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International Journal of Scientific and Research Publications, Volume 5, Issue 5, May 2015 1 ISSN 2250-3153
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Azimuthal Resistivity Sounding with the Symmetric
Schlumberger and the Alpha Wenner Arrays to study
subsurface electrical anisotropy variation with depth
Van-Dycke Sarpong Asare*, Emmanuel Gyasi*, Bismark Fofie Okyere*
* Department of Physics, Kwame Nkrumah University of Science and Technology, Kumasi
Abstract- Azimuthal apparent-resistivity measurements have been conducted using two very common resistivity electrode
configurations for the purpose of determining the extent to which each of the electrode arrays could elicit anisotropy information from
the subsurface. Apparent resistivity sounding were conducted along four different azimuths about a common center to provide
resistivity variation with azimuth. The apparent resistivities are plotted as function of azimuth in radial coordinates to produce
polygons of anisotropy for each depth of investigation. On the polar diagrams, anisotropy manifests as variation from near circular to
elliptic shapes with ellipses with high eccentricity depicting high anisotropy. With this metaphor, the strike of the anisotropy causative
subsurface feature is represented by the major axis of the ellipse. The coefficient of anisotropy was found within the range of 1.030 to
1.308 and 1.125 to 1.588 respectively for the Wenner and Schlumberger arrays indicating the Schlumberger array was more receptive
to anisotropy conditions. The predominant electrical anisotropy direction is the NW – SE. Anisotropic variation with depth was also
investigated for both electrodes arrays and a linear model was obtained. Statistical analysis at a 0.05 confidence interval was
performed on the gradients to determine whether they were significant. Coefficient of anisotropy variation with depth was found to be
insignificant for both configurations, more especially the Wenner. Thus for both arrays, expanding the electrode spacing did not
significantly reveal any significant change in the anisotropy.
Index Terms- Fractures, orientation, subsurface, anisotropy, Azimuthal Sounding
I. INTRODUCTION
Rotational resistivity sounding surveys are occasionally embarked upon to measure subsurface electrical anisotropy. In the
geophysical lexicon, a rock is said to be electrically anisotropic if the value of a vector measurement of its resistivity varies with
direction (Taylor and Flemming, 1988), (Sheriff, 2013). Subsurface anisotropy contains prints of subsurface fracturing, layering, faults
and joint systems, grain boundary cracking among others. Besides, the presence of lateral heterogeneities can produce significant
pseudo-anisotropy effect. Anisotropy is therefore jointly influenced by these factors. Fractures are important in engineering,
geotechnical, hydrogeological and environmental practice because they provide pathways for fluid flow. Many economically
significant petroleum, geothermal, and water supply reservoirs form in fractured rocks. Fracture systems control the dispersion of
chemical contaminants into and through the subsurface. They also affect the stability of engineered structures and excavations (NAP,
1996). Fracture and fracture networks are mapped by determining their orientation, density, aperture and sometimes the fracture-
filling material under the in-situ temperature and pressure conditions.
Considering the causes of electrical anisotropy such as those outlined above, the concept has very important implications in geo-
electrical resistivity survey, data inversion and interpretation. If the subsurface under investigation is anisotropic and the anisotropy is
ignored, convenient assumptions fail and actual geological depths and geologic structures are wrongly imaged and interpreted. It has
also been shown that the inversion of geoelectrical sounding data from an anisotropic underground structure with an isotropic model
can strongly distort the image of the resistivity distribution of the Earth (Changchun, 2000), (Matias 2002, Mathias and Habberjam,
1986) are few examples of papers which have dealt with the subject of the effects of anisotropy on surface resistivity measurements.
In this present paper effort is made to broadly investigate fracture anisotropy using two of the most common electrode arrays; the
alpha Wenner and the symmetric Schlumberger arrays. Specifically the paper tries to establish the effectiveness of the alpha Wenner
and symmetric Schlumberger resistivity sounding in the determination of electrical resistivity anisotropy. It also aimed at
quantitatively determining the anisotropy coefficient from both spreads and also to compare their results.
Azimuthal resistivity and its measurement
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When conducting electrical resistivity surveys with a collinear set of electrodes as described above, most of the current paths sample
the subsurface below the survey line. We can take advantage of this specific subsurface sampling by varying the azimuth of resistivity
surveys in an effort to measure directional variations of electrical properties. This technique can be sensitive to variations in a
subsurface that has preferentially aligned fractures. Line azimuths that are perpendicular to water-filled fractures for example should
exhibit higher resistivities, affording mapping of the direction of subsurface fracturing. Again, acoording to Boadi et al, the presence
of aligned vertical features and vertical to subvertical thin beds cause anisotropic behavior in rocks and observed changes in apparent
resistivity with azimuth are typically interpreted to indicate fracture anisotropy.
The sensitivity of apparent resistivity to anisotropy parameters for the traditional and special type of arrays have been studied in
(Semenov, 1975, Bolshakov et al., 1997, 1998b). Watson and Barker (2005) showed how, in the same way, lateral changes in
resistivity, which also produce pseudo-anisotropy effects in conventional surveys, can be identified using the offset Wenner technique.
There are other methods of anisotropy parameters determination. Some of these are based on measuring the second derivatives of the
electric potential from a point current source (Mousatov, et. al., 2000). This technology consists in the tensor measurements of the
electric field using specially distributed groups of transmitting and receiving electrodes (tensor array).
Theoretical considerations
The simplest form of anisotropy is the one for which the resistivity is measured respectively along and perpendicular to the bedding
plane. Rocks, predominantly shale, schist, limestones and slates, have definite anisotropic character with respect to these bedding
planes (Telford et al, 1990). Resistivity is assumed to be uniform in the horizontal direction with a value h , and in the vertical
direction has a constant value of v . Recognizing the electrical anisotropy, the equipotential surface due a point current source is an
ellipsoid symmetrical about the z axis;
21
222
2zyx
IV h
1
Where the coefficient of anisotropy
21
h
v
, (Telford et al, 1990). Considering a point a distance
1r from a current source, the
potential at that point will be
12 r
IV h
2
Introducing
21
h
v
into this equation, we have
1
21
2 r
IV hv
3
The latter equation explains that the potential is equivalent to that of an isotropic medium but of equivalent resistivity 21
hv .
In practice, the apparent resistivities are plotted as function of azimuth in radial coordinates to produce polygons of anisotropy for
each depth of investigation.
Two characteristics of this polygon namely its orientation and the anisotropy parameter, are the elements which respectively describe
and quantify the anisotropy. The first is the orientation of the best-fitting ellipse, which is given by the strike azimuth of the major axis
of the ellipse. The second consists of parameters to quantify the anisotropy (Busby, 2000). The length of the major axis of the ellipse
is numerically equivalent to the transverse resistance MAXt while the length of the minor axis is numerically equivalent to the
longitudinal resistivity MINl . The coefficient of anisotropy, λ is the root of the ratio ρt /ρi (Habberjam 1975).
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0o
045o
180o
225o
090o 270
o
135o
315o
MIN
MAX
4
The major axis of the ellipse, which can fit any of such anisotropic polygons, gives the strike direction of the fracture.
II. METHOD
The azimuthal resistivity measurements were conducted with the Terrameter SAS 4000 C by ABEM. Both Schlumberger and Wenner
soundings were conducted along four azimuthal profiles (Fig. 1) to define the variation of apparent resistivity with orientation. The
radial vertical electrical sounding involves surface measurements of VES data along four different azimuths, namely 0o – 180
o, 045
o –
225o, 090
o – 270
o and 135
o – 315
o for both array configurations. These respectively correspond to N-S, NE-SW, E-W and NW-SE
geographical azimuths. For each Schlumberger profile, the current electrode spacing (2L) was expanded from 6.0 m in steps of 4 m till
the whole profile is covered. The distance between the potential electrodes was fixed at 2.0 m. For the Wenner sounding, the inter-
electrode separation, a, was expanded from 2 m in steps of 2 m to cover the whole length of the profile.
Fig. 1 Orientation of Azimuthal profiles
III. RESULTS AND DISCUSSIONS
Presentation of Results
In this study, the data and results are organized and presented in three graphical forms: Log-log Resistivity soundings curves,
Polygons of anisotropy and anisotropy-depth scatter plots.
Apparent Resistivity Sounding Curves
From the field results apparent resistivity values were calculated along each profile and plotted against current electrode spacing a (or
AB/2), on log-log graphs. The sounding curves for the Wenner array in various azimuths are presented on one graph (Fig. 2) and those
for the Schlumberger array are also presented on a separate graph (Fig. 3).
N
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Fig. 2 Wenner Resistivity Soundings in four azimuthal directions
Fig. 3 Schlumberger Resistivity Soundings in four azimuthal directions
Azimuthal polar plots (Polygons of Anisotropy)
The apparent resistivities are plotted as function of azimuth in radial coordinates to produce polygons of anisotropy for each depth of
investigation. A set of such polygons obtained corresponding to different AB/2 or (a) separations is known as a polar diagram or
100
1000
1 10 100
0 – 180 N – S 045 – 225 NE – SW
090 – 270 E – W 135 – 315 SE – NW
100
1000
1 10 100
0 – 180 N – S 045 – 225 NE – SW
090 – 270 E – W 135 – 315 SE – NW
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anisotropy polygon. The square root of the ratio of the lengths of the major and minor axes of the best-fit ellipse is taken as a measure
of anisotropy (Fig. 3), (Mota et al., 2004). The coefficient is determined by using equation (4)
MIN
MAX
Where ρmax is the apparent resistivity measured along the ellipse major axis; ρmin apparent resistivity measured along the ellipse minor
axis.
Fig. 4 A pattern of polygon of anisotropy showing how the anisotropy coefficient and the strike direction are determined
The major axis of the ellipse, which can fit any of such anisotropic polygons, gives the strike direction of the fracture. So in the
example shown in Fig. 4, the strike direction is NW-SE etc.
a = 2 m a = 4 m a = 6 m a = 8 m a = 10 m a = 12 m
a = 14 m a = 16 m a = 18 m a = 20 m a = 22 m a = 24 m
ρMA
X ρMIN
Major Axis
N
Lines of equal resistivity
(Ohm.m) Data point at indicated
azimuth
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a = 26 m a = 28 m a = 30 m a = 32 m a = 34 m a = 36 m
a = 38 m a = 40 m a = 42 m a = 44 m a = 46 m a = 48 m
a = 50 m a = 52 m a = 54 m a = 56 m a = 58 m a = 60 m
a = 62 m a = 64 m a = 66 m
1 – 5 0o – 180
o N – S 2 – 6 045
o – 225
o NE – SW
3 – 7 090o – 270
o E – W 4 – 8 135
o – 315
o SE – NW
Fig. 5 The pattern of Azimuthal apparent resistivity in Ohm-m plotted at different depths with the Wenner Array
L = 3 m L = 5 m L = 7 m L = 9 m L = 11 m L = 13 m
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L = 15 m L = 17 m L = 19 m L = 21 m L = 23 m L = 25 m
L = 27 m L = 29 m L = 31 m L = 33 m L = 35 m L = 37 m
L = 39 m L = 41 m L = 43 m L = 45 m L = 47 m L = 49 m
L = 51 m L = 53 m L = 55 m L = 57 m L = 59 m L = 61 m
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L = 63 m L = 65 m L = 67 m L = 69 m L = 71 m L = 73 m
L = 75 m L = 77 m L = 79 m L = 81 m L = 83 m L = 85 m
L = 87 m L = 89 m L = 91 m L = 93 m L = 95 m L = 97 m
L = 99 m L = 101 m
Fig. 6 The pattern of Azimuthal apparent resistivity in Ohm-m plotted at different depths with the Schlumberger Array
Resistivity as function of azimuths is presented as polygons of anisotropy for each electrode spacing (Figs. 5 and 6). Using equation 2,
the coefficient of anisotropy (λ) is determined. This parameter is diagnostic of an anisotropy medium. In the above results i t varies
from 1.030 to 1.308 when the Wenner array was used for azimuthal sounding and for the Schlumberger array, a minimum coefficient
of 1.125 and a maximum of 1.588 were achieved.
Anisotropy variation with depth
In the previous section, the coefficient of anisotropy is calculated for each depth of investigation for both the Wenner and
Schlumberger array azimuthal measurements. Here, scatter plots of the coefficient of anisotropy versus electrode spacing (depth) are
presented (Fig. 7), Wenner and (Fig. 8), Schlumberger.
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Fig. 7 Wenner Array Scatter plot of Anisotropy versus electrode spacing (depth), with a linear regression model
Fig. 8 Schlumberger Array Scatter plot of Anisotropy versus electrode spacing (depth), with a linear regression model
A simple linear regression is fitted to each scatter plot and regression analysis performed to test the significance of the slope – that the
variation of coefficient of anisotropy with depth is indeed significant. The Wenner azimuthal resistivity sounding yielded a 0.007
anisotropy change per meter of electrode spacing while the Schlumberger sounding also yielded a 0.0013 coefficient of anisotropy
change per meter of electrode spacing.
Using the methods of least squares, a t-test of the slope of the regression lines was performed with an Excel worksheet. Fig. 8 shows
the worksheet for testing the null hypothesis that the slope of the regression line is 0 purporting that the variation in anisotropy with
depth is insignificant.
y = 0.0007x + 1.1133
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
0 20 40 60 80
Co
effi
cien
t o
f A
nis
otr
op
y
Electrode Spacing (a)/m
y = 0.0013x + 1.2713
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
0 20 40 60 80 100 120
Coef
fici
ent
of
An
isotr
op
y
Electrode Spacing (AB/2)/m
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Wenner Array
Schlumberger Array
n 33
n 49
r 0.213046
r 0.364272
Sx 19.33908
Sx 28.57738
Sy 0.064472
Sy 0.100193
b 0.00071
b 0.001277
Sy-x 0.064
Sy-x 0.094296
Sb 0.000585
Sb 0.000476
t 1.214063
t 2.681565
Df 31
Df 47
p-value 0.233892
p-value 0.010078
Alpha 0.05
Alpha 0.05
t-crit 2.039513
t-crit 2.011741
sig no
Sig Yes
confidence Interval
confidence Interval
Lower -0.00048
Lower 0.000319
Upper -0.00048
Upper 0.002235
Fig. 9 A t-test of the slopes of the regression lines for data in Figs. 7 and 8
The inspection of the azimuthal sounding curves in Figs. 2 and 3, gives the first indication of limited anisotropy
of the subsurface layers beneath the sounding point. This is demonstrated by the near congruity and trending of
the sounding curves.
At each electrode space, the coefficients of anisotropy are calculated for the various azimuths. The results are
presented as polygons of anisotropy shown in Figs. 5 and 6. Where these polygons become more elliptic in
shapes, the higher the anisotropy of the subsurface. In such instances, the major axis identifies the strike
direction of the subsurface feature that giving rise to the anisotropy effect.
It can be observed, again in Figs. 5 and 6, that most of the polygons of anisotropy that assumed elliptic
geometry strike in the NW – SE direction. The Schlumberger configuration was more sensitive to anisotropy
than the Wenner configuration.
The Wenner azimuthal resistivity sounding yielded a 0.007 anisotropy change per meter of electrode spacing
while the Schlumberger sounding also yielded a 0.0013 coefficient of anisotropy change per meter of electrode
spacing.
Depth variation in coefficient of anisotropy was studied with both arrays (Figs. 7 and 8). The coefficient of
anisotropy change per meter of electrode spacing of 0.007 and 0.0013 obtained for the Wenner and
Schlumberger arrays respectively were subject to a student t–test at a significance level of 0.05 to ascertain their
significance Fig. 9. For the Wenner array, the null hypothesis is sustained and therefore it can be concluded that
the population slope is zero and insignificant - anisotropy did not exhibit any significant variation with depth.
The hypothesis test performed on the 0.0013 regression slope obtained when the Schlumberger array azimuthal
resistivity sounding was done indicated, on the basis of the 0.05 level of significance that the slope is
significant. However, the reported confidence interval does not suggest we have very strong evidence the
regression relation is significant.
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IV. CONCLUSION
Electrical anisotropy resulting from subsurface features which cause current to have preferential flow direction
is manifested when a configuration of electrodes is rotated about a fixed point. Using two of the most common
conventional collinear electrode arrays, and without any a priori specific site information, this paper has
attempted to establish the effectiveness of alpha Wenner and symmetric Schlumberger resistivity soundings in
the determination of electrical resistivity anisotropy. It also aimed at quantitatively determining the anisotropy
coefficient from both spreads and also to compare their results.
The direction of electrical anisotropy is predominantly in the NW – SE. The Schlumberger array was found to
be more sensitive to electrical anisotropy than the alpha Wenner. The coefficient of anisotropy obtained from
the survey varies from 1.030 to 1.308 when the Wenner array was used and 1.125 to 1.588 for Schlumberger
configuration.
Coefficient of anisotropy variation with depth was found to be insignificant for both configurations, more
especially the Wenner. Thus for both arrays, expanding the electrode spacing did not significantly reveal any
significant change in the anisotropy.
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AUTHORS
First Author – Van-Dycke Sarpong Asare, MSc, Department of Physics, Kwame Nkrumah University of Science and Technology,
Kumasi. [email protected]
Second Author – Emmanuel Gyasi, BSc, Kwame Nkrumah University of Science and Technology, Kumasi
Third Author – Bismark Fofie Okyere, BSc, Kwame Nkrumah University of Science and Technology, Kumasi
Correspondence Author – Van-Dycke Sarpong Asare, MSc, Department of Physics, Kwame Nkrumah University of Science and
Technology, Kumasi. [email protected]/ [email protected] (233-244-895283)