GEOPHYSICS, VOL. 56, NO.6 (JUNE 1991); P. 874--883, 8 FIGS.
Assessment of 2-0 resistivity structures using 1-0 inversion
L. P. Beard* and F. D. Morgant
sounding data from simple models of 2-D subsurface resistivity
structures. The structures modeled are a vertical dike, a buried
fault block, a tabular prism, a square prism, and a ramp, each
infinite along one horizontal axis. All computations were
performed on a VAX 111780 computer. The forward model
results were generated using a 2-D finite-difference program. Five
to seven different soundings were computed at various locations
over each structure. These soundings were then assumed to have
been taken from a horizontally layered earth, and were interpreted using an iterative least-squares inversion approach
described by Johanssen (1977). The forward program for the
I-D inversion procedure used the linear digital filters of Ghosh
(1971), Johanssen (1975), and O'Neill (1975). Contoured crosssections for Wenner and Schlumberger arrays were compared
based on: (I) the apparent resistivity sounding data and (2) the
resistivities of the layers predicted from inversion. We found that
the Schlumberger array was usually superior to the Wenner array
in analyzing 2-D resistivity structures of low to moderate (2:1 to
10:1) resistivity contrast. The square prism model was an
important exception. We found that certain 2-D structures lend
themselves more readily to interpretation using I-D inversion
than do others. We developed rules of thumb that could serve
as guidelines in field investigations. Since a growing number of
companies use resistivity as a tool in environmental, engineering,
and groundwater investigations, such guidelines are vital,
especiallysince small companies may not have the computational
resources necessary for 2-D or 3-D inversion.
We recognize that in a 2-D or 3-D environment it is best to
use interpretational tools which assume 2-D or 3-D models. We
do not advocate the use of I-D interpretation in a 2-D or 3-D
environment. Even so, it is a fact that such analyses are performed, either inadvertently, by necessity, or by choice, so it is
important to assess the extent to which such an analysis can be
trusted and to understand the key factors affecting such an
interpretation.
ABSTRACT
Schlumberger and Wenner array resistivity soundings
over 2-D resistivity structures are interpreted using
apparent resistivity pseudosections and cross-sections
constructed from I-D inversions in order to determine the
effectiveness of I-D interpretations over such structures.
Cross-sections contoured from resistivities of inverted
"layers" show distinct differences from the apparent
resistivity pseudosections and may be used as interpretational aids. Contour lines in the cross-sections locate the
horizontal interfaces of the 2-D structures quite well. The
vertically oriented segments of the cross-section contours
are relatively undistorted in the inversion process and are
similar to the vertically oriented portions of contours in
the apparent resistivity pseudosection. A simple, empirically determined formula is used to separate the sections
into resistive and conductive zones and helps to define
the geometry of the anomaly. In order to apply the
formula, it is necessary to know whether the target is a
relative conductor or a relative resistor. Except for the
case of a square prism, the Schlumberger array appears
to hold advantages over the Wenner in qualitatively
assessing an anomaly. The primary drawback of the
Wenner array is that its expanding potential electrodes
create false anomalous zones and complicate interpretation. As might be expected, structures with long horizontal
interfaces, i.e. those more nearly I-D, yield the most
accurate interpretations.
INTRODUCTION
Geophysical data are often interpreted using a horizontally
layered earth model (I-D model) when a 2-D or a 3-D approach
might better approximate the local subsurface geometry, particularly in areas where horizontal layering does not predominate.
It is important to understand how and to what extent I-D
approximations represent the earth's true subsurface structure.
In this paper, we examine the effect of I-D inversion of resistivity
PROCEDURE
The resistivity sounding data were generated by a 2-D foward
modeling program, RESIS2D, developed by Dey and Morrison
(1979). The program uses a finite-difference approach to solve
Manuscript received by the Editor April 20, 1990; revised manuscript received December 20, 1990.
*Formerly Texas A&M; presently, Department of Geology and Geophysics, University of Utah, Salt Lake City, UT 84112.
tDepartment of Geophysics, Texas A&M University, College Station, TX 77844.
©1991 Society of Exploration Geophysicists. All rights reserved.
874
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875
Assessing 2-D Resistivity Structures
for the potential distribution due to point sources of current,
and the potential distribution is converted into apparent resistivity values. The grid used by Dey and Morrison consists of
113 horizontal nodes and 16 vertical nodes. The grid coarsens
away from the center of the air-earth interface, allowing for
accurate results with fewer nodes. Each node on the grid could
be assigned a particular resistivity. We used the 113 x 16 grid
for our vertical dike and buried fault block models, but expanded
the grid to 173 X 20 nodes for the other models. RESlS2D was
tested for the case of a two-layer earth for both Wenner and
Schlumbergerarrays, and we found it yielded apparent resistivities
to within 5 percent of our own layered forward modeling
programs. The 5 percent error appeared to be systematic, so we
implemented a small correction factor that randomized the error
and reduced it by half. This proved sufficient for our purposes.
A more elaborate approach to correcting mesh errors in the finite
difference method is described in Lowry et al. (1989). We also
tested RESIS2D for scale change effects. Scale changes usually
influenced the apparent resistivity values less than I percent
though in some cases up to 3 percent. Scaling was necessary to
obtain the appropriate number of sounding data for interpretation and inversion.
After establishing the reliability of the 2-D forward program,
we proceeded to create sounding data sets for Wenner and
Schlumberger arrays. With each model, a set of five to seven
sounding curves were generated. For soundings near the
anomalous zone, 15 to 25 apparent resistivity values were
computed. For soundings farther away, 10 to 15 values were
sufficient. The model was scaled up or down as necessary to
build a data set over 2.5 to 3 decades.
Once a sounding set was generated, these data had to be
interpolated to yield apparent resistivityvalues for specific arrays.
This was achieve" using Lagrange's interpolation formula
(Abramowitz and Stegun, 1970, p. 878).
After the interpolated apparent resistivity values were
obtained, the data were input into a I-D inverse program. An
initial guess was made as to the number of "layers" constituting
the sounding data, as wellas each layer's thickness and resistivity.
The program was then allowed to iterate to a solution. If too
few layers were chosen, a large rms error would result. If an
unnecessarily large number of layers was chosen, the thickness
of one or more layers approached zero or the resistivity of
consecutive layers was made approximately the same. If the
appropriate choice was still not obvious, a resolution matrix
(Wiggins, 1972)was employed to aid in choosing the appropriate
number of layers. If the diagonal terms of the resolution matrix
were all near I and the off-diagonal terms were near zero, good
resolution of all parameters was assumed to have been obtained.
Once a layered interpretation had been obtained for each of
the soundings, the apparent resistivities were entered on a grid
and contoured to create a cross-section. A pseudosection was
created by contouring the apparent resistivity data generated
from RESIS2D, and the sections were compared. Often additional information regarding the anomaly's geometry could be
obtained from the inverted cross-section, particularly the locations of horizontal interfaces. (Note that the term "pseudosection" has been reserved for contours of apparent resistivity
data taken from resistivity soundings, in keeping with ordinary
usage of the term. We use the term cross-section to describe
resistivities which have been contoured after I-D inversion.)
To rely only on apparent resistivity pseudosections or inverted
cross-sections to estimate the extent and geometry of an anomaly
can often be misleading. In an effort to better establish an
anomaly's true shape, we attempted to find a simple method
that would use the contours to predict the anomaly's geometry.
We were only partially successful, but we feel the method
employed could aid in field investigations, provided its limitations are understood. Our method aimed at determining a
resistivity cutoff value on the pseudosection or contoured crosssection. Any resistivities less than the cutoff value were shaded
as relative conductors. All resistivities greater than the cutoff
were left unshaded and considered to be relatively resistive. To
establish the resistivity cutoff, the highest and lowest resistivity
values were located on the pseudosection. Denote the logs of
these values Xh and Xl respectively. Let Ax=(Xh -xl)/3. If the
anomalous body was judged to be resistive, the cutoff resistivity
was calculated by
(1)
If the anomaly was judged conductive,
Pc was given by
(2)
Shading resistivity values defined by Pc had the effect of
approximately delineating the anomaly's geometry in most cases,
particularly if the Schlumberger array was used.
MODELS
Figure I illustrates the five 2-D geometries considered: (1) a
buried, vertically faulted block, (2) a vertical dike, (3) a tabular
prism, (4) a square prism, and (5) a ramp. In the first four
models, both the Schlumberger and Wenner arrays were
examined. In the fifth case, only the Schlumberger array was
considered.
Buried fault block
Figure la shows the buried fault block. The block's vertical
edge is located at zero on the x-axis and is assumed to extend
downward to infinity. The horizontal interface is 10 units deep.
The block is resistive(1000 ohm-m) with respect to the surrounding unit (200 ohm-rn).
Figure 2a shows the results of five separate Schlumberger
soundings after I-D inversion. Note that each of the soundings
inverted to two layers. In the two soundings centered directly
over the block (x = - 40, - 80), the horizontal interface is
predicted near a depth of 10 units. The upper layer resistivity
in each case is near the true value of 200 ohm-m. The lower
layer shows a somewhat lower resistivity (688 ohm-m, 6800hm-m)
than the true value due to the influence of the 200 ohm-rn
material to the right of the block. The x = 0 sounding follows
a similar pattern. The x = 40 and x = 80 soundings invert to
two layers with the lower layer showing a higher than true
resistivity due to the influence of the resistive block.
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876
Beard and Morgan
(a)
(b)
The inverted results of five Wenner soundings are shown in
Figure 2b. The inverted Wennerdata results in a two-layer pattern
very similar to that of the Schlumberger soundings, except for
the x = 0 sounding over the vertical edge of the block. Here
a four-layer inversion results, due to a more complicated sounding curve resulting from the potential electrodes expanding outward with increasing array width.
Figures 3a and 3c show apparent resistivity pseudo sections
for Schlumberger and Wenner cases, respectively. The four-layer
Wenner sounding at x = 0 is reflected in the more complicated
contour pattern. The gray region in each figure represents the
more resistive area as calculated from the resistivity cutoff filter
previously mentioned.
Contoured cross-sections based on the inverted layers of
Figures 2a and 2b are shown in Figures 3b and 3d for the
Schlumberger and Wenner arrays. The Schlumberger inversion
has the effect of concentrating the horizontally oriented contours
near the horizontal interface while the vertically oriented
contours are less obviously affected. The resistivity cutoff shows
a block-like resistive structure with interface at z = 10 units.
The vertical interface is less accurately predicted. The contoured
cross-section based on the inverted Wenner soundings shows an
accentuation of the slight stairstep pattern of Figure 3c. The
many closed contours below x = 0 revealthe effects of the fourlayer inversion.
10units
P. -IOOO.Qm
I
P "IOOO.Q·m
2
(e)
(d)
, 10units
f
P2-200n:m 20units
P "1000.Q·m
I
1
HOunits.j
(e)
P -IOOO.Q·m
2
FIG. 1. 2-D models from which Schlumberger and Wenner array
resistivity soundings were computed. (a) Resistive, vertically
faulted block. (b) Conductive vertical dike extending to the
earth's surface. (c) Conductive tabular prism. (d) Conductive
square prism. (e) Ramp structure. All structures are infinite along
strike.
SCHLUMBERGER
(0) orb
units
-80
0
-~
200
-
201
PI
P2
40
H,,,
,,
,
200
80
199
I--
>.-
680
0
-80
o
-40
1-208
196
r--
PI
20
P2
40
311
355
,,
P "200.n'm
I
,, I
100
z
o
units
0
:::;~IOO
1399
I
I
I
I
I
I
I
I
10
20
20
1011
f475
f-
119
40
~,,
198
,
,,
f--
,I
527
l-
I
7!5
I
I
I
80
571
994
57
:,I
: w200.n·m
100
--- (d) orb. z
80
997
JJ2"1000.n,'U
~
'---
units
0
201
I
I
pfIOOO.n-m
L
40
612
80
t-r- 1-527
0
20
40
6050
~
967
103
20
'--
580
80
1006
1047
997
40
4
~66
I
I
I
I
I
I
I
I
I
I
I
I
60
f--
822
536
799
l-
80
~DIKE
:... t--- BpUNDARIES
p '-100.n·m'
,I
~
-
,
30
I
I
-
~
40
1-194
I
60
I
I
,
,,,
,,
80
60
units
I
681
50
WENNER
(b) orb
X
761
60
70
~
I
I
20
(c) orb.
0
202
U\L
lOll
515
P -IOOO.n·m
2
'--
l-
~
OIKE
100 BOUNDARIES
Pi-Ioo.n·m
120
1003
1111
r.
1098
Z
FIG. 2. I-D inversions of Wenner and Schlumberger array resistivity soundings over buried fault block (Figure la) and a vertical
dike (Figure lb), Layer resistivities in ohm-m. (a) Inversions of Schlumberger array soundings over fault block. (b) Inversions of
Wenner array soundings over fault block. (c) Inversions of Schlumberger array soundings Over vertical dike. (d) Inversions of Wenner
array soundings over vertical dike.
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877
Assessing 2-D Resistivity Structures
NORMAL FAULT
-40
I
-
5I
0
I
40
I
~
VI
VI
c:
c:
;:,
:J
J:i
J:i
.s
2
~
~
:r
~
a..
:r
a..
120
~
w
w
0
0
1\
Contour Intervol = 50 !l.·m
Pc = 461!l.m
-40
WA
o
f
Contour Interval = 50 !l.m
p, =410!l.m
z
c
(d)
40
80
-40
WI
o
+---'----'---'----'----'-----'----'-----i - - X
<-=~~-----
o
200.-J
VI
'".
Conlour Intervol = 50 !l.m
Pc = 416!l.·m
Contour Intervol = 50 !l.' m
Pc = 504!l.m
FIG. 3. Buried fault block. (a) Apparent resistivity pseudosection based on five Schlumberger soundings. (b) Cross-section obtained
by contouring I-D inversions of Schlumberger soundings. (c) Apparent resistivity pseudo section based on five Wenner soundings.
(d) Cross-section obtained from contouring Wenner inversions. The following designations apply to this and to following figures:
SA = Schlumberger apparent resistivity pseudosection, WA = Wenner apparent resistivity pseudosection, SI = Schlumberger crosssection based on I-D inversions, WI = Wenner cross-section based on l-D inversions.
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878
Beard and Morgan
Based on the four cross-sections, the fault block structure is
most accurately predicted by the Schlumberger data, in particular
from the inverted cross-section.
Vertical dike
Figure lb shows a vertical dike extending to the surface and
downward to infinity. The dike has a 100ohm-m resistivity and
is surrounded by a 1000 ohm-m matrix. Schlumberger and
Wenner soundings were centered at x = 0, 20, 40, and 80 units
from the center of the dike. Using symmetry, the soundings at
x = 20, 40, and 80 units were reflected about the dike axis to
provide soundings at x = - 20, - 40, and - 80. Thus, a total
of seven soundings were contoured.
Figures 2c and 2d show the layered inversions of the apparent
resistivity data. The Schlumberger soundings off the dike yield
three-layer inversions with the upper and lower layers having a
resistivity near the true value of 1000 ohm-m and the middle
layer having a lower resistivity caused by the current electrode
of the expanding array getting near the dike. Note that the
thickness and depth of the conductive middle layer increaseswith
increasing distance of the sounding center from the dike. The
greater the distance the array center is from the dike, the farther
the electrodes may expand before the effect of the conductive
dike becomes apparent. Furthermore, the anomaly will appear
broader and less pronounced with increasing distance from the
dike. Upon inversion, the low-resistivity zones on the sounding
curves will appear as a progressively deeper and possibly thicker
conductive layer. Due to expanding potential electrodes, the Wenner data yielded more complicated inversions. At x = 0, the
three-layer inversion yielded a middle layer of 6050 ohrn-m, the
effects of which can be clearly seen in the Wenner contoured
cross-sections. At x = 20, a five-layer inversion results as both
the current and potential electrodes expand Over the dike.
Figures 4a and 4b represent a Schlumberger apparent resistivity pseudosection and a contoured cross-section based on
inverted layer data, respectively. Both contours are very similar
and the resistivity cutoff clearly indicates a dike-like feature.
Little change occurred in the inverted contour because there were
no horizontal resistivity interfaces for the inversion process
to locate.
Figures 4c and 4d show the pseudosection and cross-section
based on the Wenner soundings. Figure 4c, the apparent
resistivity pseudosection, shows no clear indication of a dike.
In the inverted contour, Figure 4d, the dike shows up in an
unusual fashion below a high-resistivity plug which is itself
beneath a low-resistivityzone. Due to the low-resistivity contrast
below z = 50 units, the resistivity cutoff filter failed to predict
a dike-like feature.
Based on the above figures, the Schlumberger array again
appears superior to the Wenner in predicting 2-D geometries.
Tabular prism
Of the 2-D structures we examined, the tabular prism was the
one most nearly representative of a layered earth. As expected,
the I-D inversion approach yielded good results in both
Schlumberger and Wenner cases. The tabular prism model is
shown in Figure 1c. The 500 ohm-m prism is buried 10 units
deep in a 1000 ohm-rn half-space. The prism is 10 units thick
and 80 wide. Figures 5a and 5b show the layered inversions based
on Schlumberger and Wenner data respectively. Symmetry was
used to reflect the x = 30, 60, and 120 soundings about the x
= 0 axis to simulate seven soundings. With both array types,
soundings over and near the prism inverted to three layers with
a low-resistivity middle layer sandwiched between two nearly
1000ohm-m layers. The x = 120sounding inverted to one layer
with a resistivity near 1000 ohm-m.
Figures 6a and 6c show the apparent resistivity pseudosections
for the Schlumberger and Wenner arrays. Figures 6b and 6d are
based on the inverted layers. All four figures indicate a prismlike structure, but the inverted contours clearly locate the upper
interface, and, to a lesser degree, the lower interface. The resistivity cutoff, especially in the inverted Schlumberger contour,
predicts prism geometry very accurately.
Square prism
The square prism model is shown in Figure ld. It is 20 units
wide, 20 thick, and is buried 10 units deep. The prism has a
resistivity of 200 ohm-m and the surrounding half-space is WOO
ohm-m, Figures 5c and 5d show the results of I-D inversion of
Schlumberger and Wenner soundings. Symmetry was used to
simulate five soundings. For both arrays, the x = 20 and x
= 40 soundings are similar. The x = 0 sounding over the prism
center inverts to two layers in the Schlumberger case and to three
layersin the Wenner case. This is due to the Schlumberger array's
stationary potential electrodes not being able to "see through"
the prism. The expanding Wenner electrodes were an advantage
in this case.
Figures 7a and 7c show apparent resistivity pseudosections.
The Wenner array's advantage is evident in comparing the
figures. The Wenner contours and cutoff indicated a buried
equidimensional body while the Schlumberger contours and
cutoff seem to indicate a dike-like structure. A small advantage
was gained by contouring the inverted Schlumberger data
(Figure 7b). A thick plug is evidenced by the resistivity cutoff.
In the Wenner case (Figure 7d), no clear interpretational
advantage was gained by contouring the inverted data.
The square prism was the only model tested in which the
Wenner array showed a decided advantage over the
Schlumberger.
Ramp
Figure le shows the ramp model and the I-D inversions based
on Schlumberger soundings. The ramp angle is 26.6 degrees to
the horizontal. Its horizontal length is 280 units. Its vertical throw
is 140 units. The unit above the ramp has a resistivity of LOO
ohrn-m while the unit below has 1000ohm-m. Taking the point
where the ramp intersects the surface as x = 0, soundings were
centered at x = - 400, - 200, -100, 100, and 200 units from
zero. Because of the poor results of the Wenner array in the case
of the normal fault, only the Schlumberger array was examined.
Figure 5e shows the results of five Schlumberger soundings over
the ramp. All the soundings over the 100 ohm-m layer inverted
to two layers with the upper layer somewhat shallower than the
true interface depth. The soundings off the ramp inverted to
three and four layers. As the left current electrode began to pass
over the ramp, the apparent resistivity initially decreased, but
as the array expanded the resistivity increased again as rnore WOO
ohm-m material was averaged in. Contours based on the apparent resistivity (Figure 8a) and on the inverted layers (Figure
8b) indicate these complications. However, note that in spite of
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879
Assessing 2-D Resistivity Structures
-40
VERTICAL DIKE
SA
0
VERTICAL DIKE
40
SI
a
-40
40
.....
III
80
900
c
III
80
c:
~
~
.ri
...
.c:i
I 120
l-
I
I-
lJ.J
Cl
lJ.J
Cl
...
.s
0
a..
120
a..
160
160
200
200
= 100 n·m
Pc = 215nm
Contour Interval
•
Z
\)
o
~
()
t
= 100 .n·m
Pc =222 n·m
Contour Interval
Z
WA
(Cl
-80
a
WI
(d)
a
-40
40
-80
80
'7~
00
---x
a
-40
0
40
80
--x
00
./
50
qj
10l
50
I
I
I
-
,10
D
100
III
C
~
...
c
.ci
150
III
C
:::J
150
.ri
c
...
~
I
I-
a..
lJ.J
100
~
0
I
Q
I- 200
200
a..
Cl
lJ.J
Cl
250
250
300
,
Z
300
Contour Interval = 100 n·m
Pc =353nm
t
z
=100 .n·m
Pc = 392 n·m
Contour Interval
4. Vertical dike. (a) Apparent resistivity pseudosection based on seven Schlumberger soundings. (b) Cross-section obtained from
contouring I-D inversions of Schlumberger soundings. (c) Apparent resistivity pseudosection based on seven Wenner soundings.
(d) Cross-section obtained from Wenner inversions.
FIG.
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880
Beard and Morgan
SCHLUMBERGER
(a) ~:ib~
30
o
20
990
L-.::z..
711
60
990
WENNER
120
30
SURFACE
996
899
q_J
60
12:
1071
2
1000
40
P,
60
80
100
(c) ~:i~;
20
0
970
-
10
P,
20
30
40
004
[]
734
608
10
860
20
-
1005
1066
40
50
60
~
-400
-300
c-
'--
-200
100
f- p",oon.
RAMP
-100
JQ1. ./'
~/'
200
124
p ·IOOOn-m
1
P,
20
40 SURFACE
998
1000
749
811
1030
961
TABULAR PRISM
P, '1000n m
PI ' 500n m
30
40
SQUARE PRISM
P, 'IOOOn-m
P ' 200n -m
I
100
1004
:ill:
~
-
0
993
0
-
-
97
9
l-.
(d) "a:i~s
SURFACE
87
100
100
-
92
80
TA8ULAR PRISM
P, 'Iooon-m
PI ' 500n m
120
50
60
1042
SQUARE PRISM
p,'IOOOn-m
PI '200nm
200
1000
510
=
859
404
407
1153
300
400
CL
SURFACE
1007
479
P,
40
100
20
120
60
996
995
53r--- 2P
-
1131
~
'-r-
-
h..
-
FIG. 5. I-D inversions of Schlumberger and Wenner array resistivity soundings over tabular
prism (Figure lc), square prism (Figure ld), and ramp (Figure le), Layer resistivities in ohm-m.
(a) Inversions of Schlumberger array soundings over tabular prism. (b) Inversions of Wenner
array soundings over tabular prism. (c) Inversions of Schlumberger array soundings over square
prism. (d) Inversions of Wenner array soundings over square prism. (e) Inversions of
Schlumberger array soundings over ramp.
the unusual contour patterns, the resistivity cutoff shows a
conductive region in the vincinity of the ramp in both cases.
The resistivity cutoff applied to the apparent resistivity data
indicates a conductive zone extending somewhat too deep while
the cutoff applied to the inverted cross-section makes the
conductive zone appear too shallow. Resistivity interpretations
based on layered earth models appear particularly ill-suited for
assessing ramp-like or sloping structures.
CONCWSIONS AND RECOMMENDATIONS
The use of contoured cross-sections based on layered interpretations of inverted apparent resistivitydata proved to be useful
in determining the subsurface structure of simple 2-D structures.
The inversemethod was especiallyeffectivein locating horizontal
resistivity interfaces while leaving information on vertical interfaces relatively unaffected. Contours based on the Schlumberger
array were usually more easily interpretable than those of the
Wenner array. The exception was the square prism where the
expanding potential electrodes of the Wenner array enabled it
to "see through" the structure. While it is true that contours
based on inverted layers are more complicated than those based
on apparent resistivity, the advantage of having horizontal
interfaces more accurately determined, combined with the use
of the resistivitycutoff to predict the geometry of the anomalous
zone, makes this method a valuable one when more sophisticated
interpretational methods are unavailable. Wedo not contend that
contours based on l-D inversions will yield a better subsurface
picture than those based on 2-D or 3-D inversion. The results
of this study indicate that 2-D subsurface geometry can be
approximately delineated using contours based on apparent
resistivity and I-D inversion.
The resistivity contrasts used in this investigation were low
to moderate - 2:1 to 10:1. Investigations of this nature using
more extreme contrasts could indicate this method's reliability
under such conditions. Furthermore, analagous work could be
done in predicting 3-D geometries using I-D inversion or 2-D
inversion.
ACKNOWLEDGMENTS
We would like to thank our colleagues at Texas A&M for their
suggestions and support, in particular Anthony Gangi, Janet
Simms, and David Lesmes. Wethank TedAsche for his assistance
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881
Assessing 2-D Resistivity Structures
TABULAR PRISM
(b)
(0)
120
-40
-120
0
-120
X
-80
SI
-40
0
40
80
120
0r-'--:~~~.ii'-'.i~~~~:;----'----T~ X
40
40
UI
:
c-
c
:>
:>
80
.Q
.0
~
2
~
:I: 120
:I:
~
~
ll.
ll.
W
W
0
0
~
160
0
160
200
200
t
z
Contour Interval = 25 n·m
-
r~iiiiii~01
-
40
-80
-40
o
40
80
120
-120
40
:>
~80
o
80
~
-40
WI
o
40
80
120
>
r-
i
c
-80
Ot=-~-~'----'--~~_-L.._--'--'--~_-L..--'---t-X
(
UI
u;
.0
e
Id)
X
= 25 n·m
Pc = 813 n·m
Z
WA
(e)
b2O
Contour Interval
f
Pc = 857 nm
10 0 0
-
)
~
:I:
:I:
~
~
ll.
~ 120
w 120
160
160
o
o
t
z
Contour Interval = 25 nm
Pc = 879 n·m
t
z
Contour Interval = 25 n·m
Pc = 825n·m
6. Tabular prism. (a) Apparent resistivity pseudosection based on seven Schlumberger soundings. (b) Cross-section obtained
from I-D inversion of Schlumberger soundings. (c) Apparent resistivity pseudo section based on seven Wenner soundings. (d) Crosssection obtained from Wenner inversions.
FIG.
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882
Assessing 2·D Resistivity Structures
SQUARE PRISM
(0)
40
f-----:'----~-~-_t
-20
-
SI
0
with RESIS2D and for his comments. Wealso thank anonymous
reviewers for their careful critiques and comments.
20
X
REFERENCES
40
~
c:
80
:x::
120
Abramowitz, M., and Stegun, I., 1970, Handbook of Mathematical
Functions: Dover Publications.
Dey, A., and Morrison, H. E, 1979, Resistivity modeling for arbitrarily
shaped two-dimensional structures: Geophys. Prosp., 20, 106-136.
Ghosh, D. P., 1971, Inverse filter coefficients for the computation of
apparent resistivity standard curves for a horizontally stratified earth:
Geophys. Prosp., 19, 769-775.
Johanssen, H. K., 1975, An interactivecomputer/graphic-display-terminal
system for interpretation of resistivity soundings: Geophys. Prosp.,
23, 449-458.
- - 1977, A man/computer interpretation system for resistivitysoundings over horizontally stratified earth: Geophys. Prosp., 25, 667-691.
Lowry, T., Allen, M. B., and Shive, P. N., 1989, Singularity removal:
A refinement of resistivity modeling techniques: Geophysics, 54,
766-774.
O'Neill, D. 1., 1975, Improved linear filter coefficients for application
in apparent resistivity computations: Bull., Austral. Soc. Explor.
Geophys., 6, 104-109.
Wiggins, R. A., 1972, The general linear inverse problem: Implication
of surface waves and free oscillationsfor earth structure: Rev. Geophys.
and Space Phys., 10, 251-285.
:l
l-
...r
c,
a,
IJJ
W
a
o
160
200
t
n'm
= 745n·m
Contour lntervo! = 50
Pc
Z
(e)
-20
'"
c:
'-c:
:l
:l
.0
80
~
~
.s
2
:x::
:x::
9~O
ln,
Ill.
IJJ
IJJ
0
20
-;;;
.c
WI
o
a
120
160
120
160
•
Z
Contour tntervcr = 50
n'm
Pc • 847 nm
t
Z
Contour Interval = 50
n· m
p c · 852 n ·m
7. Square prism. (a) Apparent resistivity pseudosection
based on five Schlumberger soundings. (b) Cross-section
obtained from I-D inversion of Schlumberger soundings. (c)
Apparent resistivitypseudosection based on five Wenner soundings. (d) Cross-section obtained from Wenner inversions.
FIG.
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Assessing 2-D Resistivity Structures
RAMP
(0)
-200
200
0
--x
~
1000..!---------------'
Contour Interval = 100 .o..m
t
z
RAMP
(b)
SA
Pc
=
208 n'm
-400
0
883
S1
-200
0
200
-x
200
1000
t
Contour Interval = 100.0.. m
z
Pc= 229.0.· m
FIG. 8. Ramp. (a) Apparent resistivity pseudosection based on five Schlumberger soundings. (b) Cross-section obtained from
Schlumberger inversions.
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