet
Fig.5 portrays the Sarma and Maru (1971) horizontal loop in-phase and quadrature profiles over a bare aluminum sheet immersed in salt water and suspended in air. The salt water enhances the in-phase anomaly by a factor of 1.4 and increases the quadrature anomaly by a factor of 50. Electric flux collection has amplified the anomaly and rotated its phase. We can conclude from this simple example that a conductive host medium increases the detectability of a buried inhomogeneity; other factors may change this conclusion as we shall see subsequently. PERCENT
ANOMALY
Fig.5. Horizontal loop in-phase (IP) and quadrature aluminum plate immersed in salt solution.
(OP) anomalies
due to a thin
The model host medium of 10.1 mhos/m conductivity scales to a full scale host medium conductivity of about lo-* mhos/m. This latter conductivity characterizes many of the areas of the world in which exploration is carried out. Hence the flux collection phenomenon must be common. It will be even more pronounced in terranes of conductivity greater than 10e2 mhos/m. The effects
of overburden
and host rock
Lowrie and West (1965) demonstrated
that conductive
overburden
rotated
133
the phase and reduced the amplitude of an anomaly due to a buried conductor. Sarma and Maru (1971) have illustrated that conductive host rock rotated the phase and increased the amplitude of an anomaly due to a buried conductor. When conductive overburden and conductive host rock are both present, the result is not readily predicted. Clearly, present quantitative interpretation of horizontal loop data, depending upon the ratio of in-phase to quadrature anomalies, is readily invalidated in conductive terranes. This result is not new to experienced geophysicists, yet quantitative interpretation of field data commonly is pursued on the assumption that the overburden or host rock do not exist. A comparison of four airborne electromagnetic coil systems: Rotary Horizontal Coplanar, Vertical Coplanar, and Vertical Coaxial
Field,
Introduction In a recent, careful, use of scaled physical models, Verma (1972) illustrated the anomalies obtained with a simulated rotary field airborne electromagnetic system over a graphite slab immersed in dilute hydrochloric acid. Verma also modeled a vertical coaxial, a vertical coplanar, and a horizontal coplanar coil system of the same 280-m coil separation as the rotary field system. While these latter configurations, because of the large separation, do not simulate any current operating airborne electromagnetic system, a comparative study of results from them and from the simulated rotary field system is enlightening One should bear in mind that the rotary field system is comprised of a horizontal coplanar coil pair and a vertical coplanar coil pair and that the output of the horizontal coplanar pair dominates an anomaly obtained with the rotary field system. The model parameters used by Verma to obtain the results to be presented here, and their full scale equivalents, are listed in Table II. Comparison of systems Fig.6 illustrates the anomaly profiles over the graphite slab when in air and when immersed in dilute hydrochloric acid. The dip of the slab is vertical. The quadrature anomaly is very small, for all four systems, when the slab is in air, but the quadrature becomes substantial when the slab is immersed in acid. The multiplication of the quadrature is approximately 15 for the horizontal coplanar and the rotary field systems, while it is approximately 8 for the coaxial system and probably less than 4 for the vertical coplanar system. The in-phase anomaly is largest for the horizontal coplanar and rotary field systems and least for the vertical coplanar system when the slab is in air. The in-phase anomalies multiply by 3.5, 3.25, 2.6, and 1.6 for rotary field, horizontal coplanar, vertical coaxial, and vertical coplanar systems, respectively, when the host medium is added. The above observations lead to the conclusion that a host medium of uniform conductivity increases detectability of a buried conductor for all four systems, but that increased detectability is most pronounced for the
134
TABLE
II
Model parameters
used by Verma (1972) --.
-
Parameter
Model
Field scale
Frequency Coil separation System height Depth to top of slab Slab length Slab width Slab thickness Slab conductivity Acid conductivity
100 kHz 0.5 m 0.17 m 0.05 m 0.505 m 0.088 m 0.02 m 26.3 *lo3 mho/m 18 mholm
400 Hz 250 m 85 m 25 m 253 m 44 m 10 m 26.3 mho/m 1.8 *lo-* mho/m
X INPHASE
-
X OUAORATURE
ANOMALY
(bl
VERTICAL
($1 VERTICAL (d)
ROTARY
COAXIAL COPLANAR FIELD
COIL
COIL
SYSTEM
COIL
SYSTEM
SYSTEM
ANOMALY
-4 * COIL
SYSTEM
e
*
SO’
D
*
0.051~
F
-
O.l?m
Qn =
Fig.6. In-phase (IP) and quadrature (OP) anomalies, due to a vertical hydrochloric acid solution, for four different coil systems.
graphite
26.3
VARIABLE
X I0?nllhI
slab in
rotary field and horizontal coplanar systems and least pronounced for the vertical coplanar system. The distortion of the ratio of in-phase to quadrature brought about by the presence of the host medium follows the same order. Quantitative interpretation of slab parameters is degenerated most for the
135
rotary field and horizontal coplanar systems and degenerated least for the vertical coplanar system when the slab is immersed in a conductive host medium. This simple illustration serves to demonstrate that different systems are affected to different degrees by the presence of a conductive host medium. Criteria for dip
Fig.7 illustrates the anomaly profiles over the same slab, in air and in acid, but the dip has been changed to 45”. X
INPHASE
ANOMALY
X OUADRATURE
I”’
-24
COPLANAR
-*I(
Us = OUN AIR1
(al
HORIZONTAL
(b)
VERTICAL
(cl (d)
VERTICAL COPLANAR COIL SYSTEM ROTARY FIELD COIL SYSTEM
COAXIAL
ANOMALY -24
COIL SYSTEM
COIL SYSTEM
Fig.7. In-phase and quadrature anomalies, immersed in a hydrochloric acid solution,
a; = O(IN AIR1
COIL SYSTEM VARIABLE 8= 45’ D- O.OSm F. 0.17 m cr. * 263 a IO’mhc,,,,
due to a graphite for four different
slab dipping at 45” and coil systems.
136
The slab in air produces asymmetrical profiles for all four systems. These profiles become almost symmetrical and hence almost identical to the profiles over a vertically dipping slab immersed in a conductive host medium. This latter result confirms earlier findings by Gaur (1959, 1963), who simulated the Hunting quadrature airborne electromagnetic system, and concluded that a conductive host medium transforms the shape of an anomaly profile so as to make all buried slabs appear to be vertical. Turam modeling Introduction The main objective of the scaled physical modeling reported in this section is a qualitative study of the effects of conductive host rock on Turam anomalies observed over dipping veins of finite extent. This work therefore represents a logical extension of Bosschart’s (1964) excellent pioneering study of the Turam method. For a vein of finite length, the departure of the dip of the vein from vertical produces dramatic changes in the shapes, phases, and amplitudes of anomalies, as we shall subsequently demonstrate. To test whether or not these changes occur for veins of infinite length, theoretical numerical modeling was performed. A subsidiary objective of the scaled physical modeling is a study of the effect of conductive host rock on the Turam anomaly observed over a horizontal circular cylinder. Interpretation of Turam data typically is based upon two critical assumptions (1) The normal magnetic field over a homogeneous earth is the magnetic field due to the transmitting loop situated in free space (Bosschart, 1964). (2) The effect, on anomalies due to buried inhomogeneities, of conductive overburden or conductive host rock is negligible (Bosschart, 1964). Hohmann (1971) has examined the effect on Turam interpretation of an overburden of limited width, constant thin depth, and infinite strike length. Swift (1971) generalized this study by allowing the overburden depth to be variable and to occur over an inhomogeneity. Both Swift and Hohmann have examined the effect of conductive host rock on the Turam anomalies due to veins of infinite strike length. The studies of Swift and Hohmann were based on theoretical formulation and clearly demonstrated that neglect of conductive overburden or of conductive host rock cannot, in general, be tolerated in interpretation of data resulting from a Turam survey. The Turam anomaly due to a buried inhomogeneity was obscured by an overburden of irregular depth in Swift’s study, while the Turam anomaly due to an inhomogeneity was shifted in phase and decreased in amplitude on account of the conductive host rock, according to Hohmann. Both Swift and Hohmann demonstrated that a free space normal magnetic field is incorrect and that a normal magnetic field that includes the effect of the conductive earth is necessary. However, Turam amplitudes and phase differences due to a conductive homogeneous half-space are approximately constant with distance. Therefore, the use of
137
the free space normal field is not too bad inasmuch as one is looking for deviations from this constant value. Swift and Hohmann have clearly advanced our basic understanding of the Turam method over that developed by Bosschart (1964). Models of infinite strike length do not conform to real occurrences. Hence, in our scaled physical modeling, an aluminum sheet, immersed in a tank of NaCl solution, was used to simulate a “perfect” conductor of finite strike length buried in a conductive half-space. The results for a vein of finite length differ markedly from those of a vein of infinite length, as a comparison of our physical and theoretical modeling demonstrates. Model measurements of the real (r, inphase) and the imaginary (i, quadrature) values of both the horizontal and the vertical components of magnetic field were made over a sheet of finite length for which the dip was discretely varied and for which the strike was parallel to one side of the loop source. Mathematical modeling over a vein of the same depth extent as the aluminum sheet, infinite length, and of similar thickness was also made. A horizontal cylinder, of axis parallel to one side of the transmitting loop, was also immersed in solution to facilitate study of a short body of revolution.
Description
of physical
models
Characteristics of inhomogeneities and host media. The scaled physical models used in these studies are summarized in Table III. The aluminum sheet, used to simulate a thin vein, and the hollow brass cylinder, used to simulate a manto, were each immersed in a tank of water in which three different salinities (1.74 * 10m2, 5.2, and 10.6 mhos/m) were used. The water simulated conductive host rock. We selected the aluminum sheet and the brass cylinder to represent “perfect” conductors at the 15 kHz frequency employed in these studies. In free space, the inhomogeneities produced no measurable quadrature magnetic field. When immersed in conducting solution, these conductors produced large quadrature magnetic fields, proof of which was one of the expectations of the study. We have not placed a horizontal linear scale on the anomaly curves because the carriage speed was only approximately constant, with the result that the precise conversion from model horizontal distance to full-scale horizontal distance may vary slightly from profile to profile. In Fig.9, 10, 11, 12, 15, 16, 17, 19, 20, 21, and 23, the left-hand ordinate corresponds to the location of the word START on Fig.8. The dot on each of the former set of figures corresponds to the vertical projection of the top of the sheet shown in Fig.8 or to the vertical projection of the axis of the cylinder. The aluminum or brass full-scale resistivities shown in Table III are lower than most massive sulphides in situ (Bosschart, 1961). The full-scale resistivities of the host media, listed in Table III, are well within the range of those normally encountered, provided the tapwater is excluded.
--
------.
N
D
;,
7
h
6
a
d
Symbol
~..~___ 4.69 *lo-* 1.004~10-’ 1.325~10~ 2.10 *lo3 8.09 .105 1.88*10-3 4.01 *1o-3 5.28+103 1.08+104 3.24m106
1,000
_._~.
_.._
9
4.5*1o-2 2.5*10-* 2.5.10-2 0.21 1.03 4.0*10-” 0.10 15 kHz 6.0 0.67
400 366 114 0.406
2.0 1.83 0.57 2.03*10-3
1,200 134 -.
5 5 42 206 0.80 20 --
200
line source to center of anomaly aluminum sheet, length aluminum sheet, depth extent aluminum sheet, thickness height of measurement above water surface depth below water surface to top of vertical aluminum sheet receiving coil, dia. brass cylinder, dia. brass cylinder, length brass cylinder, wall thickness integration distance model frequency vinyl pool, dia. solution, depth
1.88*10-4 4.01 *lo+ 5.28.10* 1.08.10’ 3.24*105
200
.
3,000 335 _____._.
12.5 12.5 105 515 2.0 50 -
22.5
1,000 916 285 1.02
500
6,000 670
25 25 ‘210 1,030 4.0 100 -
45
2,000 1,830 570 2.03
1,000
1.172.10-3 2.51 *lo-’ 3.31 *lo3 6.76 *lo’ 2.01 *IOh
500
scale factor for f = 880 Hz
Full scale dimensions, m (p, am)
o’t’ aluminum sheet = 6.09*104 mhos
7.49 ‘lo+ 1.605.10-4 2.13 -10’ 4.33 *loa 1.292.10“
200 500 .._.~~~.____ _..._
Full-scale resistivities p (nm) --scale factor for f = 220 Hz
Model dimensions (m)
3.0*107 l.4*107 10.6 5.2 I.74.1o-2
-~
Model conductivity u’ (mhos/m)
Parameter description
Aluminum sheet Brass hollow cyl. NaCl solution NaCl solution Tapwater
--
Model material
Model parameters for Turam scaled physical modeling reported here
TABLE III
4.69 *lo--’ 1.004 *lo-” 1.325.10’ 2.70 *lo4 8.09 *lo”
1,000 --.-.._
139
DIP Fig.8.
Geometry
150°
130a
of dipping
IlOo
aluminum
SO’
70’
50”
30’
sheets.
When aluminum or brass is placed in a solution, the chemical reaction between the two media produces a surface layer on the metal whose electrical impedance is unknown. Very likely this impedance is not a scaled representative of the surface impedance of a sulphide body immersed in the watersaturated host rock. This feature may then render scaled physical models of uncertain value for quantitative study of electromagnetic methods. Because the surface impedance is expected to be dominated by capacitive coupling across the double layer of charge at the surface (Marshall and Madden, 1959), the higher the frequency the less important is the surface impedance. At 15 kHz we doubt that surface impedance is important, although we have no conclusive means for proving this point. In any event, it is not important for demonstration of the principles learned from this study. Orientations of inhomogeneities Aluminum sheet: Fig.8 illustrates the nomenclature used for a dipping sheet, chosen to correspond to that selected by Bosschart (1964). The receiver traverse starts at a position 2.87 m from, and ends approximately 1.0 m from, the line source. The axis of the aluminum sheet was maintained parallel to the line source. The depth to the top of the aluminum sheet beneath the water surface was 2.5 - lo-’ m for the vertical sheet. The choice existed to orient the sheet around the top edge or around its central axis. The latter scheme was selected primarily for convenience in handling the sheet. Therefore, the depth to the top of the sheet varied considerably as did the distance from the line source to the top edge of the sheet. Brass horizontal cylinder: The horizontal axis of the brass cylinder was situated 2.0 m laterally from, 0.23 m below, and parallel to, the line source. As a cylinder is a body of revolution, dip is not a variable. The cylinder length was approximately half that of the aluminum sheet. Clearly evident in the
140
results of experiments using this model is the effect of a conductive finite length, of a geometry in which dip is of no significance. Results from physical
body of
modeling
Dipping aluminum sheet in tapwater. The first experiment designed to elucidate the nature of the response of an inhomogeneity of finite length in a conductive medium involved the aluminum sheet in tapwater. Fig.9-12 portray the real and imaginary parts of the vertical and horizontal magnetic field components. The following observations are made:
-ANOMALOUS CURVE --NORMAL CURYE *
SENSlTlVlTY
REOUCEO 81 5
-ASSUMED F’VAE BRANCH
Fig.9.
H,,
versus
distance
x for seven values
of dip of aluminum
-ANOMALOUS
Fig.10.
H,i
versus
distance
E
CURVE
sheet
in tapwater.
CURVE
x for seven values of dip of aluminum
sheet
in tapwater.
141
.
YERTlCAL OF TOP
-ANOMALOUS
OF
PROJECTION SHEET CURVE
Fig.12. Hzi versus distance x for seven values of dip of aluminum sheet in tapwater.
(1) The H,, anomaly of Fig.9 appears to be a superposition of two anomaly components, one of which is small, positive (labeled E branch in Fig.9) and dominated by relatively long spatial wavelengths, and the other of which (labeled H branch in Fig.9) is dominated by relatively short spatial wavelengths. The latter anomaly component is positive at dips of 110” or greater and negative at dips of 110” or less. Destinction between these two anomalies is not clear for dips greater than 70”. (2) The sign of the horizontal real magnetic field (H,,) reverses at a dip between 90” and llO”(Fig.9). The HX, anomaly amplitude ranges from 62% (dip = 150”) of primary field at x ? 2.0 m to -53% (dip = 30”) of primary field at x = 2.0 m. (3) The horizontal imaginary magnetic field (HXi) anomaly amplitude is very small, never exceeding 5.5% of the primary field at x = 2.0 m (Fig.10).
142
It increases in amplitude monotonically from the value of zero at a dip of 150” to a peak value of 5.5% at a dip of 30”. (4) The real part of the vertical magnetic field (Hi.,) anomaly inverts at some angle between 90” and 110” (Fig.11). The peak-to-peak amplitude, relative to background, ranges from +73% of primary field at a dip of 150” to -62% at a dip of 30”. The smallest extreme peak-to-peak anomaly occurs when the top of the sheet is nearest the line source. Distance of the top of the sheet to the line source may be more important than dip in explaining this asymmetry. (5) The quadrature part of the vertical magnetic field anomaly varies systematically from a value of zero at a dip of 150”, through 6% at a dip of 50”, to a value of 5.5% at a dip of 30” (Fig.12). (6) Fig.13 contains a summary of the peak amplitudes of HZ,. and H,i and the ratio Q of H,, to H,i plotted according to the legend of Bosschart (1964). -Where Bosschart found that Q was independent of dip, we find that Q is a function of dip even for a “perfect” conductor. The “angle of extinction” predicted by Fig.11 of Bosschart (1964) is 100” + l”, whereas we observe an extinction angle of 102”. The effect on Q of distance from the line source and of depth to the top of the sheet has not been determined. cq = 1.74
Fig.13.
X 10-2tnhor/m
Hzr, Hzi, and Q = H,,/Hzi
r
versus dip for aluminum
sheet
in tapwater.
(7) One may make a similar plot for the horizontal components as in Fig.14, where an extinction angle of 97” is now found. Once again, Q is a marked function of dip. The extraordinary agreement of our results with those of Bosschart, in terms of extinction angle, is taken as validating both sets of results. The peak amplitudes of the anomalies recorded herein are generally consistent with those found by Bosschart, even though the time constant of our circuitry integrated fields over a significant lateral distance and hence tended to smooth the curves. The conductivity contrast (1.72 * 109) between the model and the host medium is much larger than that observed in practice but much less than that employed when models are suspended in air.
143
60-
CT, = 1.74 x IO-*
mhoc
0,
mhor/
m 3.0
x IO’
/m m
40 s E
-5
20 -
-6O-
Fig.14.
Hx,r, H,i and Q = Hx,/Hxi
versus
dip for aluminum
sheet
in tapwater.
Dipping aluminum sheet in NaCl solution of conductivity, 5.2 mhos/m. If the model host medium conductivity is increased to 5.2 mhos/m the following are observed: of two (1) Again the HX ,. anomaly of Fig.15 appears to be a superposition anomalies, one of which is positive (E branch) and dominated by long spatial wavelengths, and the other of which (H branch) is positive at dips greater than 90”, negative at dips less than 90”, and is dominated by short spatial wavelengths. The E branch anomaly is much larger for a conductivity of 5.2 mhos/m than for one of 1.74 *lo-’ mhos/m. (2) In Fig.16 we have labeled an E branch and an H branch of H,,. corresponding to these quantities identified in Fig.15. An extinction angle corresponding to zero of the H branch is thus defined, but a true extinction of anomaly does not occur. (3) The “extinction angle” changes from 97” to 85” when the host conductivity is changed from 1.74 * lo-* to 5.2 mhos/m, although this angle becomes difficult to define insofar as it involves only the H branch for a conductivity of 5.2 mhos/m (compare Fig.14 and 16). (4) The positive peak H, ,. anomaly changes from +62% to +63%, while the negative peak H,, anomaly changes from -53% to -44% as the conductivity changes from 1.74 * lo-* to 5.2 mhos/m. (Compare Fig.9 and 15.) The effect of integration time could easily account for these differences. (5) The negative trough in the H,, anomaly at a dip of 150” is reduced by nearly a factor of 2 when the host conductivity changes from 1.74 * 10m2 to 5.2 mhos/m (compare Fig.9 and 15). (6) The positive peak in the H,, anomaly at a dip of 30” is increased by a factor of 3 as the host conductivity is increased from 1.74 * lo-* to 5.2 mhos/m (compare Fig.9 and 15).
HxR f
iiN
PHASE
)
= I5 ithr
Q, = 5.2mhoslm .Y~ = 3.0
X lO?mhos
Im
p = 2.0m h = 4.5
x IO-‘rn
d = 2.5
X IO-‘m
I
= 183m
b = 0.57m l
VERTICAL PROJECTION OF TOP OF SHEET
-ANOMALOUS --NORMAL ....
CURVE CURVE
ASSUMED BRANCH
PURE CURVE
E
Fig.15. tf,,. versus distance x for seven values of dip of aluminum sheet in NaCl solution ofn, = 5.2 mhos/m.
60-
rr, = 5.2 mhos/m trz
= 3.0
)I IO’
mhor
40-
/m - IO
4 w -5
-BO-
Fig.16. Hxr, Hxi, and Q a (I, = 5.2 mhos/m.
Hxr/H_xi versus dip for aluminum sheet in NaCl solution of
145
(7) The quadrature part of the horizontal changes shape as the dip is varied.
magnetic
v
Ii x,
70”
f
//
distance
( QUADRATURE
)
= 15 khr
q
=
cz
= 3.0
5.2
mhos
/m
x lO’mhos/m
p = 2.0m h = 4.5
x 10-2m
d = 2.5
X IO-*
I
=
m
1.83m
b = 0.57m
-27x
Fig.17. Hxi versus O, = 5.2 mhos/m.
field, shown in Fig.17,
.
VERTICAL OF TOP
-ANOMALOUS --NORMAL
x for seven values
of dip of aluminum
sheet
OF
PROJECTION SHEET CURVE
CURVE
in NaCl solution
of
(8) The change in amplitude of H,i is small as dip is changed from 30” to 150” (see Fig.17). (9) Q varies with dip but is, in general, small (see Fig.16). (10) HX i changes sign and increases substantially in amplitude as the conductivity of the host medium was raised from 1.74 * lo-* to 5.2 mhos/m (compare Fig.10 and 17). (11) The H,, component appears to reach true extinction at 90” (see Fig.18). Dipping aluminum sheet in NaCl solution of conductivity, 10.6 mhoslm. Exaggeration of all effects noted for the aluminum sheet in a host medium of conductivity 5.2 mhos/m is evident in Fig.19-21 pertaining to a host medium conductivity of 10.6 mhos/m. The following relative features are noted: (1) The relative contributions of the anomaly components, of short and long spatial wavelength, change as host medium conductivity is changed (compare Fig.15 and 19). (2) The H branch “extinction angle” for H,, is changed from 85” for a host of 5.2 mhos/m (Fig.16) to 71” for a host of 10.6 mhos/m (Fig.22), but a strong HXT anomaly exists for any angle when the host medium is of conductivity 10.6 mhos/m.
146
H,,
(IN
f
PHASE)
= 15 khz
Q,
= 5.2
mhosf
cr2 = 3.0
m
X lO?mhas
Im
p = 2.0m h = 4.5
X 10v2m
d = 2.5
x 16’m
I =
1.83m
b
= 0.57m
*
VERTICAL OF TOP
PROJECTION OF SHEET
-ANOMALOUS
CURVE
--NORMAL
Fig.18. LY+~versus distance of (J, = 5.2 mhos/m.
x for seven values of dip of aluminum
76%
CURVE
sheet in NaCl solution
68%
150"
1
l1O0
1
130”
40%
90"
& i-
~
--
_
~
,
-_
/
--.
Ii,,
1
50”
30” 21%
(IN
PHASE)
.
f
= 15khz
ot
= to.6
mhosfm
me = 3.0
X 107mhor/m
p = 2.0m
- - _
‘._
.-
h = 4.5
X ld2m
d = 2.5
x IO-“m
I
= 1.83m
b
= 0.57111
l
~
Fig.19. H,, versus distance o, = 10.6 mhos/m.
-26%
for seven values of dip of aluminum
-
VERTICAL PROJECTION OF TOP OF SHEET ANOMALOUS
CURVE
--NORMAL
CURVE
...- ASSUMED BRANCH
PURE CURVE
E
sheet in NaCl solution
of
/ -Id 147
go*
-37%
H,, ( OUADRATURE 1 f = 15 khz QI = 10.6mhos /m q = 3.0 x IO’mhor /m p h d I
= = = =
2.0m 4.5 X id* m 2.5 X Idem 1.83m
b = 0.57m . VERTICAL PROJECTION OF TOP OF SHEET -ANOMALOUS CURVE --NORMAL CURVE
Fig.20. H,i versus o1 = 10.6 mhos/m.
distance
x for seven values of dip of aluminum
I
sheet
in NaCl solution
H,, .( IN PHASE 1 f = I5 khz * 10.6 mhos /m = 3.0 I IO’mhos /m
d I b .
= 2.5 X IO-*m = I.63m = 0.57m VERTICAL PROJECTION OF TOP OF SHEET -ANOMALOUS CURVE --NORMAL CURVE
Fig.21. Hz, versus distance of o1 = 10.6 mhos/m.
x for seven values of dip of aluminum
sheet
in NaCl solution
of
-60L
I
Fig.22. H,,, H,i, and Q = Hx,./H,i versus dip for aluminum 0, = 10.6 mhos/m.
sheet in NaCl solution
of
(3) The amplitude of the positive peak of HX, at all dips is increased for a host of 10.6 mhos/m relative to that observed for a host of 5.2 mhos/m. The accompanying negative peak is reduced as the conductivity of the host increases from 5.2 to 10.6 mhos/m (compare Fig.15 and 19). (4) Both the H,i, and its change of amplitude with dip, increase as the host conductivity changes from 5.2 to 10.6 mhos/m (compare Fig.17 and 20). The Q, meanwhile, becomes slightly more negative and it is a slightly more pronounced function of dip. (Compare Fig.16 and 22.) (5) The amplitude of the peak-to-peak Hz, anomaly is increased for all dips, as the host conductivity is raised from 1.74 - lo-* to 5.2 mhos/m to 10.6 mhos/m. (Compare Fig.11, 18 and 21.) An illustration of the orientation of the ellipse of pol~ization at the surface of the host medium, relative to the dip of the aluminum sheet at which H branch extinction occurs, is contained in Fig.23. No quantitative relationship between ellipse parameters and H branch extinction angle is evident, but qualitatively the “extinction” angle rotates counter-clockwise when the major axis of the ellipse rotates clockwise. Horizontal
cylinder. Fig.24 portrays the anomalies in H,,., Hxi, Hz,., and H,i for three values of host conductivity. From this single figure we observe that: (1) The negative peak of H,, decreases as conductivity increases. (2) The anomaly in HXi first changes sign, then increases as host conductivity increases. increases, while the (3) The positive peak of Hz, increases as conductivity negative peak remains virtually unchanged.
149
-
SOURCE
MEASURING
SURFACE
Fig.23. Theoretical polarization ellipses, at a height earth, in relation to dipping aluminum sheet.
of 4.5~10.* m above a two-layered
BACKGROUND CONDUCTIVITY mhos /m
0.0174
i-- L!!! LIIT!Li / _ q -_ I, c/ii J’
ILL..,..,,..
Hxn UN
PHASE1
Fig.24. H,,, a horizontal
Hxi, Hz,,
cylinder.
and Hz; versus distance
I HORIZONTAL BRASS CYLlNDER AXIS PARALLEL TO WRE A - t.03m 6 = o.etm
,-
,/’
,-!; I
/’
5.2
.
/
i’
I’
/I
IO 6
T - 4xto‘Jm Q, * A3 INDICATED 4 - 1.4llo’mho~/s
p = 2.Om h = 4.3 “IO% 6 * 4 5 x Id% f = ekhr l “2RTlCAt PROJECTiON OF AXIS OF CYLINDER - ANWALOUS CURYE --NORMAL CURVE
I/
/’
.
x, for three values of conductivity
o,, over
150
(4) The increases. (5) The increasing (6) The increasing
anomaly
in Hzi first changes sign, then increases as host conductivity
normal or background host conductivity. normal or background host conductivity.
gradient
in H,i and H,i both increase with
gradient
in H,,
and Hz, both decrease
with
interpretation of results A line source situated on or over a conductive half-space, when energized with alternating current, will induce eddy currents in the half-space. If, then, an inhomogeneity of much greater conductivity than the half-space is immersed in the half-space, eddy current induction in the inhomogeneity may be conceived as originating in two mechanisms. First, for half-space of very low conductivity, currents in the half-space may be neglected and eddy currents are induced in the highly conducting inhomogeneity by magnetic field induction in the inhomogeneity. Second, for an inhomogeneity of finite length situated in a fairly conductive half-space, one may view the inhomogeneity as an electric flux collector, i.e., the currents are locally diverted from the half-space and concentrated in the more conductive inhomogeneity. Current density is increased in the inhomogeneity and decreased adjacent to it. For an inhomogeneity of infinite strike length, parallel to the inducing electric field, this flux collection mechanism does not seem to be operative as subsequent discussion will illustrate. In this framework, the dominant part of the “E branch anomaly”, if such can be considered to exist separately, would seem to arise in electric flux collection and to be represented, therefore, by a -line of poles. The “H branch anomaly”, again in this debatable framework, would seem to arise in magnetic induction and to be represented, therefore, by a line of dipoles. An alternate explanation for the phenomenon of anomaly enhancement, for bodies of finite length, is that the surfa%e electromagnetic fields arise in a suEerpositizn of induced electric sources JE and induced magnetic sources JM, the JE contribution being negligible when the host medium is free space. Results from computer modeling The integral equation formulation for electromagnetic scattering, as established by Hohmann (1971) for the Turam method, has been used to calculate the real and imaginary parts of the vertical and horizontal magnetic field components near a thin slab of infinite strike length located near an infinite line source of current. Fig.25 displays the Re (H,) anomaly profiles so calculated. The model parameters are listed in Table IV. These parameters are very close to those used in the scaled physical modeling of the Turam system. The slab thickness was, by computational limi~tions, selected as 0.04 m rather than the 0.002 m used for the physical models. This extra thickness is not expected to change the basic conclusions since the results found here are consistent with those found by Hohmann (1971) for a slab of quite different cross-section.
151
Fig.25. Turam anomaly 45”, when host medium
TABLE
profiles of Re(H,) is of (a) 1.74.10.’
observed over an aluminum sheet dipping at mhoslm and (b) 1.06-10’ mhos/m.
IV
Model parameters
for Turam mathematical
modeling Thick dike
Thin dike Parameters
model
full scale (scaling factor 200)
model
full-scale
Conductor length Conductor thickness Conductor depth eitent Depth to top of conductor Height of observation Frequency Conductivity of half-space
infinite 0.04 m 0.56 m 0.025 m 0.045 m 1.5.10’ Hz as quoted
infinite 8m 112 m 5m 9m -
infinite -
infinite 15 m 150 m _25, 50,100,150 0 500 Hz 2*10-’ mhos/m
-
m
152
The real in-phase anomaly is decreased substantially, regardless of dip, as a result of raising the host rock conductivity from 1.74 - lo-’ to 10.6 mhos/m in the model system. This effect clearly must be due to attenuation of the downgoing primary wave and of the upgoing secondary wave. Electric flux collection, as we have phrased it, does not seem to be present, when all media are of infinite strike length. In other words, current lines for a two-dimensional model are everywhere parallel to the infinite direction for a line source parallel to that direction such that current diversion is not present. We are now faced with an observation that a conductive host medium increases the anomaly for a thin slab or sheet of finite length while it seems to decrease the anomaly for a thin slab or sheet of infinite length. A study of the effect of length of a conductor buried in a conductive host medium clearly is in order, but so far has not been reported for any method. The importance of the impedance between buried conductor and host medium, noted earlier, is of fundamental importance to this issue. Fig.26 indicates that the imaginary part of H, increases as the conductivity of the host medium increases; hence a phase rotation arises due to the high conductivity of the host medium.
x
= 8
____----
0
- 1.0 ,LlNE
- 2.0
I I.0
SOURCE
I
I I5
I
I 20
I
I 2.5
I
I 3.0
I
I 3.5
I
I 4.0
I
I 45
I
I 5.0
METERS
Fig.26. Turam anomaly 45”, when host medium
profiles of Zm(H,) observed over an aluminum sheet dipping at is of conductivity (a) 1.74-10-2 mhos/m, and (b) 1.06*10’ mhos/m.
Fig.27 indicates that the anomaly of the real part of Hz decreases while the anomaly of the imaginary part of Hz increases with increasing conductivity of the host medium. Conclusions Clearly, conductive host rock can have a profound effect on Turam anomalies. It is evident that a conductive host medium can: (1) cause the ratio of real to imaginary magnetic field components due to
153
METERS r-7
Fig.27. Turam anomaly profiles of Re (Hz ) and Im (Hz ) observed over an aluminum sheet dipping at 45”, when host medium is of conductivity (a) 1.74*10~’ mhos/m, and (b) 1.06~ 10’ mhos/m.
an inhomogeneity to be a function of dip of inhomogeneity, conductivity of host medium, position in space relative to the inhomogeneity, plus strike of the inhomogeneity. (2) invalidate the quantitative interpretation of Turam data in terms of depth of burial and conductivity-thickness product. The range of host medium conductivities which produce the results noted is well within the range of conductivities encountered throughout the world. The dramatic difference of the effect of host medium conductivity upon the anomaly due to a slab of infinite as opposed to one of finite extent is indicated in the foregoing results. Thus we tentatively conclude that the use of models of infinite strike length can be misleading in this respect. Further study of this observation is required, however. Tilt angle and ellipticity
near a line source
Rather than measure the amplitude and phase of a magnetic field component, one might measure the tilt angle and ellipticity of the magnetic field in order to ‘locate subsurface conductors in the vicinity of a large loop or a line source. Such measurements using a large horizontal rectangular loop, operating
154
at a single frequency, have been made by Paterson et al. (1973), and multifrequency measurements will be made using the 14-frequency EM system described subsequently. Fig.28 and 29 show theoretical results for a two-dimensional conductor energized by a line source. The former figure is for a poor conductor (3 mhos), while the latter figure pertains to a good conductor (30 mhos). These curves were computed using the numerical modeling program described by Hohmann (1971). A frequency of 500 Hz and a background resistivity of 500 L?m were used for the calculations. Results are shown for the following depths of burial: 25, 50,100, and 150 m. The three important points to note in Fig.28 and 29 are: (1) The inflection point for the left side of the tilt angle anomaly occurs directly over the inhomogeneity. (2) The ellipticity curves for a good conductor are quite different from
too -
-80
L
Y
k
z
Z60 D
w
d z 4o 4 IJ
+
-
20
-
0.4
-
f
0
100
200
300
DISTANCE
400
(METERS)
500
-500
hz
600
Fig.28. Theoretical tilt angle (CX) and ellipticity (e) profiles a homogeneous half-space; conductivity contrast is 10”.
700
over a two-dimensional
slab in
155
04
= u
03
I= a.
702
HOMOGENEOUS
EARTH
ii 01
0
0
100
200
300
DISTANCE
Fig.29. Theoretical conductor buried
400
500
600
700
(METERS)
tilt angle (a) and ellipticity in a homogeneous half-space;
(E) profiles over a two-dimensional conductivity contrast is 10’.
slab
those for a poor conductor, thus providing a means of discrimination. (3) A large ellipticity anomaly occurs for a good conductor even at a depth of burial of 150 m. Tilt angle and ellipticity measurements would appear to be quite useful for detecting and evaluating subsurface inhomogeneities with this particular prospecting system. The dramatic change of ellipticity anomaly with change of host rock conductivity is clear evidence of the sensitivity of this magnetic field descriptor to changes in the geological model. The tilt angle is not nearly as sensitive a descriptor. SOUNDING
Vertical Loop data Fig.3 depicts the curves of tilt angle and ellipticity as functions of frequency of an observed electromagnetic field. One attempts to deduce,
via
156
forward or inverse methods, the conductivity and the thickness of each layer in an assumed horizontally stratified earth from such curves. Lateral variation in layer conductivity or thickness are ignored or treated lightly. As noted earlier, Fig.3a, b, c, d, and e depict the tilt angle and ellipticity versus frequency curves at distances of 300, 450, 900, 1,500, and 2,400 ft. from the center of a vertical loop of 30 ft. diameter. The curves illustrate (a) systematic translation along the frequency axis as the transmitter-receiver separation varies, and (b) broadening of the (Yand E curves as r increases. whether the transition in curve shape with Z-is due to horizontal layering or to vertical inhomogeneities is, of course, unknown at this stage. Quantitative study of these data is in progress. For each set of tilt angle and ellipticity curves of Fig.3, corresponding to a given transmitter-receiver separation, a layered model may be found, via forward or inverse methods, which will provide theoretical curves fitting the observational ones. The five models so obtained may then be “patched together”, as is standard practice in resistivity sounding, to obtain an approximate geoelectric section. Insofar as the parametric sounding curves of Fig.3 vary from site to site, rather than merely translate along the frequency axis, one might conclude that the earth is inhomogeneous laterally. Models of a laterally and vertically inhomogeneous earth are then required to fit all observational data. The combined parametric and geometric sounding was required to permit recognition of the heterogeneity of the true earth. Vertical Loop
uersus Horizontal
Loop
in sounding
As noted earlier, a horizontal loop will induce horizontal current flow in a horizontally layered earth. The conductivity of conductive horizontal layers may be deduced from the resulting data. A vertical loop will induce currents both within horizontal layers and across the layer boundaries. The resistivity-thickness product of a resistive layer, and the conductivity of a conductive layer presumably may be deduced from the resulting data. Systematic study of the relative virtues of vertical loop and horizontal loop electromagnetic systems in sounding, and comparison of them with resistivity sounding, are now in progress at the University of Utah. Madden (1971) provides useful guidelines for analysis of the problem. App~ica~i~~s of sounding
The data of Fig.2 and 3 were obtained while mapping water-bearing strata in Curlew Valley, Utah. The exploration problem under study was a hydrological one. Keller (1970) has reported on application of electromagnetic sounding to geothermal resource detection, while Frischknecht (1967) reported on application of the method to detection of the top of liquid lava at Kilauea Iki crater and on measurement of the electrical conductivity of the molten basalt. References to application of electromagnetic sounding to mining
157
problems are scarce. Hohmann et al. (1970) describe an attempt to measure the induced electrical polarization phenomenon inductively. However, systematic application of the electromagnetic sounding method to determine the depth and conductivity of overburden covering a lateral conductivity anomaly in the bedrock is seldom attempted, evidently. In view of the fact that conductive overburden shifts the phase, changes the amplitude, and changes the shape of anomalies due to buried conductors detected by electromagnetic profiling (Roy, 1970), and thereby markedly degrades quantitative interpretation of the profiling data, this seems unusual. On the other side of the coin, the resistiuity method is used occasionally to determine conductivity and thickness of overburden covering a buried electromagnetic profiling anomaly. To us it seems logical that the electromagnetic method should be used for sounding the depth and the conductivity of overburden in areas in which electromagnetic profiling is performed to search for buried inhomogeneities such as massive sulphide deposits. Inversion of Horizontal Loop sounding data To illustrate the features of the inverse method described during our discussion earlier of the theory of the inverse problem (p.128) we have chosen a particular two-layered earth model (conductive overburden case) shown in Fig.30. We have elected, arbitrarily, to use parametric, horizontal loop sounding. The transmitter-receiver separation is fixed at 200 m and eight transmitter frequencies are used: 21,42,84,168, 336,672, 1,344, and 2,688 Hz. The analysis is strictly theoretical in the sense that the “observed data” (Oj of equation (2)) are theoretically generated for the model in Fig.30.
Fig.30. Configuration coplanar loop system,
for parametric
sounding
of a two-layered
earth
with a horizontal
An initial parameter guess, Xi of p, = 10 Qm, p2 = 100 52m, and d = 20 m was made and the percent parameter change as a function of iteration is shown in Fig.31 for the vertical magnetic field component. Note that convergence to the correct parameter values has occurred after seven iterations. A similar result for the horizontal magnetic component, not shown, can be obtained only if the initial guess is within 10% for each parameter and the incremental change in parameter value after each iteration is severely controlled (Glenn et
158
0
2
1
4
6
6
10
ITERATIONS Fig.31.
Percent
parameter
change
versus iteration
of inversion.
al., 1972). The problem of resolution that arises here can be discerned readily from an examination of the theoretical model curves shown in Fig.32 and Fig.33. The theoretical curves for the vertical magnetic field component (Fig.32) have more individual character than do the curves for the horizontal magnetic field component (Fig.33) over the typical induction number range considered appropriate for geoexploration problems. To describe the problem one need only to look at curve 3 of Fig.32 and Fig.33 which corresponds to the model in Fig.30 (that is, d/r = 0.125). Curve 3 for the horizontal magnetic field component could be shifted either to the right or to the left and would become nearly coincident with curves 2 or 4 because of similarity in shape of curves 2, 3, and 4. This fact would preclude using the horizontal magnetic field component in a parametric sounding mode in conductive overburden regions. In contrast curve 3 for the vertical magnetic field component, parametric sounding (Fig.32), would not coincide with either curve 2 or curve 4 if shifted to the right or to the left because, now, all three curves are of similar shape. For geometric sounding the reverse argument is true. Lateral separation between curves, on the induction number axis, may be used in addition to curve shape in order to minimize ambiguity in either forward or inverse interpretation. Thus one need only alter the d/r ratio by varying r, measure the offset on the induction number axis, and determine the correct curve. Therefore, for direct curve-matching or inversion interpretations to be successful one should have a general knowledge of the character of the magnetic field variations over a variety of terranes before the experiment is performed. One way to approach this problem is through the inversion scheme (Glenn et al., 1973). The S matrix obtained by using the inversion scheme provides a means to assess the relative information contained in each observed data point in terms
d UT’
INDUCTION NUMBER (w+)‘4
Fig.32.
Fig.33
2
5
10
2
5
‘7’
INOUCTION NUMBER (+)4
Fig.32. Normalized /HZ1versus induction number B for parametric sounding over a twolayered earth with a horizontal loop system. The loop radius is 10 m; the ratio K’ of first layer to second layer conductivity is 0.1. Fig.33. Normalized lH,I versus induction number B for parametric sounding over a twolayered earth with a horizontal loop system. The loop radius is 10 m; the ratio K of first layer to second layer conductivity is 0.1
FREQUENCY thz)
Fig.34.
Information
density matrix resulting from inversion of data pertinent to Fig.30.
of its contribution to the resolution of the particular model under study. As an illustration, the S matrix for the model in Fig.30 is shown in Fig.34. For this model the resolution matrix R is the identity matrix and is not shown but the information density matrix is not an identity matrix since m = 8 and
160
p = it = 3 (see Table I). The structure of the S matrix should approach that of an identity matrix; that is, the optimum S matrix for uniform information distribution would have rows approaching delta functions which are centered on the diagonals (Glenn et al., 19’73). From Fig.34 we observe that little information is contributed to the resolution of the model for the two lowest frequencies. This result may be observed from the theoretical curves of Fig.32. For the model studied here these two low frequencies, 21 and 42 Hz, would correspond to induction numbers less than one, a region where there is little individual character difference between the model curves. The inherent power of the inversion method lies not only in its application to interpretation but also to experimental design as illustrated by the preceding discussion.
Introduction In the last few years, several methods have been developed for numerical evaluation of electromagnetic scattering from two-dimensional earth structures, i.e., earth structures which are infinitely extended in the horizontal y direction. A suitable set of references appears in Geophysics, 36(l). We have used one of these methods, the finite element method, to compute the scattering from the model earth structures used in this section. The long axis of a two-dimensional inhomogeneity is taken to be the y axis; the x axis is horizontal and normal to y while the z axis is vertical as in Fig.35. The electromagnetic wave equations are decoupled if two modes are assumed. The TE mode pertains to a wave in which the electric vector is in the y direction, i.e., parallel to the long axis of the inhomogeneity. The TM mode pertains
TE
mode g
TM mode
= jEy
i = 3Hy
Fig.35. Illustrations of TE and TM modes relative to two-dimensional
inhomogeneities.
161
to a wave in which the magnetic vector is parallel to the long axis of the inhomogeneity. The cross-section of a twodimensional inhomogeneity can be arbitrary. A horizontally layered structure is a trivial case. Conductive
dike model
Description
of model
Fig.36 portrays a vertical dike model of infinite depth and strike length in an otherwise homogeneous bedrock, overlain by soil overburden. The resistivities selected are typical of the Canadian Precambrian Shield, provided the dike model is used to simulate a fault zone. The depth of overburden is 30 m and the width of the fault zone is either 30 or 60 m. We shall study the effect of the fault zone on electromagnetic sounding-profiling with AMT and the effect of the overburden on lateral profiling with both AMT and AFMAG. A frequency of 1,000 Hz is chosen for the profiling while the range of frequencies l-l,000 Hz is chosen for the AMT sounding-profiling. 20-
a:
2
TE
15-
I.d
IO-
2.
Dg
5 I-
=30m d f
I
w i 7
mods
=60m = IOOOhz
5-
600
I 900
500
I 900
0 -5-
-930
- 600
-300
-6M)
-300
OISTANCE
0
300
-IO-15-20
t
-
0.1 -
? i
0.05 0 -900
p, *
DISTANCE
lo3n-nl
‘t
METER?,’
0
t\
GROUND
30m SCALE
Fig.36. AFMAG TE mode tilt angle and ellipticity of conductive fault with overburden.
profiles
across
two-dimensional
model
162
AFMAG profiling Fig.36 also contains plots of tilt angle and ellipticity versus horizontal distance normal to the fault zone for the TE mode, when the overburden is present. Fig.37 contains the same information when the overburden is absent but the top of the fault zone remains at, 30 m. The tilt angle is virtually unchanged in shape or amplitude, over a fault zone of 30 m thickness, when the selected overburden is added. On the other hand, the elliptic&y changes significantly from the overburden to the non-overburden case. The rise in TE
mods
f
:
d
= 30m
1000
hz
3
F
a
r: w
ao50 -900
-600
0
-300
OtSTANCE
300 (METERS)
600
/ 900
AIR GROUND
/j * I04&rn SCALE 0
METERS
300
Fig.37. AFMAG TE mode tilt angle and ellipticity of conductive fault without overburden.
profiles
across two-dimensional
model
ellipticity beyond 400 m from the axis of the fault zone in Fig.36, presumably arises in phase shift of the fields scattered from the fault zone; when the overburden is absent, this phase shift is not large. It is difficult to visualize any physical explanation for the increase in flank ellipticity with increase in thickness of the fault zone, but it may be due to coupling between the induced currents within the overburden and within the fault zone. We have not computed the tilt angle and ellipticity profiles beyond 1,200 m from the axis of the fault zone because of four factors: (1) The tilt angle and ellipticity are slowly varying functions of distance beyond 1,200 m and we anticipate decreases to zero beyond 1,800 m from the axis of the fault zone.
163
(2) The model boundaries are 1,800 m on either side of the axis of the fault zone and boundary effects are expected within a few hundred meters of the boundaries. (3) It is impractical, because of finite computer storage, to extend the model to a size that will ensure that the tilt angle and ellipticity go to zero as distance from the fault zone increases. (4) From a practical viewpoint, field profiles would seldom extend more than 1,200 m from the axis of an inhomogeneity. Customarily one attempts, in interpretation of electromagnetic survey data, to obtain the conductivity-thickness (ot) product, the dip, the length, the depth, and the depth extent of an inhomogeneity. Ward et al. (1968) describe an interpretation scheme for AFMAG, based on the use of two frequencies over disc models in fr.ee space. One could develop a similar interpretation scheme based on tilt angle and ellipticity at a single frequency rather than tilt angle at two frequencies. However, if realistic overburden, and bedrock resistivities are substituted for free space values, used in presently available interpretation schemes, the interpretation is materially altered. The central zero values of tilt angle and ellipticity are clear markers of the axis of the buried fault zone.
a;
6-
L %
4
3
% 2-
d * 30m
-
TE
----
TM f
d. -900
I - 800
1 300
I -300
d DISTANCE
W&w&N mode mode
‘1000hz 1 600
900
(METERS) 0
X
AIR 30J
/!
Fig.38. AMT of conductive
GROUND
* IO’P-In
apparent resistivity (pa) versus traverse distance across two-dimensional fault with and without overburden for TE and TM modes.
model
164
As is well known, TM mode excitation produces no tilt of the major axis of the ellipse of magnetic field polarization and the field is linearly polarized. AMT profiling
Fig.38 portrays the AMT apparent resistivity plotted versus horizontal distance for both TE and TM modes. An overburden of lo3 Qrn resistivity and 30 m thickness is present for one set of calculations and is absent for another. The fault width is selected both as 30 and 60 m for the submodels which include an overburden. The TE mode, for each model, produces the anomaly of largest amplitude and half-width. The TM mode anomaly extends only over a lateral distance of 300 m for each model and the apparent resistivity beyond 150 m on either side of the fault zone is that of an appropriate one- or two-layered half-space. In this instance, then, the TM mode is best for detection of vertical structures provided amplitude of anomaly, and not resolution, of adjacent structures, is taken as the main criterion for detectability. The 30 m overburden markedly attenuates the TM mode anomaly from the 30 m fault zone, but the TE mode fault zone anomaly is affected only slightly. Increasing the thickness of the fault zone from 30 m to 60 m increases the TE and TM mode anomalies appreciably. The apparent resistivity for a two-layered earth, without an inhomogeneity, is shown for comparison in Fig.38. AMT sounding-profiling
Fig.39a is a plot, in frequency-distance space, of contours of TE mode AMT apparent resistivity. A broad inhomogeneity is suggested by the contours which are not clear evidence for either a narrow vertical fault zone nor a horizontally layered structure. The induced currents flow parallel to the fault zone in the overburden and along the fault zone itself. Fig.39b is a plot, in frequency-distance space, of contours of TM mode AMT apparent resistivity. Both the vertical fault zone and the horizontal layering are clearly evident in the contoured data. The induced currents flow normal to the fault zone in the overburden and transversely through the fault zone itself. The TM mode produces the larger fault zone anomaly at 1 Hz, but the smaller fault anomaly at 100 Hz and above. Conclusions
Vozoff (1971) previously studied a similar model for the TE mode and drew the following conclusions: (1) The frequency at which peak response occurs is, to first order, independent of bedrock resistivity for bedrock as resistive as lo3 Rm. (2) The peak Hz/H, ratio (approximately equal to tilt angle) depends on overburden thickness, overburden resistivity, and bedrock resistivity.
165
DISTANCE
( METERS)
DISTANCE
3” /
_-600
-3 00
(METERS) 0
600
300
900
’ Onnn
(bl 0
TM
mode AIR
I
Fig.39. Contours in frequency-distance resistivities across a buried fault.
space
of TE and TM mode
AMT apparent
(3) The overburden attenuates the peak Hz/H, anomaly according to the induction number B = (0~ w ) ‘12d where d is the depth of overburden. To these conclusions we add the following: (1) The apparent resistivity may be decreased in the vicinity of a conductive fault zone for both modes, but the apparent resistivity contours, in frequencydistance space, are quite different for the two modes. (2) Both TE and TM mode AMT depth sounding in an inhomogeneous terrane would lead to errors in estimates of overburden depth and resistivity within several hundred meters of the fault zone, but the TM mode fault zone anomaly is least extended laterally. (3) Since a fault zone alters sounding interpretation and overburden alters profiling interpretation, then continuous sounding-profiling is required for maximum interpretability of either sounding or profiling data in areas where both layering and inhomogeneities are expected. (4) A wide range of frequencies, preferably covering several decades, is required for maximum interpretability of sounding-profiling data.
166
Effect
of surface topography
Description
of model
Parry and Ward (1971) used an integral equation formulation to compute the 1,000 Hz TE mode scattering from a ridge. Their calculations pertain to measurements well above the ridge. For AMT and ground AFMAG purposes, it is necessary to calculate the scattered field components on the surface topography. Fig.40 describes a ridge 90 m high superimposed upon a 30-m deep layer of overburden under which lies resistive bedrock. A gravel ridge and gravel overburden such as a glacial esker and a layer of glacial gravel might be represented by the dimensions and resistivities selected. The bedrock is highly resistive as might be expected in the Precambrian Shield of Canada.
TE
mode
f = IOOOhr
-900
-600
-300 DISTANCE
600 ‘t
SOM
AIR
Gf7CUND
IOU--l
Fig.40. profile
Two-dimensional across it.
AFMAG
900
METEf%”
model
of surface
topography
and AFMAG
TE mode
tilt angle
profiling
The 1,000 Hz AFMAG TE mode tilt angle and ellipticity profiles over the ridge are illustrated in Fig.40. The peak-to-peak tilt angle anomaly is 20”, a value consistent with the lesser vertical field peak-to-peak anomaly obtained by Parry and Ward (1971) at an elevation of 150 m above the ridge.
167
The TE mode ellipticity varies systematically across the ridge. It is zero at the axis of the ridge and reaches peak values of 0.14 at 300 m on either side of the ridge. The TE mode ellipticity anomaly is larger and the TE mode tilt angle anomaly is smaller, for the ridge represented, compared to the fault zone and overburden combined (compare Fig.40 with Fig.36).
AMT profiling The apparent resistivity deduced from AMT continuous sounding-profiling at 1,000 Hz is drawn above the sketch of the ridge in Fig.41. A small central resistivity low, flanked by slight high values, is evident in the TE mode data. The central low and flanking highs are much larger for the TM mode than for the TE mode.
AIR
P,=103n-ml &=
GROUND
104n-m SCALE 0
METERS
300
f.looohz Fig.41. Two-dimensional model apparent resistitities across it.
of surface
topography
and AMT TE mode
and TM mode
Buried topography Depression
in bedrock surface
Faults frequently offset the bedrock topographic surface to produce a local thickening of the overburden, but otherwise do not affect the geoelectric section. Fig.42 portrays the TE mode 1,000 Hz tilt angle and ellipticity profiles across such a feature. Note the peak-to-peak tilt angle anomaly of +7 to -8” and the peak ellipticity anomaly in excess of 0.07. Both anomalies
I5
TE
z
mode
f=iooohz
-900
Fig.42. it.
-600
-300 DISTANCE
Two”di~ensional
600
900
’ (MET&i0
model
of buried
topography
and AFMAG
tilt angle profile
across
might be erroneously interpreted to indicate a vertical conductor located about 175 m to the left of the fault (compare Fig.37 and 42 for example).
Depression
in bedrock
surface plus conductive
fault zone
causing the bedrock depression is conductive by virtue of increased porosity associated with shattered rock, the model of Fig.43 might pertain. In comparison with the responses over a fault zone buried beneath overburden as in Fig.36, we note that the depressed bedrock makes the following disturbances in TE mode, 1,000 Hz responses: (1) the peak tilt angle at the left of the fault zone is shifted about 200 m to the left, (2) the peak-to-peak tilt angle increases, comparable with that over a fault zone of 60 m width buried beneath a uniform layer of overburden and (3) the peak ellipticity at the left of the fault zone is decreased, but is increased slightly at the right of the fault. The tilt angle profile could readily be interpreted as arising in a fault zone alone, but the ellipticity profile warns that the geoelectric section is complex. Evidently, both tilt angle and ellipticity should be recorded in an AFMAG survey. If the
fault
169
TE
mode
qi 1
-900
-390
- 600
0 DISTANCE
300
Fig.43. Two-dimensional model of buried and ellipticity profiles across it.
Conductive topography
,
600
topography
fault zone with overburden,
Description
--do
(METERS)
with fault and AFMAG
surface topography
tilt angle
and buried
of model
Fig.44 illustrates a simplified version of a rather common geological crosssection. A fault zone of resistivity 10’ Rm separates two blocks of the same country rock, the left-hand block being rotated and downdropped at the fault. A general layer of overburden, thickening to a ridge at the fault, hides the subsurface structure. This model represents the superposition of the previous several models. Whether one was attempting to find the thickness of overburden via sounding or the location of the fault zone via profiling, all elements of the geologic section would need to be taken into account. Dual-mode broad-band continuous sounding-profiling becomes highly desirable in such situations. Let us draw this conclusion, however, by studying finite element computations over this complex structure. AFMAG
profiling
Fig.44 also contains
TE mode tilt angle and ellipticity
profiles over the
170
02 = a15
u
F 5
d
O’ 0.05 0
-900
-600
-300D16TANCE0
wrE3F%
Fig.&. Two-dimensional model ellipticity profiles across it.
600
900
of inhomogeneous
earth,
and AFMAG
tilt angle and
structure with the fault zone width 0, 30, and 60 m. With no fault zone present, d = 0, the tilt angle profile is dominated by the combination of surface and subsurface topography (compare Fig.40 and 42 with 44). The tilt angle anomaly increases and the el1ipticit.y anomaly decreases in magnitude as the thickness d or induction number B = (opw )li2d of the fault zone increases.
Fig.45 contains the TE and TM mode AMT apparent resistivity profiles across the same structure. The TE mode anomaly increases with thickness of the fault zone; but surface and subsurface topography contribute modestly to it. Compare duplicates of the curves of Fig.41 with the other curves of Fig.45. The TM mode anomaly increases only slightly with thickness of the fault zone, it is dominated by the effect of surface topo~aphy and made asymmetrical by the effect of buried topography. AMT sounding-~rofi~~rzg
Fig46a,
b are plots, in frequency-distance
space, of contours
of TE mode
171
‘+m
0-
TOP0
l-d 2-d
ONLY = =
/
Om 30m
GROUND
v
SCALE METERS
Fig.45. earth.
AMT apparent
resistivity
profiles
across
two-dimensional
model
of an inhomogeneous
and TM mode, respectively, AMT apparent resistivity computed for the geometrical model shown in Fig.46c. Note that the resistivities of the media of this model were selected to be ten times lower than those of Fig.45b. The model now would simulate a sulphide deposit buried beneath a clay overburden and a clay ridge. However, if the values of frequency shown in Fig.46a or Fig.46b were multiplied by 10, the resistivities of Fig.46 could be multiplied by 10 and the model would again simulate a fault zone beneath gravel. Frequencies as high or higher than lo4 Hz, are required to reveal the shallow structure of Fig.45b, whereas frequencies of lo3 Hz are adequate to reveal the shallow structure of Fig.46c. The TE mode apparent resistivity plot of Fig.46a still suggests a broad inhomogeneity as for the simpler model producing the results of Fig.39a. Comparing Fig.46a with Fig.39a we observe asymmetry in the contours of the former figure, which may indicate a structural complexity. There are, however, no diagnostic criteria permitting Fig.46a to be interpreted in terms of a vertical fault zone, a horizontally layered structure, surface topography nor buried topography, as separate entities. The TM mode apparent resistivity plot of Fig.46a clearly reveals the complexity of the structure. A narrow central zone of the apparent resistivities,
172
DISTANCE
IMETERS)
((1)
DISTANCE
103n-In
mode
IMETERS)
(b)
Pz =
TE
u-
Pa-lo’n-m
TM mode
SCALE OF=-=METERS
‘O”
Fig.46. Contours in frequency-distance space of TE and TM mode AMT resistivities across two-dimensional model of an inhomogeneous earth.
apparent
less than 70 am, due to the buried fault zone, appears to be shifted to the left by the buried topography, and is flanked on either side by zones of slightly higher apparent resistivities. Beyond these latter zones, the resistivities rise again. The surface topography presumably produces the slightly higher resistivities near the center of Fig.46b, and also adds to the low at the left and contributes a slight low at the right. Frequencies in excess of 10’ Hz clearly reveal a horizontally layered structure of overburden and bedrock at distances in excess of 500 m on either side of the fault. Frequencies less than 10’ Hz do not appear to detect the horizontal stratification at such distances. If the resistivities of the media of Fig.46c were multiplied by 10 to comply with Fig.45b, horizontal stratification would be detected only if frequencies well in excess of lo3 Hz were employed.
173
Conclusions For two-dimensional complex geologic cross-sections, we can draw the following conclusions: (1) The amplitude and the shape of the AFMAG TE mode tilt angle and ellipticity anomalies are governed not. only by a buried fault zone but also by surface and buried topography adjacent to it and by the mode of excitation. (2) The amplitude and the shape of the TE mode AMT apparent resistivity anomaly is much more affected by a fault zone than by surface or buried topography adjacent to it. (3) The amplitude and the shape of the TM mode AMT apparent resistivity profile is dominated by the surface topography. (4) Provided the fault zone exhibits a larger induction number than the irregular overburden above it, the effect of the fault zone can be emphasized and the overburden de-emphasized by using lower frequencies. (5) The effect of the overburden can be emphasized relative to the fault zone by using higher frequencies. (6) The surface topography, the buried topography, and the fault zone will all affect the interpretation of overburden sounding data. According to our calculations these effects carry laterally for several hundreds of meters. (7) As frequency is varied for a sounding, the relative contributions of the surface topography, buried topography, and fault zone will each vary in the vicinity of the structure. (8) Dual-mode broad-band continuous sounding-profiling, provides the maximum amount of data for interpretation. The degree to which this amount of data can be exploited, and the economics of attempting to acquire this amount of information, require field study for evaluation. This field study is in progress. (9) Measurement of both tilt angle and ellipticity is to be preferred to measurement of tilt angle alone in an AFMAG survey, because, as a minimum, ellipticity seems to be a more sensitive indicator of complexity than tilt angle, while tilt angle is more readily interpretable. It is axiomatic that ambiguity of interpretation is made more apparent, and sometimes may be reduced, by measurement of two parameters rather than one. The anatomy
of an anomaly
The examples presented indicate that interpretation of AFMAG and AMT electromagnetic profiling data is ambiguous unless evaluation can be made of the effects of surface topography, buried topography, overburden resistivity, and bedrock resistivity. Further the examples indicate that interpretation of AMT electromagnetic sounding data is ambiguous unless surface topography and buried inhomogeneities, such as fault zones, are evaluated. The maximum information is provided when dual-mode, broad-band, continuous soundingprofiling is carried out. Whether or not all of this acquired information can be assimilated and will lead to improved interpretation remains to be established
174
by field studies. However, it can be said that a warning signal on the complexity of a geologic structure is provided when this full information is provided, but is usually lacking if both modes, broad band, or continuous sounding-profiling are not utilized. SUMMARY
OF LIMITATIONS
OF ELECTROMAGNETIC
EXPLORATION
Introduction The data presented so far permit us to make a summary of the limitations of electromagnetic sounding and profiling introduced by a complex geoelectric section. This summary appears below first under profiling and then under sounding.
Profiling Table V contains a summary of the deleterious effects introduced by overburden, host rock, and topography on interpretation of electromagnetic profiling data. This table is based on observations by Hedstrom and Parasnis (1958), Gaur (1959,1963), Lowrie and West (1965), Roy (1970), Hohmann (1971), Sarma and Mar-u (1971), Swift (1971), Vozoff (1971), Verma (1972), and on data presented in this paper.
Sounding Lateral inhomogeneities such as faults, surface topography, and buried topography all invalidate deduction of layer thicknesses and conductivities results in this paper illustrate. A 14-FREQUENCY
SOUNDING-PROFILING
as
SYSTEM
Introduction The authors have been studying the theory for tilt angle and ellipticity sounding and profiling for several years (Ward, 1967b; Dey and Ward, 1970; Ryu et al., 1970). We have published one case history of application of tilt angle and ellipticity sounding (Ryu et al., 1972). Fig.2 and 3 of this paper were obtained with a new 14-frequency tilt angle and ellipticity electromagnetic system suited to sounding, profiling, or continuous sounding-profiling and it is this system which we shall next describe.
Transmitting
system
The transmitter is capable of supplying up to 20 A, to either one of two transmitting coils at frequencies of 10.5, 21, 42, 84, 168, 336, 672, 1344,
175
TABLE
V
Summary of effects of overburden, host rock, surface topography and buried topography problem
Methods for which effect has been observed ~~___
Ingredient
Effect
Interpretation
Overburden
rotates phase
depth estimates invalid
horizontal loop
decreases amplitude
ot estimates invalid
TURAM AFMAG AMT VLF rotary field airborne
Host rock
rotates phase increases amplitude for shallow conductors
depth estimates invalid
horizontal loop
ot estimates invalid
TURAM
dip estimates invalid
AFMAG
expected to decrease amplitude for deep conductors
AMT VLF rotary field airborne
changes shape of profiles Surface and buried topography
hunting airborne
fall-off laws changed introduces geologic noise
depth estimates invalid
TURAM
ot estimates invalid
AFMAG
distorts or obscures anomalies
dip estimates invalid
AMT
anomalies not recognized
2688, 5376, 10752,21504,43008, and 86016 Hz. These frequencies are in geometric progression with a common ratio of 2 and are chosen to avoid 60 Hz and its harmonics. One transmitting coil is 200 ft in diameter when used as a circular horizontal loop while it is roughly 280 ft long by 33 ft high when erected on masts as a fixed vertical loop. The number of turns used on the loop range up to 10. A maximum magnetic moment of 2.92 *10’ A - turns * m2 is available with this loop, but the actual turns, current, and hence moment vary with frequency. A second loop may be used as a 30-ft diameter circular loop for orientation in either the horizontal or vertical planes. The maximum number of turns which may be connected in this loop is 38 while the maximum current is 20 A; a maximum moment of 2.81. lo4 A +turns - mz results. Fig.47 depicts this latter loop when erected in a vertical plane; it may be rotated about the vertical diameter when in this orientation. Table VI illustrates the several configurations possible with this transmitting system
VI
I, 0 = cylindrical f = frequency
Sounding
--
loop
coordinates
vertical loop
horizontal
vertical
___~
vertical _-- _~_I_-
horizontal
rotatable
vertical loop
._~
horizontal
.._ _____
“TURAM”
..-“__
._~
Profiling
-
--
1Cfrequency
Orientation of transmitting loop
for generalized
Technique
techniques
Function
_.-
Operational
TABLE
__
large or small
large or small
small
large or small
~___.
on axis of loop
on any radius
plane of loop
on any radius
~_
Location of point observation
system
-._. -
Transmitting loop size
.._~
electromagnetic
r,e,f
plane of vertical loop
r, f __~-
r,e,f
vertical plane through axis of loop ~__ _.._._^___~
r,e,f
plane normal to plane of loop
-
Variable parameters geometric
vertical radial
~-~--.
Plane of measurement
Fig.47. system.
Pictorial
description
of small loop
in vertical
plane,
of 14-frequency
elect] romagnel tic
178
Receiving
system
Two orthogonal receiving coils operating into a phase-sensitive detector permit measurement of tilt angle to a precision of 0.1” and of ellipticity to 2%. Accuracies are estimated as 0.5” and 5% for tilt angle and ellipticity, respectively. One such receiving coil system is used for the frequency range 10.5~2,688 Hz while another such system is used for the frequency range 5,376~86,016 Hz. Fig.48 depicts one receiving coil system. Table VI notes the manner of measurement of tilt angle and ellipticity for the several possible transmitter configurations. The operating principle of the orthogonal receiving coil system is quite similar to the principle of an AFMAG receiver as described by Ward (1967b). Ellipticity is not normally measured in an AFMAG survey nor in any other electromagnetic prospecting tilt angle system. Its measurement was, however, included in the Bieler-Watson method employed in Australia as early as 1928 (Broughton-Edge and Laby, 1931). Referring to Fig.49, the output of one coil, the reference coil, gates the output of the other, the signal coil, via a phase-sensitive detector. Thus for a linearly polarized field, the instantaneous detector output will be positive, zero, or negative according to the signal coil orientation relative t,o the field vector as illustrated in Fig.49. Because a phasesensitive detector is employed, an output will be recorded only for that part of the signal voltage which is in phase with the reference voltage. In a field which is elliptically polarized, the phase of the component along the axis of the reference coil governs the output of the phase sensitive detector. When the reference coil is oriented along the major axis of the ellipse, the output of the detector is zero, but it is positive or negative when the reference coil assumes another orientation. Thus by rotating the coil system about its axis, the signal coil is readily aligned along the minor axis and the reference coil along the major axis. Measurement of the signal coil and reference coil outputs then yields a voltage ratio proportional to the ellipticity. Preliminary
results obtained
with 14-frequency
system
Fig.2 and 3 illustrate preliminary results obtained ostensibly horizontally layered medium. Future use of the lo-frequency
with the system over an
system
Quantitative interpretation of the data obtained with the system has yet to be made. The amount of information collected for Fig.3 is comparable to the amount of information we normally expect to obtain in a combined resistivity-induced polarization survey. In the latter instance we commonly use two frequencies, five separations, and a large number of transmitter locations. With the 16frequency electromagnetic system we expect to use up to three transmitter locations, five to fifteen transmitter-receiver
Fig.48. system.
Pictorial
description
of one receiving
coil unit for 14-frequency
electromagnetic
180
REFAWCE COIL NET NEGATIVE METER
READING
NET POSITNE
METER
READING
0
I
+ ---INET ZERO METER READING
Fig.49.
Principle
of orthogonal
coil,
phase sensitive
detector,
receiving
unit
‘oo’“oo* 10,000-
i
z
IOOO-
!i
& IL
100
“0
12
4I
DISTANCE
Fig.50.
Contours,
61
FROM
6I
10 I
I2 I
14
16
16
20
TRANSMITTER-HUNDREDS
in frequency-distance
22
24
OF
space,
26 I
FEET
of tilt angle observed
near a vertical
loop,
separations and, of course, fourteen frequencies. The selection of precise values for number of transmitter locations, number of transmitter-receiver separations, and number of frequencies will depend upon optimization studies using the inverse method of interpretation to identify the density of informa-
181
tion and upon economic and logistical studies. The intent is to seek to make the electromagnetic method more cost-effective than the combined resistivityinduced polarization method when used in the same application. One possible data presentation scheme is contained in Fig.48 where tilt angle is contoured in frequency-distance space. Such diagrams for observed tilt angle and ellipticity would be used for comparison with similar diagrams obtained by forward problem solution. However, this would be intended only as a guide for initial guesses for the primary interpretation via inversion. Either the TE mode or the TM mode, or both, can be induced in a subsurface inhomogeneity depending upon the location and orientation of the transmitting coil relative to the inhomogeneity. It is entirely possible that with the generalized approach we have initiated in instrumentation, field technique, and interpretation we can significantly improve the application of the electromagnetic method in conductive terranes. ACKNOWLEDGEMENTS
Results presented here have been obtained in research sponsored by the National Science Foundation under grants GA 24421 and GA 31021, and by the National Aeronautics and Space Administration under contracts NASB5078, NAS9-11475, and NAS9-12168. O.P. Verma generously permitted use of unpublished data from scaled physical modeling. Mrs Kay Suiter typed the manuscript, Falko Friemann supervised drafting of the figures, Dennis Buzzell assisted with the field observations and S.A. Ward assisted with the Turam modeling; we are indebted to all of them. We are grateful to McPhar Geophysics Limited for designing and producing the 14-frequency electromagnetic system and for sharing in its cost. REFERENCES Backus, G.E. and Gilbert, J.T., 1967. Numerical applications of a formalism for geophysical inverse problem. Geophys. J. R. Astron. Sot. B, 15: 247-276. Backus, G.E. and Gilbert, J.T., 1968. The resolving power of gross earth data. Geophys. J. R. Astron. Sot., 16: 169-205. Backus, G.E. and Gilbert, J.T., 1970. Uniqueness in the inversion of inaccurate gross earth data. Philos. Trans. R. Sot. Lond., A, 266: 123-192. Bosschart, R.A., 1961. On the occurrence of low resistivity geological conductors. Geophys. Prospect., 9: 203-212. Bosschart, R.A., 1964. Analytical Interpretation of Fixed Source Electromagnetic Prospecting Data. Thesis, Technische Hogeschool, Delft, The Netherlands, 103 pp. Broughton-Edge, A.B. and Laby, T.H., 1931. Geophysical Prospecting, The Report of the Imperial Geophysical Experimental Survey of Australia. Cambridge University Press, Cambridge, England, 372 pp. Dey, A. and Ward, S.H., 1970. Inductive sounding of a layered earth with a horizontal magnetic dipole. Geophysics, 35: 660--703.
182
Frischknecht, F.C., 1967. Fields about an oscillating magnetic dipole over a two-layer earth, and application to ground and airborne electromagnetic surveys. Q., Colo. School Mines, 62(l): l-326. Gaur, V.K., 1959. Model Experiments Simulating Conditions Encountered in Airborne Electromagnetic Prospecting. Thesis, University of London, London, England. Gaur, V.K., 1963. Electromagnetic model experiments simulating an airborne method of prospecting. Bull. Natl. Geophys. Res. Inst., 1: 167-174. Glenn, W.E., Ryu, J., Ward, S.H., Peeples, W.J. and Phillips, R.J., 1973. Inversion of vertical magnetic dipole data over a layered structure, 3. Geophysics, 38(6): 1109-1129. Grant, F.S. and West, G.F., 1965. Interpretation Theory in Applied Geophysics. McGraw Hill, New York, 583 pp. Hedstrom, E.H. and Parasnis, D.S., 1958. Some model experiments relating to electromagnetic prospecting with special reference to airborne work. Geophys. Prospect., 4: 322-341. Hohmann, G.W., 1971. Electromagnetic scattering by conductors in the earth near a line source of current. Geophysics, 36(l): 101-131. Hohmann, G.W., Kintzinger, P.R., Van Voorhis, G.D. and Ward, SW., 1970. Evaluation of the measurement of induced electrical polarization with an inductive system. Geophysics, 35: 901-915. Inman Jr., J.R., Ryu, J. and Ward, S.H., 1973. Resistivity inversion. Geophysics, 38(6): 1088-1108. Jackson, D.D., 1972. Interpretation of inaccurate, insufficient and inconsistent data. Geophys. J. R. Astron. Sot., 28: 97-109. Keller, G.V., 1970. Induction methods in prospecting for hot water. Geothermics, Spec. Issue 2, 2(l): 318-332. Keller, G.V. and Frischknecht, F.C., 1966. Electrical Methods in Geophysical Prospecting. Pergamon, New York, N.Y., 517 pp. Lanczos, C., 1961. Linear Differential Operators. Van Nostrand, London, England, 539 pp. Lowrie, W. and West, G.F., 1965. The effect of conducting overburden on electromagnetic prospecting measurements. Geophysics, 30: 624-632. Madden, T.R., 1971. The resolving power of geoelectric measurements for delineating resistive zones within the crust. In: J.G. Heacock (Editor), The Structure and Physical Properties of the Earth’s Crust. American Geophysical Union, Washington, D.C., pp. 95-105. Marshall, D.J. and Madden, T.R., 1959. Induced polarization: a study of its causes. Geophysics, 24: 790-816. Parry, J.R. and Ward, S.H., 1971, Electromagnetic scattering from cylinders of arbitrary cross-section in a conductive half-space. Geophysics, 36(l): 67-100. Paterson, N.R., Hewitt, R.P. and Dockery, B., 1973. Extra low frequency (ELF) EM surveys with the EM-25 in Western Australia. In: B.D. Johnson, D.S. Parasnis and K. Vozoff (Editors), Geophysics of the Earth and the Oceans, Part III. Geoexploration, 12( 2/3): 226 (abstract). Roy, A., 1970. On the effect of overburden on EM anomalies, a review. Geophysics, 35(4): 646-659. Ryu, J., Morrison, H.F. and Ward, S.H., 1970. Electromagnetic fields about a loop source of current. Geophysics, 35: 862-896. Ryu, J., Morrison, H.F. and Ward, S.H., 1972. Electromagnetic depth sounding across Santa Clara Valley. Geophysics, 37(2): 351-374. Sarma, D.G. and Maru, V.M., 1971. A study of some effects of a conducting host rock with a new modeling apparatus. Geophysics, 36(l): 166-183. Swift Jr., C.M., 1971. Theoretical magnetotelluric and Turam response from twodimensional inhomogeneities. Geophysics, 36(l): 38-52. Vanyan, L.L., 1967. Electromagnetic depth sounding. Selected and translated by G.V. Keller, Consultants Bureau, New York, N.Y., 312 pp.
183
Verma, O.P., 1972. Electromagnetic Model Experiments Simulating Conditions Encountered in Geophysical Prospecting. Thesis, University of Roorkee, Roorkee, India, 143 pp. Vozoff, K., 1971. The effect of overburden on vertical component anomalies in AFMAG and VLF exploration: a computer model study. Geophysics, 36(l): 53-57. Ward, S.H., 1967a. Electromagnetic theory for geophysical applications. In: Mining Geophysics, II. Society of Exploration Geophysicists, Tulsa, Okla., pp.lO-196. Ward, S.H., 1967b. The electromagnetic method. In: Mining Geophysics, II. Society of Exploration Geophysicists, Tulsa, Okla., pp.224-372. Ward, S.H., O’Brien, D.P., Parry, J.R. and McKnight, B.K., 1968. AFMAG --. Interpretation. Geophysics, 33(4): 621-644. Ward, S.H., Peeples, W.J. and Ryu, J., 1973. Analysis of geoelectromagnetic data. In: Methods in Computational Physics, 13. Geophysics, 38(5): 1109-1129. Wiggins, R.A., 1972. The generalized inverse problem. In: Reviews of Geophysics and Snace Physics, 10: 251-286.