Different Kinds of Noise and Ways for Their Removing

CHAPTER 3

Different Kinds of Noise and Ways for Their Removing Chapter Outline 3.1 Instrumental Noise 15 3.1.1 3.1.2 3.1.3 3.1.4 3.1.5

Gravimeter 15 Magnetometer 15 Temperature Device 16 Electrodes in SP Method 16 Resistivity 16

3.2 Technogenic Noise 16 3.3 Temporal Variations 17 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5

Gravity Field 17 Magnetic Field 17 Temperature Field 18 SP Field 19 Resistivity 20

3.4 Terrain Relief Influence 3.4.1 3.4.2 3.4.3 3.4.4 3.4.5

20

Magnetics 20 Temperature 25 Gravity 26 Resistivity 28 Self Potential 29

3.5 Complex Geological Media and Noised Environment References 31

29

It is well known that geophysical observations are often complicated by a lot of factors (Eppelbaum and Khesin, 2012). Detailed investigation of these noises enabled to develop a generalized scheme of their classification (Fig. 3.1). Let us briefly consider these disturbances. Artificial noise. The first component of this noise is industrial component. This component comprises power lines, cables, buildings, different underground and transport communications and strongly affects practically all potential fields applied in geophysics (a list of all this noise is reflecting in self-potential (SP) methods). Instrumental component is associated with the properties of geophysical instruments, such as a “shift zero” of gravimeters and magnetometers. Difficulties of electrodes grounding are of some Geophysical Potential Fields. https://doi.org/10.1016/B978-0-12-811685-2.00003-5 Copyright © 2019 Elsevier Inc. All rights reserved.

13

14 Chapter 3 significance for geophysical potential fields with electrode scheme of measurements, such as resistivity and SP methods. It is one of typical technical problems arising in arid and semiarid regions. Finally, the last component of artificial noise is absence of information about the earlier performed geophysical observations at the site under study that did not allow to utilize these data by planning geophysical investigations and their analysis (Eppelbaum and Khesin, 2012). Natural disturbances. The first component of nonstationary noise comprises temporary variations of geophysical fields, such as tidal variations in gravity field, ionosphere disturbances influencing magnetic field, and climatic changes affecting temperature and SP fields. The second component of nonstationary noise reflects meteorological conditions (rains, lighting, snow, hurricanes, etc.) obviously disturbing observations of all potential fields. The first and the most important component of the geological-geophysical

Figure 3.1 A generalized scheme of different kinds of noise appearing in potential field investigations. After Eppelbaum, L.V., 2011. Study of magnetic anomalies over archaeological targets in urban conditions. Physics and Chemistry of the Earth 36 (16), 1318 1330, with modifications.

Different Kinds of Noise and Ways for Their Removing 15 and environmental factors is the physical limitation indicating is the suggested potential field applicable in the concrete situation (ratio signal/noise, observation grid, proposed depth of occurring of anomalous target, etc.) Soil-vegetable factors are associated with some soil types (e.g., waterlogged ground and loose ground in deserts) and dense vegetation complicating movement with geophysical equipment. Uneven terrain relief effect causes the physical limitations by equipment transportation and geophysical data measurements. Interpreting this disturbing effect is generally twofold for potential and quasi-potential fields: first, there is the effect of the form and physical properties of the topographic bodies forming the relief and, second, there is the effect of variations in the distance from the measurement point to the hidden target (Khesin et al., 1996). Complex structure of geological section is most important. Variety of anomalous sources is composed from two factors: variable surrounding medium and variety of anomalous targets. Both these factors are very crucial and strongly complicate interpretation of all potential fields. Oblique polarization (magnetization) complicates magnetic, SP, thermal and resistivity fields. Oblique polarization disturbs these geophysical fields in the following manner: the major extremum is shifted from the projection of the upper edge of object on the plan, and an additional extremum may appear (Khesin et al., 1996). Oblique magnetization is a characteristic peculiarity for the majority regions of the world.

3.1 Instrumental Noise 3.1.1 Gravimeter Instrumental noise in gravimeter (‘shift zero’) is well known. It is caused by instability of gravity equipment by environmental conditions changing (temperature, pressure, humidity, presence of small electric currents, etc.). For removing this noise were developed different methods: from repeated measurements at initial point with following introducing corrections to all observed points to practically automated correction in the microgravimeters of last generation (e.g., Hao et al., 2016).

3.1.2 Magnetometer Magnetometer “shift zero” by equal temperature conditions is very smalldabout 0.02 nT per year and usually is not considered (however, it is important by temporal magnetic variations analysis). Unequal temperature environments increase this value, but even by these conditions “shift zero” with modern magnetometers consists of insignificant value.

16 Chapter 3

3.1.3 Temperature Device The first temperature devices applied for borehole measurements had a low quality (about 0.2e0.5
C.). Present accuracy of temperature devices consists of 0.01e0.001
C (Eppelbaum et al., 2014; Huynh, 2015) and even higher. At the same time, accuracy of heat flow q (q ¼ lgrad T ¼ l dt/dz) is comparatively lowdabout 10%e12%. It is caused by insufficient accuracy of the thermal conductivity l determination in field conditions, whereas parameter graduate T is measured with a high accuracy.

3.1.4 Electrodes in SP Method Let us say we have for first electrode: U1 þ e1 (U1 is the first “geological” signal, and e1 is the noise of accumulated in the first electrode). For the second electrode, we have correspondingly U2 þ e2 (U2 is the second “geological” signal, and e2 is the noise of accumulated in the second electrode). We measure the value (Semenov, 1980) DU1 ¼ ðU1 þ e1 Þ

ðU2 þ e2 Þ:

(3.1)

If we will change electrodes by their places, we will receive DU2 ¼ ðU1 þ e2 Þ

ðU2 þ e1 Þ:

(3.2)

If we will calculate difference between DU1 and DU2, we will receive vU ¼ DU1

DU2 ¼ ½U1 þ e1

U2

e2 

½U1 þ e2

ðe1

e2 Þ ¼

U2

e1  ¼ 2ðe1

e2 Þ

(3.3)

or vU : 2

(3.4)

If the value (e1 e2) is significant, the electrodes must be replaced.

3.1.5 Resistivity Instrumental noise in the resistivity method is usually associated with the quality of electrodes and may be removed calculated by different methods (e.g., Perrone et al., 2014).

3.2 Technogenic Noise Technogenic noise in potential geophysical fields may be caused by different factors. The main kinds of the noise and their influence to potential fields are compiled in Table 3.1.

Different Kinds of Noise and Ways for Their Removing 17 Table 3.1: Influence of different kinds of technogenic noise to potential fields. Technogenic Noise Fields Gravity Magnetic Thermal Electric SP

Buildings 



C

Electric Power Lines

Underground Cables and Pipes

Transport Communications

Agricultural Enterprises C C, C -

C

C

C







C -,  C

C C

C -,  C

C not influence, - week influence,  strong influence.

3.3 Temporal Variations Temporal variations exist in all potential geophysical fields excluding different modifications of resistivity method. In this method, temporal variations may be caused by geodynamical factors only.

3.3.1 Gravity Field Gravity field temporal variations are caused mainly by tidal effects (we assume that instrumental “shift zero” has been removed). Methodology of removing tidal effects is well known (e.g., Elkins, 1943; Yacoby and Smilde, 2009).

3.3.2 Magnetic Field A procedure of magnetic variations elimination by the way of synchronous (quasisynchronous) magnetic observations in the area under study and at the control point (CP) disposed in the vicinity of the area is well known (e.g., Parasnis, 1986; Telford et al., 2004). The amplitudes of magnetic temporal variations observations observed at CP are subtracted from the field magnetic observations. In the case of time noncoinciding between the CP and areal (profile) measurements, a simple linear filtering is applied. However, in the case of precise magnetic observations, this method is an insufficient one. The accuracy of high-precision investigations (archeology, environmental investigations, military examinations, etc.) should not exceed the value of 0.1e0.2 nT or less (Becker, 1995). At the same time, the presence of both natural (basalts, diabases, gabbro, etc.) and artificial (iron and iron-containing) objects with high magnetization may cause secondary variation effects, which may inflate the actual value. Conventional procedures for eliminating temporary (primary) magnetic variations are based on the trivial additive expression

18 Chapter 3 DTðx; y; tÞ ¼

l X i 1

ai þ

k X

nj ;

(3.5)

j 1

where t is the time, x and y are the spatial coordinates, DT(x, y, t) is the magnetic field P P registered along a profile, li 1 ai is the sum of “useful” anomalies and kj 1 nj is the sum of the noise component caused by temporary variations. This formula provides only a simple subtraction of the noise component from the observed magnetic field and cannot be used to calculate the effect of secondary variations. Given that the secondary variation effect also depends on the intensity of the primary variations, the typical model of magnetic observations may be described in the following way (Eppelbaum and Mishne, 1995; Eppelbaum et al., 2001): 8 2 39 k l k < = X X X nð j; tÞ þ S x; y; ai 4 nð j; tÞ5 ; (3.6) DTðx; y; tÞ ¼ : ; j 1 i 1 j 1 P P P where kj 1 nð j; tÞ is the field variations in time, and li 1 Sfx; y; ai ½ kj 1 nð j; tÞg is the sum of the effects from anomalous objects and geological inhomogeneities of the medium with regard to their dependence on the field variations. Measurements at points along the profile are made at different times t (2) to obtain a solvable set of algebraic equations to extract the desired signal DT with sufficient accuracy.

3.3.3 Temperature Field Various methods of geothermal surveying and data processing have been developed for eliminating the temporal variations of temperature in near-surface temperature survey. The procedure suggested by Parasnis (1971) speeds up the field works but does not allow to remove seasonal variations. The other method consists of conducting a long-term geothermal investigation of the area under study and selecting a period when seasonal variations are minimal for the field survey (Dobrynina et al., 1985). However, this method suffers from such drawbacks as long duration, and hence nonapplicability of the results, since the time of fieldwork is frequently set by organizational factors, etc. Two other methods are worth mentioning: (1) synchronous measurements of the temperature variations within the field survey (Khutorskoi et al., 1983) similar to the well-known method of eliminating magnetic field variations in magnetic prospecting and (2) measurement of the temperature simultaneously at all points of the profile (Chekalyuk et al., 1974). However, in the first method it is not always possible to avoid the influence of temperature waves delayed in diffusing from the surface. The second method (it should be noted that there is

Different Kinds of Noise and Ways for Their Removing 19 not a real proof that such a procedure allows to remove all temporary variations) demands simultaneous use of many temperature-measuring devices which impede the surveying. A method for eliminating temporary variations using repeated observations with subsequent linear filtering of the results was suggested by Eppelbaum and Mishne (1987). It is known that a regional thermal field is stable in time (Lyubimova, 1968) and temperature-wave propagation in the medium is linear (Tikhonov and Samarsky, 1963). Taking into consideration these factors, a model of the total temperature field, recorded in the layer with annual temperature oscillations, can be represented in the following form: Qi ¼ Ti þ

t X

sð jÞ f ðt

jÞ;

(3.7)

j t t0

where Qi(t) is the observation at the ith point (borehole); Ti is the temperature conditioned by redistributing the deep heat flow caused by the object with contrasting conductivity; s( j) is the average temperature at a certain depth Dh at time j along the region including the district under investigation (data from meteorological stations are employed); f(t j) is the weight step function reflecting the temperature effect at the depth Dh, at time t j on the temperature measured in the borehole, at depth h at time j; and t0 is the delay time of temperature waves diffusing down the surface. Noises are assumed to be autocorrelative, and the autocorrelation matrix for noises R(tej) can be written in the form: 9 1 > = jj  j jt 2 ; (3.8) Rðt jÞ ¼ 1 þ ðt jÞ > ; 0 jt jj  j where J is some defined parameter. Measurements at the observation points, made at different times t, enable one to obtain a solvable set of algebraic equations that allow the desired signal Ti to be extracted with the required accuracy (Eppelbaum, 1999). Later publications (for instance, Kumar and Kaleita, 2003; Smerdon et al., 2004) confirm applicability of this physical-mathematical model.

3.3.4 SP Field Parasnis (1986) has been carried out SP measurements in Akulla region (Sweden) seven times in the period of 1960e1967. These measurements show a good repeatability despite the fact that they were conducted under different climatic conditions.

20 Chapter 3

3.3.5 Resistivity Variations in temperature during time-lapse electrical resistivity studies introduce changes in electrical conductivity. Compensation of such variations is analyzed by Hayley et al. (2010). Other temporal resistivity variations usually are associated with changing of geometrical and physical characteristics of the geological objects: underground water level, their salinity, pores of some rocks, etc. Sometimes temporal electric resistivity anomalies are signatures of the dangerous geodynamic events at a depth (see section 13.4).

3.4 Terrain Relief Influence The elimination of the effects of terrain relief is crucially important for geophysical studies of mountainous regions. A rugged terrain relief has an effect not only on transportation, complicating geophysical prospecting under mountainous conditions (in particular, routes are not always located across the strike of the target, which limits the interpretation). The terrain relief effect also manifests itself in nonstationary and stationary topographic anomalies. Nonstationary anomalies are customarily identified visually during fieldwork or by special measurement methods. For instance, filtration SP anomalies are classified as nonstationary anomalies. Usually their gradient is considerably less than that of “ore” anomalies, and a mirror reflection of the topographical shape by the SP anomaly is used to reject false anomalies. When the SP survey profile crosses a mountainous river with a stony bed, a kinetic electric field is observed, which appears as a potential minimum against the background of its total increase due to filtration on the valley slopes. The potential of such a field grows along the stream. Magnetic anomalies on tops of hills, when associated with lightning (magnetization of outcropping rocks is severely altered in its vicinity), can also fall into this category, as well as thermal anomalies due to varying meteorological conditions (their effect can be excluded by repeated measurements at different time intervals). The main features of terrain correction are similar to corrections for stationary noise effects incorporated into results of geophysical measurements. First, the form and physical properties of topographic masses (i.e., relief-forming morphostructures) are responsible for the effects of these masses in the anomalous field, which mask anomaly effects from hidden targets.

3.4.1 Magnetics There is a clear correlation between the elevations of the measurement point (H) and the magnetic field DZ (DT) for a relatively homogeneous magnetic medium. In the case of direct magnetization, the field maxima correspond to ridges of the “magnetic” relief, while the minima correspond to the valleys.

Different Kinds of Noise and Ways for Their Removing 21 An analytical approach was suggested by Khesin (1976) that applied the linear relation DZ (H) to a typical element of mountainous regionsda slope (inclined ledge, or step). All the main types of relief can be approximated by one or another combination of slopes. Thus although crude, this is a simple and effective method for eliminating the effect of magnetized rock relief. It only uses the data concerning the recorded field and terrain relief. To apply this technique, a correlation field is drawn up between DZ (DT) and H values, and then their average as a straight line is plotted. The terrain correction is determined by the regression equation DZr ¼ c þ bH;

(3.9)

where b and c are the factors of a linear equation computed using the least-squares method (the b dimension is nT/m; the subscript “r” indicates that it is a relief correction). The regression line (3.9) is drawn on the basis of many measurement points from the data obtained under the conditions of a medium close to uniform and as distant as possible from sharp bends in the terrain relief. It was shown (Khesin et al., 1996) that 8J cos a ; (3.10) R where J is the topographic mass magnetization, a is an acute angle between the slope face and horizon, and R is the slope length across the strike. b¼

Therefore, the J value can be determined by the angular coefficient of the regression line. Elimination of the topographic effect by the correlation technique allows for practically complete smoothing out of the anomalies caused by morphostructures (Fig. 3.2A). When excluding the topographic effect from the observed field (Fig. 3.2B), the corrected DZ graph coincides closely with the magnetic field caused by a flat-dipping thin bed (magnetite deposit) under oblique magnetization. Along with the linear approximation of the relationship between the field and the height, approximations in the form of the square trinomial (parabolic equation) can also be used. Judging by the type of the parabola, one can get useful interpretation evidence. If its vertex is at the top, the vertical gradient decreases with height, which is characteristic of a uniform medium. If, however, it is at the bottom, there are significant heterogeneities present in the section. The parabolic characteristics contain other information as well, including assessing the presence of a heterogeneity (i.e., additional source) and even its features. However, it has been statistically proven that the parabolic approximation U(H) can be replaced by the linear approximation when the correlation between the magnetic field and the relief is known (Khesin et al., 1996). To reduce correlation distortions, in general it is recommended to plot approximation lines for each individual element of the topography. In regions with flat-dipping geological

22 Chapter 3

(A)

(B)

(C)

Figure 3.2 Terrain correction by the correlation method for the ground profile (survey on a 1:25,000 scale) in the Dashkesan mining district, Lesser Caucasus, Azerbaijan (Khesin et al., 1996): (A) calculated magnetic fields and approximating lines DZ (H) for the model c; (B) the same for the observed field; (C) petromagnetic section (gK is the hidden apophysis of the Dashkesan intrusive). I, II, III, IY are the profile portions where correlation DZ (H) was calculated. DZ field: (1) computed by the model c, (2) the same, corrected, (3) observed, (4) the same, corrected.

Different Kinds of Noise and Ways for Their Removing 23 boundaries, rock outcropping onto the Earth’s surface may differ markedly from those of the section on the whole. In such regions it is preferable to draw a unified approximating line by the correlation plotted for the whole surveying sheet. It is advisable to first determine the areas of correlation by visual analysis of geophysical and topographic maps (Fig. 3.3). The results of the correlation terrain correction in the Mekhmana mining district are a good example (Fig. 3.4). Regioning of the terrain relief was carried out in this district by comparing the dip angles with magnetic susceptibility data (see Fig. 3.3). No correlations were observed in areas 1, 4, and 5, which can be explained theoretically by the ratio of the inclination angles for the relief and magnetization. For area 2, the correlation takes the following form DZ ¼ 0:765ðH

1150Þ;

(3.11)

Figure 3.3 Topography regioning in the Mekhmana mining district, NE Lesser Caucasus (Azerbaijan), by the inclination angles as compared to magnetic susceptibility. (1) area with similar inclination angles and number; (2) magnetic susceptibility isolines (in 10 3 SI unit). After Khesin, B.E., Alexeyev, V.V. and Eppelbaum, L.V., 1996. Interpretation of Geophysical Fields in Complicated Environments. Ser.: Modern Approaches in Geophysics. Kluwer Academic Publishers (Springer), Boston Dordrecht London.

24 Chapter 3

Figure 3.4 Terrain correction by the correlation method in the Mekhmana mining district (Lesser Caucasus). (A) observed magnetic field Zan, (B) magnetic field Zc corrected for topographic effect. (1 3) isolines (n,100 nT): (1) positive, (2) zero, (3) negative field; (4) sites of intense local anomalies: (a) positive, (b) negative. After Khesin, B.E., Alexeyev, V.V. and Eppelbaum, L.V., 1996. Interpretation of Geophysical Fields in Complicated Environments, Ser.: Modern Approaches in Geophysics. Boston Dordrecht London, Kluwer Academic Publishers (Springer).

whereas for area three it takes the form DZ ¼ 1:135ðH

1280Þ;

(3.12)

where H is measured in meters and Z in nanotesla. In Fig. 3.4, the isogam map Zc drawn up for areas two and three is compared with the initial field chart. The figure shows that the anomalies and other field features presented in the initial chart have undergone drastic changes. The field pattern becomes simpler and the anomaly strikes showed a marked deviation, such that some of them are smoothed. This allows for considerable reduction in interpretation errors, and primarily Type I errors (i.e., “false positives”) (see section 4.6). This method can be used to improve the choice of level for reducing the field to one plane. When plotting a correlation chart, the areas with the largest dispersion with respect to the averaging line correspond to the elevation of the points under which the targets are situated. The presence of dispersion in itself is indicative of the hidden source present in the section.

Different Kinds of Noise and Ways for Their Removing 25 The advantage of the correlation technique is that it can rapidly reveal the influence of terrain relief as well as the presence and certain peculiarities of hidden sources, in addition to suppressing or reducing the noise caused by the terrain relief. It can also solve additional problems, such as determining the mean magnetization of the medium and the vertical gradients of magnetic field. Eppelbaum (2010) suggested conducting a magnetic survey using remotely operated vehicles (ROVs) to determine the upper geological section magnetization (including inclined ROV observations over flat surfaces). Analysis of the spectral composition of the geophysical and height field makes the correlation method more precise (Erofeyev and Avteneyev, 1971). The magnetic field spectrum is much more highly differentiated and wider than the height spectrum. For this reason, a higher correlation is obtained when using average values than the observed values of DZ or DT. If high-frequency magnetic components are involved in the correlation, the correlations turn out to be lower. These weaker correlations at high frequency testify to the presence of such geological sources as ore bodies or dikes.

3.4.2 Temperature The applicability of the above technique developed in magnetic prospecting to thermal data analysis is substantiated by the following findings. The inverse dependence of the surface temperature on the height of observations was pointed out by Bullard (1940) and was noted subsequently by many investigators. Lachenbruch (1968) made a calculation of the change in heat flow that governs the temperature variation observed on an inclined slope. A comparison between the plots of the vertical magnetic field component

Figure 3.5 Comparison of plots of (A) the magnetic field vertical component Z, and (B) relative heat flow q/qo over (C) a slope in terrain (after Eppelbaum, 2009; the curve (B) is from Lachenbruch, 1968).

26 Chapter 3

Figure 3.6 Temperature cross-section for a hill near Wilbur (Washington, USA) as inferred from measured temperatures in three drill holes shown in the section. After Blackwell, D.D., Steele, J.L. and Brott, C.A., 1980. The terrain effect on terrestrial heat flow. Journal of Geophysical Research 85 (B9), 4757 4772, with modifications.

(at vertical magnetization J) and the relative amount of the heat flow q/qo is presented in Fig. 3.5. The inverse correlation between the relief height and amplitudes of temperature values clearly confirm the data presented in Fig. 3.6 (correspondingly, and correlation coefficient between aforementioned values will be negative). Fig. 3.7 illustrates the application of the correlation technique for eliminating the topographic effect in the district of the Gyzylbulagh gold-pyrite deposit. The equation for the terrain relief correction takes the form Tappr ¼ 15.6 0.07H, where the correlation coefficient between the temperature T and the height H is 0.8. Once the inclined relief effect has been eliminated, the anomalies from disturbing objects (massive ore in the southwestern part of the profile, and a vast zone of disseminated ore in the northeastern part) are more pronounced (Fig. 3.7).

3.4.3 Gravity According to the theoretical analysis (Khesin and Alexeyev, 1986; Khesin et al., 1996), the potentialities of the statistical reduction have broad prospects in gravimetric prospecting at regional and especially detailed investigation (Khesin et al., 1988). Statistical reduction, which automatically reduces defects of the Bouguer reduction described in the literature and employs a simple correlation technique, since except the surrounding relief correction, all the corrections exhibit linear dependence on the

Different Kinds of Noise and Ways for Their Removing 27 (A) Tobser,°C

(B) 15

Tobser

T,°C Tcorr,°C

16

1

14

14

Tcorr

H, m

0

13

780 1

(C)

H, m 1 37

64 83

800 tuffs of liparite dacite porphyrites

800

fault

760

zone of brecciation

720

disseminated pyrite chalcopyrite ore

680

massive pyrite chalcopyrite ore

Figure 3.7 Correlation technique for reducing the terrain relief effect in near-surface thermal prospecting in a district of the Gyzylbulagh gold-pyrite deposit (the Lesser Caucasus, Daghliq (Mountainous) Garabagh, Azerbaijan): (A) plots of observed and corrected temperature values, (B) correlation, (C) geological section. Drill holes 1, 37 and 64 continue below the section. Drill hole 83 terminates as shown (Eppelbaum et al., 2014).

observation point height. It can be shown that proceeding from the analytical expression of the inclined ledge (slope) gravitation, the attraction of typical relief forms is also linearly dependent on the height on the observation point. According to (Khesin and Alexeyev, 1986) Dg ¼ c þ bh;

(3.13)

where c ¼ 2GsaHo, b ¼ 2pGs, G is the gravitational constant, s is the density of rocks forming the ledge; a is the acute angle between the inclined face of the ledge and its base, Ho is the vertical ledge thickness, h is the difference in levels between the observation point and the ledge base (if the ledge base is at the sea level, then h ¼ H). The relationship between Dg and heights h becomes a correlation due to the presence of density inhomogeneities in the volume of the slope and beneath it, and also as a result of the deviation of the earth’s surface from the inclined step.

28 Chapter 3 Further inspection of the gravitational anomaly over the slope formed of homogeneous rocks discloses that corrections for relief gr in all points of the slope are equal and proportional to the ledge thickness and to the inclination angle of the relief. Therefore, on a homogeneous slope Bouguer anomalies DgB are constant and equal to the attraction of the ledge to the point at its base DgB ¼ 2GsaHo :

(3.14)

When a < 0, then DgB < 0. When s ¼ 2.67 g/cm3 and a ¼ 30
, it is found that DgB ¼ egr ¼ 18.6 Ho (mGal), where Ho is presented in kilometers. The estimation of gr value thus obtained is supported by the results of computing terrain corrections. In practice, these corrections are added to DgB which is usually used as an alternative to the anomalous value in topographic reduction (DgT). Therefore, Bouguer anomalies (assumed to be local topographic anomalies) must be equal to zero, provided that the intermediate layer is calculated correctly and geologic inhomogeneities are absent. Owing to the above defect of the Bouguer reduction, the correlation Dg ¼ f(H) is registered.

3.4.4 Resistivity Classic resistivity anomalies are usually inversely correlated with the topographic forms (Fig. 3.8). Nevertheless, what about the electric resistivity tomography anomalies? In the recently published work, Modin et al. (2018) comprehensively studied this question. To

ρa, Ohm·m 1600 ΔZ, nT

ρa

800

400 0 400 ΔZ

1200

+ + 1

+ + +

+

+

+ +

+ + + + +

+ 2 +

Figure 3.8 Topographic anomalies in ra (apparent resistivity, electric profiling AMNB) and DZ (vertical component of magnetic field) on a copper-molybdenum deposit of the Lesser Caucasus. After Khesin, B.E., 1969. Ore Geophysics in Mountainous Regions, Nedra, Moscow (in Russian), with modifications.

Different Kinds of Noise and Ways for Their Removing 29 solve this problem, the authors performed physical modeling on large homogeneous sand embankment with artificial complex surface topography. After that Modin et al. (2018) have performed mathematical modeling by use of integral equations. In both cases was proved and concluded that the inverse correlation relationship with heights of relief does not change.

3.4.5 Self-Potential In the SP method, relief influence is twofold. On the one hand, the rugged terrain relief caused by electromotive force can create negative SP anomalies over the positive landforms. Comparison of the SP graphs with topographic data usually makes it possible to identify anomalies of this type by the characteristic mirror image of the terrain in them. From the other side, as follows from detailed SP measurements of Ernstson and Schrerer (1986), at the inclined surface the SP field directly increases with relief form heightening (Fig. 3.9). So, is should taking into account that in the field SP practice can occur as single effects and their combinations.

Figure 3.9 SP observations at inclined relief. After Ernstson, K. and Scherer, V., 1986. Self-potential variations with time and their relation to hydrogeologic and meteorological parameters. Geophysics 51 (10), 1967 1977.

3.5 Complex Geological Media and Noised Environment The combination of methods of potential field interpretation under rugged terrain relief and oblique polarization of objects is compiled to the flowchart presented in Fig. 3.10. This flowchart indicates that selection of necessary algorithms and software packages is

Figure 3.10 Flowchart of a system of geophysical fields quantitative interpretation for complex physicalegeological environments. After Eppelbaum, L.V., Itkis, S.E., 2003. Geophysical examination of the archaeological site Emmaus-Nicopolis (central Israel). In: Collection of Papers of the XIXth International UNESCO Symposium “New Perspectives to Save the Cultural Heritage”, Antalya, Turkey, 395e400, with modifications.

Different Kinds of Noise and Ways for Their Removing 31 not a simple process and demands a careful consideration. As a whole, such a system can assist in optimizing the selection of working algorithms for geophysical methods with final optimization of testing wells and mines location and parametrization, thus ensuring a considerable economy.

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