Effects of Lateral Heterogeneity on ID D.C. Resistivity and
Transient Electromagnetic Soundings in Kuwait
by
Nasruddin Abbas Nazerali
S.B. Physics, 2005, M.Eng. Civil and Environmental Engineering, 2007
Massachusetts Institute of Technology
SUBMITTED TO THE DEPARTMENT OF EARTH, ATMOSPHERIC AND PLANETARY
SCIENCES IN PARTIAL FULFILLMENT OF THE REQUIEMENTS FOR THE DEGREE OF
ARCHIVES
MASTER OF SCIENCE IN GEOPHYSICS
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
SEP 28 2015
September, 2015
LIBRARIES
c 2015 MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Signature of Author:
Signature redacted
Department of Earth, Atmospheric and Planetary Sciences
Certified by:
Signature redacted
&I
I/
Z7-)
Signature redactec
Accepted by:
August 28, 2015
Frank Dale Morgan
Professor of Geophysics
Thesis Supervisor
-17 ',
Robert D. van der Hilst
Department Head, Earth, Atmospheric and Planetary Sciences
2
Effects of Lateral Heterogeneity on ID D.C. Resistivity and Transient
Electromagnetic Soundings in Kuwait
By
Nasruddin Abbas Nazerali
Submitted to the Department of Earth, Atmospheric and Planetary Sciences on August
28, 2015 in Partial Fulfillment of the Requirements for the Degree of Master of Science
in Geophysics
ABSTRACT
Aquifer storage and recovery (ASR) of treated wastewater is a viable sustainable water
management option for Kuwait. A geophysical survey to characterize the target aquifer in the
Dammam Formation was conducted to obtain one-dimensional (lD) resistivity using the D.C.
resistivity (DCR) and transient electromagnetic (TEM) methods.
For DCR, we implement a systematic approach to obtain a 1 D vertical profile using
fixed-thickness and variable-thickness layer inversion techniques in succession. The optimal
model has 6 layers above the half-space depth of 101 m, consisting of 3 surface layers down to
15 m depth and 3 intermediate layers, which correspond to the formations of the Kuwait Group
overlying the Dammam Formation. Anomalies in the data which cannot be attributed to noise or
error are not adequately fit by the best set of ID models. The possibility that lateral
heterogeneity explains the variation in the data is explored using approximate 2D resistivity
inversion. A comparison of the 1 D vertical profile obtained from the approximate 2D image
with the ID layered model indicates that, in our case, ID analysis provides a sufficient picture of
the subsurface despite the evidence of possible lateral heterogeneities in the subsurface. Such
heterogeneity is explained by the occurrence of gatch (caliche) in the Fars and Ghar formations
of the Kuwait Group.
The comparison between DCR and TEM indicates that the TEM data is not sensitive to a
relatively resistive layer that is resolved by the ID DCR inversion, or to the resistive
heterogeneities that are indicated in the DCR data with respect to the best fit. We obtain the top
of the Dammam formation - or the aquitard on top of the Dammam - as the model half-space
depth at approximately 100 m below the surface in both data sets.
Thesis Supervisor: Frank Dale Morgan
Title: Professor of Geophysics
3
BIOGRAPHICAL NOTE
Nasruddin Nazerali received an S.B. in Physics in 2005 and an M.Eng. in Civil and
Environmental Engineering in 2007, both from MIT. In between the two, he taught high school
mathematics in Potomac, Maryland. In the Geophysics program in the Department of Earth,
Atmospheric and Planetary Sciences, his research interests were: electromagnetic methods,
inverse methods, GPS, earthquakes, and innovations in instrumentation, field logistics and
interpretation of geophysical exploration.
ACKNOWLEDGEMENTS
The author would like to acknowledge the Kuwait Foundation for the Advancement of
Sciences for funding this research through the Kuwait-MIT Center for Natural Resources and the
Environment (KUMIT-CNRE). We also gratefully acknowledge the support of Massachusetts
Institute of Technology through the Robert R. Shrock, and Theodore R. Madden fellowships. We
thank our colleagues at Kuwait Institute of Scientific Research who helped us to perform the field
experiment described in this work, in particular, Mr. Asim Al-Khalid and Mr. Bandar Rahman.
We wish to thank Dr. Amina Hamzaoui, who served as executive director of KUMIT-CNRE, and
was instrumental in facilitating all aspects of the project. We thank Professors Nafi Toksoz,
Thomas Herring, and Taylor Perron for kindly serving on the thesis committee and providing
invaluable insights and advice on improving the research. Drs. Daniel Burns and Srinivas Ravela
also kindly offered their helpful suggestions to improve the thesis. We acknowledge our direct
collaborators in this research without whose diligent work the project would not be possible: D.A.
Coles, B. Minsley, A. Mukhopadhyay, F. Al-Ruwaih and F.D. Morgan. The thesis supervisor,
Professor Frank Dale Morgan, was instrumental in astutely guiding the project from conception to
completion. We offer our deepest gratitude to him. We offer thanks to all family, friends and
colleagues who offered their support in many ways, and our final call is Praise to God, Lord of the
Worlds.
4
CONTENTS
1. Introdu ction ............................................................................................
. .. 9
2 . M eth o dolog y ...............................................................................................
10
2 .1 S tu dy A rea ......................................................................................
10
2 .2 L ithology ...................................................................................
2.2.1 Umm er Radhuma Aquifer .......................................................
. 11
11
2.2.2 Dammam Aquifer .................................................................
12
2.2.3 Kuwait Group Aquifer and Surface Sediments .................................
13
2 .3 D C R .........................................................................................
2 .4 TE M ..............................................................................................
3 . D ata Analysis.........................................................................................
. .. 13
14
. .. 15
3.1 D C R ID A nalysis ..............................................................................
15
3.2 TEM ID A nalysis ..........................................................................
17
3.3 DCR Approximate 2D Analysis .............................................................
18
3.3.1 Alternative 2D Parameterization and Inverse Models .......................... 22
3.4 Comparison of 1 D Vertical Profiles from 1 D and Approximate 2D Inversion ........ 25
4 . D iscu ssion .............................................................................................
5 . C on clu sion ................................................................................................
. 26
29
5
6. Appendix A. Determining the Optimal Number of Layers in 1 D DCR Inversion
.........
44
7. Appendix B. Exploring the Limits of ID DCR Models in Fitting Vertical Electrical Sounding
D ata ............................................................................................................
55
8. Appendix C. Alternative ID and Approximate 2D DCR Inverse Models ....................
57
9. Appendix D. Raw Data of DCR and TEM Experiments ............................................
97
10 . R eferen ces...............................................................................................1
12
6
LIST OF FIGURES
Figure 1. Map of Kuwait with contours of the top elevation of the Dammam Formation
in meters above mean sea level. The experiment site in Kabd is marked in red.
Figure 2. Experiment set-up showing relative placements and dimensions of the DCR
and TEM arrays.
Figure 3. Left panel: DCR data and best fit model. Right panel: residuals.
Figure 4. Best one dimensional resistivity model with depth from DCR data inversion.
Figure 5. TEM data as normalized induced voltage vs. time, and a homogeneous model
fit to the data.
Figure 6. Left panel: TEM data and best fit model. Right panel: residuals.
Figure 7. Best one dimensional resistivity model with depth from TEM data inversion.
Figure 8. The model grid and starting model for approximate 2D inversion. Note the
symmetry from the central point of the array.
Figure 9. The best resistivity model with lateral structure only in layer 3 - using
approximate 2D DCR inversion.
Figure 10. A zoomed-in contour plot, with 7 contour levels, of the approximate 2D
inverse model shown in figure 9.
Figure 11. Left panel: DCR data and best fit model with approximate 2D inversion.
Right panel: residuals.
7
Figure 12. A comparison of the ID vertical profiles obtained by 1D inversion and
approximate 2D inversion.
Figure 13. A comparison of the lithological and stratigraphic interpretation obtained
from the literature with the 1 D DCR and TEM resistivity layered models.
8
1. INTRODUCTION
Aquifer storage and recovery (ASR) of treated wastewater in Kuwait is a viable means of
water resource management and sustainable development to meet projected water demands.
Kuwait has the largest domestic water consumption in the world, 500 liters/cap/day in 2011
(Gulf News, 2011), which is supplied by desalinated seawater (90%) and brackish groundwater
(10%), (Fadlemawla and Al-Otaibi, 2005). Al-Otaibi and Mukhopadhyay, (2005), and
Fadlemawla and Al-Otaibi, (2005), indicate that only 30% of treated wastewater is being reused,
and contributes to 25% of the irrigated agriculture needs, the remaining supply being from the
over-exploited brackish groundwater aquifers. Therefore, if the treated wastewater could be
stored rather than disposed of in the Gulf Sea, it could serve the double purpose of restoring
over-exploited aquifers and encouraging more efficient use of the existing water supply, for
example, by increasing its use in irrigated agriculture.
The Kabd well-field has been chosen for a pilot ASR study due to its proximity to one of
the larger capacity treatment facilities, and the hydrogeology that is known of the area due to the
test wells and boreholes needs to be supplemented by more extensive coverage using surface
geophysical methods. Such methods are a cost-effective means to characterize the target aquifer,
and for subsequent monitoring of injection, storage and recovery phases (e.g., Minsley et al.
2010). In Kuwait, the relatively deeper carbonate aquifer (Dammam Formation) is preferred to
the overlying clastic aquifer in the Kuwait Group due to the compatibility in geochemistry
between the native water and injected waters (Mukhopadhyay et al., 1998), specifically due to
better efficiency due to less clogging from dissolution and re-precipitation of minerals.
Mukhopadhyay and Al-Otaibi, (2002), and Minsley et al. (2010) have shown synthetic
hydrogeophysical models that indicate electrical resistivity as a sensitive parameter for surface
9
geophysical measurements due to the contrast in bulk resistivity caused by the low salinity (high
resistivity) of the injected compared to the native waters. Previous work in electrical resistivity
soundings has focused on the shallow groundwater in Northern Kuwait (Al-Ruwaih and Ali,
1986).
As part of a feasibility study to determine the most effective electrical-resistivity method
to survey the 100 sq.km. well-field, we used D.C. resistivity (DCR) and time-domain (transient)
electromagnetic (TEM) sounding methods at one site in Kabd. The goal of both experiments
was to obtain the 1 D layered resistivity structure and specifically to obtain the resistivity, depth,
and thickness of the Dammam formation. The depth to the top of the Dammam formation in the
Kabd area is expected to be at 130 to 180 m below the surface, and with a thickness between140
to 160 m.
The following section describes the analysis of the DCR and TEM data. The DCR
analysis points to complexity in the data that is not adequately explained by the best fit 1 D
models. The hypothesis that the ID data is corrupted by 'geological noise' (Frischknecht, et al.,
in Nabighian, ed., 1987) or 'model structural error' (Kennedy and O'Hagan, 2001) due to actual
heterogeneous resistivity structure beneath the array of electrodes is further explored in an
approximate 2D inversion.
2. METHODOLOGY
2.1 Study Area
The Kabd area is part of a region with many water wells. The exact location of the field
tests was N29 6.09'E47'40.471' (3222.2 km N, 760.3 km E UTM zone 38N, shown in figure 1).
This coordinate served as the mid-point in the DCR electrode array, which was along a North-
10
South strike. The same line was also the eastern edge in the TEM sounding square loop
transmitter. Figure 2 shows the lay out and relative dimensions of the two experiments.
The goal of both the DCR and TEM methods is to obtain the one dimensional (lD)
layered resistivity structure of the subsurface with depth. The assumption that the structure
within the length scale of the survey is one dimensional may be justified by the known geology,
but must be verified by the experiments. Such vertical electrical soundings could be repeated
throughout the well field in order to yield an approximate understanding of the 3D structure of
the aquifer system.
2.2 Lithology
The hydrogeology of Kuwait has been reviewed in several papers, and the stratigraphy
and regional structure of the aquifer systems are well known from the coring done at water and
oil well fields. The following is a brief summary following Alsharhan, et al., (2001). The
Dammam aquifer is discussed in more detail, including hydrochemical tests of the compatibility
of the aquifer with injected waters, by Mukhopadhyay, et al., (1998).
2.2.1 Umm er Radhuma Aquifer
The Cenozoic (Paleocene, early Eocene Age) Umm er Radhuma formation overlies the
Mesozoic Aruma. This aquifer is more important in Eastern Saudi Arabia, but more saline in
Kuwait, increasing from 4000 mg/l in the southwest to 35,000 mg/l in the northeast. It is
composed mostly of anyhdritic, dolomitic and marly limestone, increasing in thickness from
north to south from ~420m to 600m. It is overlain by the Rus aquiclude which separates it from
the Dammam formation.
11
2.2.2 Dammam Aquifer
The Radhuma (Umm er Radhuma), Rus, and Dammam formations together compose the
Hasa Group. This middle to early Eocene formation was deposited in marine and continental
environments and ranges in thickness from 180m to 210m. It is composed of soft, chalky, shelly
and porous limestone and hard crystalline dolomitic limestone, with chert bands occurring
mostly near the top. The formation is recharged in outcrops in southern Iraq and northeastern
Saudi Arabia. The salinity increases from southeast to northwest from 2500 to 150,000 mg/l,
with Na>Ca>Mg for anions and S0 4>Cl>HCO 3 for cations. The piezometric surface map also
shows the general water movement in this direction. The hydraulic gradient is generally upward
into the overlying Kuwait Group, with the reverse applying in certain areas. It is semi2
confined/confined with average transmissivity 580 m 2/d and effective permeability 2.8E-12 m
increasing to the north. Karstification has caused vuggy and moldic porosity, with an average
value from laboratory core samples of 18%, with a range of 4 to 27% (Al-Sulaimi and AlRuwaih, 2004; and Mukhopadhyay, et al. 1998). The structure of the Dammam formation also
controls the geomorphology of Kuwait to a large extent as the overlying Kuwait Group and
surface sediments lie conformably on top of it (Al-Sulaimi and El-Rabaa, 1994.)
The depth of the Dammam formation at the experiment site can be expected to be
between 130 to 180 m based on the wells and boreholes near to the site (figure 1), and its
thickness is expected to be between 140 and 160 m. A resistivity well log from well SH-OW-7
which is about 2.6 km away from our site is used as a reference for the lithology in the area.
12
2.2.3 Kuwait Group Aquifer and Surface Sediments
The Kuwait Group is composed from bottom to top of the Miocene Ghar and Lower Fars
formations and the Pleistocene Dibdibba formation. The Lower Fars formation is composed of
calcareous sandstone and limestone with some shale, and acts as an aquitard between the upper
and lower Kuwait Group, the Dibdibba and the Ghar. The Ghar formation is composed of
sandstone and conglomerates with some shale in the lower part, which along with the chert on
top of Dammam forms an aquitard. The formation has generally brackish water. The Dibdibba
formation consists of gravels, gravel and sand, conglomeratic sandstones, siltstone and shale.
This formation is permeable and hosts fresh water in shallow parts below wadis and depressions.
The overlying sediment is composed of windblown sand, wadi alluvium, playa silts and clays,
beach sands and limestones. The Ghar and Lower Fars formations are the host material for the
formation of gatch (caliche).
2.3 DCR
A Schlumberger array (see, e.g. Telford, et al., 1990) was used to collect apparent
resistivity data up to a maximum current electrode spacing of 498 m, determined by the available
field work time. The Schlumberger array is a 1 D array, with a linear and center-symmetric
spread of four electrodes. The outer electrodes (for current injection) are equally spaced on a
logarithmic scale reflecting the decrease of resolution with increasing separation, and
corresponding increase in the depth sensitivity. The inner electrodes (voltage measurement) are
maintained in place for a number of measurements such that we obtain 23 data points with only 6
blocks of move-out in order to maintain a good voltage signal-to-noise ratio. Such an array
provides an approximate depth of investigation of 125m to 200m based on the portion of current
injected that penetrates beyond a given depth (Telford, ct al., 1990). The actual maximum depth
13
sensitivity and resolution of the field data depends on the resistivity structure and is seen from
the optimal inverse resistivity models that fit the data. The measurements were conducted with
the Zonge GDP multi-purpose receiver system and the transmitter signal was generated with a
car-battery powered 400 W ZeroTEM transmitter of the same company (Zonge, 2015).
DCR inversion is carried out with three different algorithms, (i) fixed layer thickness, (ii)
variable layer thickness programs, and (iii) a two-dimensional finite difference program
developed to compare one dimensional and approximately two dimensional parameterization of
the subsurface resistivity.
2.4 TEM
The TEM soundings were conducted with a central or in-loop configuration, consisting of
a 190 by 190 m 2 square loop of one turn, and an induced voltage receiver antenna in the center
(the Zonge TEM/3 antenna, which has a moment of 10 4 M 2 . The transmitter moment (current
magnitude multiplied by transmitter loop area) and the number of cycles of data stacking
determine the time range of the data above the noise floor which in turn affects the maximum
depth of investigation. The transmitter waveform consists of a sum of square waves such that
there is an on+/off/on-/off sequence. The antenna measures the induced voltage decay due to the
changing magnetic field caused by induction in the subsurface during the off-time of the primary
current signal. The earliest time that the signal at the receiver can be sampled gets larger as the
transmitter loop size increases, because it takes a longer time for the primary signal to turn off.
Therefore, by choosing a large transmitter moment, we sacrifice the ability to resolve shallow
structure using fast and early sampling of the induced voltage (Spies, 1989; and Fitterman and
Stewart, 1986). Smaller loop sizes were also tried in the field. The 190m loop data proved to be
the only one with a sufficient range of data above the noise floor of ~10- 8 V/M 2. In our case the
14
data ranges from 44.14 pts to 7.731 ins, which, using the concept of diffusion depth (e.g., Ward
and Hohmann, in Nabighian, ed., 1987), indicates an approximate minimum depth of
investigation of 22 m (no shallower than 22 m) and a maximum of ~290 m, assuming an average
resistivity structure of ~7 im. Note that depth of investigation calculations are only
approximate due to the use of diffusion depth,
conductivity in Siemens/meter, to
6
TD
4
6
TD
= '(2t/ajio), [t, time in seconds,
G7,
x 10-7 N/A 2 is the vacuum permeability]. Diffusion depth
is appropriate for an impulse source rather than for an alternating on-off current source, and
also due to the assumption of a homogenous average resistivity.
For TEM inversion, we use a program, eml dinv, developed by Auken and Christiansen,
(2007). The program solves for the resistivity and thickness of a specified number of layers of
the subsurface with a damped non-linear least squares algorithm.
3. DATA ANALYSIS
3.1 DCR 1D Analysis
DCR ID analysis is carried out in a sequential use of two different inversion methods:
(a) a fixed-layer-thickness model in which a number of layers and their thickness distribution is
set and fixed at the beginning and the resistivity values are solved for and (b) a variable-layerthickness model in which the same parameters are set at the beginning, but the thickness of the
layers is allowed to vary and is solved for along with the resistivities. The first step (a) is carried
out with a search over inversion starting parameters (number of layers, maximum depth, and
initial homogeneous resistivity) to obtain a range of models to characterize the error space. We
draw the following conclusions: (1) The optimal (fewest) number of layers that fit the data is 6
above a basement half-space; (2) No one dimensional model can account for the curvature
observed in the data, which has a higher spatial frequency than can be explained solely by one15
dimensional resistivity contrasts. Specifically, the best fitting apparent resistivity curve does not
fit the curvature of the data for electrode spacings greater than L = 50 m. The best model with 6
distinct layers above the half-space is used as a starting model for further analysis. Figures 3 and
4 show the observed apparent resistivity data, best data-fit, and the corresponding ID DCR
model. A-priori model constraints were not applied; however, we favor, in general, the models
with the least number of parameters which fit our data adequately as described below and in the
approximate 2D analysis described in the section on DCR approximate 2D analysis.
The approach of using a fixed layer thickness code in a systematic search of inverse
models followed by a variable layer thickness code suggests an extension and simplification of
the work of Simms and Morgan (1992), who showed that the 'variable parameter scheme'
obtains the most accurate inverse results in synthetic tests and suggests using the F-Test to obtain
the minimum number of layers. Gupta et al., (1997), describe a "straightforward inversion"
which closely corresponds with our fixed thickness layer inversion, and also address the task of
determining sharp layer boundaries from the smooth inverse models (Israil, et al., 2004).
However, we propose a simpler sequential application of two distinct algorithms to obtain an
optimal ID model. Further work is being done with synthetic models in the manner of Simms
and Morgan, (1992), to formalize and benchmark an automated algorithm instead of a sequential
approach. We also suggest that this simple sequential approach is better in practice and in
computation time to Bayesian approaches which incorporate a penalty with increasing number of
layers in order to solve the inverse problem with the most 'parsimonious' dimensionality (e.g,
Malinverno, 2002).
16
3.2 TEM ID Analysis
TEM data is dependent to a large extent on the half-space resistivity, especially the late
time asymptote (Ward and Hohmann in Nabighian, ed., 1987). This motivated us to pre-process
our TEM data to accentuate the variation by plotting the residual variation relative to a
homogeneous model. The observed TEM data and homogeneous best fit are shown in figure 5,
plotted with induced voltage on the horizontal axis and time increasing downwards on the
vertical axis. We then plot the log of the ratio of the raw data to the fitted model, as shown in
figure 6 in red circle markers. This transformation has an advantage over conventional
calculations of apparent resistivity from induced voltage data (Raiche, 1983; Spies and Eggers,
1986) because it clearly highlights the variation in the data. The data as displayed shows three
segments, or two turning points, possibly enumerating the number of layers that depart from the
homogenous model.
The TEM data is inverted for layer resistivities and thicknesses, and the data is indeed
only able to resolve two distinct layers above the model half-space. The data and best fit are
displayed in figure 6, and the ID vertical profile is shown in figure 7. The TEM model, figure 7,
is seen to correspond on average to the DCR model, figure 4, with (1) a resistive top layer that
averages out the 3 top layers of the DCR model, (2) a conductive middle layer without the 2
additional intermediate resistivity layers in the DCR model and (3) a basement layer which is
more conductive than the basement of the DCR model.
We note that unlike the DCR data, the TEM data and fit do not show any evidence of a
systematic misfit. The misfit between the DCR best fit model and data is postulated in the next
section to arise from lateral heterogeneity that is not accounted for in a ID layered model. The
fact that the transmitter and receiver dipoles move along the surface in the DCR survey and that
17
the transmitter loop and receiver antenna are stationary in the TEM survey accounts for the
relative insensitivity of the latter to heterogeneity. Moreover, as the geometry of the experiment
set-up shows in figure 2, there is an offset of 95 meters between the central axis of the DCR and
TEM arrays, and the lateral subsurface volumes that are investigated do not exactly coincide. As
shown in the next section, the anomaly encountered in the DCR data is relatively resistive
whereas the TEM method is known to be more sensitive to conductive anomalies (Fitterman and
Stewart, 1986). This may be an additional factor explaining why the resistive intermediate layer
in the ID DCR or the resistive anomaly in the approximate 2D DCR model are not encountered
in the TEM model.
3.3 DCR Approximate 2D Analysis
The results of DCR 1 D analysis point to the possibility that 1 D model parameterization is
not enough to adequately fit the data. (Refer to appendices A and B for more detail.) In order to
obtain greater depth sensitivity the Schlumberger array and other 1 D DCR acquisition techniques
symmetrically spread the transmitter and receiver dipoles. Therefore, the measurements are also
sensitive to laterally varying volumes in the subsurface and not only to layers as postulated in 1 D
analysis. As the ID experiment is not designed to resolve such lateral variations, any such
heterogeneity in the subsurface is understood in the literature as model structural error (Kennedy
and O'Hagan, 2001) or geologic noise (Frischknecht, et al., in Nabighian, ed., 1987). In
analyzing Schlumberger array data in an approximate 2D inversion, we note again that the data is
severely limited in terms of the design, namely that there is no lateral profiling, and the quantity
of data compared to the number of 2D resistivity grids that are being modeled. Therefore, it is
justified to treat the approximate 2D analysis as a 'noise' analysis in the 1 D data, and to use the
18
best fitting 1 D model as a starting model on top of which lateral variation is parsimoniously
added.
In order to analyze the data in an approximate-2D scheme, we first make an appropriate
2D finite difference grid and solve the Poisson equation using the method outlined in Dey and
Morrison, (1979). In the x-direction (horizontally) we accommodate every position (23 data
points) of the 4 electrode spread and include an extra grid point in between the electrode
positions, along with five boundary blocks outside the imaging domain (with width 6, 15, 100,
500, and 500 meters each). In the z-direction (vertically) we use the optimal 6 layer model
obtained in the 1 D analysis with a seventh layer serving as a half-space as well as three boundary
blocks (the layer at the half-space depth has 200 m thickness and the boundary blocks have
thickness 300, 500, and 500 meters each).
The model grid and starting model are illustrated in figure 8. The best ID model is the
starting model for the inversion. The horizontal cells that are added follow 2 simple criteria: (i)
we only allow variation in layers 1 to 5 as the sensitivity to variation in cells at depth is seen to
be very small, and (ii) we don't include the whole horizontal spread, but only from the left half
of the model from the edge at L = 270 up to 30 m from the center, and the mirror image on the
right half of the model because of the radial symmetry of the array. These criteria are devised on
the observation that the systematic misfit (see figure 3) only occurs from approximately L = 60
to 249 m, and that the symmetry of the array does not allow a distinction between the left or right
of center. The inversion proceeds to solve for layer resistivities for the layers that do not have
lateral cells, and the lateral cell resistivities for the approximate-2D portions. The LevenbergMarquardt algorithm is used for the inversion with log-rescaling and parameter bounds
implemented following Kim and Kim, (2011). As the inverse problem as formalized here is
19
highly underdetermined and ill-conditioned, this approach helps to improve the inversion
stability. The effectiveness of using ID models as starting models for 2D inversion to improve
the stability of the inverse problem, has been shown in the context of 2D data sets (e.g., Olayinka
and Yaramanci, 2000).
To explore the likely depth of the lateral variation, we performed multiple inversions with
lateral variation in the 5 top layers individually and in combination for a total of 30 different
cases. Operating on the principle that the lowest data misfit for the least number of layers is the
best answer, we pick the model with only layer 3 as the target location for the heterogeneous
structure. This model ranks 4 th out of the 30 cases. The first 4 ranked models are all within 1%
root-mean-square-error, and have (1) layer 3 and 4, (2) layer 3, 4 and 5, (3) layer 3 and 5, and (4)
layer 3 only. Refer to Appendix C for the other models with more parameter complexity. We
show the results of our chosen best model in figures 9 to 11: figure 9 a 'pseudocolor' plot; figure
10, a smoothed contour plot, displaying model features in a more geologically realistic way; and
figure 11, the apparent resistivity data and fit. Note that the model is radially symmetric about a
vertical axis at the center of the array, and the model plot in figure 10 shows only one side of the
electrode lay-out.
Previous work has investigated the efficacy of ID data acquisition and interpretation in
subsurface models that have 2D variation. Beard and Morgan, (1991), performed synthetic
studies on how ID Schlumberger and Wenner resistivity soundings resolve 2D structures such as
fault blocks, dikes, buried prisms, and ramps. If such simple anomalies are known to be either
conductive or resistive, they showed that a series of ID inverse models can be combined to
approximate the shape and location of the 2D anomalies. They note that the more smoothly
varying the 2D structure is, the better is the reconstruction, and that the Schlumberger array is
20
superior to the Wenner array in this regard. Duch and Sorensen, (1994), extend the work, with a
field study using Wenner array profiling/sounding and assess the similarity of inversions of
adjacent soundings using 2 or 3 layers with the inversions of the profiling data.
Most other work on DCR surveys involving a series of ID data sets has revolved around
treating a set of adjacent ID data sets or VES (vertical electrical sounding) from a 2D
perspective, instead of simply concatenating a series of 1 D vertical profiles to characterize the
study area (e.g., Uchida, 1991; El-Qady, et al. 1999; Gyulai and Omos, 1999; Gyulai, et al.,
2010). Alternatively, some researchers have taken profiling data and applied ID inversions with
lateral constraints to favor smoothly varying 2D sections. This type of ID or 2D 'laterally
constrained inversion' (LCI) aims to combine the lateral resolution of combined 1 D data sets
with the sharp layer boundary resolution of ID inversions (E.g., Auken and Christiansen, 2004;
Auken et al 2005; Wisen, et al., 2005; Santos, 2004, Miorelli, 2011; Schamper, et al., 2012).
In our case, we need to assess the validity of 1 D interpretation of a single sounding. As
the foregoing analysis and discussion has shown, data pre-processing and systematic exploration
of ID models rules out the possibility that the anomalous features in the data are either noise or
erroneous outliers, or that they can be adequately explained by ID layered models alone. We are
presently developing a diagnostic data analysis tool to make such assessments in near real-time.
In this study, we present a sequential analysis of 1 D and approximate-2D inversion models in
order to determine whether lateral heterogeneity is affecting VES data. Based on a parsimonious
parametrization, we are able to provide a reasonable geological interpretation of this type of
geologic noise.
21
3.3.1 Alternative 2D Parameterization and Inverse Models
In the absence of external constraints, we have chosen one 'best' approximate 2D model
for the foregoing and subsequent analysis based on the criterion that a model with less
parameters which fits the data adequately is better than a model with more parameters.
Moreover, we perform the approximate 2D inversion by using the 'best' ID inverse model as a
starting model and baseline for comparison with the 2D models. Given that we have a ID VES
data set, this approach is more feasible than parameterizing the 2D domain in the conventional
manner with a 2D grid in the whole domain and adding a model-norm penalty to the objective
function or applying various smoothness constraints in the inversion. Both of the above choices
of best ID baseline model and the best approximate 2D model lead to a consideration of how
disparate the alternative parameterizations and resultant inverse models are, and therefore how
robust is the approximate 2D interpretation of our DCR data. These questions are further
examined in appendices A and C.
Firstly, we can see that the ID inverse model which minimizes the Li norm of the misfit
instead of the L2 norm has slightly different layer depths/thicknesses and resistivities especially
for the middle three layers and the half-space (figure A6, Appendix A). However, in comparing,
e.g., figure 10 to the corresponding figure for the LI case, figure C16, of Appendix C, we can
conclude that the conductive and resistive anomalies are present in both cases in the same pattern
and with the same geometries. The Li model fits the data points for L between 50 and 100m and
also for L greater than 150m by sacrificing the two data points for L between 100 and 150m as
outliers, which are both relatively resistive, whereas the L2 model fits all the data points equally
well by leaving residuals with a pattern of conductive-resistive-conductive relative to the data
points between L = 50 and 200m (compare figures A4 and A5). Conceivably the pattern of
22
anomalies would be different between the approximate 2D models based on the L2 and LI
baseline models, but this is not observed to be so in comparing the sets of figures 9 to 12, C2 to
C13 for L2 on the one hand, and C15 to C30 for LI cases on the other.
We can observe from best set of approximate 2D models in Appendix C that all four best
models have lateral cells in layer 3, and the lowest rmse models have layers 3 and 4 in the L2
case or layers 3 and 5 in the LI case. In all cases the inversion proceeded to a large maximum
iteration number and took conservative steps in decreasing the damping factor in the LevenbergMarquardt algorithm. It was attempted in this manner to make the comparisons independent of
the inversion behavior and stopping criteria. As expected, the cases with deeper layers, layers 4
and 5, in addition to layer 3 (figures 9 to 12), have the heterogeneous structures extend deeper
and also wider (e.g., compare figure 10 and figure C11), with the model which has all layers 3 to
5, figure C7 for L2 case, and figure C20 for the LI case, showing the resistive anomaly
extending under the conductive anomaly between 50m to l00m laterally. These geometries and
depths of the resistive anomaly conform to the hypothesis of the occurrence gatch in the Kuwait
Group formations. In the comparison of the vertical profiles obtained from the approximate 2D
inversions with the best ID model, we observe a greater or lesser effect based on the inclusion of
more layers of lateral heterogeneity as can be expected. In some of the cases, such as shown in
figure C12 as compared to figure 12, the pattern of relative resistive and conductive layer
transitions can be reversed, even though the magnitude differences in resistivity are negligible. It
should be noted that the parameterization of the approximate 2D inversions with a full 2D grid
independent of the best 1 D models (even if we do use the 1 D models as starting resistivities for
the 2D inversion) would be better suited to examine the effect of lateral heterogeneity on the
vertical profiles, as layer depths would not be effectively fixed as we have done in our analysis.
23
Finally, we can compare a third set of different parameterization for the 1 D and
approximate 2D inversion to our results presented in this section. Figures C31 through C38
illustrate a set of inversions which are all done with the 2D modeling and inversion code, and
therefore forego the investigation into the optimal-fewest number of layers using the fixedthickness and variable-thickness ID codes (Appendix A). With the knowledge that resolution is
diminished with increasing depth, layers of thickness logarithmically increasing with depth are
assigned and a 1 D inverse model is obtained (figures C3 1, C32) by inverting for the resistivities
of these layers. This ID model is used as a starting model for an approximate 2D inversion in a
similar way to the foregoing discussion, with the difference that in this instance, we have not
imposed the symmetry of the image from the center of the array. The best approximate 2D
model which has heterogeneity in layers 3 to 8 of the 15 layers is shown with the associated
contour-map, data and fit, comparison of vertical profiles, in figures C33 to C36. And finally a
comparison with the other available models (TEM and well-log) and the corresponding
lithological interpretation are presented in figures C37 and C38. We can compare figure C34
with the closest corresponding figure with the alternative parameterization, figure C7, which has
layers 3, 4 and 5 for the L2 baseline model. What is immediately apparent is that the anomalies
in the log-fixed-thickness case of figure C34, the heterogeneities are more extensive in width and
shallower in depth. The resistive patch at 5 meters depth in is almost extensive as a thin layer,
but has lens shaped pieces between 50 m to 200 m offset. The associated conductive anomalies
lie on top of the resistive anomalies, conforming to the expectation that these could be lenses of
perched water on top of the gatch layers/patches. In comparing figure 13 and figure C37, we
note that the resistivity magnitude of the log-fixed-thickness inverse model is higher on the
average than the models obtained with 1 D DCR codes (whether variable thickness as in figure 13
24
or the fixed thickness models shown in Appendix A) and is therefore closer to the magnitude of
the well-log. This can be explained by the observation that in ID DCR modeling the product of
resistivity and thickness of a given layer is uniquely resolved but not either parameter separately.
Therefore the thinner layers at intermediate depths of 10 m to 100m, in the fixed-thickness case
all have higher resistivities. We also observe in figure C37 that the half-space depth assigned for
the 15 layers coincides with the depth of a notable jump in resistivity shown in the well-log at
-150 m. The fact that both the ID inverse model and the well-log are showing a relatively
resistive layer would lead us to postulate this depth as a possible transition to the Dammam
aquifer or the aquitard overlying it. Nonetheless, the matching depths are also a factor of
coincidence in the log-increasing thickness parameterization of the 15 layers and has not been
artificially imposed, nor should too much weight be given in the interpretation of these matching
depths.
3.4 Comparison of 1D Vertical Profiles from 1D and Approximate 2D Inversion
Comparing the 1 D vertical profile obtained in a 1 D inversion, which does not account for
heterogeneity, to the vertical profile obtained in an approximate 2D inversion (the area weighted
average of resistivity of the lateral blocks), which accounts for heterogeneity, helps to determine
whether 1 D acquisition of data in the context of the near surface of Kuwait in the Kabd region
will be sufficient to characterize the basic hydrogeological lithology. By area weighted average
we mean than in our best approximate 2D inverse model, the lateral cells of layer 3 are averaged
by summing the product of the area (AxAz) of each cell and the resistivity, and dividing by the
sum of the areas of all the cells. This average value is used as an alternative to the value of
resistivity at zero offset, or the middle of the array as the layer resistivity for comparison. Either
one of these two ways was found to be suitable for the comparison. The comparison illustrated
25
in figure 12 shows that there is minimal difference between the two 1 D vertical profiles, and that
we can cautiously conclude that the 1 D data acquisition and interpretation is generally accurate
despite the evidence of heterogeneity. Note also that our comparison does not account for
variation of the layered structure in terms of the depths of the layer transitions because we used
our best ID model as a starting model for the approximate 2D inversions.
4. DISCUSSION
The litho-stratigraphy that is deduced from the literature (e.g., Alsharhan, et al., 2001)
matches, in large part, with the resistivity layers obtained from the 1D DCR inversion. In figure
13, we show our interpretation of the matching stratigraphy obtained from core samples and
well-logging (e.g., Al-Ruwaih and Ben-Essa 2004; Al-Ruwaih and Qabazard, 2005; and
Mukhopadhyay, et al., 1998) alongside the vertical profiles obtained from the resistivity (DCR
and TEM) sounding models. The top 3 layers show decreasing resistivity from the surface,
possibly indicating increasing moisture content with depth; we have interpreted these to be the
surface sediments. The following 3 layers indicate alternating relative low and high resistivities,
corresponding with the expectation of the succession of Kuwait Group aquifers separated by an
aquitard. The last half-space layer is semi-infinite and therefore does not resolve separate units
of the Dammam aquifer or the aquitard overlying it. Its depth indicates where we would expect
the top of the formation at this location. In the same figure, we also show the formation
resistivity ranges for the Dammam aquifer and the Kuwait Group aquifer. These range estimates
are obtained from laboratory investigations on core samples from the Kuwait Group
(Mukhopadhyay, et al., 2004), the Dammam Formation (Mukhopadhyay, et al. 1998), and from
the groundwater conductivities from these aquifers (Al-Ruwaih, 2001).
26
The approximate 2D analysis of our DCR data indicates the possible presence of lateral
heterogeneities which are relatively resistive within the length of the experiment, with adjacent
conductive lenses.
The resistive heterogeneities are likely due to the occurrence of gatch. Gatch
is an evaporite deposit which occurs in Kuwait as a "partially to highly cemented calcareous
patch or irregular lens of different shapes and sizes (as a) common and characteristic feature of
the Lower Kuwait Group sand" (Al-Sulaimi, 1988). Gatch has been studied in Kuwait on
regional and local scales, including (1) a country wide map for construction material resource
(Youash, 1984, Al-Sulaimi, et al., 1990; Al-Sanad, et al. 1990), (2) presence of gatch in Kuwait
city from excavations and borehole cores (Al-Sulaimi, 1988) as well as surface geophysical
methods (Al-Fahad and Al-Senafy, 2003) and (3) field investigation of gatch hydraulic
conductivity (~1.9e-6 m/s) in surface oil contamination areas (Al-Sarawi, et al., 1998) and soil
aquifer treatment experiments (Viswanathan, et al., 1999). Surface geological maps (e.g., AlSulaimi, et al., 1997) can also be used as a guide to locations where the Ghar and Lower Fars
formations outcrop and gatch can be expected in the shallow subsurface.
The adjacent low resistivity lenses (associated with both the smaller and larger patches of
high resistivity centered around 50 m and 125 m offset from the center respectively) could be
explained by the presence of water, the downward percolation of which has been blocked by the
relatively low permeability gatch and accumulated to some extent to the sides of the gatch. The
very low resistivity values in these lenses indicate that the fluid in the pore-spaces has high
salinity which would point to a deeper source such as brines from oil reservoirs that could have
spilled on the surface. However, if the water is accumulating from percolating rainwater as it
would be reasonable to expect, these small shallow lenses of water are worth investigating as a
potential source of water for small scale use. At our experimental site, shallow wells can be used
27
to sample cores and water content to verify the hypothesis of these two sources of heterogeneity.
Depending on the outcome of core and water sampling, shallow patches of gatch can be a future
target for geophysical imaging in the exploration for water.
The Ghar and Lower Fars formations (middle and lower member) of the Kuwait Group
are known to be the host material for gatch. We propose gatch to be the cause of the
heterogeneity that is seen in the 1 D DCR data although our chosen inverse model shows the
anomalies in the layer overlying the Ghar formation. Gatch may occur in discontinuous patches
as seen in the approximate 2D image (figures 9 and 10) and at length scales similar to the station
spacing in a geophysical survey of the whole well field. Therefore, a study of the occurrence of
gatch in the Kabd area is warranted before proceeding to such a larger survey. Ground
penetrating radar (GPR) imaging or 2D/3D DCR imaging in conjunction with borehole core
sampling can be used to determine (1) whether the heterogeneity that is postulated in this paper
is encountered, and (2) if the vertical profiles obtained from 2D or 3D images compare to the
approximate results of our ID soundings. In figure 12, we show that accounting for the
heterogeneities in the relatively shallow structure at our test site does not have a large effect on
the vertical profile compared to the imaging that does not account for heterogeneity. Moreover,
the limited maximum depth of investigation of our DCR experiment does not support further
inferences regarding the Dammam aquifer.
The TEM inverse model shows an average correspondence with the DCR models.
Notably, the TEM data is seen to be insensitive to the lateral heterogeneities that are indicated in
the DCR data analysis. With respect to the target aquifer, the depth of investigation of the TEM
data is also limited to confirming the expected depth of the top of the Dammam Formation
determined by the DCR analysis.
28
5. CONCLUSION
We conducted two 1 D resistivity imaging experiments using DC resistivity and time
domain electromagnetic sounding at one site in the Kabd well field in Kuwait. The data analysis
shows evidence that the target aquifer for the aquifer storage and recovery project is at the deeper
limits of the sensitivity of both experiments, and further that there is some heterogeneity in the
relatively shallow subsurface, likely due to the occurrence of gatch. In future geophysical
investigations of the Kabd area of Kuwait or similar arid environments, we suggest an initial
exploratory survey using relatively fast techniques such as GPR, or 2D DCR. GPR would be a
suitable method, as the topmost sediments in a desert setting are expected to be relatively dry,
resulting in good depth resolution (see, e.g., Kruse, et al., 2000). Such an initial survey,
completed on a smaller scale can help to decide what type of survey, whether a series of 1 D or
2D, or a full 3D imaging, is best suited to characterize the larger study area.
We note that the central-loop TEM method has an advantage over DCR in field
deployment, as the transmitter and receiver are stationary, and heterogeneities near electrodes
may thus be avoided. If the loop size is decreased, so that earlier times of the induced transient
can be measured, and the transmitter power and data stacking time are increased in order to
increase the number of data points above the noise threshold, TEM can be a viable method for
ID sounding in the Kabd well field. However, if 2D or 3D imaging is deemed to be necessary,
automated acquisition and high-powered transmitters can be used to deploy DCR to advantage,
both in terms of speed and resolution.
We performed approximate 2D analysis of our 1 D DCR sounding data to account for
features that could not be adequately fit by ID layering. The heterogeneities in this approximate
2D image have high resistivity, horizontally elongated shape and the correct depth range,
29
indicating that gatch is present in the relatively shallow subsurface. A comparison of the 1 D
vertical profile obtained from the approximate 2D image with the 1 D layered model indicates
that, in our particular experiment, ID analysis provides a sufficient picture of the subsurface
despite the evidence that the best 1 D fits do not capture a clear anomalous pattern in the data
caused by possible lateral heterogeneities in the subsurface.
30
JNI
Iraq
330-
U
Iz3250
3200
3150
Saudi Arabia
31
650
700
750
goo
850
60
UTM Easting (km)
Figure 1. Map of Kuwait with contours of the top elevation of the Dammam Formation
in meters above mean sea level. The experiment site in Kabd is marked in red.
31
Experiment Set-up
tN
DCR Schlumberger Array
maximum electrode spread
498 m
TEM transmitter
19o by 190 sq. m
receiver
antenna
DCR array center at
N290 6.og' E47* 40.471'
Figure 2. Experiment set-up showing relative placements and dimensions of the DCR
and TEM arrays.
32
Residuals
DCR Data and Best Fit
0
0
50
-
500
0
100
100-
0
0
p
-Jwtk
150
150H
0-
200
200F
250
250
-0
o Data
-Best
300
Fit [1.5 Om; 10.4% rmse]
102
Apparent Resistivity (Om)
3001
-40
-20
0
20
40
% Residual
Figure 3. Left panel: DCR data and best fit model. Right panel: residuals.
33
Best I D Resistivity Model with Depth
SII I li1i 11111iI I I
I
50-
.0
0
1'5
I
100
'
I
'
'
'
'
1
'
'
'
'
'
101
1'
102
'
'
'
'
'
'
'
'
1
103
Resistivity (em)
Figure 4. Best one dimensional resistivity model with depth from DCR data inversion.
34
TEM Data and Homogenous Model Fit
100
10
-I
I0
0 TEM Data
-Homogeneous
.3
- --
10 .2-
-
10
Fit
-22
10 -8107
10 -610'
10~-
Induced Voltage I Receiver Moment (Volts/m2
Figure 5. TEM data as normalized induced voltage vs. time, and a homogeneous model
fit to the data.
35
TEM Data and Best Fit
10
10
__
0-3
Residuals
10
1
-3
--
-2-
~- 1
'U-
-
-
--- - --
10'b
104
o Data
-
Best Fit [7.5e-9 V/m 2 ; 0.2 % rmse]
-0.4
-0.2
0
log(VIVhomog)
0.2
0.4-10
0
10
% Residuals
Figure 6. Left panel: TEM data and best fit model. Right panel: residuals.
36
Best TEM 1 D Model with Depth
0
50
'
'
'
'
'
''
'
'
''I
1 1 1
y
'
'
'
' '
''11
-
E
CL
100
1501
IC iO
10
102
103
Resistivity (Qm)
Figure 7. Best one dimensional resistivity model with depth from TEM data inversion.
37
C~0
C4
E
U1
0
0
CD4
0
0
0
I
0)
0
U,
0D
0
LO
0
0
0
CD
(w) Li)dea
Figure 8. The model grid and starting
model for approximate 2D inversion. Note the symmetry from the central point of the array.
38
E
CI
Cj.
-
>1
D
0
0
SIn
I-
...
0
0
E
ui
-
n1
0
-
I
I
0
0
0
0
CD
(wu) Lidea
Figure 9. The best resistivity model with
lateral structure only in layer 3 - using approximate 2D DCR inversion.
39
E
C
0
0
0
0
It,
I
0
0
0
0
U
0
LO)
0
Cd
0
IO
C41
O
0
(w) qIdea
Figure 10. A zoomed-in contour plot, with 7 contour
levels, of the approximate 2D inverse model shown in figure 9.
40
DCR Data and 2D Best Fit
n
-j
Residuals
0
50-
50
100-
100
150-
150
-o
I
0-
0-
200-
20U
)
250
-
-
-e
o Data
Best Fit [1.92cm; 3.6% rmse]
'2 nn0
I
309
"3
102
Apparent Resistivity (em)
-10
0
% Residual
10
Figure 11. Left panel: DCR data and best fit model with approximate 2D inversion.
Right panel: residuals.
41
0
I
ID
Cross Sections Compared
II
-
---
-
50-
- -
- -- II
Approx 2D
Best I D
El
0.
0)
100-
150100
II
101
I
I I I
I I I I II
102
Resistivity (nm)
Figure 12. A comparison of the 1 D vertical profiles obtained by 1 D inversion and
approximate 2D inversion.
42
0
I
Best I D Resistivity Models with Depth
I II
I
I.I
I
I
I
I
I
II
lI
I
Surface sediments
Dibdibba (Upper
KG Aquifer)
Expected resistivity of KG aquifers
Upper Fars
Aquitard
50
model
model
-DCR
-TEM
#-ft
-
E
0.
Resistivity well-log
100
--
- -
-
-
Lower Fars and Gha,
(Lower KG Aquifer)
Chertified limestone
Aquitard on top
Of Dammam Formatio n
150'
1C
0
I
II I
I I I I I1111
101
I
I
ExI pected resistivity of Dammam aquifers
I
III
i
I
I
102
I I I
103
Resistivity (0m)
Figure 13. A comparison of the lithological and stratigraphic interpretation obtained
from the literature with the 1 D DCR and TEM resistivity layered models.
43
Appendix A: Determining the Optimal Number of Layers in ID DCR Inversion
We adopt a novel two-step approach to analyze the DCR data. In step 1, we explore
inverse models with fixed layer thickness. We perform a search over starting parameters of the
inversion program, namely, (i) number of layers (10 to 75), (ii) maximum depth (50to 500 in),
and (iii) homogeneous starting resistivity (1 to 1000 Um). The variation in inverse results which
are close to a global minimum shows a measure of uncertainty which can be depicted as errorbars on the predicted data (figures Al, A2), and as a resistivity vs depth solution cloud, or again
as error bars on resistivity values for the subset of models with the same number of layers (figure
A3).
We note that we have been able to obtain two distinct families of models from one set of
inversions as illustrated by figures Al and A2, and the ID cross sections compared in figure A3.
Even though the inversion algorithm minimizes the L2 norm of the objective function, we can
rank our set of inverse results according to those that minimize the L2 or the Li norm of the
misfit between observed and predicted data. This allows us to interpret which features of the
resistivity vs depth models are affected by what appear to be systematic misfits in the data, and
to decide whether or not to treat some set of points as outliers and minimize their influence in the
interpretation. Such a choice in interpretation does affect some salient features of our model
interpretation as can be seen by a comparison in figure A3, specifically, the depth and resistivity
of the basement (half-space) of the models are quite different. The Ll model has basement depth
at 70 m and basement resistivity -70 Qm, whereas the corresponding values for the L2 model are
150m and -430 fm. We see a fair correspondence between the two models up to 40 in depth.
We notice visually that the largest variation is indicated in the parameters at larger depth, namely
the depth and resistivity of the basement (or model-half-space).
44
Compared to case of the L2 quantification of error, the Li ranking shows that (i) there is
more variation in the predicted data in the neighborhood of the global minimum shown by the
larger error-bars (note that this is not accounted for by the inclusion of 33 more models in this
case compared to the previous one), and (ii) the best fit line treats the data points at L = 104 and
L = 139 as outliers and fits the rest of the data better. The second observation is in keeping with
the feature that the LI measure of the misfit does not weigh (and try to fit) outliers as much as
the L2 measure. From the residuals and the best fit plot with error-bars, we infer that the range
of inverse results obtained do not adequately fit the data from spacing L = 50 onwards.
Specifically, the variation of apparent resistivity with L has a higher spatial frequency in the data
than can be captured by 1 D modeling to within the expected uncertainty.
Both fixed-thickness layer models in figure A3 lead us to conclude that the resistivity
structure has 6 distinct layers above the half-space. The discrete approximation of the layered
structure from step 1 is used to determine the number of layers to use in a more accurate
inversion for layer thicknesses and resistivities. To proceed, we again present two sets of results
in the second step of the DCR analysis. In the second inversion program, we can actually choose
to minimize the L2 or the LI norm of the objective function. In figure A4, we present the best fit
and residuals according to the L2 norm minimization. Figure A5 shows the best fit and residuals
according to LI minimization. The overall fit is slightly worse than in the case of the L2
minimum model: 1.7 Qm; 10.5% rmse, compared to 1.5 Um, 10.4% rmse, but it is noticeable
that the data points from L= 33 onwards are fit better in the LI case, with the exception (and at
the expense of) the points L = 104 and L = 139, which are treated as outliers. Figure A6 shows
all of the ID models for comparison.
45
The two variable thickness models corresponding to L2 and Li minimum have
differences from
5 th
layer and below, the most significant being the basement is 10 m shallower
and 200 fm higher resistivity in the Li model compared to the L2 model. Figures A4 and A5
illustrate the difference between the two models clearly by showing that the LI model does not
weigh the misfit at data points L= 104, and L = 139 as heavily as the L2 norm, resulting in these
points being treated as outliers in the fitting. Interestingly, we notice a similarity between the
models corresponding to LI and L2 minimum in the fixed and variable thickness inverse models
(yellow and green for Li, red and blue for L2 in figure A6), even though in the case of the fixed
thickness inversion the distinction between the two measures of error is simply obtained by
ranking of the inverse results. Figures Al and A2 also show correspondence with figures A4 and
A5 in the data and best fit lines between the two types of inversion programs. We can make the
observation that the best models in the LI case compared to the L2 have shallower half-space
depths, and show similarity to some of the models in the L2 case.
To illustrate the steps taken to determine the optimal (minimum) number of layers to be
used in the variable thickness inversion model from the results of the fixed thickness layer
inverse models, we show a set of plots in sequence in figure A7 corresponding to the best L2
ranked model. We may simply use a smoothed version of the many layered fixed thickness
model to obtain an estimate of the number of turning points in the 1 D cross section. These
would correspond to the number of distinct layers. We could visually ascertain from the top
panel of figure A7 showing the smooth section, and certainly from the second panel showing the
integrated section that there are 6 distinct segments. However, further processing as shown in
the bottom panel, such as taking stationary points of the second derivative of the integrated (or
the first derivative of the smoothed section), can be a method of obtaining the optimal number of
46
layers in an automated algorithm. This approach suggests an extension and simplification of the
work of Simms and Morgan (1992), who have shown that the 'variable parameter scheme'
obtains the most accurate inverse results in synthetic tests and suggests using the F-Test to obtain
the minimum number of layers. Gupta et al., 1997, describe a "straightforward inversion" which
as some correspondence with our fixed thickness layer inversion, and also address the task of
determining sharp layer boundaries from the smooth inverse models (Israil, et al., 2004).
However, we propose a simpler sequential application of two distinct algorithms to obtain an
optimal 1 D model. Further work with synthetic models in the manner of Simms and Morgan,
1992, can be done to formalize and benchmark an automated algorithm instead of the sequential
approach described in this appendix. We also suggest that the present approach is better in
practice and in computation time to Bayesian approaches which incorporate a penalty with
increasing number of layers in order to solve the inverse problem and solve for the most
'parsimonious' dimensionality (e.g, Malinverno, 2002).
47
Data and Model Fit
Residuals
0
0
00 lw
50KF
100
_01
- ---- 150-
0
0.. ...
0
,150
- ..........
.
EJ
200-
200
250
-
-
......
0
0.2
log(d/p)
250
-
o
-
1 00K_
50
Data
Best Model 1.7Qm; 9_8% RMSE
2a of 45 best
300 L
3UU-
102
Apparent Resistivity (Om)
-0.2
0.4
0.6
Figure Al. Left panel: best fitting model-prediction in black and data points in red.
Error bars are shown for the best 45 solutions at each point at 2 times the standard deviation.
Note that the apparent resistivity is displayed in log scale in order to clearly show the deviation
of the model from the data. Right panel: residuals of the data from the best fit line.
48
Residuals
Data and Model Fit
0
0
50-
50-
100-
1 00
0-
-0
.-. -..
.
EJ 150-
0-
-J
150
200
-
200
- ..............
250
250
o Data
Best Model 1.80m, 10.0% RMSE
300
I I I
I
2o of 78 best
I111111
I
-3UU
-
-
102
Apparent Resistivity (em)
-0.2
0
0.2
log(d/p)
0.4
0.6
A2. Left panel: best fitting model-prediction in black and data points in red. Error bars
are shown for the best 78 solutions (ranked by Li measure of misfit) at each point at 2 times the
standard deviation.
FIGURE
49
Best Models Comparison
I
0
-
I I
i
best fixed thickness LI rank
best fixed thickness L2 rank
50 H
0.
E
100 F-
1 0
10
101
Resistivity (nm)
-
-I
'
1i
-
III
102
Figure A3. The best models according to L2 and LI ranking of the misfits. The error bars,
which are too small in the case of the LI rank to be noticed are showing the variation in
resistivity of the subset of models with the same number of layers, the best 6 in the LI case and
the best 4 in the L2 case.
50
Residuals
Data and Model Fit
0
0
rko*
. - - -
50
100-
100--
00
-J 150-
-
50-
0-
EJ 150--
0
0
200
-
-
200
---~~ ~
250
250 --
-
o
-
--..
--
Data
Best L2 Model 1.47260m; 10.4% rmse
3001
102
Apparent Resistivity (f m)
300'
-0.4
-0.2
0
log(d/p)
0.2
0.4
FIGURE A4. Best fit and data, left panel, residual, right panel, for variable layer thickness
inversion, L2 minimization
51
Data and Model Fit
0
Residuals
0
O mr
50-
100-
150-
50
100-
-0
0
EJ
150-
-j
-
.
.......
.....
o
200-
200-
250-
250-
-I-
Data
Best Li Model 1.6591nm; 10.5% rnse
300
-'
102
Apparent Resistivity (Qm)
300kL
-0.2
0
0.2
log(d/p)
0.4
0.6
FIGURE A5. Best fit and data, left panel, residual, right panel, for variable layer thickness
inversion, Li minimization
52
Best Models Comparison
0
-best
-
-
best fixed thickness LI rank
L2 rank
rank
fixed thickneee L2
fixed thickness
best
best L2 6 Layers
best LI 6 Layers
501F-
E
C.
100[K
150L 0
10
I
I
I
I
~Nj~
I
I
II
.111
101
Resistivity (em)
102
Figure A6. A comparison of the fixed thickness and variable thickness optimal models showing
the correspondences between the outcome of the two algorithms in minimizing L2 or Li
measures of misfit
53
B.t FCkd
T
Ac1%-
M
yLfyerd
ModsI
-
0-
---
Bedt Layered Mde
--- smOOO1*d Mo"de
40
100
120
40
1
1010
10,
Rewiahw* (Cm)
Snocwd Resiseuyd b tg
Festmad
0emond Derihsumoftu 0iasgnd Made
-
O
10
d Re.*ety Plot
20j
30
4
Socod 0
40
00
60
-1
70-
?O60
0
60
100
160
Figure A7. Illustrating steps that can be taken to obtain the optimal number of distinct layers
that can be used in a variable layer thickness inversion from a many-layered fixed layer thickness
model.
54
Appendix B: Exploring the Limits of ID DCR Models in Fitting Vertical Electrical
Sounding Data
In Appendix A, we explored a family of models which characterize the global minimum
of the model to data error space. We notice that as more models near to the minimum are
included the best fit apparent resistivity lines can approach closer to the anomalous data points,
from L = 60 and up (refer to figures Al and A2.) However, the overall fit is always sacrificed in
the attempt to fit the anomalous data points better. In order to obtain more certainty that 1 D
layers are inadequate to fit the data to better than ~10% rmse and capture the turning points in
the apparent resistivity curve, we perform a posterior error analysis, which is illustrated in figure
B 1. Firstly, the initial surface layers are ruled out of the parameter search due to the insensitivity
that is observed with respect to data beyond a certain electrode spacing. We then perform a
search over the thickness and resistivity values and keep the best set of models, as shown in
figure B1, which plots the data and the ID cross section on the same figure for easier reference
and comparison. We can conclude from the figure that extremes in layer thickness or resistivity
are not able to adequately characterize the curvature in the data that is not fit by the best layered
model. We also performed a posterior error analysis in the conventional way to obtain limits in
apparent resistivity due only to extremes in resistivity of the best 6 layer model with the
thicknesses as determined in appendix A. The two data points between L = 150 and 200 are not
within the error bars thus obtained. These observations lead to the hypothesis that lateral
heterogeneity is affecting the data, as explored in section 3.3.
55
Synthetic Data and Models Analysis
50
|
b UU
-----------------------10
-
in
CL
-
---------------
C
150
10
rmse =1.55 Pct rmse =10.3%
rmse =1.69 Pct rmse =12.7%
200
-
rmse =1.81 Pct rmse =14.50
rmse =4.31 Pct rmse =20.3*
rmse =3.1 8 Pet rmse =55.50
5
101
10"
10
1
2
102
"
10
'
"
' ' ' '' "' '
10-2
10
10
10
10
Apparent Resistivity/Resistivity Om
Figure BI. Synthetic data and models analysis based on the best layered model plotted
along with the apparent resistivity data, showing that overall fit is sacrificed by fitting certain
anomalous portions of the data.
56
Appendix C Alternative 1D and Approximate 2D DCR Inverse Models
The strategy in approximate 2D inversion of DCR data was to favor the least complex
model that would fit the data to an appropriate level. The result that was chosen for further
analysis in section 3.3- 3.4 had only 1 layer with lateral heterogeneity, and the baseline ID
structure corresponded with the inverse model that minimizes L2 measure of misfit. Here we
provide for completeness the other low rnse models for the L2 baseline model (figures CI to
C13) and a matching set of figures corresponding with a baseline ID LI model (figures C14 to
C30). (Please refer to appendix A for more detail on the Li and L2 models). Finally, we also
provide the approximate 2D inverse model that uses a completely different set of
parameterization for the baseline ID model. Specifically, we use the 2D code to make a ID
inversion for a fixed thickness distribution of layers - with logarithmically increasing thickness
with depth reflecting decreasing resolution with depth. We then perform the approximate 2D
inversion with the same set of constraints described for the earlier set of models, with the
difference that the symmetry of the 2D image on the left and right of the array center is not
imposed - the anomalies are only on one side of the image and the layer parameters extend
wherever there are no 2D parameters and the ambiguity of the location of the heterogeneities to
the left or right of the center remains (figures C31 to C38). These three alternative sets of
models (L2, Li and fixed thickness) demonstrate the robustness of the results and the expected
variation of the results due to final model parameter errors and variation due to parameterization.
In the ranking of the Li and L2 sets of inverse models, the 4 case numbers that are the best sets
of models correspond to: Case 3, layer 3 only; Case 13, layers 3 and 4; Case 14, layers 3 and 5;
Case 24, layers 3, 4 and 5. The rest of the case numbers shown in figures Cl and C14, and the
matching layer combinations are given in the following table. Note that the case numbers 1 to 30
57
correspond with all the combinations that can be obtained by assigning layers 1 to 5, e.g., case 1
which has only layer 1, all the way to case 30 which has all layers 1 through 5 with lateral cells
in the inversion. In choosing and presenting results, the cases with the first thin layer in the
parameterization were left out as the sensitivity near the electrodes in this layer can dominate the
inverse results.
Case Number
Layer combination
2
2
3
3
4
4
5
5
10
2,3
11
2,4
12
2, 5
13
3,4
14
3,5
15
4,5
22
2,3,4
23
2,3,5
24
3,4,5
29
2,3,4,5
Table C1. Case numbers in the approximate 2D inversion with corresponding layer
combinations.
58
14 Solutions with L2 Starting Model
0.1
0.09
0.08-
0.07
0.060
U)
0.05-
0.04
13
0.030.02
0.01
0
1
2
3
4
5
6
7
8
9
10 11 12
13 14
Ranking
Figure Cl. Ranking of L2-baseline approximate 2D models. See the text for
corresponding structure of the case numbers. Note the rinse values use the log of the ratio of the
data to the predicted data as a measure of residual.
59
C4
qm
0
0
40
0
.
0D
0
am
0
CD
U")
0
U)
o
Figure C2. L2 case 14 (layers 3, 5) pseudoand
logio of resistivity in Um for the color
and
offset,
color plot. Scales are in meters for depth
scale.
60
CM
V
I
0
0
0
LC)
0
0
.5
I
E
0
0
Le)
CD)
a
*
0
In
-
S
0
In
Figure C3. L2 case 14 (layers 3, 5) contour plot.
Scales are in meters for depth and offset, and logio of resistivity in Um for the color scale.
61
I D Cross Sections Compared
0
-Approx
2D
Best I D
50 F
E
0.
100
150
FL
0
50
100
150
200
250
300
Resistivity (em)
Figure C4. L2 case 14 (layers 3, 5), comparison of vertical profiles.
62
Data and Model Fit
0
d=W&I
Residuals
0
V0
50 H
50 [F
0-
.--%
100 F-
100 H
150 H
150 H
200 [
200 H
250
250 H
I
I
o Data
-Best
300
Fit 1.92Qm; 3.3% rmse
102
Apparent Resistivity (em)
300'
-10
0
Pct Residual
10
Figure C5. L2 case 14 (layers 3, 5), left panel: data and best fit; right panel: percent
residuals.
63
IfO
I0
C*4
L
0
0
c~I
4a~
0
0L
0
0
0
0
0
4)
U)
0
0
I
U)
U)
w)
0
0
I
o
0
0
T""
0
Figure C6. L2 case 24 (layers 3, 4, 5)
pseudo-color plot. Scales are in meters for depth and offset, and logio of resistivity in Urm for the
color scale.
64
VEO
00
.
0
OL0
0
0
CD
LO Figure C7. L2 case 24 (layers 3, 4, 5) contour plot.
Scales are in meters for depth and offset, and loglo of resistivity in Qm for the color scale.
65
1D Cross Sections Compared
0
-Approx
2D
-Best
ID
50 1
100
150
0
50
100
150
200
Resistivity (Qm)
250
300
Figure C8. L2 case 24 (layers 3, 4, 5), comparison of vertical profiles.
66
Data and Model Fit
Residuals
0
0
5o
50 F
100
1001-
-J 150
150 H
a
C
200 I-
200
250
o Data
Best Fit 1.91 Qm; 3.3% rmse
300
'
'
I0
02
Apparent Resistivity (Um)
250 F-
4
300'
-10
10
0
Pct Residual
Figure C9. L2 case 24 (layers 3, 4, 5), left panel: data and best fit; right panel: percent
residuals.
67
Ien
UO
Vn
TM-6
D4
0
0
C~J
4w.
0
0
0
0
0
0
0
4-
a
U-
0
0
I
0
0
C,1
o
o
In
o
o
o
In
Figure C10. L2 case 13 (layers 3, 4)
pseudo-color plot. Scales are in meters for depth and offset, and logio of resistivity in Urm for the
color scale.
68
LC)
W)
0
0
0
0
In
I
0
0
0
0
CU
U
E
0
0
I
S
(I)
0
0
N
I
0
0
U,
(N
I
0
0
In
Figure C11. L2 case 13 (layers 3, 4) contour plot.
Scales are in meters for depth and offset, and logio of resistivity in Um for the color scale.
69
1D Cross Sections Compared
0
-Approx
-
2D
Best 1D
50
E
0.
100
'
150
0
50
100
200
150
Resistivity (Um)
250
300
Figure Cl 2. L2 case 13 (layers 3, 4), comparison of vertical profiles.
70
Residuals
Data and Model Fit
0
0
)
-o
E1
50 F-
50 F
100 H
100 V
150 H
150 H
0
0-
200 H
200 1-
r
250 Io Data
- Best Fit 1.91m; 3.3% rmse
0 I
300 i
I 02
Apparent Resistivity (Um)
250 H
300'
-10
0
10
Pct Residual
Figure C13. L2 case 13 (layers 3, 4), left panel: data and best fit; right panel: percent
residuals.
71
14 Solutions with LI Starting Model
0.09
0.080.070.06E
0.050.04:92 f 914
0.030.02-
0.01
0
0
10
5
15
ranking
Figure C14. Ranking of LI-baseline approximate 2D models. See the text for
corresponding structure of the case numbers. Note the rmse values use the log of the ratio of the
data to the predicted data as a measure of residual.
72
EV
M
0
0
CM~
0
0*a
0
75
U
0
0
0)
U)
I
0
0
C14
o
0
If
O
0
0
I4W
Figure C15. LI case 3 (layer 3) pseudocolor plot. Scales are in meters for depth and offset, and logio of resistivity in nm for the color
scale.
73
oC0
0
LM
00
0
C
E
o
0
In
CO
.0
e
LO Figure C 16. L I case 3 (layer 3) contour plot. Scales
are in meters for depth and offset, and logio of resistivity in Urm for the color scale.
74
ID
Cross Sections Compared
0
-Approx
2D
Best I D
50
I-
100
'
150
0
50
100
150
200
Resistivity (Qm)
250
300
Figure C17. LI case 3 (layer 3), comparison of vertical profiles.
75
Residuals
Data and Model Fit
0
0
50 F
50 F
100 1-
m .7
100
-j
150 H
150
200
-
0
200 H
250 [-
250 H
0
0
o Data
-
Best Fit 2.23 Qm; 3.4% rmse
'
300
I 02
Apparent Resistivity (am)
300'
.10
0
10
Pct Residual
Figure C18. LI case 3 (layer 3), left panel: data and best fit; right panel: percent
residuals.
76
In
CM
0
0
0
0
L.
0
0
0D
0
0
0
U)
U)
0
U)
40
Q
0
In
o
0
0
10
Figure C19. LI case 24 (layers 3, 4, 5)
pseudo-color plot. Scales are in meters for depth and offset, and logio of resistivity in Um for the
color scale.
77
In)
to
N
0W
0
0
0
0
C)
0
E
0
11
.O
0n
0
nos
a
o
0
Figure C20. LI case 24 (layers 3, 4, 5) contour plot.
Scales are in meters for depth and offset, and logio of resistivity in im for the color scale.
78
I D Cross Sections Compared
0
I
-Approx
2D
-Best
ID
F-I
*0
CL
100
150
0
I
I
I
50
100
150
Resistivity (Um)
II
200
I
250
300
Figure C21. LI case 24 (layers 3, 4, 5), comparison of vertical profiles.
79
Residuals
Data and Model Fit
0
0
50 -4
50-
100-
100
150 -
150-
200-
200-
250 -
250-
_-
o Data
-Best
Fit 2.58Qm; 3.4% rmse
300'
1
102
Apparent Resistivity (Qm)
I
300
-10
0
10
Pct Residual
Figure C22. LI case 24 (layers 3, 4, 5), left panel: data and best fit; right panel: percent
residuals.
80
0
C4 .4r:
IO
In
W-
0D
0D
0
cV"
LO
0
0
I
U
a-
U)
4)
CY.
o
0
IC)
o
o
O
in
Figure C23. LI case 13 (layers 3, 4)
pseudo-color plot. Scales are in meters for depth and offset, and logio of resistivity in Um for the
color scale.
81
LO
L
00
U
0
00
In
U-
o
to
U)
Figure C24. LI case 13 (layers 3, 4) contour plot.
Scales are in meters for depth and offset, and logio of resistivity in Urn for the color scale.
82
I D Cross Sections Compared
0
-Approx
-
2D
Best I D
50
E-
U-
100
150
0
50
100
150
200
250
300
Resistivity (Qm)
Figure C25. Li case 13 (layers 3, 4), comparison of vertical profiles.
83
Residuals
Data and Model Fit
0
0
50-
50
100-
100-
N150 -
150-
-j
200-
200-
-
250
_-
-
250 o Data
Best Fit 2.56Qm; 3.4% rmse
300'
1
102
Apparent Resistivity (Um)
300
-10
0
10
Pct Residual
Figure C26. LI case 13 (layers 3, 4), left panel: data and best fit; right panel: percent
residuals.
84
to
C4
W)
C4
Vn
T-
(N
0 A
0
0D
.5
0D
0
4)
0D
.l)
0D
0D
I
1
0
in
Figure C27. Li case 14 (layers 3, 5)
pseudo-color plot. Scales are in meters for depth and offset, and logio of resistivity in Um for the
color scale.
85
a,
LC
C
a
L
C
O0
0
L0
$O%
L.n
O
oD
0
0
Ln
Figure C28. Ll case 14 (layers 3, 5) contour plot.
logio
of resistivity in fOm for the color scale.
offset,
and
Scales are in meters for depth and
86
I D Cross Sections Compared
0
I
-Approx
2D
-Best
ID
II
50
9
100
150
0
50
100
150
200
250
300
Resistivity Ulm)
Figure C29. LI case 14 (layers 3, 5), comparison of vertical profiles.
87
Data and Model Fit
0
Residuals
0
mO-O
00
-e
50K
50F
0-
-J
100 b
100 K
150
150 F-
-e
0
200 [-
200 H
250 1
250 K
o Data
Best Fit 2.240m; 3.3% rmse
'
300
300'
-
02
Apparent Resistivity (0m)
-10
0
10
Pct Residual
Figure C30. LI case 14 (layers 3, 5), left panel: data and best fit; right panel: percent
residuals.
88
ID Cross Section
10
0
10
10
102
100
101
102
3
Resistivity (ftm)
Figure C31. 1D DCR inverse model, using fixed thickness layers, with logarithmic
increasing thickness with depth distribution. This alternative parameterization inversion was
done with the 2D code.
89
Data and Model Fit
Residuals
0 -T
0
ID
U
50
-
50
0'
0
100
Data
Best 1 D Model Fit
1.400m; 9.6% rmse
0*
100-
i
-J
-- o
0
150
150
0-
200 F-
200
250
101
102
Apparent Resistivity (0m)
2581
-. 4-0.2 0 0.2
log(d/p)
Figure C32. Apparent resistivity data and best fit corresponding to the model shown in
figure C3 1, left panel; residuals plotted as log of the ratio of the data to the best fit (predicted),
right panel.
90
Aprpoximate 2D Model
log10 (Resistivity
Qm)
3.5
3
50
2.5
100
2
Ea-
0.
1.5
150
1
200
0.5
250
-200
-100
0
100
Electrode Positions (m)
200
-
Figure C33. Approximate 2D DCR inverse model with the starting baseline 1D model
shown in figure C3 1. Note that in this case, compared to the approximate 2D models shown
earlier, only one side of the array is parameterized with 2D cells and symmetry is not imposed
the position of the anomalies is therefore ambiguous whether on the right or the left of the array
center.
91
Approximate 2D Subdomain
0
10glo (Resistivity Qm)
2.5
5
10
2
15
-
20
1.5
L 25
30
35
0.5
40
4
-250
-200
-150
-100
Electrode Positions (m)
-50
Figure C34. A contour plot of a zoomed in portion of the approximate 2D inverse model
shown in figure C33. Note the different color scale.
92
Residuals
Data and Model Fit
0
0
--
I
0
50
~0
0 Data
-
P
Best Fit
0.55Qm; 2.2% rmse
-10 0
'
100
I
I
-i
150
I
0 -P
200
0
-2(
0-0
250
101
102
Apparent Resistivity (Um)
-0.1
0.1
0
log(d/p)
Figure C35. Apparent resistivity data and best fit corresponding to the model shown in
figure C33, left panel; residuals plotted as log of the ratio of the data to the best fit (predicted),
right panel.
93
ID Cross Sections Comparison
I II
I
I
I III I 1 I
I
I
I
I
I t I I
I
100
E
1D Model
Approx 2D
zero-offset cross secti n
4.d
101
F
I
-
-
m m m -
m
--
U
I
II
102
I
0
ENEENNEONMENEENOW
II
I
I
100
10 1
I I II II I I IIII
102
II
.
II I I I
3
Resistivity (am)
Figure C36. A comparison of the vertical resistivity profile of the ID and approximate
2D inverse models. The cross section of the 2D model is taken at the middle of the image, and
the resistivity of the layers with lateral resistivity heterogeneity are not average (area-weighted
average) as with the previous comparisons shown. This comparison shows how the layered
parameters compare, in case we do and we do not account for any heterogeneous structures.
94
ID Cross Sections Comparison
0
I1I I I
I
odel-
-DCRM
50 F-
""DCR- A pprox 2D
"'-.TEM M xdel
rusisIt vity well-log
a
-
-
i
I--
-
.1001E
150
I I I
K
II
II
I
I
I
I
I
I
I
200 H
I
' I'
250
100
101
I'
102
Resistivity (Qm)
104
Figure C37. A comparison of the ID and approximate 2D inversion models in cross
section, with the best 1 D TEM inverse model and the resistivity well log, obtained from a well
2.6 km away from the field experiment site. Note that the resistivity magnitudes of the DCR
inversion in this parameterization compare more favorably with the well log data, whereas the
earlier set of parameterizations (LI and L2 from the 1 D code) correspond more to the
magnitudes obtained from TEM inversion.
95
Cross Sections Comparison
1D
sedl
Dibdibba 0
(Upper KG Ao luffer) -
I I I
ents
IIj
m
m
Rsistivity ae of KG aquifers
I
Upper Fars Aquitard
50
I
Lower Fars ai id Ghar
(Lower KG A luifer)
100
I
I
U
I
I
calcareous sand
U
gravelly sand
siliclfi .. ca sroU.Lvs91
Che;f;lim;;;oe, aq;ulard
on top of Dammam Formation
chertifled dolomite
E
150
Depth and resistivily range of Damram Formaftk n
I
&
I
DCR Model
gU
A
"I
-
2001
- DCR- Approx 2D
- - TEM Model
I
100
101
I II
I I I II
102
103
104
Resistivity (Qm)
Figure C38. Alternative lithological interpretation based on fixed thickness (logarithmic
increasing with depth) parameterization of DCR inversions. Compare with figure 13.
96
Appendix D Raw Data of DCR and TEM Experiments
We provide the raw data for DCR (table DI), and show a figure with the data points
picked for analysis using a summary figure displaying the data, figure DI. The outliers have
been eliminated. The nearly-overlapping data points for short L spacing include points that were
obtained according to optimal experimental design. Nonetheless, the SEM (standard error of the
mean) of these points proved higher than the nearby points that were following a logarithmically
increasing spacing of conventional use in Schlumberger arrays, and were therefore also
discarded.
We provide the TEM data (table D2) and summary figures (figures D2 and D3). The
pages of the TEM data file can be interpreted with the aid of the following key: (A) 1 Hz
switching current signal and 512 cycles of stacking for the transient induced voltage (sampled at
the appropriate gates corresponding to the signal frequency) and (B) similarly for 8 Hz signal
and 2048 cycles. And finally, blocks 130 and 132 correspond with ambient noise measurements
(no transmitter signal) obtained with the sampling and stacking system of cases A and B above
respectively. The data that was used for the analysis in this study was 190 by 190 m loop, 8Hz
(block 110).
Loop Size
Data Block
Loop Size
Data Block
190
107
190
110
100
116
100
113
50
128
50
125
50 repeat
129
18
095
Case A 1 Hz, 512 cycles
Case B 8 Hz, 2048 cycles
97
The data picked for TEM inverse analysis was the 190m square loop data at 8Hz, 2048
cycles. This data set was the only one with sufficient range at early and late times above the
ambient noise floor. The smaller loop sizes were not operated with higher frequencies and we
therefore did not have earlier samples of the voltage transient to provide complementary
information on the data from the 190m loop. All of the field data, as well as synthetic data with
the same sampling and data range computed for simple layered models, were analyzed in inverse
modeling. Apart from the chosen data set, the inversions were not robust with respect to initial
parametrization such as number of layers, and initial resistivity and depth distribution.
phi
V
I
L
Data Block
No. cycles
Freq
SEM
I
1
2
0.1
1.1
1391
66.94
1.92
0.5
8
2
2
0.1
19.53
-11.2
68.68
0.52
0.5
8
3
4
2.7
2.7
0.1
1.2
7.21
0.4
-14.7
-765.7
51.05
54.25
0.86
11.21
0.5
0.5
8
8
5
3.6
0.1
44.8
1.4
65.15
-1.18
0.5
8
6
3.6
1.5
57.6
-444.7
51.06
13.8
0.5
8
7
4.8
0.1
8
4.8
2.1
26.46
268.9
7.8
-1130.3
82.07
85.59
5.37
1.79
0.5
0.5
8
8
9
10
6.4
6.4
0.1
2.8
9.06
382.9
-5.3
-2.8
62.99
68.07
10.41
0.35
0.5
0.5
8
8
11
8.6
0.1
3.83
11.9
59.88
15.43
0.5
8
64.28
43.42
0.6
93.32
0.5
0.5
8
8
12
13
8.6
10
3.7
0.1
213.9
1.81
-3.6
-18.3
14
10
1
19
13.8
47.89
3.25
0.5
8
15
10
4.3
132.5
-7.2
52.9
1.06
0.5
8
16
17
12
1
9.75
30.4
43.09
7.72
8
12
5.2
77.02
-2.3
44.12
1.77
0.5
0.5
18
13
1
12.3
-7.7
71.92
6.16
0.5
8
19
13
5.6
115.5
-5.8
79.68
0.89
0.5
8
8
20
15
1
16.33
10.3
157.8
5.39
0.5
8
21
15
31.8
4
0.83
0.5
8
18
171.1
17.04
164.2
22
6.5
3
89.15
2.47
0.5
8
23
18
7.7
81.02
-4.7
116.6
1.13
0.5
8
24
25
26
27
21
21
24
28
3
9
3
3
14.43
68.77
15.92
7.32
2
-6.1
1166
46.1
127.9
138.2
0.35
159.2
3.18
1.4
3.62
17.24
0.5
0.5
0.5
0.5
8
8
8
8
28
32
6
11.11
706
126.7
6.17
0.5
16
29
37
9
7.89
30.6
133.1
30.2
0.5
16
30
43
9
5.12
-17.1
141.7
9.82
0.5
16
31
50
9
3.17
-23.5
133.6
15.04
0.5
16
27.3
24.86
30.5
53
0.5
0.5
0.5
0.5
16
16
16
16
58
67
77
90
9
9
9
20
2.68
1.27
1.56
3.39
16.1
39.9
97.7
-1081
167
112.6
76
0.227
36
90
-1161.6
0.427
63
0.5
16
104
20
20
3.28
37
1.97
950.3
107.7
95.3
0.5
16
38
120
20
2.83
1348
0.2
64.1
0.5
16
39
139
20
2.01
212
217.4
86.9
1
32
40
41
161
186
30
30
2.12
1.63
134.3
88.4
279
290.1
39.8
36.76
1
1
32
32
42
216
30
1.22
220.9
227.9
91.5
1
32
43
249
30
1.07
-6.6
249.9
66.73
1
32
32
33
34
35
Table D1. DCR raw data
99
Raw Data And Picked Data
0
pO
010
*
-
50
0
.E
o>
0
0 0
L 100
00
S15000
-
0
0
raw data
*
picked data
corrected L
'
250
10-2
10,1
100
102
10
Apparent Resistivity 9m
(Volta ge/C urrent)ir(L 2 . 1 2 )/(21)
77, 1 9 to 1
20
10 3
105
Figure D1. DCR apparent resistivity data and picked data
100
0095
TEM 0618 2008-02-12 15:16:25 12.2v INL 42.5% 36.1 DegC
Tx 0.00000 Rx
1 N OUT
26u 30.52u
2048 Cyc Tx Curr
1 213.6u
8 Hz
0.00
0000 0.018u
54.62u 0.646
I Hz
1 4.5007
Rho I
Mag I
Wn
54.62u 4.5007
0.6457
85.14u 1.3378
0.6919
115.7u 54.047m 3.5269
146.2u 11.956m 6.5268
176.7u 28.351m 2.6759
207.2u 22.490m 2.3944
252.4u 17.357m 2.0484
313.6u 12.491m 1.7765
374.7u 9.5993m 1.5737
450.2u 7.0736m 1.4206
541.9u 5.2237m 1.2763
661.9u 3.7230m 1.1462
829.1u 2.5991m 1.0008
1.027m 1.8293m 0.8854
1.269m 1.3271m 0.7704
1.573m 967.42u 0.6653
1.965m 701.70u 0.5685
2.481m 506.93u 0.4790
3.119m 380.92u 0.3957
3.907m 291.18u 0.3251
4.893m 216.47u 0.2723
6.148m 164.32u 0.2236
7.742m 117.75u 0.1902
9.714m 76.978u 0.1730
12.20m 54.790u 0.1485
15.35m 40.374u 0.1241
19.31m 26.093u 0.1132
24.29m 19.205u 94.724m
0107
TEM 0618 2008-02-13 11:45:44 12.3v INL 43.8% 27.2 DegC
Tx 0.00000 Rx
1 N OUT
1 488.3u
64u 122.1u
1 Hz
512 Cyc Tx Curr
1.24
0400 28.23u
1 -0.1363
212.3u 16.02
1 Hz
Rho 1
Mag 1
Wn
212.3u -0.1363
16.023
334.4u -90.044m 9.9055
Page 1
0
0
Table D2. TEM raw data - pg. 1, continued overleaf...
101
456.4u -63.329m
7.4560
578.5u -46.457m
6.1752
-35.186m
-27.392m
-19.756m
-13.379m
-9.5311m
-6.5544m
-4.4442m
-2.8779m
-1.7049m
-1.0115m
-590.12u
5.4017
4.8838
4.3612
3.9310
3.6576
3.4535
3.2812
3.1386
3.0548
3.0269
3.0441
6.285m -330.12u
7.855m -171.95u
3.1347
3.3394
9.916m -83.035u
12.47m -32.943u
15.62m -4.2424u
3.6795
4.6524
12.530
700.6u
822.6u
1.003m
1.248m
1.493m
1.794m
2.162m
2.641m
3.310m
4.101m
5.071m
19.56m
7.3281u
5.9803
24.59m
30.96m
38.85m
22.288u
41.928u
37.358u
1.9466
0.8700
0.6436
48.78m
44.071u
0.3944
61.40m 20.220u
77.23m -11.352u
97.17m -36.239u
0.122 -24.860u
13.387u
0.154
0.5008u
0.194
0.4520
0.4531
0.1425
0.1248
0.1287
0.7835
0110
TEM 0618 2008-02-13 11:56:24 12.2v INL
1 N OUT
Tx 0.00000 Rx
1
8 Hz
Hz
Wn
44.14u
74.66u
105.2u
135.7u
166.2u
196.7u
2048 Cyc Tx Curr
44.14u
1 -0.3289
Mag 1
-0.3289
-0.2806
-0.2419
-0.2102
-0.1842
-0.1624
42.5%
28.3 DegC
26u
30.52u
1 244.1u
0300
92.30u
1.51
122.0
0
Rho 1
122.01
56.490
35.233
25.299
19.706
16.179
Page 2
Table D2. TEM data - pg. 2, continued overleaf...
102
241.9u
303.1u
364.2u
439.7u
531.5u
651.4u
818.6u
1.016m
1.259m
1.562m
1.955m
2.470m
3.108m
3.896m
4.882m
6.138m
7.731m
9.703m
12.19m
15.34m
19.30m
24.28m
12.877
-0.1364
-0.1097
10.225
-89.951m 8.5952
-71.839m 7.2950
-56.070m 6.2744
-41.783m 5.4376
-29.141m 4.7251
-20.159m 4.2114
-13.641m 3.8259
-8.9588m 3.5322
-5.6149m 3.3197
-3.3986m 3.1415
-2.0196m 3.0305
-1.1722m 2.9884
-674.33u 2.9664
-378.39u 2.9776
-212.16u 2.9807
-121.09u 2.9665
-70.605u 2.9070
-45.324u 2.6623
-32.999u 2.2439
-23.665u 1.9096
0113
TEM 0618 2008-02-13 13:04:12 12.2v INL 41.1% 30.6 DegC
Tx 0.00000 Rx
1 N OUT
8 Hz
2048 Cyc Tx Curr
1 213.6u
26u 30.52u
1 Hz
1 -0.3712
41.62u 52.75
0300 88.96u
1.92
Wn
Mag I
Rho 1
41.62u -0.3712
52.748
72.14u -0.2753
25.743
102.7u -0.2115
17.046
133.2u -0.1671
12.926
163.7u -0.1350
10.568
194.2u -0.1110
9.0538
239.4u -85.633m 7.5953
300.6u -62.696m 6.3989
361.7u -47.645m 5.6442
437.2u -35.386m 5.0180
528.9u -25.669m 4.5243
648.9u -17.795m 4.1083
816.1u -11.547m 3.7411
1.014m -7.5097m 3.4710
Page 3
0
Table D2. TEM data - pg. 3, continued overleaf...
103
1.256m
1.560m
1.952m
2.468m
3.106m
3.894m
4.880m
6.135m
7.729m
9.701m
12.18m
15.34m
19.30m
24.28m
-4.8028m
-2.9864m
-1.7685m
-995.88u
-546.63u
-285.21u
-141.03u
-65.581u
-33.214u
-27.061u
-40.401u
-65.368u
-100.5lu
-140.33u
3.2715
3.1305
3.0539
3.0311
3.0819
3.2618
3.5807
4.0731
4.3630
3.4245
1.7929
0.8865
0.4539
0.2477
0116
TEM 0618 2008-02-13 13:21:53 12.2v INL 41.8% 30.0 DegC
1 N OUT
Tx 0.00000 Rx
64u 122.1u
1 488.3u
512 Cyc Tx Curr
1 Hz
1.24
0500 28.37u
1 -71.998m 240.3u 8.474
1 Hz
Rho 1
Mag 1
Wn
240.3u -71.998m 8.4742
362.4u -41.753m 6.1448
484.4u -26.862m 5.0822
606.5u -18.436m 4.4912
728.6u -13.351m 4.1027
850.6u -10.040m 3.8324
1.031m -6.9788m 3.5423
1.276m -4.5485m 3.3048
1.521m -3.1572m 3.1475
1.822m -2.1186m 3.0364
2.190m -1.4114m 2.9319
2.669m -894.68u 2.8556
3.338m -525.97u 2.8036
4.129m -318.82u 2.7459
5.099m -188.45u 2.7434
6.313m -113.63u 2.6921
7.883m -68.360u 2.6090
9.944m -37.454u 2.6459
12.50m -15.308u 3.2830
15.65m 1.2461u 12.014
19.59m 11.267u 1.9031
24.62m 16.803u 0.9967
Page 4
0
Table D2. TEM data - pg. 4, continued overleaf...
104
30.99m 32.529u
38.88m 41.314u
48.81m 45.057u
61.42m 35.713u
77.26m 19.625u
97.19m 0.5632u
0.122 -17.726u
0.154 -14.017u
34.207u
0.194
0.4372
0.2554
0.1650
0.1313
0.1336
0.9721
66.430m
53.009m
19.921m
0125
TEM 0618 2008-02-13 14:20:26 12.2v INL 41.8% 30.0 DegC
1 N OUT
Tx 0.00000 Rx
26u 30.52u
1 183.1u
2048 Cyc Tx Curr
8 Hz
0400 85.08u
1.10
32.11u 52.29
1 -0.1800
1 Hz
Rho l
Mag 1
Wn
32.11u -0.1800
52.287
62.62u -0.1211
22.366
93.14u -87.286m 14.353
123.7u -65.562m 10.831
154.2u -50.838m 8.8849
184.7u -40.486m 7.6534
229.9u -29.989m 6.4912
291.1u -21.051m 5.5462
352.2u -15.502m 4.9502
427.7u -11.152m 4.4607
519.4u -7.8629m 4.0726
639.4u -5.3302m 3.7327
806.6u -3.3913m 3.4264
1.004m -2.1766m 3.1950
1.247m -1.3851m 3.0122
1.550m -861.88u 2.8739
1.943m -517.86u 2.7709
2.458m -303.15u 2.6754
3.096m -177.78u 2.5994
3.884m -105.65u 2.5200
4.870m -63.339u 2.4309
6.126m -39.571u 2.2696
7.719m -27.035u 1.9902
9.691m -20.728u 1.6260
12.18m -18.064u 1.2184
15.33m -17.579u 0.8453
19.29m -17.267u 0.5834
Page 5
0
Table D2. TEM data - pg. 5, continued overleaf...
105
24.27m -18.627u
0.3781
0128
TEM 0618 2008-02-13 14:35:28 12.2v INL 41.8% 30.0 DegC
1 N OUT
Tx 0.00000 Rx
64u 122.1u
1 366.2u
256 Cyc Tx Curr
1 Hz
1.37
0510 48.31u
1 -43.440m 139.2u 11.70
1 Hz
Rho I
Mag 1
Wn
139.2u -43.440m 11.697
261.3u -20.261m 6.8105
383.4u -11.486m 5.2485
505.4u -7.2374m 4.5046
627.5u -4.9493m 4.0466
749.6u -3.5660m 3.7440
930.3u -2.3830m 3.4173
1.175m -1.4923m 3.1635
1.419m -1.0162m 2.9826
1.721m -674.53u 2.8422
2.089m -452.98u 2.6855
2.568m -292.21u 2.5483
3.237m -182.61u 2.3708
4.028m -118.40u 2.1981
4.998m -74.651u 2.0870
6.212m -54.467u 1.7919
7.782m -30.894u 1.7964
9.843m -15.541u 1.9199
12.39m -3.4352u 3.5762
15.55m 11.171u 1.1168
19.49m 24.665u 0.4518
24.51m 44.284u 0.2087
30.89m 67.508u 0.1072
38.78m 75.400u 68.173m
48.71m 84.942u 43.053m
61.32m 49.810u 41.870m
77.15m -33.929u 36.884m
97.09m -119.14u 10.884m
0.122 -98.955u 8.3890m
76.571u 6.7895m
0.154
45.378u 6.5538m
0.194
0129
TEM 0618 2008-02-13 14:46:23 12.2v INL 41.8%
Page 6
0
30.0 DegC
Table D2. TEM data - pg. 6, continued overleaf...
106
0.00000 Rx
1 N OUT
1 Hz
512 Cyc Tx Curr
1 -43.023m 139.2u
1 Hz
Rho I
Wn
Mag I
139.2u -43.023m 11.773
261.3u -20.095m 6.8481
383.4u -11.390m 5.2778
505.4u -7.1817m 4.5279
627.5u -4.9006m 4.0734
749.6u -3.5281m 3.7708
930.3u -2.3432m 3.4558
1.175m -1.4584m 3.2123
1.419m -983.46u 3.0485
1.721m -647.69u 2.9202
2.089m -430.94u 2.7763
2.568m -272.92u 2.6670
3.237m -160.77u 2.5808
4.028m -101.17u 2.4410
4.998m -63.520u 2.3242
6.212m -42.139u 2.1263
7.782m -31.069u 1.7897
9.843m -17.520u 1.7725
12.39m -17.110u 1.2262
15.55m -13.510u 0.9839
19.49m -7.3674u 1.0112
24.51m -4.1497u 1.0118
30.89m -0.5767u 2.5656
38.78m -1.5455u 0.9102
48.71m -7.8832u 0.2100
61.32m -21.737u 72.774m
77.15m -36.706u 34.999m
97.09m -34.807u 24.720m
0.122 -11.411u 35.409m
0.154
0.5184u 0.1897
0.194 -22.971u 10.318m
Tx
64u 122.1u
1 366.2u
1.37
11.77
0510 24.82u
0130
TEM 0618 2008-02-13 14:56:55 12.2v INL 41.8% 30.0 DegC
1 N OUT
Tx 0.00000 Rx
64u 122.1u
1 366.2u
512 Cyc Tx Curr
1 Hz
1.37
0510 21.52u
4189
1 -6.4092u 139.2u
I Hz
Rho 1
Wn
Mag I
139.2u -6.4092u 4189.4
Page 7
0
0
Table D2. TEM data - pg. 7, continued overleaf...
107
261.3u
383.4u
505.4u
627.5u
749.6u
930.3u
1.175m
1.419m
1.721m
2.089m
2.568m
3.237m
4.028m
4.998m
6.212m
7.782m
9.843m
12.39m
15.55m
19.49m
24.51m
30.89m
38.78m
48.71m
61.32m
77.15m
97.09m
0.122
0.154
0.194
-20.768u
-15.593u
-4.2525u
-23.004u
-11.982u
-10.535u
-10.944u
-16.058u
-16.349u
-20.445u
-14.332u
-12.015u
-16.345u
-13.419u
-14.392u
-13.455u
-11.375u
-10.904u
-13.162u
-12.764u
-9.7888u
-2.4765u
0.6058u
8.7691u
4.5266u
-1.5171u
-6.1613u
4.4399u
7.8288u
-17.552u
669.93
428.07
642.12
145.30
166.89
126.86
83.810
47.366
33.937
21.185
19.019
14.546
8.2290
6.5524
4.3517
3.1265
2.3639
1.6558
1.0011
0.7010
0.5710
0.9711
1.6994
0.1956
0.2071
0.2928
78.411m
66.438m
31.051m
12.346m
0132
TEM 0618 2008-02-13 15:03:17 12.2v INL 42.5% 30.0 DegC
1 N OUT
Tx 0.00000 Rx
26u 30.52u
1 183.1u
8 Hz
2048 Cyc Tx Curr
1.37
7266
0640 110.6u
1 Hz
1 109.85u 32.11u
Rho 1
Wn
Mag 1
32.11u 109.85u 7266.0
62.62u 136.07u 2068.9
93.14u 121.07u 1154.0
123.7u 135.66u 667.02
154.2u 138.74u 454.97
184.7u 103.32u 409.83
Page 8
0
Table D2. TEM data -pg.8, continued overleaf...
108
229.9u 126.28u
291.lu 133.28u
352.2u 128.52u
427.7u 130.16u
519.4u 131.83u
639.4u 130.20u
806.6u 126.25u
1.004m 122.89u
1.247m 123.27u
1.55Gm 116.75u
1.943m 116.90u
2.458m 112.65u
3.096m 108.80u
3.884m 102.25u
4.870m 94.671u
6.126m 84.226u
7.719m 70.139u
9.691m 49.479u
12.18m 23.385u
15.33m -8.8806u
19.29m -47.059u
24.27m -87.800u
248.92
162.06
120.85
86.696
62.171
44.337
30.733
21.710
15.111
10.896
7.4739
5.1761
3.6061
2.5754
1.8595
1.3716
1.0541
0.9104
1.0258
1.3326
0.2990
0.1345
Page 9
Table D2. TEM data - pg. 9
109
Different Loop Sizes at 8Hz 2048 cycles
101
x
x
100
x
0
18m
50m
0
loom
190m
V
0noise
9
)P0
10*1
a
~ a 0a
x
10-2
0
0
X.o
xC
00
x
00
V
00
0 10-3
x
0
V
a x0
V
10
8
0/
10~S
10.6
10~1
100
101
time (ms)
Figure D2. TEM data for various loop sizes and the ambient noise magnitude for 8Hz
transmitted signal and 2048 cycles of stacking. Note the last 3 noise measurements are negative
in sign.
110
Different Loop Sizes at I Hz 512 cycles
10 0
o
0
V
10 .1
0
a
noise
o
So
I 0-2
50m
loom
190m
1
o
0
o
a0 0 0e
a
CO
0
a
10-3
0
aa
V
01
a
0
0 10-4
0
S0
'
0
Ift
0
0
10
106
0
0
7
10- 1
-1
10
100
10 1
102
time (ms)
Figure D3. TEM data for various loop sizes and the ambient noise magnitude for 1Hz
transmitted signal and 512 cycles of data stacking. Note that apart from points 24 to 26 and 29 to
30, the noise measurements are negative in sign.
111
REFERENCES
1. Al-Ruwaih, F.M., and H.O. Ali, 1986, Resistivity measurements for groundwater
-
investigation in Umm Al-Aish area, North of Kuwait: Journal of Hydrology, 88, 185
198
2. Al-Fahad, K.G., and M.A. Al-Senafy, 2003, Exploration of subsurface water and calcrete
with seismic refraction and surface resistivity techniques in Kuwait City in J.A.A. Jones
and T.G. Vardanian, eds., The Rational Use and Conservation of Water Resources in a
Changing Environment, Yerevan State University
3.
Al-Otaibi, M., and A. Mukhopadhyay, 2005, Options for managing water resources in
Kuwait: The Arabian Journal for Science and Engineering, 30, #2C, 55-68
4. Al-Ruwaih, F.M., 2001, Hydrochemical investigation on the clastic and carbonate
aquifers of Kuwait: Bulletin of Engineering Geology and the Environment, 60, 301-314
5. Al-Ruwaih, F.M., and S.A. Ben-Essa, 2004, Hydrogeological and Hydrochemical Study
of the Al-Shagaya Field-F, Kuwait: Bulletin of Engineering Geology and the
Environment, 63, 57-70
6.
Al-Ruwaih, F.M., and H.A. Qabazard, 2005, Aquifer characteristics and water quality of
Miocene-Pleistocene sediment, Kuwait: Bulletin of Engineering Geology and the
Environment, 64, 175-191
7.
Al-Sanad, H.A., F.M Shaqour, S.R. Hencher, and A.C. Lumsden, 1990, The influence of
changing groundwater levels on the geotechnical, behaviour of desert sands: Quarterly
Journal of Engineering Geology, London, 23, 357-364
112
8. Al-Sarawi, M., M.S. Massoud, and S.A. Wahba, 1998, Physical properties and indicators
of oil penetration in soils contaminated with oil lakes in the Greater Burgan oil fields of
Kuwait: Water, Air, and Soil Pollution, 102, 1-15
9. Alsharhan, A.S., Z.A. Rizk, A.E.M. Nairn, D.W. Bakhit, and S.A. Alhajari, 2001,
Hydrogeology of an arid Region: The Arabian Gulf and Adjoining Areas: Elsevier.
10. Al-Sulaimi, J.S., M, Mollah, and M. Matti, 1990, Geotechnical properties of calcrete soil
(gatch): Engineering Geology, 28, 191-204
11. Al-Sulaimi, J.S., 1988, Calcrete and Near Surface Geology of Kuwait City and suburbs,
Kuwait, Arabian Gulf: Sedimentary Geology, 54, 331-345
12. Al-Sulaimi, J.S., F.J. Khalaf, and A. Mukhopadhyay, 1997, Geomorphological analysis
of paleo drainage systems and their environmental implications: Environmental Geology,
29, 94-111
13. Auken, E., and A.V. Christiansen, Layered and laterally constrained 2D inversion of
resistivity data: Geophysics, 2004, 69, #3, 752-761
14. Auken, E., A. Christiansen, B.H. Jacobsen, and N. Foged, 2005, Piecewise ID laterally
constrained inversion of resistivity data: Geophysical Prospecting, 53, 497-506
15. Auken, E., and A. Christiansen, 2012, eml dinv and EMMA computer programs and
literature, Hydrogeophysics Group, University of Aarhus, Denmark,
http://www.aarhusgeo.com/, accessed November, 2012
16. Beard, L.P., and F.D. Morgan, 1991, Assessment of 2-D resistivity structures using ID
inversion: Geophysics, 56, #6, 874-883
17. Duch, Peter M., and Kurt I. Sorensen, 1994, When is ID 2D? Interpretation of
Geoelectrical Sections: Symposium on the Application of Geophysics to Engineering and
113
Environmental Problems, Environmental and Engineering Geophysical Society,
Extended Abstracts, 967-976. doi: 10.4133/1.2922123
18. Dey, A., and H.F. Morrison, 1979, Resistivity Modeling for Arbitrarily Shaped TwoDimensional Structures: Geophysical Prospecting, 27, 106-136
19. El-Qady, G., C. Sakamoto, and K. Ushijima, 1999, 2-D inversion of VES data in Saqqara
archaeological area, Egypt: Earth, Planets and Space, 51, 1091-1098
20. Fadlemawla, A., and M. Al-Otaibi, 2005, Analysis of the water resource status in Kuwait:
Water Resources Management, 19, 555-570
21. Fitterman, D.V., and A.P. Stewart, 1986, Transient electromagnetic sounding for
groundwater: Geophysics, 52, 995-1005
22. Frischknecht, F.C., V.F. Labson, B.R. Spies, and W.L. Anderson, 1991, Profiling
Methods Using Small Sources, in M.N. Nabighian, ed., Electromagnetic Methods in
Applied Geophysics, Vol. 2, Application: Society of Exploration Geophysicists
23. Gulf News, 2011, "Kuwait Has World's Highest Water Consumption",
http://gulfnews.com/news/gulf/kuwait/kuwait-has-world-s-highest-water-consumption-
1.798870, accessed 10 August 2014.
24. Gupta, Pravin K., Sri Niwas, and Vinod K. Gaur, 1997, Straightforward inversion of
vertical electrical sounding data: Geophysics, 62, no. 3, 775-785
25. Gyulai,
A., and T. Ormos, 1999, A new procedure for the interpretation of VES data: 1.5-
D simultaneous inversion method: Journal of Applied Geophysics, 41, 1-17
26. Gyulai, A., T. Ormos, and M. Dobroka, 2010, A quick 2-D geoelectric inversion method
using series expansion: Journal of Applied Geophysics, 72, 232-241
114
27. Israil, M., T., Pravin K. Gupta, and D.K. Tyagi, 2004, Determining sharp layer
boundaries from straightforward inversion of resistivity sounding data: Journal of the
Indian Geophysical Union, 8, No. 2, 125-133
28. Kennedy, M. C. and A. O'Hagan, 2001, Bayesian calibration of computer models:
Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63, 425-464
29. Kim, Hee Joon, and YoungHee Kim, 2011, A unified transformation function for lower
and upper bounding constraints on model parameters in electrical and electromagnetic
inversion: Journal of Geophysical Engineering, 8, 21-26
30. Kruse, S.E., J.C. Schneider, D.J. Campagna, J.A. Inman, and T.D. Hickey, 2000, Ground
penetrating radar imaging of cap rock, caliche and carbonate strata: Journal of Applied
Geophysics, 43, 239-249
31. Malinverno, A., 2002, Parsimonious Bayesian Markov Chain Monte Carlo Inversion in a
Nonlinear Geophysical Problem: Geophysical Journal International, 151, 675-688
32. Minsley, B.J., J. Ajo-Franklin, A. Mukhopadhyay, and F.D. Morgan, 2010,
Hydrogeophysical methods for analyzing aquifer storage and recovery systems,
Groundwater, 49, #2, 250-269
33. Miorelli, F., 2011, Joint Laterally Constrained Inversion of CSEM and MT Data:
7 3 rd
Conference & Exhibition, EAGE, Extended Abstracts, C025
34. Mukhopadhyay, A., E. Al-Awadi, M.N. Al-Senafy, and P.C. Smith, 1998, Laboratory
investigations of compatibility of the Dammam Formation Aquifer with desalinated
freshwater at a pilot recharge site in Kuwait: Journal of Arid Environments, 40, 27-42
115
35. Mukhopadhyay, A., E. Al-Awadi, R. Osuki, K. Hadi, F. Al-Ruwaih, M. Turner, and A.
Akber, 2004, Laboratory investigations of compatibility of the Kuwait Group aquifer,
Kuwait, with possible injection waters: Journal of Hydrology, 285, 158-176
36. Mukhopadhyay, A., and M. Al-Otaibi, 2002, Numerical Simulation of Freshwater
Storage in the Dammam Formation, Kuwait: The Arabian Journal for Science and
Engineering, 27, #2B, 127-150
37. Olayinka, A.I., and U. Yaramanci, 2000, Use of block inversion in the 2-D interpretation
of apparent resistivity data and its comparison with smooth inversion: Journal of Applied
Geophysics, 45, 63-81
38. Raiche, S., 1983, Comparison of apparent resistivity functions for transient
electromagnetic sounding data: Geophysics, 48, 787-789
39. Santos, F.A.M., 2004, 1-D laterally constrained inversion of EM34 profiling data: Journal
of Applied Geophysics, 56, 123-134
40. Schamper, C., F. Rejiba, and R. Guerin, 2012, 1D single-site and laterally constrained
inversion of multifrequency and multicomponent ground-based electromagnetic
induction data - Application to the investigation of near-surface clayey overburden:
Geophysics, 77, #4, WB19-WB35
41. Simms, J.E., and F.D. Morgan, 1992, Comparison of four least-squares inversion
schemes for studying equivalence in one-dimensional resistivity interpretation:
Geophysics, 57, no. 10, 1282-1293
42. Spies, B.R., and D.E. Eggers, 1986, The use and misuse of apparent resistivity in
electromagnetic methods: Geophysics, 51, 1462-1471
116
43. Telford, W.M., L.P. Geldart and R.E. Sheriff, 1990, Applied Geophysics, 2nd ed.,
Cambridge University Press
44. Uchida, T., 1991, Two-Dimensional Resistivity Inversion for Schlumberger Sounding:
Butsuri-Tansa, 44, #1, 1-17
45. Viswanathan, M.N., M.N. Al Senafy, T. Rashid, E. Al-Awadi, and K. Al-Fahad, 1999,
Improvement of tertiary wastewater quality by soil aquifer treatment: Water Science and
Technology, 40, #7, 159-163
46. Ward, S.H., and G.W. Hohmann, 1987, Electromagnetic Theory for Geophysical
Applications, in M.N. Nabighian, ed., Electromagnetic Methods in Applied Geophysics,
Volume 1, Theory, Society of Exploration Geophysicists
47. Wisdn, R., E. Auken, and T. Dahlin, 2005, Combination of ID laterally constrained
inversion and 2D smooth inversion of resistivity data with a priori data from boreholes:
Near Surface Geophysics, 71-79
48. Youash, Y., 1984, Geology and mineral resources of Kuwait: Proceedings of the
2 7th
International Geological Congress, Non-Metallic Mineral Ores, 15, 31-121
117