Chapter 12 Groundwater Exploration

401

CHAPTER 12 GROUNDWATER EXPLORATION

12.1

GEOLOGIC AND HYDROLOGIC METHODS

Preliminary conclusions on the occurrence of groundwater can often be made with the aid of aerial photographs, regional geologic maps, and geologic field reconnaissance. The use of aerial photographs to obtain geologic information is commonly called photogeology. The main objective of photogeology is to contribute to geologic mapping, i.e., mapping the distribution of rock types and structures.

Interpretation of aerial photographs permits inferences as

to the composition of rock types but does not permit identification of mineral types or estimates of absolute ages of rocks.

Rock types with distinctive

water-yielding properties can be identified through petrographic studies. The position, thickness, and continuity of aquifers, aquitards, and aquicludes can be determined with stratigraphic techniques.

Aquifers which have been

displaced by earth movements can be located by structural studies in conjunction with stratigraphic work. In mapping the distribution of rock types and structures, maximum use of aerial photographs is achieved by integrating photogeologic studies with field investigations.

In general, a preliminary photogeologic study should

precede the field investigation (Ray, 1960) because it may indicate areas that must be mapped principally by field methods; it may reduce or eliminate extensive field surveys in some areas; it may direct attention to certain areas where detailed field study is justified; and it generally provides a basis for organizing the geologic plan of field study.

The amount of geclogic

information that can be obtained from aerial photographs depends on the type of terrain, climate environment, and

nature

of

sedimentary

terrains,

with

consequent

differ enti a1 erosion

characteristics that are prominent on aerial photographs. regions usually yield the greatest amount of

Arid and semiarid

information from aerial

photographs, because they generally have a larger area of rock outcrop and a greater number of plant-rock associations than other climatic areas. Aerial photographs can provide much assistance to geologic mapping in groundwater investigations, particularly in areas covered by surficial materials (Howe, 1958). As an aid in groundwater mapping, evaluations are made of surface expressions of soils materials, such as landform, drainage, erosion, relative photographic tone, color, vegetation cover, and land use. For example, coarse-textured drainage or even absence of drainage may indicate highly permeable materials; in low-permeability soils, drainage will commonly be fine-textured or ponds may be numerous.

Coarse- or fine-

textured drainage is related mainly to the relative resistance of the surficial materials to erosion, and thus related to permeability and grain size. Coarse materials are normally permeable and resistant to erosion, and have a coarse-textured drainage. Fine materials are commonly impermeable and less resistant to erosion, and have a fine-textured drainage. In addition, the landform may suggest the materials that compose it, thus permitting an evaluation of porosity and permeability.

Furthermore, the presence of

groundwater may be suggested directly by aerial photographs, as when vegetation is prominent along edges of a terrace gravel cap. Terrace deposits are commonly favorable reservoirs for groundwater storage.

The type of

vegetation a t the margins of a gravel cap may make possible inferences as to the general water quality. For example, cottonwood usually grows where the water is potable, whereas salt cedar is tolerant of water with relatively high salt content. For best results in prospecting for groundwater, geologic and hydrologic methods should proceed together.

Hydrologic methods include studies of the

location and quantity of groundwater recharged and discharged at the surface. The rate and quantity of groundwater recharge is influenced by conditions relating to precipitation and to the intake facilities. In humid regions, more than one-third of the precipitation may become groundwater, whereas in

semiarid regions the recharge may be only a few percent of the precipitation,

geophysical methods are based on measurements at t h e earth's surface of anomalies in physical forces which must be interpreted in t e r m s of subsurface geology. These methods are advisable where geologic structures and bodies

are not exposed, since geophysical measurements are in general more expensive Although surface than geologic and hydrologic reconnaissance surveys. geophysical methods are frequently inexact or difficult to interpret, they have proved useful for locating and analyzing groundwater. Success in applying these methods depends on t h e existence of sufficient contrasts in t h e physical proper ties (electrical conductivity, elasti city, density, magnetic susceptibility, etc.) of subsurface formations. 12.2.A Electrical Resistivity Methods In t h e electrical resistivity method, as in other surface geophysical methods, t h e distinctness of surface indications depends on t h e contrasts in t h e physical properties of geologic formations and their vicinity. An essential characteristic f o r t h e usability of any geophysical method is continuity of physical properties.

In t h e resistivity method, used for determining depths of horizontal formations, these physical properties must remain continuous in a horizontal direction since t h e spacing of transmitting and receiving units is changed horizontally to obtain increased depth penetration.

The resistivity of rocks and formations varies widely with t h e material and its porosity, grain packing, water content, and conductivity. Resistivities of igneous and metamorphic rocks may range from 10 to 107 ohm-m, whereas those of unconsolidated formations may vary from 1 to 103 ohm-m.

Heiland

(1946) presented an extensive tabulation of t h e resistivities of elements and minerals, ores, rocks with conductive mineral impregnations, igneous and metamorphic rocks, consolidated sediments, unconsolidated formations and oil formations. In general, t h e resistivity of a rock or formation can be expressed by: (12.1) in which p = resistivity of t h e rock or formation, pw = resistivity of t h e water filling, t h e voids, a = porosity, and c is a constant depending on t h e arrangement of t h e voids. If it is assumed t h a t groundwater fills all of t h e

geophysical methods are based on measurements at t h e earth's surface of anomalies in physical forces which must be interpreted in t e r m s of subsurface geology. These methods are advisable where geologic structures and bodies

are not exposed, since geophysical measurements are in general more expensive Although surface than geologic and hydrologic reconnaissance surveys. geophysical methods are frequently inexact or difficult to interpret, they have proved useful for locating and analyzing groundwater. Success in applying these methods depends on t h e existence of sufficient contrasts in t h e physical proper ties (electrical conductivity, elasti city, density, magnetic susceptibility, etc.) of subsurface formations. 12.2.A Electrical Resistivity Methods In t h e electrical resistivity method, as in other surface geophysical methods, t h e distinctness of surface indications depends on t h e contrasts in t h e physical properties of geologic formations and their vicinity. An essential characteristic f o r t h e usability of any geophysical method is continuity of physical properties.

In t h e resistivity method, used for determining depths of horizontal formations, these physical properties must remain continuous in a horizontal direction since t h e spacing of transmitting and receiving units is changed horizontally to obtain increased depth penetration.

The resistivity of rocks and formations varies widely with t h e material and its porosity, grain packing, water content, and conductivity. Resistivities of igneous and metamorphic rocks may range from 10 to 107 ohm-m, whereas those of unconsolidated formations may vary from 1 to 103 ohm-m.

Heiland

(1946) presented an extensive tabulation of t h e resistivities of elements and minerals, ores, rocks with conductive mineral impregnations, igneous and metamorphic rocks, consolidated sediments, unconsolidated formations and oil formations. In general, t h e resistivity of a rock or formation can be expressed by: (12.1) in which p = resistivity of t h e rock or formation, pw = resistivity of t h e water filling, t h e voids, a = porosity, and c is a constant depending on t h e arrangement of t h e voids. If it is assumed t h a t groundwater fills all of t h e

405

voids of a n isotropic aquifer packed uniformly with spherical mineral grains, aquifer resistivity can be expressed by (Heiland, 1946): P =

3 -a 201

(12.2)

Pw

The electrical resistivity method i s applicable to depth determinations of horizontal formations and t h e mapping of dipping strata.

This method

measures t h e potential difference between t w o points and t h e current in t h e primary circuit. T h e ratio of potential difference and current, multiplied by

a f a c t o r t h a t depends on t h e spacing of t h e electrodes, gives t h e resistivity of t h e ground. T h a t is a t r u e resistivity only if t h e medium is homogeneous; if layers of different conductivities are present, i t is an apparent resistivity. Apparent resistivity is commonly calculated by t h e s a m e formula t h a t applies to homogeneous ground. Consider an electric current I entering a homogeneous and isotropic ground of resistivity p by means of two electrodes C1 and C2 (Fig. 12.la). If t h e current flows from C1 and C2, t h e potential V at any point P is vP

=

pr ( L -1- ) 271

rl

r2

(b) Figure

Schematic representation of electrode arrangements.

(12.3)

Similarly, the potential difference between two points P1 and P2 (Fig. 12.lb) is

-

=

v

=

1

1

r2

r3

p 2a I (r lL - - - -

+

1

-1

r4

(12.4)

Thus, the resistivity is

- 2aV P - I

1

(12.5)

+ - 1)

(q-5-5 r4 1

1

Equation (12.5) holds for any position of the electrodes C1, C2, P1, and P2. Various electrode spacing arrangements have been adopted in practice.

The

most common arrangements are discussed below. In the Wenner arrangement, shown in Fig. 12.2a, the potential electrodes are placed on a line with the current electrodes, so that all electrodes are equidistant from one another. If a is the distance between t h e electrodes,

r1 -- r4 = a and r2 = r3 = 2a.

Then, from eq. (12.51, the resistivity is

Figure 12.2

Schematic of (a) Wenner, (b) Schlumberger, (c) asymmetrical double, and (d) double equidistant electrode arrangements for the measurement of earth resistivity. =

2raV/I

(12.6)

In the Schlumberger arrangement, shown in Fig. 12.2b, the potential electrodes are close together. If 2 is the distance between the current electrodes and a the potential-electrode interval, rl = r4 = (Z-a)/2, r2 = r3 = (2+a)/2, and the resistivity

In the asymmetrical double electrode arrangement, shown in Fig. 12.2c,

the potential electrodes are situated at equal intervals from one current electrode but asymmetrical with respect to the center. With rl = a, r2 = Z-a, r3 = 2a, and r4 = Z-2a, the resistivity is

In the double equidistant electrode arrangement, shown in Fig. 12.2d, the potential electrodes are placed at equal intervals from one current electrode whereas t h e second current electrode is far removed. With rl =

a, r2 = r4 =

and r3 = 2a, (12.9)

4mV/ I

The resistivity method can be applied in two ways.

In t h e first, t h e

electrode spacing is kept constant (i.e., constant depth penetration) and t h e arrangement as a whole is moved over t h e ground.

This procedure is called

resistivity mapping or electrical trenching. Resistivity mapping is well adapted for locating vertical boundaries buried less than 100 m deep.

Measurements

made at various field stations are shown graphically as resistivity traverses. A traverse traced with a constant spacing of 5 m at a buried gravel deposit (Fig. 12.3) indicates the boundary of t h e deposit as t h e resistivity drops below

a certain minimum, about 250 ohm-m in this case. In the second way, measurements are made at one location (the center of the measuring arrangement) from which t h e spacing of t h e electrodes is gradually increased to pick up changes in resistivity with depth. In this manner, t h e depth

400 -

-

200 -

-

0. Figure 12.3

Resistivity traverse of a buried gravel deposit.

Y

U

0

20

3

-

' E 40-

-

2 60-

-

U

2 80-

-

100-

-

c

40

0

W 3 60

-0

m 80

c

u

c

El00

n

20-

CT

t

I 20

I20

Figure drilling.

I

Resistivity curve obtained by resistivity sounding or electrical

penetration is increased and t h e apparent resistivity is obtained as a function This procedure is called resistivity sounding or electrical drilling.

of depth.

It is used for determining depths of horizontal boundaries such as the water table, surfaces of stratified rocks, and bedrock.

Figure 12.4 illustrates the

resistivity curve of subsurface deposits obtained by this procedure.

The

apparent resistivity measured by this procedure is affected by the entire depth of penetration.

Thus, the greater t h e number of layers penetrated,

the more difficult i t is to interpret t h e resistivity sounding (Tattam, 1937; Heiland, 1946). Interpretation of resistivity data may be made qualitatively and quantitatively.

Qualitative interpretation, based on the appearance of the curves,

is used mainly in resistivity mapping, with a decline in apparent resistivity indicating t h e approach of formations or bodies of better conductivity, and vice versa.

Quantitative interpretation is based primarily on type curves.

The type-curve method involves the construction of field (data) and theoretical (type) curves. Interpretation consists of placing the data curves over the type curves and determining the depth by interpolation.

The type curves

are constructed for given conductivity ratios and for various layer thicknesses or depths. The data curves have apparent resistivities plotted as ordinates, and t h e lengths of the electrode arrangement plotted as abscissas. This

410

method of depth determination is applicable mainly to two- and three-layer conditions (Mooney and Wetzel, 1956; Zohdy et al., 1974). The electrical resistivity method has been widely used for groundwater investigations.

Its greatest success has been with two-layer problems (Gay

and Kosten, 1956; Kelly, 19621, particularly in locating subsurface fresh-water salt-water boundaries (Swartz, 1937, 1939, 1940). successful also in locating:

The method has been

municipal water supplies in unconsolidated

materials (Bays and Folk, 1944; Buhle, 1953); alluvium-bedrock boundaries in river valleys (Foster and Buhle, 1951; Norris and Spicer, 1958; McGinnis and Kempton, 1961; Kelly, 1962); and sand or gravel layers overlain by clay and silt (Workman and Leighton, 1937; Foster and Buhle, 1951).

The resistivity

method is limited to relatively simple geologic structures unless additional information is available from other geophysical methods or from drilling. Because m e t a l pipes, wire, rails, and o t h e r structures in c o n t a c t with t h e ground disturb t h e flow of electricity in t h e vicinity of t h e electrodes, t h e resistivity method is limited also to areas f r e e from such disturbing elements. 12.2.B

Seismic Methods

Seismic methods measure t h e reactions of geologic bodies to physical fields. In seismic exploration, an explosive is detonated at or near t h e surface and

t h e elastic impulses or vibrations are picked up by seismometers (also referred

to as d e t e c t o r s or geophones) and recorded on magnetic t a p e or photographic paper. The time lapse between generation and detection of t h e vibrations is referred to as t r a v e l time. The fan-shooting method provides t h e simplest way of determining t h e nature or character of t h e media occurring between t h e point of explosion (shot point) and a number of detectors. In this method, d e t e c t o r s are spread at equal distances from t h e shot point, thus giving t h e appearance of a fan. The area to be explored is then covered with a series of overlapping fans. A medium t h a t transmits elastic waves at high speed, such as bedrock, will be indicated by a f a s t e r travel time than expected f o r t h e particular distance and area. Plots of t r a v e l times f o r each f a n arrangement can rapidly outline t h e presence of a buried s t r e a m channel, anticline, or similar structure (Heiland, 1946). Because t h e depth of these structures is not indicated by

411

Figure 12.5 Fan-shooting method for mapping a buried stream channel overlying bedrock (Davis and Dewiest, 1966). this method, fan-shooting indications need to be detailed by other geophysical methods.

Figure 12.5 illustrates t h e use of t h e fan-shooting method for

mapping a buried s t r e a m channel overlying bedrock (Heiland, 1946; Davis and Dewiest, 1966). A second method of seismic prospecting is t h e refraction method, in

which t h e travel times of first impulses or arrivals are determined as functions of t h e distance of d e t e c t o r s arranged in a straight line from t h e shot point. The change of travel time with distance, commonly referred to as t h e travel-time curve, gives information on t h e t r u e velocities and depths of t h e refracting beds. Consider a wave traversing t h e boundary between t w o layers with transmission velocities v1 and v2 (Fig. 12.6).

T h e wave will b e refracted

according to Snell's law

-ss ii nn- ri - -

V

1

V

2

(12.10)

412

?8

Figure

Refraction and reflection wave paths.

D \ \ \ \ \ \ \

C Figure

Refraction wave paths.

in which i and r are the angles between t h e normal t o the boundary and the rays in the layers with velocities v1 and v2, respectively.

Let us assume

that v1 < v2.

For a ray in layer 1 striking the boundary, there is a critical angle of incidence ic for which r = 90' and the refracted wave is then parallel to the boundary, traveling with t h e velocity of layer 2. In this case, sin r = 1 and eq. (12.10) becomes sin i

C

=

vl/v2

For any i > i

C'

(12.11)

there can be no refracted ray in layer 2 and therefore no

penetration into this layer, and all the energy incident at such an angle is reflected. Thus, total reflection occurs for any angles i > ic. Let us now consider a two-layer case (Fig. 12.7) in which a circular wave generated by an explosion at point A expands uniformly in the upper

413

layer. The latter is a homogeneous isotropic layer with uniform thickness z and transmission velocity vl and is underlain by a second layer with a higher velocity, v2. Waves striking the boundary between the layers will be partially reflected into the upper layer and partially refracted into the lower layer. The refractions will, in general, occur according to eq. (12.10). The wave refracted at the critical angle may be thought of as a disturbance traveling along the boundary with velocity v2. Because each point on the advancing wave front in the upper layer may be considered as a new source of waves, the disturbance traveling along the boundary can be considered as producing waves at the lower end of the upper layer. The wave front of these latter disturbances progresses in the upper layer along rays also at the critical angle. Consequently, wave energy can be considered as being refracted to the boundary between the layers along a path AB at the critical angle ic, being refracted along that boundary along paths such as BC, and ultimately being refracted to the ground surface along paths such as CD at the critical angle ic. The path ABCD is a minimum-time path. Let us consider again a two-layer case in which the upper layer, with uniform thickness z and velocity vl, is underlain by a second layer with velocity v > v1 (Fig. 12.8). A number of detectors are set along the ground 2 surface (from the shot point to a distant point) at measured distances apart. The first waves to reach a detector travel horizontally in the upper layer at a velocity v1 and arrive at a detector at a distance x at times

tl

=

X/Vl

(12.12)

Therefore, the travel-time or time-distance curve begins as a straight line with a slope l/vl. A t a certain distance xc, a wave that has been refracted along the boundary reaches the ground surface at the same time as one that has traveled the direct horizontal path in layer 1. This happens when the time lost by traveling the distances AB and CD at the slower velocity v1 is gained by traveling the distance BC at the higher velocity v2. A t distances greater than this critical distance xc, a refracted wave reaches the ground surface first (first arrival). The time reauired for a wave to travel this refracted path is

414

c

.-

I

Shot Point

l

l

’

I

I

I

I

I-xc-td-x

Figure t2

I

,Detectors

Minimum-time path and travel-time curve for two layers.

- AB - v1

BC

CD

v2

v1

- + - + -

(12.13)

Using eq. (12.11) and t h e geometry of t h e figure, it can b e shown t h a t t2

- 2 2 cos i v1

+

x v2

(12.14)

It is evident from eq. (12.14) t h a t t h e slope of t h e travel-time curve beyond xc is l/v2.

Therefore, t h e presence of t h e boundary between t h e layers is

indicated by t h e intersection of t h e t w o segments of t h e travel-time curve. The travel-time curve permits t h e depth z to be calculated in various ways.

With t h e critical distance xc and t h e transmission velocities v1 and

v2 known, t h e depth can be expressed as

415

Intercept time for a two-layer case.

Figure

(12.15) Also, projecting t h e slope of t h e t2 segment of t h e travel-time curve back to zero distance (Fig. 12.9) allows us to determine the intercept time

ti.

Then, z = -t i 2

v2 v1 2 2 1/2

(v2

-

(12.16)

vl)

Finally, using a point on t h e t2 segment of t h e travel-time curve gives z

=

v v 2 1 (t2 - 5 ) V 2 2 1/2 2 2(v2 - v,)

(12.17)

Because of its utility in deriving relations on t h e time that a wave requires to traverse a refracted path, t h e concept of delay time is now introduced by means of a n example. Referring to Fig. 12.10, t h e delay time td associated with t h e segment AB of t h e ray trajectory is t h e additional t i m e required t o travel t h e distance s at velocity v1 over t h e t i m e required

to travel t h e distance d at velocity v2.

That is, (12.18)

418

time required for a wave to t r a v e l t h e path ABCDE is equal to t h a t required to travel t h e path ABCD plus t h e additional t i m e for t h e path DE. Thus, t h e total t i m e will be

t2

- 2 cos i v1

+

x V

+

+ey

=

(22

1

2

+

y ) cos i V 1

+

x

(12.21)

v2

I t is evident t h a t t h e t i m e is t h e same as if shot and d e t e c t o r were at t h e average elevation z + (y/2).

The equivalent path for this average elevation

is shown by t h e dotted lines of Fig. 12.11. A situation similar to t h a t just considered is t h e case of a boundary between two layers which is dipping at a n angle $ with t h e horizontal. If

t h e slope is downward from t h e shot point toward t h e d e t e c t o r (Fig. 12.121, t h e total time is given by

t2

=

(22 + x s i n $1

cos i + v1

x cos $ v2

(12.22)

Shot

Figure

Refraction path in shooting down dip.

417

in which zn = thickness of nth layer (for the top layer, n = 1); vn = sound velocity in nth layer (reciprocal of slope for nth straight section of data

= intercept of extended straight line for nth layer with t i(n) axis (Fig. 12.9). Also available a r e expressions that take into account t h e continuous variation of velocity with depth (Nettleton, 1940; Heiland, 1946). curve); and t

The velocity distributions t h a t have had practical application in seismic exploration are those in which the velocity increases linearly and exponentially with depth (Slotnick, 1936).

Refraction data are easier to interpret when

contrasts in the velocity of energy propagation are large.

In these cases

t h e rays can be assumed t o be perpendicular t o t h e interfaces.

In most

refraction work, interpretation is based on t h e assumption of uniform velocity within each bed. The situations considered so far have assumed that the shot point and detectors are located on a plane ground surface and that t h e refracting beds

are parallel t o that surface.

Because those assumptions are ordinarily not

valid in practice, i t is usually necessary t o employ travel-time relations that take into account differences in elevations of t h e wave source and detector

or slopes of refracting layers. If t h e detector is at height y above the shot point (Fig. 12.111, the

Figure

Shot point and detectors at different elevations.

418

time required for a wave to t r a v e l t h e path ABCDE is equal to t h a t required to travel t h e path ABCD plus t h e additional t i m e for t h e path DE. Thus, t h e total t i m e will be

t2

- 2 cos i v1

+

x V

+

+ey

=

(22

1

2

+

y ) cos i V 1

+

x

(12.21)

v2

I t is evident t h a t t h e t i m e is t h e same as if shot and d e t e c t o r were at t h e average elevation z + (y/2).

The equivalent path for this average elevation

is shown by t h e dotted lines of Fig. 12.11. A situation similar to t h a t just considered is t h e case of a boundary between two layers which is dipping at a n angle $ with t h e horizontal. If

t h e slope is downward from t h e shot point toward t h e d e t e c t o r (Fig. 12.121, t h e total time is given by

t2

=

(22 + x s i n $1

cos i + v1

x cos $ v2

(12.22)

Shot

Figure

Refraction path in shooting down dip.

419 The slope of t h e t2 segment of t h e travel-time curve is

m- =

s i n ( i + $1

=

"1

s i n ( i + $) v [sin i 2

( 12.23)

and t h e apparent velocity indicated by t h e slope of t h e curve is v2[sin i/sin (i + $11, which is less than t h e t r u e velocity v2 of t h e lower layer by t h e ratio sin i/sin (i + $1. If t h e slope is upward from t h e shot point toward t h e d e t e c t o r (Fig. 12.131, t h e t i m e becomes t2

=

(22 - x s i n $ )

cos i + -

x cos

v1

v2

(12.24)

The slope of t h e t2 segment of t h e travel-time curve is now

m+ = s i n ( i - $1

-- s i n ( i

-

$)

(12.25) "1 and t h e apparent velocity indicated by t h e slope of t h e curve is v2[sin i/sin

(i -

v2 s i n i

$)I, which is greater than t h e t i m e velocity v2 of t h e lower layer by

t h e f a c t o r sin i/sin (i - $). To s e p a r a t e t h e e f f e c t s of dip and velocity, refraction profiles need to be shot in opposite directions (Fig. 12.14). From eqs. (12.23) and (12.25)

-_-----

_----_ + _ _ - - - -

Figure 12J3 Refraction path in shooting up dip.

Distance

Travel-time curves for sloping layers.

Figure

(12.26)

( 12.27

The relationship between the apparent and tru e velocities and t h e angle of dip is v2

- - - sln

- 2 co s (e m-

+ m+

(12.28)

or, for a small dip angle, v2

=

+

2/(m- + m )

(12.29)

The depth to sloping beds can be calculated with expressions similar to those for horizontal layers. A t the critical distance for the down-dip

421

case X

- c - - 2 2 cos i

+

+

$I)

v1

v1

v1

X c sin(i

(12.30) X

z = 2 cosC i [ 1 - s i n ( i + $I11 Recall t h a t z is measured perpendicularly from t h e shot point to t h e sloping layer (Fig. 12.12).

T h e vertical distance between t h e shot point and the

sloping layer is

z

V

- sin(i +$)I - x c 11 2 cos i cos $I

= - -Z cos $I

(12.31)

Similarly, for t h e up-dip case z

V

= -

Z

= xc

cos $I

[ l - s i n ( i - $I)] 2 cos i cos $I

(12.32)

Also, for either t h e down-dip or t h e up-dip case, t h e intercept t i m e is

ti

- 22 cos i

(12.33)

v1

for which

z

V

= - -z

cos $I

-

ti 1 ' 2 cos i cos $I

(12.34)

Finally, for t h e down-dip case (eq. 12.221, using a point on t h e t2 segment of t h e travel-time curve yields

z

V

= - -z

cos 6

-

t 2 v1 2 cos i cos $I

- -x s i n ( i + 2

$I)

cos i cos $I

( 12.35)

Similarly, for t h e up-dip case

z

V

=

t,v, L l

2 cos i cos $I

x s i n ( i - $I) 2 cos i cos $I

(12.36)

422 A third (and most accurate) method of seismic prospecting is reflection

shooting.

In this method, measurements are made of t h e t i m e it takes f o r

a n elastic impulse to t r a v e l to and from a reflecting bed.

The depths of

t h e reflecting surfaces can be calculated from t h e travel times.

The basic

difference between reflection and refraction techniques is in t h e location of t h e d e t e c t o r s with respect to t h e shot point. In t h e refraction method t h e distances between t h e shot point and detectors are several times t h e depth of t h e beds being mapped, and only f i r s t arrivals on t h e records are used. In reflecting shooting these distances are a fraction of t h e depth of t h e beds being mapped, and impulses a f t e r t h e f i r s t arrivals are used.

In general,

instrumentation and interpretation are much more involved f o r reflection work than f o r refraction work (McDonald and Wantland, 1961; Dudley et al., 1964). The main difficulty in interpreting reflection results is to recognize reflections when t h e recordings are greatly disturbed and show o t h e r irregularities.

The reflection method is t r e a t e d in detail in textbooks of

geophysics (Nettleton, 1940; Heiland, 1946; Jakosky, 1950; Dobrin, 1952). Reflection techniques have been widely used in geophysical prospecting for oil but not in exploration for groundwater.

Reflection shooting is more

costly than o t h e r methods. As a m a t t e r of fact, t h e equipment and personnel ordinarily needed in seismic prospecting in general makes it t h e most expensive of all geophysical methods. 12.2.C

Gravity Methods

Gravity methods are based on measuring any variations in t h e gravitational field at t h e earth's surface.

Because t h e gravitational e f f e c t s of bodies or

masses are proportional to t h e density differences among themselves and their vicinity, gravity methods are suitable for locating structures in stratified formations.

As such, these methods lack t h e depth control possessed by

seismic or electrical procedures.

Usually, reconnaissance gravity surveys are

relatively rapid and inexpensive but give only general information, often inadequate. Gravity methods have been used widely in prospecting for oil.

Variations in t h e gravitational field have been measured by pendulums, gravimeters, and torsion balances (Nettleton, 1940; Heiland, 1946; Jakosky, 1950; Dobrin, 1952).

Pendulums and gravimeters measure t h e relative value

423 of gravity, whereas torsion balances measure t h e gradient of gravity (gravity force per unit horizontal distance). T h e measured variation in gravity is interpreted in t e r m s of probable subsurface mass distributions, which in turn form t h e basis for inferences about probable geologic conditions. Gravity methods have been used in oil exploration to determine general geologic structure, to map basement topography, and to locate buried ridges, domes, anticlines, salt domes, volcanic dikes, intrusions, terraces, and faults. The method has little application to groundwater exploration. Under ideal circumstances, gravity variations might

be used successfully

in

determining t h e depths of thick alluvial deposits bordering a mountain area or t h e locations of intrusive bodies constituting a n aquifer boundary (Todd, 1959). 12.2.D

Magnetic Methods

Magnetic methods are based on t h e measurement of small variations in t h e earth's magnetic field. As in gravity methods and in contrast to electrical and seismic methods, magnetic prospecting utilizes a natural field of force. The latter consists of t h e field of geologic bodies and t h e terrestrial magnetic field. Thus, in magnetic methods, measurements are made of anomalies in t h e earth's magnetic field t h a t result from geologic bodies that differ from each other in degrees of magnetism. The source of magnetic anomalies is magnetized material in t h e rocks. Because of t h e spontaneous nature of t h e subsurface effects, magnetic methods lack depth control. Furthermore, for geologic bodies to be detectable, their s i z e has to increase in proportion to

depth. Measurements of anomalies in t h e earth's magnetic field are probably t h e simplest, least expensive, and fastest of all geophysical measurements (Heiland, 1946). Relative values of magnetic intensity are measured by instruments called magnetometers. The measured variation is interpreted in t e r m s of t h e probable subsurface distribution of magnetic material. The

latter, in turn, must be explained in t e r m s of reasonable geologic conditions so t h a t inferences c a n b e made as to subsurface geology pertinent to t h e detection of local geologic structure. Thus, magnetic methods are similar to gravity methods in t h a t their interpretation is not unique.

Natural magnetic anomalies are ordinarily related to geologic bodies at great depth or to local variations which are seldom related to groundwater occurrence.

Groundwater studies can derive some assistance from magnetic

exploration when water occurs in troughs underlain by crystalline or igreous rocks or in porous magnetic igneous rocks, or when water movement is blocked by faults or igneous dikes.

Magnetic prospecting is useful also in

locating buried metal, such as pipe and abandoned well casing. 12.3

SUBSURFACE METHODS

If geologic and groundwater conditions cannot be inferred from work or the

surface, test drilling and/or subsurface geophysical techniques will be needed to obtain the desired information.

Although both drilling and geophysics are

preferred, economic considerations often demand that one be selected.

12.3.A

Test Drilling and Geologic Logs

Information on subsurface conditions can be obtained by drilling small-diameter holes, seldom exceeding 8 to 10 in, called test holes. Specifically, test holes provide information on depths to water, physical character and thickness of aquifers, and water quality.

Test holes can be used as observation wells for

measuring water levels or for conducting aquifer tests. If a test hole appears adequate as a site for a regular well, it can be redrilled or reamed to a larger diameter to form a production well. Where aquifers are less than 50 ft (15 m) below the surface, test drilling can be done rapidly, usually at a low cost in flat land underlain by soft materials.

Several well-drilling methods are suitable for test dri:ling;

used most commonly are cable-tool and rotary methods.

The choice of a

method depends on the purpose of the drilling as well as geologic and economic factors. If water quality is to be investigated during drilling, the cable-tool method is better. If rapid geologic reconnaissance of a region is the purpose, rotary methods are generally selected. During drilling, systematic samples should be collected of the materials penetrated, preferably at intervals not exceeding 10 f t and a t every change in formation. Samples should be placed in proper containers in the fielS and labeled with the location of the hole, the date, and the depth from vhich

425

( t)

I

F*"l +g+/*&

,#&+&

Figure 1215 A driller's log. each was obtained.

These can then be referred to in preparing a record, or

log, of t h e geologic formations encountered and in analyzing grain-size distribution.

Geologic logs furnish valuable information on the location of

water-bearing zones and final design of a well casing. for correlations between wells.

They are useful also

A log constructed from drilling samples is

shown in Fig. 12.15. 12.3 .B

Geophysical Methods

Subsurface geophysical methods, also referred to as geophysical logging techniques or simply well logging, have been widely used in the petroleum

industry during t h e past 50 years.

Several of the techniques have been used

also in connection with the location and construction of water wells. Well logging signifies any operation in which some characteristic data of the formations penetrated by a drill hole are recorded as a function of depth. Many of the logging methods are restricted to open holes, although surveys on aspects such as radioactivity and temperature can be performed in cased holes. 12.3.B.1

Spontaneous potential logging

The spontaneous or self-potential (SP)log is a record of naturally occurring potential differences between a stationary surface electrode, whose potential is constant, and an electrode immersed in a mud-filled drill hole, whose potential varies as it is moved along the hole. Thus, the SP log is a record of the variations in potential of the down-hole electrode. In general, the SP log consists of a rather well-defined base line having deflections to the left.

The base line usually corresponds to shale, whereas the deflections

generally indicate permeable beds. The SP log is used primarily to delineate permeable and porous beds and to determine the resistivity of waters which saturate permeable formations. The potential variations are caused by currents flowing around the intersection of t h e permeable formation, the mud column, and the shale bed (Fig. 12.16). The currents are generated largely by electrochemical electromotive forces (which occur where the formation water in the permeable beds, the drilling mud, and the shale join together) and, to a lesser extent,

by electrokinetic electromotive forces (which are produced by the mud filtrate passing through the pores of the permeable formation). If both formation water and mud filtrate are essentially sodium chloride solutions, the electrochemical component of the spontaneous electromotive force can be expressed as (Wyllie, 1949; Schlumberger, 1958a) E

(12.37)

in which K is a coefficient depending mostly on temperature, and aw and "mf are respectively t h e chemical activities of the formation water and mud

427

Figure 12.16

Schematic of spontaneous potential and current distribution in

a permeable sand lying between two shale beds. filtrate. Since, for most situations, t h e chemical activities of sodium chloride solutions are inversely proportional to their resistivities, eq. (12.37) can be rewritten for practical purposes as

in which R m f and R w are respectively t h e resistivities of t h e mud f i l t r a t e and formation water. Equation (12.38) provides t h e basis for t h e determination of R w from t h e SP curve. If t h e SP current were to be prevented from flowing by placing insulating plugs at t h e t o p and bottom of a permeable bed, t h e difference

of t h e potentials in t h e mud between t h e plugs and outside t h e plugs is called t h e s t a t i c PP (SSP) of t h e bed (in clean formations) or t h e pseudo-static SP (PSP) (in formations containing interstitial shale or clay). In clean formations,

SSP = - E (Fig. 12.16).

The PSP depends on t h e resistivity of t h e formation;

t h e higher t h e resistivity t h e smaller t h e PSP.

If t h e values of aw and amf

428

are t h e same for a shaly sand as for a clean sand, t h e PSP of t h e shaly sand will b e smaller than t h e SSP of t h e clean sand.

In low-porosity

formations, a small amount of interstitial shale reduces t h e SP deflection appreciably.

In high-porosity sands t h e PSP is practically equal to t h e SSP

if t h e shale content does not exceed a few percent. The deflection on t h e SP log opposite a given formation may be influenced by (Schlumberger, 1958a):

t h e thickness of t h e formation; t h e

resistivity of t h e formation, Rt; t h e resistivity of t h e surrounding formations, Rs; t h e resistivity of t h e mud, R,; depth of invasion.

t h e diameter of t h e borehole; and t h e

In general, for relatively soft formations such as sand

and shale series (Fig. 12.161, when t h e permeable bed is thick and when R t = R m t h e amplitude of t h e SP deflection is nearly equal to t h e SSP in clean sand or to t h e PSP in shaly sand.

Under these conditions, t h e SP curves

define t h e boundaries of t h e bed with great precision.

For thin beds, on t h e

other hand, t h e amplitude of t h e S P deflection is less than t h e SSP or PSP.

Moreover, t h e thinner t h e bed t h e smaller t h e deflection. When R t >> Rm, t h e boundaries of t h e bed are marked less precisely because t h e SP curves are rounded off. In this case, with other conditions remaining t h e same, t h e amplitude of t h e deflection is less than when R t = R,. The resistivity of t h e mud appears to a f f e c t t h e SP curve considerably. If t h e salinities of both t h e formation water and t h e mud are very high, t h e electrochemical potentials are very small. Also, t h e smaller t h e R m with respect to Rt, t h e wider t h e deflection opposite t h e permeable beds. Commonly, when t h e bore hole is filled with very conductive mud t h e SP curve shows very small deflections. An increase in hole diameter or t h e presence of a n invaded zone a f f e c t t h e SP curve in similar manners. Either f a c t o r tends to widen t h e deflections on t h e S P log. The main purpose of quantitative analysis of t h e SP log is to determine RW'

Equation (12.38) provides t h e basis f o r t h e determination of R w from

t h e SP curve when drilling muds do not contain gypsum or calcium chloride, as is usually t h e case, and when formation waters are of high salinity. Under

these conditions, as regards SP, muds and formation waters generally behave as solutions of sodium chloride, and t h e SSP is equal to eq. (12.38). For

formation waters of comparatively low salinities, t h e SSP is n o longer equal

to eq. (12.38).

Regardless of t h e salinity of formation waters, however, t h e

SSP c a n be expressed as

SSP =

-

(12.39)

in which Rwe is an equivalent resistivity. which 0.08 < R w < 0.3 ohm-m at 75'F,

For sodium chloride waters in

Rwe does not differ much from Rw.

On t h e other hand, for fresh formation waters (Rw > 0.3 ohm-m at 75')

or for more concentrated sodium chloride solutions (Rw < 0.08 ohm-m at 75'),

Rwe differs from Rw. The first s t e p in t h e determination of R w from t h e SP log is t o measure t h e value of t h e static SP, SSP. The latter is measured with respect

to a reference line, t h e shale line, which c a n b e t r a c e d along t h e e x t r e m e edges of t h e curve (Fig. 12.17). The shale line is usually a straight vertical line. If several thick permeable beds are present, it is convenient also to trace a sand line along t h e edges of t h e curve corresponding to t h e permeable beds. The SSP is then read as t h e difference between t h e sand and shale lines (Fig. 12.17). If a hole is too shallow, as in many water wells, a sand line cannot b e traced, so each permeable bed must be t r e a t e d individually. In thin permeable beds, a geometric correction f a c t o r (Schlumberger, 1958a) must be applied in order to find t h e exact ratio of t h e measured SP to t h e SSP.

The second s t e p is to select t h e value of K corresponding to t h e formation temperature (Fig. 12.18). If t h e formation temperature is not recorded on t h e log but t h e bottom-hole temperature is known, t h e former can be estimated from an available c h a r t (Schlumberger, 1958b).

If no

bottom-hole temperature is available, t h e temperature of t h e formation can

also be estimated from t h e s a m e c h a r t (Schlumberger, 1958b) provided t h a t t h e mean surface temperature and t h e geothermal gradient are known. The

relation is of t h e form T(OF) = A + (G Depth/100 ft), where A is t h e mean 0 0 surface temperature in F and G is t h e geothermal gradient in F/100 ft. T h e third s t e p is to read t h e value of Rmf at a given temperature from t h e log heading. This value is known from direct measurements on samples of mud, using a n appropriate filter press.

By means of Fig. 12.19,

430 = IOOOF 70 F

30 mv

-H+ 2000

2100

2200

2300

2400

2500 Figure 12.17

Portion of an electric log of a well penetrating sand and

shale.

z T z z l 70

6530

Figure 12.18

130

50

70

90

Temperature

150

110

Relation of temperature to electrochemical constant.

431

Figure

Relation of temperature and resistivity to NaCl concentration.

t h e recorded value of R m f c a n b e converted to t h a t corresponding to t h e formation temperature.

When direct measurements on mud samples are not

available, Rmf can be closely approximated by t h e relation Rmf = 0.75 R m , particularly in muds where NaCl is t h e major dissolved solid (Schlumberger, 1958b).

The value of R m is always recorded in t h e log heading. The fourth s t e p is to substitute t h e values of SSP, K, and R m f into

either eq. (12.38) and solve f o r Rw, or into eq. (12.39) and solve f o r Rwe. In t h e latter case, t h e value of R w can be estimated from t h e calculated

value of Rwe by use of an Rw-Rwe c h a r t (Schlumberger, 1958b). The value of R w can be related to NaCl concentration by use of Fig. 12.19. The determination of R w from an SP log can perhaps best be illustrated by t h e following example. From t h e SP log in Fig. 12.17, SP = -54 mv. From Fig. 12.18, K = 73 mv at 100°F. From Fig. 12.19, R m f = 0.9 ohm-m at 100°F. Substituting these values of SP, K, and R m f into eq. (12.38) gives R w = 0.2 ohm-m at 100°F. In this case, t h e estimated salinity (from Fig. 12.19) equals 23,000 ppm as NaC1. It should be pointed out t h a t in groundwater investigations, w a t e r samples are always analyzed so t h a t t h e main advantage

432

of running a n electric log is to show where to set screen most economically and to best advantage. 12.3.B.2

Resistivity logging

Resistivity methods are adapted to t h e investigation of large or small volumes of material around a borehole, from a few cubic inches to 100 cubic f t or more (Leroy, 1950; Schlumberger, 1958a; Lynch, 1962; P a t t e n and Bennett, 1963). Logs corresponding to measuring devices for investigating comparatively

large volumes of material include t h e normal and lateral logs, t h e laterolog, and t h e induction log.

These logs have been used for t h e delineation and

correlation of formations, a n d for t h e analysis of reservoirs in t e r m s of porosity and fluid saturation. Conventional resistivity devices such as normals and laterals involve t h e measurement of potentials resulting from electric currents flowing from

electrodes in t h e borehole into adjacent formations (Fig 12.20).

The

measurements are a f f e c t e d by t h e mud column and by t h e adjacent formations. The surveying current is constrained only by t h e location of t h e electrodes between which t h e current flows. The electrode system making up t h e sonde consists of t w o electrodes for emitting current and t w o o t h e r electrodes for potential measurement.

Depending on t h e physical configuration of t h e

electrodes, a device can give a n a c c u r a t e representation of thick layers but may not be good for showing thin breaks. Similarly, another device which may be suitable for locating formation boundaries may not permit t h e estimation of fluid content. Various electrode devices are in existence; only two shown in Fig. 12.20. In t h e normal device (Fig. 12.20a), t h e point of measurement of t h e readings is a point halfway between electrodes A and M, and t h e spacing is t h e distance AM. The point of measurement of readings

for t h e lateral device (Fig. 12.20b) is a point 0, midway between electrodes M and N, and t h e spacing is t h e distance AO.

Sometimes t h r e e resistivity

curves are recorded with t h r e e different electrode arrangements to get a more complete picture of t h e formations encountered in a borehole.

Usually,

t h e t h r e e curves of t h e conventional log are run with a short normal arrangement (AM = 16 to 18 in), a long normal (AM = 64 in) or a short lateral ( A 0 = 6 to 9 ft), and a long lateral ( A 0 = 18 f t 8 in).

In general, t h e short

433

\ \ -

--

\’

<<

---r,---_

Figure

Schematic of (a) normal and (b) AMN lateral devices.

normal is useful for locating formation boundaries but is not well adapted for showing t r u e resistivities since it is a f f e c t e d by invasion. The long normal is well adapted for finding t r u e resistivities in thick formations but is not efficient for picking formation boundaries.

The lateral is usually more suitable f o r detecting thin resistive formations than t h e o t h e r devices, but it is not efficient for a c c u r a t e formation definition. Information t h a t is more complete and a c c u r a t e than t h a t provided by this combination of three

resistivity curves can be obtained with other devices, such as t h e laterolog, induction log, microlog, or microlaterolog. The laterolog also uses electrodes, but t h e electric current flows into

t h e formations as a sheet of limited thickness.

Since it indicates bed

boundaries much more sharply than do conventional devices, thus, it is well adapted to investigations of thin formations. The laterolog works best when It has been widely used for determining t r u e resistivities in Rmf/Rw < freshwater formations drilled with relatively fresh muds.

Induction logs measure t h e conductivity of formations by means of induced alternating currents. In this case, insulated coils are mounted on a sonde which is lowered into t h e borehole. The response can b e restricted to a horizontal slice of formation of limited vertical thickness. The mud column and t h e adjacent formations have little or no e f f e c t on t h e results. Induction logging can be used in wells drilled with oil-base mud, water-base mud, or n o liquid at all in t h e hole. It works best in s o f t or moderately consolidated formations drilled with fresh muds. The combination of induction log, short normal and SP log, commonly called t h e induction-electrical log, has been used more extensively in fresh mud than have conventional logs. Unfocused (microlog) and focused (microlaterolog) microdevices are used for measuring t h e resistivities of small volumes of formation just behind t h e walls of t h e drill hole. With microdevices, t h e e f f e c t of t h e mud column on t h e measurement is practically removed.

Also, t h e delineation of

formations is more accurate than with t h e resistivity devices discussed earlier. A microlog is recorded with electrodes placed at distances of a f e w inches or less from each other on a rubber pad which is pressed against t h e walls of t h e hole. The resistivity measurements are considerably a f f e c t e d by t h e presence of mud cakes, making it possible to d e t e c t permeable formations and their boundaries. Microlog sondes usually include a second pad, located opposite t h e first one. The distance between t h e outer f a c e s of t h e two pads is continuously recorded, thus providing an a c c u r a t e record of hole diameter or microcaliper log. The microlog is valuable for determining permeable beds in areas where hard or well-consolidated formations predominate. It is also valuable for a detailed representation of t h e beds in moderately consolidated formations. It is one of t h e tools which can be used to determine t h e formation f a c t o r in soft or moderately consolidated formations. When t h e formation porosity is less than about 15%, however, t h e microlog does not provide a very a c c u r a t e determination of t h e resistivity of t h e flushed zone and, accordingly, of formation f a c t o r and porosity. Figure 12.21 illustrates t h e microlog and conventional resistivity curves in a hypothetical borehole penetrating sand and shale beds. Three sand beds are identified although intervals 1, 2, 3, and shale.

contain substantial amounts of

435

Resistivity Microlog 0

20 0

Portions of microlog and conventional resistivity curves in a borehole penetrating sand and shale. Figure

The microlaterolog device consists of a very small center electrode and three concentric ring electrodes spaced one inch or less from each other. The electrodes are mounted on a rubber pad which is pressed against the walls of the hole. As in the microlog sonde, the equipment also includes a microcaliper, which provides a detailed record of mud cakes and cavings.

Unlike t h e microlog device, t h e microlaterolog involves a focusing system t h a t minimizes t h e e f f e c t of t h e mud c a k e on t h e measurement, even eliminating t h e e f f e c t when t h e mud cake is not thick. T h e resistivity measurements are nearly equal or equal to t h e resistivity of t h e formations flushed by mud filtrate. In any type of formation, t h e microlaterolog can be used to give t h e value of t h e resistivity of t h e flushed zone when t h e mud cake thickness is less than 3/8 inch thick. When the mud c a k e is thicker than 3/8 inch, t h e value of t h e flushed zone resistivity can be found by employing appropriate correct ion charts (Schlum berger, 1958b). 12.3.B.3

Radioactivity logging

Radioactivity logging comprises gamma-ray Gamma-ray formations.

logging consists of

logging and neutron logging.

measuring t h e natural radioactivity of

Although several sources of natural radioactivity found in

formations e m i t alpha rays (helium nuclei), beta rays (electrons), and gamma rays (electromagnetic radiation), t h e last are t h e only ones which c a n p e n e t r a t e any appreciable distance through t h e formation and sonde into a detector. The radioactive elements which produce natural g a m m a radiation are those a

belonging to t h e radioactive families of uranium and thorium (e.g., U238 and Th232), and also t h e radioactive isotope of potassium (K ). It is t h e radiation emitted by these elements which is detected and measured in gamma-ray logging. The radioactivity is measured by a sonde, slowly moved up t h e hole, which contains a gamma-ray detector, usually a scintillation counter. The counter uses a thin crystal which e m i t s a small flash of light when reached by a gamma ray, and a photomultiplier which transmits an electrical impulse to t h e surface when t h e light strikes it. At t h e surface, t h e impulse is converted into electrical voltage and recorded on film. The recorded voltage is proportional to t h e radioactivity encountered in t h e hole.

431

The gamma-ray log is employed mainly for bed definition and correlation. Since high concentrations of radioactive elements are usually found in shales, the gamma-ray log essentially differentiates shales from other formations. In general, shales are more radioactive than sands, sandstones, limestones, etc.

The gamma-ray log can be recorded in open or cased holes filled with any fluid. The gamma ray curve shows a positive deflection with an increase in radioactivity (Fig. 12.22). In this respect, the gamma-ray log is somewhat similar to the SP log, which also indicates the presence of shales by deflections to the right. Unlike the SP curve, however, t h e gamma-ray log is not affected by mud salinity. In open holes drilled with high-salinity mud t h e SP curve lacks resolution, whereas the gamma-ray log generally differentiates the shales from the other formations. Because t h e gamma-ray log can be recorded in cased wells, it can be used for depth

control in perforating jobs.

Gamma ray log pg Ra eq/ton 0

4

8

12

16 20

Neutron log std counts/sec

180 260 340 420 5

Figure Portions of gamma and neutron logs run through a hypothetical sequence of sands and shales.

438

Neutron logging .consists in measuring radiation induced in or reflected from formations as a result of bombarding them with neutrons.

Neutrons

are emitted from a source contained in a sonde and collide with other nuclei in the natural media surrounding the borehole. Eventually they are slowed down, reaching a velocity comparable to the thermal motion of the environment, and are absorbed or captured. Capture is effected by the atoms of hydrogen, chlorine, sodium, etc., and results in gamma radiation. Hydrogen atoms are the most effective in slowing neutrons. Since the radiation detector employed in neutron logging is shielded from the source, the counter is essentially responsive to only gamma rays, i.e., to t h e surrounding hydrogen content. When abundant hydrogen surrounds t h e neutron source, the neutrons are slowed and captured near the source, with a resultant low level of activity registered by the counter. On the other hand, when the hydrogen concentration is small, neutrons travel to the vicinity of the source prior to capture, with a resultant measure of higher activity. Therefore, the counting rate decreases for increasing hydrogen concentration of the environment, and vice versa. For water-bearing formations, the counting rate is essentially responsive to

.

porosity In many cases, the neutron log provides fairly reliable porosity values. Neutron-log

439

The neutron log is useful for porosity estimation.

As with other

logging techniques, neutron logging is useful for formation delineation and for correlation. The neutron log, like t h e gamma-ray log, can b e made in cased holes or in open holes, in empty holes, or in holes drilled with water-base

mud or oil-base mud. It is recorded with t h e s a m e cable and truck Used for electrical logging and gamma-ray logging. T h e combination of neutron

log and gamma-ray log is valuable for surveying cased wells since it provides a qualitative record of shales, tight formations, and porous sections. 12.3.B.4

Sonic logging

In essence, sonic logging involves measuring t h e t i m e required for a sound wave t o t r a v e l across a formation. The t r a v e l t i m e is inversely proportional

to t h e speed of sound in t h e formation. As t h e sonic sonde is moved up t h e borehole, a continuous recording is made of t r a v e l times versus depth. The sonic log c a n b e used in all types of formations, with any type of mud. In high-porosity soft formations, t h e sonic log is responsive to t h e nature of t h e fluids filling t h e voids; thus it may give indications of fluid saturation. In low-porosity formations t h a t are moderate to hard, it is a f f e c t e d by t h e amount of fluid in the formations; thus, it gives reliable indications of porosity. The sonic log is particularly well suited f o r correlation purposes. 12.3.B.5

Temperature logging

The rate of increase, referred to as t h e geothermal gradient, depends upon t h e heat conductivity of the formations and t h e location under consideration. In general, temperature gradients are Temperature increases with depth.

high in formations with low heat conductivities, and vice versa. Temperatures

in a drill hole depend on both t h e geothermal gradient and t h e mud circulation. A strong mud circulation in a drill hole allows t h e mud to be mixed thoroughly and t h e mud temperature to become fairly uniform. A f t e r t h e drill pipe is removed, t h e mud temperature at each depth gradually approaches t h e temperature of t h e corresponding surrounding formation. Temperatures in a drill hole are measured with a temperature-sensitive resistance thermometer. As t h e thermometer is slowly lowered into the hole, voltages corresponding to t h e measured resistances are transmitted to t h e surface, where they are continuously recorded.

Temperature logs have

been used for locating t h e top of new cement behind a casing (Bays and Folk, 1944; Schlumberger, 1958a) since t h e heat generated during setting increases t h e temperature of t h e fluid within t h e casing (Fig. 12.23).

They have been used also for locating t h e depth of lost circulation (Schlumberger, Because t h e mud lost to a formation is constantly replaced in t h e

1958a).

drill hole by a mud pump, measured temperatures until t h e point of lost

Figure 12.23 cement

.

Schematic of temperature log in a cased well showing top of

circulation would tend to be cooler than t h e t e m p e r a t u r e of t h e formations. Below t h e point of lost circulation, t h e mud will nearly match t h e natural formation in temperature since it will have been dormant f o r s o m e time. A temperature discontinuity would thus be discerned at t h a t depth (Fig. 12.24). Temperature logs are a n important method of locating gas-producing zones (Schlumberger, 1958a; Davis and Dewiest, 1966).

During gas production,

expansion of t h e gas has a considerable cooling e f f e c t on t h e drill-hole temperature. Temperature may drop 20°F or more opposite a gas-producing zone. Temperature logs assist t h e interpretation of electrical logs. In t h e petroleum industry they have been used f o r correlation with t h e electrical

log for depth control in perforation operations.

441 Temperature increase

0

: u

c ._ 5

9

Figure circulation. 12.3.B.6

Temperature log in a hypothetical well showing depth of lost

Section-gauge logging

The diameter of a drill hole can be measured with a section-gauge instrument. Both a conventional section gauge, sometimes referred to as a caliper, and

a microcaliper (see Section 12.3.B.2) are used in t h e field. As t h e instrument is moved along in t h e hole, t h e size of t h e hole is recorded continuously at

t h e surface. Measurements of hole diameter provided by section-gauge logging

are of use in interpreting electrical and radiation logs and in estimating c e m e n t and gravel requirements for t h e well. 12.3.B.7

Other logging techniques

Other subsurface geophysical techniques are used (Bays and Folk, 1944; Leroy, 1950; Jones and Skibitzke, 1956; Schlumberger, 1958a; Lynch and Breitenbach, 1964). Of these, fluid-velocity and fluid-resistivity surveys are perhaps most useful in groundwater investigations.

Fluid-velocity logs provide a record of

flow velocities in wells, which can indicate formations t h a t contribute water

to existing wells and leaks around and through casings.

Fluid-resistivity

442

surveys provide a record of t h e electrical resistivity of fluids in wells, which' is of use in determining contamination zones in existing wells.

Information

derived from well logs is of course most reliable when based on t h e results of several types of logs. In t h e petroleum industry, t h e advantages of having t h e additional information provided by various surveys have been recognized for several decades. I t has become t h e industry's general p r a c t i c e to run electrical, radioactivity, andlor sonic logs, supplemented by other devices, when a hole has been drilled or at intervals during t h e drilling.

In t h e w e t e r

industry, only a few wells are surveyed by more than four devices, perhaps because of t h e added expense.

Small and relatively inexpensive devices are

now available which have been specifically developed for use in water wells.

443

REFERENCES

Ackermann, W. C., 1969. Costs of wells and pumps.

Ground Water, 7:35-37.

Water Well J., ll:8 pp. Anonymous, 1969. Finding ways to save pumping costs. Johnson Driller's J., 41:l-4. Ahrens, T. P., 1957.

Well design criteria.

Babbitt, H. E. and D. H. Caldwell, 1948. The f r e e surface around and interference between gravity wells. Univ. Illinois Bull. Eng. Exp. St. 374, 60 pp. Developments in t h e application of Bays, C. A. and S. H. Folk, 1944. geophysics to ground-water problems. Illinois State Geol. Survey Circ. 108, 25 pp. Bear, J., 1972. Dynamics of Fluids in Porous Media. New York, 764 pp.

American Elsevier,

Bentall, R., 1963. Methods of determining permeability, transmissivity, and drawdown. U.S. Geol. Surv. Water-Supply Paper 1536-1, 243-341. Bertam, G. E., 1940. An experimental investigation of protective filters. Harvard Soil Mechanics Series 7, 21 pp. Blair, A. H., 1970.

Well screens and gravel packs.

Blanchard, A. and J. T. Dewan, 1953. The Petro. E

Ground Water, 8:10:21.

The calibration of gamma ray logs.

Bligh, W. G. (See E. W. Lane, 1935. Security from under-seepage, masonry d a m s on e a r t h foundations. Trans. Am. Soc. Civil Engrs., p. 1235). Bonnet, M., J. Forkasiewicz, and P. Peaudecerf, 1970. M'ethodes d'interpr'etation d e pompages d'essai e n nappe libre. Bur. Rech. Geol. Min. Rep. 70 SGN 359 HYD, Orleans, France. Boulton, N. S., 1951. The flow pattern near a gravity well in a uniform water-bearing medium. J. Inst. Civ. Eng., 36:534-550. Boulton, N. S., 1954a. The drawdown of t h e water table under non-steady conditions near a pumped well in a n unconfined formation. Proc. Inst. Civ. Eng., 3:564-579. Boulton, N. S., 1954b. Unsteady radial flow to a pumped well allowing for delayed yield from storage. Proc. Gen. Assembly Rome, Intern. Assoc. Sci. Hydrol. Publ. 37, 472-477. Boulton, N. S., 1963. Analysis of d a t a from nonequilibrium pumping tests allowing for delayed yield from storage. Proc. Inst. Civ. Eng., 26:469-482. Boulton, N. S., 1970. Analysis of d a t a from pumping tests in unconfined anisotropic aquifers. J. Hydrol., 10:369-378. Boulton, N. S. and J. M. A. Pontin, 1971. An extended theory of delayed yield from storage applied to pumping tests in unconfined anisotropic aquifers. J. Hydrol., 14:53-65.

444 Boussinesq, M. J., 1904. Recherches theoretique sur l'ecoulement des nappes d'eau infiltrees dans le sol et sur debit des sources. Jour. de Math. Pures et Appl., 10:5-78. Bouwer, H., 1978. Groundwater Hydrology.

McGraw-Hill, New York, 480 pp.

Brahtz, J. H. A., 1936. Pressures due t o percolating water and their influence upon stresses in hydraulic structures. 2nd Congr. on Large Dams, 5:43-7 1. Brons, F. and V. E. Marting, 1961. The effect of restricted fluid entry on well productivity. J. Pet. Technol., 13:172-174. Buhle, M. B., 1953. Earth resistivity in ground water studies in Illinois. Eng., 5:395-399.

Min.

Burt, T. P. and P. J. Williams, 1976. Hydraulic conductivity in frozen soils. Earth Surface Processes, 1:349-360. Campbell, M. D. and J. H. Lehr, 1974. Water W e l l Technology. New York, 681 pp.

McGraw-Hill,

Carslaw, H. S. and J. C. Jaeger, 1959. Conduction of Heat in Solids, 2nd ed., Oxford Univ. Press, London, 510 pp. Childs, E. C., 1953. in porous beds.

A new laboratory for t h e study of t h e flow of fluids Inst. Civil Eng., Proc. IIk134-141.

Childs, E. C., 1969. The Physical Basis of Soil Water Phenomena. Interscience, 493 pp.

Wiley

Childs, E. C. and E. G. Youngs, 1961. A study of some three-dimensional field-drainage problems. Soil Sci., 92:15-24. Cooper, H. H., Jr. and C. E. Jacob, 1946. A generalized graphical method for evaluating for m a t ion constants and summarizing well-field his tory. Trans. Am. Geophys. Un., 27:526-534. Dagan, G., 1967a. A method for determining the permeability and effective porosity of unconfined anisotropic aquifers. Water Resour. Res., 3:10591071. Dagan, G., 1967b. A method for determining t h e permeability and effective porosity of unconfined anisotropic aquifers. Hydraul. Lab. Rep. P. N. 1/1967, Technion Israel Inst. of Tech., Haifa. Darcy, H., 1856. Les Fontaines Publiques de la Ville de Dijon. V. Dalmont, Paris, 570, 590-594. Davis, S. N. and R. J. M. Dewiest, 1966. Hydrogeology. John Wiley & Sons, New York, 463 pp. Dewan, J. T., 1956. Neutron log correction charts for borehole conditions and bed thickness. J. Petro Technology, 8. Dixon, R. M., 1976. Comment on Derivation of a n equation of infiltration by H. J. Morel-Seytoux and J. Kohanji. Water Resour. Res., 12:116-118. Dobrin, M. B., 1952. Introduction t o Geophysical Prospecting. N e w York, 435 pp.

McGraw-Hill,

445 Donnan, W. W., V. S. Aronovici and H. F. Blaney, 1947. investigations in irrigated areas of Imperial Mimeographed report, U.S. Dept. of Agriculture.

Report on drainage Valley, California.

Dudley, W. W. Jr., and others, 1964. Geophysical studies in Nevada relating to hydrogeology. Desert Research Inst., Univ. of Nevada, Tech. Rept. 2, 46 PPDupuit, J., 1863. Etudes Th’eoriques et Pratiques sur le Movcement des Eaux Travers les Terrains Perm’eables. dans les Canaux D’ecouverts et 2nd ed., Dunod, Paris, 304 pp. Ferris, J. G., D. B. Knowles, R. H. Brown, and R. W. Stallman, 1962. Theory of aquifer tests. U.S. Geol. Surv. Water-Supply Paper 1536-E, 174 pp. Forchheimer, P., 1930. Hydraulik. 3rd ed., B. G. Teubner, Leipzig and Bulin, 595 pp. Foster, J. W. and M. B. Buhle, 1951. An integrated geophysical investigation of aquifers in glacial drift near Champaign-Urbana, Illinois. Econ. Geol., 46:367-397. Freeze, R. A., 1971. Three-dimensional, transient saturated-unsaturated flow in a groundwater basin. Water Resour. Res., 7:347-366. Gardner, W. R., 1958. Some steady-state solutions of t h e unsaturated flow equation with application to evaporation from a water table, Soil Sci., 85:228-232. Gardner, W., T. R. Collier, and D. Farr, 1934. Groundwater, P a r t J: Fundamental principles governing its physical control. Utah Agric. Exp. Sta. Bul. 252. Gay, L. 0. and M. Kosten, 1956. Some applications of geophysical methods to geological problems in t h e Gold Coast. Gold Coast Geol. Survey Bull. 21, 37 pp. Glover, R. E., 1964. Ground water movement. Eng. Monogr. 31, Chief Engineer, U.S. Bureau of Reclamation, Denver, Colo., 81 pp. Green, W. H. and G. A. Ampt, 1911. Studies in soil physics I. air and water through soils. J. Agr. Sci., 4:l-24.

The flow of

Hall, H. P., 1955. An investigation of steady flow toward a gravity well. Houille Blanche, 10:8-35. Hall, F. R. and A. F. Moench, 1972. Application of t h e convolution equation to stream-aquifer relationships. Water Resour. Res., 8:487-493. Hansen, V. E., 1952. Complicated well problems solved by t h e membrane analog. Amer. Geophys. Union Trans., 33:912-916. Hantush, M. S., 1956. Analysis of d a t a from pumping tests in leaky aquifers. Trans. Am. Geophys. Un., 37:702-714. Hantush, M. S., 1960a. Modification of t h e theory of leaky aquifers. Geop hys. Res., 6 5 :3713-3 7 2 5. Hantush, M. S., 1960b. Tables of t h e function H(u, 8). Library of Congress, Wash., D.C.

J.

Document 6427, U S .

446 Hantush, M. S., 1962. Aquifer tests on partially penetrating wells. Am. Soc. Civ. Eng., 127:284-308.

Trans.

Hantush, M. S., 1963. Growth of a groundwater ridge in response to deep percolation. Symp. on Transient Ground Water Hydraul., Ft. Collins, Colo., 118. Hantush, M. S., 1964. Hydraulics of wells. In: Advances in Hydroscience, vol. 1, V. T. Chow (ed.), Academic Press, New York, 281-432. Hantush, M. S., 1967. Growth and decay of groundwater mounds in response to uniform percolation. Water Resour. Res., 3:227-234. Hantush, M. S. and C. E. Jacob, 1955. Nonsteady radial flow in a n infinite leaky aquifer. Trans. Am. Geophys. Un., 36:95-100. Haushild, W. and G. Kruse, 1962. Unsteady flow of ground water into a surface reservoir. Trans. Am. SOC. Civ. Eng., 127:408-415. Harr, M., 1962. Groundwater and Seepage. New York, 315 pp. Heiland, C. A., 1946. 1013 pp.

McGraw-Hill Book Co., Inc.,

Geophysical Exploration.

Hirschfeld, R. C. and S. J. Poulos, 1973. John Wiley & Sons, 454 pp.

Prentice-Hall,

New York,

Embankment-Dam Engineering.

Hollyday, E. F. and P. R. Seaber, 1968. Estimating cost of groundwater withdrawal for river basin planning. Ground Water, 6:15-23. Hooghoudt, S. B., 1936. Bijdragen tot d e Kennis van eenige Natuurkundige Grootheden van den Grond. No. 4, Versl. Land Ond. 42.B. Hooghoudt, S. B., 1940. Bijdragen tot d e kennis van eenige natuurkundige grootheden van den grond, 7. Verslag, Landboruuk, Onderzock, 46:515707. Howe, R. H. L., 1958. Procedures of applying air photo interpretation in t h e location of ground water. Photogramm. Eng., 24:35-49. Huisman, L., 1972. 336 pp.

Groundwater Recovery.

Iterson, F. K., Th van 1916-17. De Ingenieur.

Winchester Press, New York,

Eenige Theoretische Beschouwingen ver kwel.

Jackson, R. D., 1972. On t h e calculation of hydraulic conductivity. Soil Sci. Soc. Amer. Proc., 36:380-382. Jacob, C. E., 1947. Drawdown test to determine effective radius of artesian well. Trans. Am. Soc. Civ. Eng., 112:1047-1070. Jacob, C. E. 1950. Flow of ground water. In: Engineering Hydraulics, H. Rouse (ed.), John Wiley & Sons, New York, 321-386. Jakosky, J. J., 1950. Exploration Geophysics. 2nd ed., Times Mirror Press, Los Angeles, 1195 pp.

447 Jeppson, R. W. and R. W. Nelson, 1970. Inverse formulation and finitedifference solution to partially s a t u r a t e d seepage from canals. Soil Sci. SOC. Am. Proc., 34:9-14. Johnson, E. E., Inc., 1966. Ground Water and Wells. Johnson Div., Universal Oil Products Co., St. Paul, Minnesota, 440 pp. Jones, P. H. and H. E. Skibitzke, 1956. Subsurface geophysical methods in ground-water hydrology. In: Advances in Geophysics, H. E. Landsberg (ed.), vol. 3, Academic Press, New York, 241-300. Jumikis, A. R., 1962. New Jersey.

Soil Mechanics.

D. van Nostrand Inc., Princeton,

Kelly, S. F., 1962. Geophysical exploration f o r w a t e r by electrical resistivity. J. New England Water Works ASSOC., 76:118-189. Kirkham, D., 1940. Artificial drainage of land: Streamline experiments. The artesian basin-11. Amer. Geophys. Union Trans., 21:587-593. Kirkham, D., 1945. Artificial drainage of land: Streamline experiments. The artesian basin-111. Amer. Geophys. Union Trans., 26:393-406. Kirkham, D., 1946. Proposed method f o r field measurement of permeability of soil below a water table. Soil Sci. Soc. Amer. Proc., 10:58-68. Kirkham, D., 1958. Seepage of steady rainfall through soil into drains. Geophys. Union Trans., 39:892-908.

Amer.

Koenig, L., 1960a. Survey and analysis of well stimulation performance. Am. Water Works ASSOC., 52:333-350. Koenig, L., 1960b. Economic aspects of water well stimulation. Water Works ASSOC., 52:631-637.

J.

J. Am.

Koenig, L., 1960c. Effects of stimulation on well operating costs and i t s J. Am. Water Works Assoc., performance on old and new wells. 5 2 :14 9 9-1512. Koenig, L., 1961. Relation between aquifer permeability and improvement achieved by well stimulation. J. Am. Water Works ASSOC., 53:652-670. Kostiakov, A. N., 1932. On t h e dynamics of t h e coefficient of water percolation in soils and t h e necessity for studying it from a dynamic view for purposes of amelioration. Trans. 6th Comm. Int. Soc. Soil Sci., Russian P a r t A:17-21. Kozeny, J., 1932. Hydrologische Grundlagen des Dgnversuches. Comm. Int. Soc. Soil Sci., A:42-67.

Trans. Sixth

Kutilek, M., 1972. Non-Darcian flow of water in soils - laminar region. In: Fundamentals of Transport Phenomena in Porous Media, Intern. Assoc. f o r Hydraul. Res., Elsevier Publ. Co., Amsterdam, 327-340. Leroy, L. W. (editor), 1950. Subsurface Geologic Methods. 2nd ed., Colorado School of Mines, Golden, Colo., 1166 pp. Lennox, D. H., 1966. Analysis and application of step-drawdc-m test. Hydraul. Div., Am. SOC. Civ. Eng., 92:25-48.

J.

448 Lohman, S. W., 1972. Groundwater hydraulics. Paper 708, 70 pp. Luthin, J. N. and A. Haig, 1972. pipes. Hilgardia, 41:23 5-245.

Some f a c t o r s affecting flow into drain

Lutz, J. R. and W. D. Kemper, 1959. a f f e c t e d by clay-water interaction. Lynch, E. J., 1962. 422 pp.

U.S. Geol. Surv. Prof.

Intrinsic permeability of clay as Soil Sci., 88:83-90.

Formation Evaluation.

Lynch, E. J. and E. A. Breitenbach, 1964. evaluation. World Oil, 158:llO-118.

Harper and Row, New York,

Recent developments in formation

Maasland, M., 1956. The relationship between permeability and t h e discharge, Bull. 1, Water Conservation and depth and spacing of tile drains. Irrigation Commission, New South Wales. Maasland, M., 1959. Water table fluctuations induced by intermittent recharge. J. Geophys. Res., 64:549-559. Mariiio, M. A., 1964. Growth and Decay of Groundwater Ridges in Response to Deep Percolation. M.S. Thesis, New Mexico Institute of Mining and Technology, Socorro, N. M., 129 pp.

Mariiio, M. A., 1967. Hele-Shaw model study of t h e growth and decay of groundwater ridges. J. Geophys. Res., 72:1195-1205. Mariiio, M. A., 1973. Water-table fluctuations in semipervious streamunconfined aquifer systems. J. Hydrol., 19:43-52. Marifio, M. A., 1974a. Growth and decay of groundwater mounds induced by percolation. J. Hydrol., 2 2: 2 9 5-301.

Mariiio, M. A., 1974b. Rise and decline of t h e w a t e r t a b l e induced by vertical recharge. J. Hydrol., 23:289-298.

Marifio, M. A., 1974c. Water table fluctuation in response t o recharge. brig. Drain. Div., Am. SOC. Civ. Eng., 100:117-125.

J.

Marifio, M. A., 1975a. Digital simulation model of aquifer response to s t r e a m stage fluctuation. J. Hydrol., 25:51-58. Marifio, M. A., 1975b. Artificial groundwater recharge. area. J. Hydrol., 25:201-208.

I. Circular recharging

Marifio, M. A., 1975c. Artificial groundwater recharge. recharging area. J. Hydrol., 26:29-37.

II. Rectangular

Mariiio, M. A., 1978. Solute transport in a saturated-unsaturated porous In: Modeling, Identification and Control in Environmental medium. Systems, G. C. Vansteenkiste (ed.), North-Holland Publ. Co., Amsterdam, 269-281. Marifio, M. A. and W. W-G. Yeh, 1972. Nonsteady flow in a recharge well-unconfined aquifer system. J. Hydrol., 16:159-176.

449

Marifio, M. A. and W. W-G. Yeh, 1973a. A discrete space continuous time modelling approach to nonsteady flow in a leaky aquifer system of finite configuration. J. Hydrol., 2 0:25 5-266. Marifio, M. A. and W. W-G. Yeh, 1973b. Identification of parameters in finite leaky aquifer system. J. Hydraul. Div., Am. SOC. Civ. Eng., 99:319-336. Marifio, M. A. and G. B. Matanga, 1978. A Galerkin-finite element simulation of solute transport in subsurface drainage systems. In: Finite Elements in Water Resources, C. A. Brebbia, W. G. Gray and G. F. Pinder (eds.), Pentech Press, London, 1.51-1.67. Marshall, T. J., 1957. Permeability and t h e size distribution of pores. 180:664-6 6 5.

Nature,

McDonald, H. R. and D. Wantland, 1961. Geophysical procedures in ground water study. Trans. Am. SOC. Civil Eng., 126:122-135. McGinnis, L. D. and J. P. Kempton, 1961. Integrated seismic, resistivity, and geologic studies of glacial deposits. Illinois State Geol. Survey Circ. 323, 23 pp. McLachlan, N. M., 1956. Bessel Function for Engineers. London, 239 pp.

Oxford Univ. Press,

Miles, D. L. and R. L. Longenbaugh, 1968. Evaluation of irrigation pumping plant efficiencies and costs in t h e High Plains of eastern Colorado. Colo. State Univ. Exp. St. General Series No. 876. Millington, R. J. and J. P. Quirk, 1960. Trans. Int. Cong. Soil Sci., I:97-106.

Transport in porous media.

7th

Mooney, H. M. and W. W. Wetzel, 1956. The potentials about a point electrode and apparent resistivity curves f o r two-, t h r e e , and four-layered earth. Univ. of Minnesota Press, Minneapolis, 146 pp. (plus curves).

Morris, D. A. and A. I. Johnson, 1967. Summary of hydrologic and physical properties of rock and soil materials. U.S.G.S. Water Supply Paper 1839-D. Muskat, M., 1937. The Flow of Homogeneous Fluids through Porous Media. McGraw-Hill, New York (Second Printing by J. W. Edwards, Ann Arbor, Michigan, 1946, 763 pp.) Najamii, M., D. Kirkham and M. D. Dougal, 1978. Tube drainage in stratified soil above a n aquifer. J. Irrig. and Drain., ASCE, 104:209-228. Nelson, A. G. and C. D. Busch, 1967. Cost of pumping irrigation water in c e n t r a l Arizona. Univ. Arizona Tech. Bull. 182, 44 pp. Nettleton, L. L., 1940. New York, 444 pp.

Geophysical Prospecting for Oil.

McGraw-Hill,

Neuman, S. P., 1972. Theory of flow in unconfined aquifers considering delayed response of t h e water table. Water Resour. Res., 8:1031-1045. Neuman, S. P., 1973a. Supplementary comments on theory of flow in unconfined aquifers considering delayed response of t h e water table. Water Resour. Res., 9:1102-1103.

450 Neuman, S. P., 1973b. Saturated-unsaturated seepage by finite elements. Hydraul. Div., Am. Soc. Civ. Eng., 99:2233-2250.

J.

Neuman, S. P., 1974. Effect of partial penetration on flow in unconfined aquifer considering delayed gravity response. Water Resour. Res., 10:303-312. Analysis of pumping test data from anisotropic Neuman, S. P., 1975. unconfined aquifers considering delayed gravity response. Water Resour. Res., 11:329-342. Neuman, S. P., 1979. 15:899-908.

Perspective on 'delayed yield.'

Water Resour. Res.,

Neuman, S. P. and P. A. Witherspoon, 1969a. Theory of flow in a confined two aquifer system. Water Resour. Res., 5:803-816. Neuman, S. P. and P. A. Witherspoon, 1969b. Applicability of current theories of flow in leaky aquifers. Water Resour. Res., 5:817-829. Neuman, S. P. and P. A. Witherspoon, 1972. Field determination of t h e hydraulic properties of leaky multiple aquifer systems. Water Resour. Res., 8:1284-1298. Nisle, R. G., 1958. The effect of partial penetration on pressure build-up in oil wells. Trans. Am. Inst. Min. Metal. Pet. Eng., 213:85-90. Norris, S. E. and H. C. Spicer, 1958. Geological and geophysical study of the preglacial Teays Valley in west-central Ohio. U.S. Geol. Survey Water-Supply Paper 1460-E, 192-232. Olsen, H. W., 1966. Darcy's law in saturated kaolinite. Water Resour. Res., 2:28 7-29 5. Patten, E. P. and G. D. Bennett, 1963. Application of electrical radioactive well logging t o ground-water hydrology. U.S. Geol. Survey Water-Supply Paper 1544-D, 60 pp. Peterson, D. F., 1957. 122:502-517.

Hydraulics of wells.

Trans. Am. Soc. Civ. Eng.,

Prickett, T. A., 1965. Qpe-curve solution t o aquifer tests under water-table conditions. Ground Water, 3:5-14. Ray, R. G., 1960. Aerial photographs in geologic interpretation and mapping. U.S. Geol. Survey Prof. Paper 373, 230 pp. Rhoades, J. D., 1974. Drainage for salinity control. Agriculture, Amer. Soc. Ag., Memeo 17.

In: Drainage for

Rorabaugh, M. I., 1953. Graphical and theoretical analysis of step-drawdown test of artesian well. Proc. Am. Soc. Civ. Eng., vol. 79, separate no. 362, 23 pp. Rubin, J., 1968. Theoretical analysis of two-dimensional transient flow of water in unsaturated and partly saturated soils. Soil Sci. Soc. Am. Proc., 32:607-615.

451

Russell, J. L., 1934. 24:544-573.

Scientific research in soil drainage.

J. Agric. Sci.,

Schaffernak, F., 1917. Uber die Standsicherheit durchlassiger geschut ter Damme Allgem. Bauzeitung. Schleicher, G., 1975.

The well driller's blues.

Schlichting, E. and U. Schwertmann, 1973. Comm. V and VI of Int. Soil Sci. Soc.

Irrig. Age, 9:38-43. Psuedogley and gley.

Trans.

Schlumberger W e l l Surveying Corporation, 1958a. Introduction t o Schlumberger well logging. Schlumberger W e l l Survey. Corp. Document 8, Houston, Texas, 176 pp. Schlumberger Well Surveying Corporation, 1958b. Log interpretation charts. Schlumberger Well Survey Corp., Houston, Texas. Schmid, P. and J. Luthin, 1964. The drainage of sloping lands. J. Geophys. Res 69:1525-1530.

.,

Sheahan, N. T., 1971. Water, 9:25-29.

Type-curve solution of step-drawdown test.

Ground

Skaggs, R. W., L. E. Huggins, E. J. Monke and G. R. Foster, 1969. Experimental evaluation of infiltration equations. Trans. ASAE, 12:822-828. Slotnick, M. M., 1936. On seismic computation, I. Geophysics, 1:9-22; Geophysics, 1:299-305. Smith, H. F. 1954. Gravel packing w a t e r wells. Illinois State Water Survey Circ. 44, Urbana, Ill. Stallman, R. W., 1961. Boulton's integral for pumping test analysis. U.S. Geol. Surv. Prof. Papers 400-C, Geol. Surv. Res. 1961, Short Papers in Geol. Hydrol. Sci. Articles 147-292, C-24 t o C-29. Sternberg, Y. M., 1973. Water, 11:5-8.

Efficiency of partially penetrating wells.

Streltsova, T. D., 1972a. Unconfined aquifer and slow drainage. 16:117-124.

Ground

J. Hydrol.,

Streltsova, T. D., 1972b. Unsteady radial flow in a n unconfined aquifer. Water Resour. Res., 8:1059-1066. Streltsova, T. D., 1973. Flow near a pumped well in a n unconfined aquifer under nonsteady conditions. Water Resour. Res., 9:227-235. Streltsova, T. D., 1974. Drawdown in a compressible unconfined aquifer. J. Hydraul. Div., Am. Soc. Civ. Eng., 100:1601-1616. Summers, W. K., 1972. Specific capacities of wells in crystalline rocks. Ground Water, 10:37-47. Swartz, J. H., 1937. Resistivity studies of some salt-water boundaries in the Hawaiian Islands. Trans. Am. Geophys. Union, 18:387-393. Swartz, J. H., 1939. Geophysical investigations in t h e Hawaiian Islands. Trans. Am. Geophys. Union, 20:292-298.

452

Swartz, J. H., 1940. Geophysical investigations on Lanai. In H. T. Steams, Geology and ground-water resources in Hawaii. Terr. Hawaii Div. of Hydrography Bull. 6, 97-115. Swartzendruber, D. and M. R. Huberty, 1958. Use of infiltration equation parameters to evaluate infiltration differences in t h e field. EOS Trans. Amer. Geophys. Union, 39:84-93. Swartzendruber, D., 1969. The flow of water in unsaturated soils. In: Flow through Porous Media, R. J. M. Dewiest (ed.), Academic Press, New York, 215-292. Talsma, T., 1963. The control of saline groundwater. Landbouwhogeschool. Wageningen, The Netherlands, 63:l-68. Talsma, T., 1967. 5:37-46.

Leaching of tile-drained saline solis.

Meded.

Aust. J. Soil Res.,

T a t t a m , C. M., 1937. The application of electrical resistivity prospecting to ground water problems. Colorado School of Mines Quart., 32:117-138. Taylor, D. W., 1948. New York.

Fundamentals of Soil Mechanics.

John Wiley & Sons,

Thesis, C. V., 1935. The relation between t h e lowering of t h e piezometric surface and t h e rate and duration of discharge of a well using groundwater storage. Trans. Am. Geophys. Un., 16:519-524. Theil, T. and G. S. Taylor, 1960. Utilizing a sand tank model to study some moisture flow problems in drainage. Int. Congr. Soil Sci. Trans. 7th (Madison, Wis.), vol. 1, Comm, 1:473-479. Todd, D. K., 1959. Ground Water Hydrology. 336 pp.

John Wiley & Sons, New York,

Van Schilfgaarde, J., 1963. Design of tile drainage for falling water tables. Amer. Soc. Civil Eng. Proc., 89:l-11. Grafische Berekening Drainafstanden. Van Someren, C. L., Undated. Cultuurtechnische Dienst Ministrie van Landbouw, Visserijen. Visocky, A. P., 1970. Values of W(u, r/m, y). Presented in W. C. Walton, Groundwater Resources Evaluation, McGraw-Hill, New York, Table 3.3, p. 140. Volker, A. and J. Dijkstra, 1955. Determination des salinitds des eaus dans le sous-sol du Zuiderzee par prospection gdophysique. Geophys. Prospecting 3:111-12 5. Walton, W. C., 1960. Leaky artesian aquifer conditions in Illinois, Ill. State Water Surv. Rept. Invest. 39, 27 pp. Walton, W. C., 1962. Selected analytical methods for well and aquifer evaluation. Illinois State Water Survey Bull. 49, 81 pp. Walton, W. C., 1970. New York, 664 pp.

Groundwater Resource Evaluation,

McGraw-Hill,

453 Wenzel, L. K., 1942. Methods f o r determining permeability of water-bearing material with special r e f e r e n c e to discharging-well methods. U.S. Geol. Surv. Water-Supply Paper 887, 192 pp. Werner, P. W., 1953. On non-artesian groundwater flow. 25:37-43.

Geofis. Pura Appl.,

Werner, P. W., 1957. Some problems in non-artesian ground-water flow. Trans. Am. Geophys. Un., 38:511-518. Wesseling, J., 1964. A comparison of t h e steady-state drain spacing formulas J. of Hooghoudt and Kirkham in connection with design practice. Hydrol., 2:25-32. Williamson, R. E. and G. J. Kriz, 1970. Response of agricultural crops to flooding, depth of water table and soil gaseous composition. Amer. Soc. Agric. Eng. Trans., 13:216-220. Witherspoon, P. A., I. Javandel, S. P. Neuman, and R. A. Freeze, 1967. Interpretation of Aquifer Gas Storage Conditions from Water Pumping Tests. American Gas ASSOC., New York. Workman, L. E. and M. M. Leighton, 1937. Search for ground water by t h e electrical resistivity method. Trans. Am. Geophys. Union, 18:403-409. Wyllie, M. J. R., 1949. Statistical study of accuracy of some connate-water resistivity determinations made from self-potential log data. Am. Assoc. Petro. Geol. Bull., 33:1892-1900. Yeh, W. W-G., 1970. Nonsteady flow to s u r f a c e reservoir. Am. Soc. Civ. Eng., 96:609-618.

J. Hydraul. Div.,

Zee, C-H., D. R. Peterson, and R. 0. Bock, 1957. Flow into a well by electric and membrane analogy. Amer. Soc. Civil Eng., Trans., 122:10881112. Zohdy, A. A. R., G. P. Eaton and D. R. Mabey, 1974. Application of surface geophysics to ground water investigations. Chap. D1 In Techniques of water resources investigations of t h e U.S. Geological Survey. U.S. Govern. Printing Office No. 2401-02543, Wash., D.C., 116 pp.