![The dense 1977 magnetometer array (dots) relative to regional geology in Namibia [(a), Otjiwarongo study region indicated], and the proposed conductor, determined with the 1972 and 1977 arrays and Schlumberger sounding data (see text), crossing mainly Namibia and Botswana, in relation to a simplified Bouguer anomaly map [(b), the Otjiwarongo and Katima Mulilo study regions are indicated] (van Zijl and de Beer, 1983).](https://www.researchgate.net/profile/Alan-Jones-13/publication/262690120/figure/fig1/AS:613999863402533@1523400383989/The-dense-1977-magnetometer-array-dots-relative-to-regional-geology-in-Namibia-a_Q320.jpg)
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Case History
An audio-magnetotelluric investigation of the Otjiwarongo
and Katima Mulilo regions, Namibia
Pieter-Ewald Share1, Alan G. Jones2, Mark R. Muller2, David T. Khoza3,
Marion P. Miensopust4, and Susan J. Webb5
ABSTRACT
As an additional opportunistic component to the southern
African magnetotelluric experiment, natural-source audio-
magnetotelluric (AMT) data were acquired during phase IV
to investigate the local-scale electric conductivity subsurface
structure in the Otjiwarongo and Katima Mulilo regions
(Namibia) as an aid in locating the installation points for
high-voltage direct current earth electrodes. The study showed
that the shallow subsurface of areas containing one measure-
ment site in the Otjiwarongo region and three sites in the Ka-
tima Mulilo region have appropriate high conductivities for
the optimal placement of the earth electrodes. Both of the
AMT surveys are situated close to the edge of the orogenic
Neo-Proterozoic Damara mobile belt (DMB). Previous studies
all suggest the existence of a highly conductive midcrustal
zone, which correlates well with the spatial location of the
DMB. Two-dimensional inverse modeling of the Otjiwarongo
AMT data confirms the existence of the high-conductive zone
at midcrustal depths (10–15 km). The high conductivity of the
DMB is explained by the presence of interconnected graphite
in the marble units present. The Katima Mulilo inversion re-
sults are characterized by a conductive upper crustal layer that
does not form part of the DMB conductive belt. It was deduced
that at the uppermost subsurface (maximum ∼200 m), Kala-
hari sediments are responsible for the high conductivity ob-
served, whereas at greater depth (up to 6 km), its cause
remains enigmatic, albeit the hypothesis of ironstone or graph-
ite being present and causing the observed conductive upper
crust.
INTRODUCTION
The southern African magnetotelluric experiment (SAMTEX)
was a multinational project initiated in 2003 to study the electric
conductivity subsurface structure of southern Africa by means of
the magnetotelluric method (MT, Cagnaird, 1953;Chave and Jones,
2012), and to infer from it the tectonic processes involved in the
formation of the southern African subcontinent (Figure 1). MT data
were recorded at more than 740 locations covering an area that ex-
ceeds 1,000,000 km2(Jones et al., 2009b). The consortium mem-
bers that formed SAMTEX come from academia, government, and
industry (see the Acknowledgments in Jones et al., 2009b).
SAMTEX data have been used by various researchers in their
scientific endeavors. There has been a comparison of electric
and seismic anisotropy at lithospheric depths by means of analysis
of MT data from SAMTEX and S-wave splitting of teleseismic
Manuscript received by the Editor 30 April 2013; revised manuscript received 15 January 2014; published online 27 May 2014.
1Formerly Dublin Institute for Advanced Studies, School of Cosmic Physics, Dublin, Ireland and University of the Witwatersrand Johannesburg, Schoolof
Geosciences, Johannesburg, South Africa; presently Council for Scientific and Industrial Research, Centre for Mining Innovation, Auckland Park. E-mail:
pshare@csir.co.za.
2Dublin Institute for Advanced Studies, School of Cosmic Physics, Dublin, Ireland. E-mail: alan@cp.dias.ie; mark.muller@dias.ie.
3Formerly Dublin Institute for Advanced Studies, School of Cosmic Physics, Dublin, Ireland; presently Anglo American Technical Solutions and University
of the Witwatersrand Johannesburg, School of Geosciences, Johannesburg, South Africa. E-mail: david.khoza@angloamerican.com.
4Formerly Dublin Institute for Advanced Studies, School of Cosmic Physics, Dublin, Ireland; presently Federal Institute for Geosciences and Natural
Resources, Geozentrum Hannover, Hannover, Germany. E-mail: marion.miensopust@bgr.de.
5University of the Witwatersrand Johannesburg, School of Geosciences, Johannesburg, South Africa. E-mail: susan.webb@wits.ac.za.
© 2014 Society of Exploration Geophysicists. All rights reserved.
B151
GEOPHYSICS, VOL. 79, NO. 4 (JULY-AUGUST 2014); P. B151–B171, 22 FIGS., 2 TABLES.
10.1190/GEO2013-0171.1
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events from a southern African seismic experiment (Hamilton et al.,
2006), leading to a new model explaining the anisotropy observed at
lithospheric depths in the Kaapvaal region. More recently, litho-
spheric 2D conductivity models have been produced for parts of
South Africa, Namibia, and Botswana that indicate variations in
conductivity between the older cratonic regions and younger
surrounding mobile belts (Muller et al., 2009;Evans et al., 2011;
Miensopust et al., 2011;Khoza et al., 2013). Furthermore, the con-
ductivity models were used to make inferences about the thermal,
mechanical, and chemical properties of the geologic terranes (Fullea
et al., 2011) and to provide control on laboratory measurements of
water in olivine (Jones et al., 2012). The correlation between dia-
mond prospectivity and regional resistive/conductive boundaries in
Namibia and South Africa has also been examined with SAMTEX
results (Jones et al., 2009b;2013;Muller et al., 2009).
During phase IV of SAMTEX, in conjunction with deeper prob-
ing of the earth, a study with shallower imaging objectives was
undertaken in northern and northeastern Namibia. Two localized
surveys were undertaken after a new consortium member, ABB
of Sweden for NamPower of Namibia, expressed specific interest
in the shallow subsurface in the regions close to the towns of Otji-
warongo and Katima Mulilo. The conductivity information in the
Otjiwarongo and Katima Mulilo regions is needed for optimal
placement of high-voltage direct current (HVDC) earth electrodes.
Owing to the shallow target depths under investigation, the high-
frequency (typically 10–10,000 Hz) counterpart of MT and the
audio-magnetotelluric (AMT) method were used. An AMT survey
requires a dense spacing of sites to best define the extent of struc-
tures within the shallow subsurface (approximately 5 km). In the
current study, the intersite spacing ranged from 5 to 20 km
(Figures 2and 3), in contrast to the minimum 20 km spacing
for SAMTEX MT sites. AMT data were recorded at a total of
22 locations, of which 13 were situated in the Otjiwarongo region
(Figure 2) and nine in the Katima Mulilo region (Figure 3). To pro-
vide greater depth resolution, broadband-magnetotelluric (BBMT)
data (0.001–100 Hz) were also acquired at six of the 13 locations in
Figure 1. The more than 740 MT sites installed during SAMTEX
plotted on a map of southern Africa’s geologic provinces (after
Nguuri et al., 2001). The two squares indicate the audio-magneto-
telluric arrays installed close to the towns of Otjiwarongo (left) and
Katima Mulilo (right) that are central to the current study.
Figure 2. Locations of the 13 AMT sites installed during SAMTEX
phase IV close to the town of Otjiwarongo, plotted on top of a high-
resolution aeromagnetic map (200-m line spacing) of the area (cour-
tesy of the Ministry of Mines and Energy, Geological Survey
of Namibia). Sites ELG001A, ELG002A, ELG003A, ELG007A,
ELG013A, and ELG014A have collocated BBMT and AMT data.
Figure 3. Locations of the nine AMT sites (site names starting with
ELZ) installed during SAMTEX phase IV close to the town of Ka-
tima Mulilo, plotted on top of a high-resolution aeromagnetic map
(200-m line spacing) of the area (courtesy of the Ministry of Mines
and Energy, Geological Survey of Namibia). Sites ELZ101A,
ELZ102A, ELZ201A, and ELZ204A have collocated BBMT and
AMT data. The other sites shown, CPV027, CPV028, CPV029,
RAK053, and RAK054, are BBMT sites also used in the current
study and were installed prior to, or during, the installation of
the AMT array.
B152 Share et al.
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the Otjiwarongo region, and four of the nine locations in the Katima
Mulilo region.
The aim of the current study is to exploit the data from the two
AMT arrays with existing modeling tools to find the best possible
model of the subsurface conductivity structure for each area, up to
midcrustal depths (20 km). Where available, BBMT data were used
to resolve subsurface conductivity structure to even greater crustal
depths. Modeling of MT data involves processing of the recorded
electric and magnetic time-varying fields and obtaining appropriate
frequency response curves for each site. The calculated responses
are then analyzed for dimensionality and a choice of a 1D, 2D, or
3D inversion approach is made. In the present study, a 2D inversion
approach is justified and deemed appropriate. Subsequently, gal-
vanic distortion of the electric field is removed from the MT re-
sponses and geoelectric strike angles are obtained that best
represent the regions’predominant 2D structural trends. The cor-
rected responses are derived in the obtained strike angles and used
as input to a 2D inversion algorithm (incorporated in the program
WinGLink®) to obtain the subsurface conductivity models. After
robust models (where all structures within the obtained models
are required by the data) with low misfit errors are obtained, the
results, together with models derived from other geophysical data
sets, are correlated with existing geologic data to facilitate in con-
straining interpretation, where the geology is unknown. The con-
ductivity models will also be used in recommending locations
for the placement of the HVDC earth electrodes in the Otjiwarongo
and Katima Mulilo regions.
GEOLOGY OF THE OTJIWARONGO
AND KATIMA MULILO REGIONS
In general, the crust beneath the two studyregions, and, in fact, for
most parts of Namibia andBotswana (Singletary et al., 2003), consists
of Neo-Proterozoic orogenic belts; theDamara belt in the Otjiwarongo
region, andthe Ghanzi-Chobe belt in the Katima Mulilo region. Large
parts of the Damara belt are exposed in Namibia, but the Ghanzi-
Chobe belt, except for a few sparse outcrops, is totally covered by
Phanerozoic sediments. Geophysical data have in the past (Hutchins
and Reeves, 1980) and present (SAMTEX) been used to investigate
structures to crustal depths in the poorly exposed areas, and inferences
about the geology underneath the sedimentary cover have been made.
Through geophysical investigations, and the analysis of available geo-
logic information, the Ghanzi-Chobe and Damara belts have been de-
fined as interconnected (Key and Rundle, 1981) and is currently
collectively termed the Damara mobile belt (DMB, Figure 1).
The DMB separates the composite Kalahari (Jacobs et al., 2008)
and Congo (Begg et al., 2009) cratons in northern Namibia and Bot-
swana, and was deposited during extensive rifting between the two
cratons. Studies suggest initial deposition of Ghanzi-Chobe sedi-
ments (Modie, 2000), followed by later deposition of Damara sedi-
ments 1000–900Ma(Tankard et al., 1982, p. 316) to at least 600 Ma
(Miller, 1983). Apart from deposition, extensional faulting also took
place during rifting between the Kalahari and Congo cratons and the
faults were partly reactivated as thrusts during later continental col-
lision (Miller, 1983). Today, the collisional thrusts manifest them-
selves as lineaments on the surface, and in southern Africa many
observed regional lineaments are shear zones with large displace-
ment (Coward and Daly, 1984). In the Damara belt specifically,
shear zones separate regions of different stratigraphic and structural
evolutions, in which its variability is primarily related to the different
stages of deformation and metamorphism that took place across the
belt (Miller, 1983;Daly, 1986). The four main zones identified in the
Damara belt are the northern zone, central zone, southern zone, and
southern margin zone (Gray et al., 2006). One of the major shear
zones, separating the central and northern zones, is locally termed
the Othohorongo thrust (Miller, 2008,p.13–16, its southwest exten-
sion is called “Autseib Fault”) and is located approximately 15 km
south of the Otjiwarongo study region (Figure 4).
The Damara belt sequence consists of Archaean-Proterozoic base-
ment outcrops, clastic sediments and minor volcanics of the Nosib
group (1000–830 Ma) filling the fault-bounded troughs of rifted
basement (Martin and Porada, 1977), carbonates of the Otavi group
(830–760 Ma) rimming the ocean basins between cratons, turbidites
of the Swakop group (830–760 Ma) within the ocean basins and
foreland basin deposits of the Mulden and Nama groups (approxi-
mately 650 Ma, Gray et al., 2006) (Figure 4). The clastic sediments
and carbonates of the Nosib and Otavi groups can be correlated with
sequences in the Ghanzi group in northern Botswana (Ghanzi-Chobe
belt). The Ghanzi group, together with volcanics of the Kgwebe for-
mation (1100 Ma), which it disconformably overlies (Modie, 2000),
constitute the rifted zone in northern Botswana. The northeast-trend-
ing metasedimentary and metaigneous rocks west of the rifted zone
in Botswana are considered as extensions of the main part of the
Damara belt in Botswana (Singletary et al., 2003). Due to the
300-m-thick sedimentary cover in northern Namibia and Botswana
(Thomas and Shaw, 1990), it is difficult to state the exact basement
composition beneath the Katima Mulilo study region. An extrapo-
lation of geology from maps created using sparse outcrops, borehole
data, and geophysical results in northern Botswana (Figure 5) into
the Caprivi strip (a narrow eastward protrusion of Namibia separat-
ing Angola and Zambia from Botswana) shows the Kwando com-
plex (Mesoproterozoic granite gneiss intrusion) and/or rocks of the
Ghanzi group forming the basement beneath the Katima Mulilo
study region. It is suggested (Catuneanu et al., 2005) that overlying
these basement rocks in the study region are Karoo basin shales,
sandstones, and weathered basalts, which are, in turn, overlain by
the thick Kalahari sedimentary cover.
CRUSTAL ELECTRIC CONDUCTIVITY
Factors controlling conductivity
The extrinsic petrological and physical factors, on which conduc-
tivity is greatly dependant, are more easily explained and distin-
guished when coupled with the three conduction mechanisms
(charge transport processes) present in the earth. The first conduc-
tion mechanism, electronic conduction, is important when highly
conductive minerals (e.g., graphite, iron, or any metallic ore) form
an interconnected or partially interconnected network within the
host rock matrix (Nover, 2005). Another factor that influences con-
ductivity is the presence of partial melt (Nover, 2005), which facil-
itates ionic conduction and generally explains high conductivities
associated with volcanic areas. Its contribution to the total conduc-
tivity is directly related to the amount (melt fraction is dependent on
temperature, Roberts and Tyburczy, 1999) and interconnectivity of
the melts. The third conduction type, electrolytic conduction, domi-
nates in fluid-filled porous rocks and varies with the petrophysical
factors within the rock, namely, the size, orientation, interconnec-
tivity, etc., of the pores and on the chemistry of the fluid and its
interaction with the host rock (Nover, 2005). As with electronic
Audio-magnetotellurics in north Namibia B153
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conduction and the presence of partial melt, the conductivity of
fluid-filled porous rocks also depend on the amount and intercon-
nectivity of the conducting phase (Jones, 1999). When no conduc-
tive phase is present, the final charge transport process, namely
semiconduction, dominates. Semiconduction is most prominent
in the earth’s upper mantle and depends on thermodynamical fac-
tors such as temperature, oxygen fugacity (partial pressure of oxy-
gen), and pressure to a lesser extent (Shankland, 1975;Jones et al.,
2009a;Fullea et al., 2011).
Previous crustal conductivity studies in northern
Namibia and Botswana
The first major investigation of the conductivity of northern
Namibia and Botswana was a magnetovariational study in 1972
(de Beer et al., 1976). The study comprised 25 3C magnetometers
spanning across an area that included central and northern Namibia,
Botswana, and western Zimbabwe. The study resulted in the dis-
covery of a long east–west-trending conductor crossing the survey
area at depth. Characteristically, the magnetovariational method has
poor depth resolution, and the surface outline of the conductor
could only be accurately determined within an error that depends
on the station spacing (50–150 km). Therefore, a second more dense
magnetometer array covering only Namibia with a station spacing
of approximately 60 km was installed in 1977 (de Beer et al., 1982)
(Figure 6a). The greater spatial accuracy showed the conductor in
Namibia to be curved rather than linear (Figure 6b), following the
trend of the central zone of the DMB. Its depth, or more accurately
depth to the anomalous induced currents flowing within it, was de-
termined to be less than 45 km (de Beer et al., 1982). Installation of
the magnetometer array was accompanied by
several DC soundings using a Schlumberger con-
figuration. These soundings inferred the top of
the conductor to vary from 3 to 10 km (de Beer
et al., 1982). In addition, inversions of the
Schlumberger sounding curves inferred that the
resistivity of the conductor was less than
20 Ωm and that of the surrounding upper crust
ranged from 5000 to more than 20,000 Ωm.
In a more recent study, densely spaced (4–
12 km) MT stations were deployed across the
western end of the conductor (Figure7a)byRitter
et al. (2003). Similar to earlier studies, an anoma-
lous highly conductive middle to lower crust (re-
sistivity as low as 5 Ωm) and a resistive upper
crust (5000–15,000 Ωm) were detected (Ritter
et al., 2003)(Figure7b). In addition, the high-
station density led to the discovery of anisotropic
conductivities within, and parallel to, the Water-
berg Fault/Omaruru Lineament (Weckmann et al.,
2003), which is one of the tectonostratigraphic
zone boundaries of the DMB (Figure 7b).
Van Zijl and de Beer (1983) suggest that the
most plausible explanation for the high conduc-
tivity is the presence of serpentinite, thought to
be the only rock that could develop the necessary
high conductivity at midcrustal temperatures.
Early experiments suggested that serpentine
was conducting as a consequence of bound water
(Stesky and Brace, 1973), but Olhoeft (1981)
demonstrates that those results were in error,
and the most recent ones show serpentine not in-
trinsically to be conducting (Reynard et al.,
2011). There is, though, a highly conductive min-
eral associated with the process, namely, magne-
tite, and, if distributed appropriately on well-
connected grain boundaries, it can drastically in-
crease the conductivity of a rock (Pakhomenko
et al., 1973). The process of serpentinization re-
quires a large amount of water and van Zijl and
de Beer (1983) admit explaining the origin of it
during DMB formation, either originating from
the mantle or being introduced by subduction, re-
mains the only problem with the serpentinite
Figure 4. Locations of the 13 AMT sites installed in the Otjiwarongo region, plotted on
top of a geologic map of the area (courtesy of the Ministry of Mines and Energy, Geo-
logical Survey of Namibia). The solid line in the southeastern corner of the map depicts
the Othohorongo thrust.
B154 Share et al.
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model. Recent advances in understanding conductive anomalies at
crustal depths point to the greater presence of fluids, fault gouge, sul-
fides, or graphite in shear zones as a more plausible explanation for
the conductor (Ritter et al., 1999). Graphite-bearing marble units are
widespread in the stratigraphy forming part of the conductor and Rit-
ter et al. (2003) state that it is the most plausible cause of the high
conductivity observed. Also, motion along shear planes is the ideal
mechanism to ensure an interconnected network of conductive graph-
ite over large distances.
DATA ANALYSIS AND INVERSION
AMT and collocated BBMT data
Programs included in the Phoenix Geophysics® software pack-
age were used for most of the data processing in the current study.
The program SSMT2000 was used to precondition the time-series
data, convert it from the time domain to frequency domain and cal-
culate impedance estimates. Impedances were estimated using the
stacking cascade decimation scheme incorporated into SSMT2000,
which is identical to method four in Jones et al. (1989). In most
cases, recording took place at a local site with at least one remote
reference site recording simultaneously (see Gamble et al., 1979, for
the remote referencing method). In all cases, where data from a re-
mote site were available the remote magnetic fields were used in the
impedance estimation of the local site, and where more than one
remote site recorded simultaneously, multiple impedance estimates
were obtained using data from each remote site. For logistical rea-
sons, two AMT sites in the Otjiwarongo region, ELG002A and
ELG004B, had no remote sites and were sub-
sequently processed locally using their respective
local magnetic fields.
The program MTeditor (also part of the Phoe-
nix Geophysics package) was used to evaluate
the calculated impedances and response curves.
During evaluation, the remote-reference imped-
ance estimate that was smoothest and contains
the least amount of noise (if more than one esti-
mate was available) was selected and outliers
from the set of impedance estimates (calculated
from the set of time sections) at each frequency
were removed. At all sites, editing produced
smoother, less noisy, and thus more reliable re-
sponse curves. The one consistent poorly esti-
mated frequency range that could also not be
improved with editing was the AMT dead band
(Garcia and Jones, 2002). After obtaining satis-
factory response curves from all data at the loca-
tion, the AMT responses with collocated BBMT
data were merged (merged sites are hereinafter
indicated by the letter m after the site name)
and, together with the sites where either only
AMT or only BBMT data were acquired, rotated
from magnetic to true north.
Galvanic distortion removal and
geoelectric strike analysis
Galvanic distortion is defined (Groom and
Bahr, 1992;Utada and Munekane, 2000) as all
the effects that charges accumulating on the surface of small (in
an inductive sense) 3D heterogeneities, normally located close to
the surface, have on the electromagnetic (EM) fields induced in
larger background regional structures. In the present study, the re-
moval of galvanic distortion and determination of geoelectric strike
is done simultaneously, using an extended form of the classical
Groom-Bailey decomposition (Groom and Bailey, 1989) developed
by McNeice and Jones (2001), which is suited for multisite, multi-
frequency analysis. With the multisite, multifrequency analysis a
global minimum misfit solution is sought to produce a geoelectric
strike direction and galvanic distortion parameters for a range of
frequencies and set of sites. Excluded in the determined galvanic
distortion parameters is any frequency-independent scaling, other-
wise known as static shifting, present in the impedance estimates.
The code used in the current study for strike analysis that incorpo-
rates the extended form of the Groom-Bailey decomposition, is
hereinafter referred to as strike.
First, to obtain an understanding of the dimensionality of subsur-
face conductivity structure in the Otjiwarongo and Katima Mulilo
regions, the program strike was used to calculate a geoelectric strike
angle for each site over all available frequencies (Figure 8a and 8b).
In all calculations, an error floor of 3.5%, which corresponds to
approximately 2° in phase and 7% in apparent resistivity, of the ab-
solute value of the largest impedance was assigned to the calculated
impedances. The program derives a strike angle that, together with
the calculated distortion parameters, form part of a Groom-Bailey
model (GB-model) that has the lowest possible misfit (GB-error)
with the data. Given the assigned error floor, a GB-error of two
or lower is defined as adequate for a calculated GB-model to
Figure 5. Subsurface Precambrian geology of Botswana, modified from Singletary et al.
(2003), showing the probable extensions of Kwando complex and Ghanzi group rocks
into the Caprivi strip (Namibia) and forming the basement beneath the Katima Mulilo
study region (indicated by the square).
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describe a measured data set; i.e., 95% of the model values lie
within 2σof the data estimates. A GB-error greater than two indi-
cates (beside noisy data) that distortion is severe and/or the regional
conductivity structure is 3D, and/or that the calculated errors are far
too small. This is often a problem with parametric error estimates,
especially when there are large numbers of estimates, because the
assumption that each estimate is independent from all others and
introduces new information is incorrect. Chave and Jones (1997)
show that jackknife error estimates, which make no assumptions
whatsoever about error distribution, are factors of 3–5 larger than
parametric error estimates when there are large numbers of data.
Inherent to the MT method is a 90° ambiguity in the determina-
tion of strike that is resolved with external information such as geol-
ogy and other geophysical data. In the Otjiwarongo region, the
calculated strike angles were rotated, if needed, by 90° to align
as best possible with structural trends in geology (Figure 4) and
regional magnetic data (Figure 2). Due to thick sedimentary cover
in the Katima Mulilo region, no structural information was avail-
able, and regional magnetic data were used to remove the ambiguity
in strike determination (Figure 3).
Most of the GB-errors associated with the single site strike analy-
sis in the Otjiwarongo region are at or below two; therefore, the
assumption of a 2D regional structure for each individual site is
valid (Figure 8a). In the Katima Mulilo region, all the GB-errors
associated with the single site strike analysis are also at or below
two (Figure 8b), thus, the 2D assumption is also valid. In addition,
because many sites have small average phase differences between
the transverse electric (TE, horizontal electric field is polarized, and
currents flow, parallel to dominant strike) and transverse magnetic
(TM, horizontal magnetic field is polarized parallel to dominant
strike and current flows 90° to it) modes (Figure 8b), a 1D inversion
can even provide a good approximation of the regional conductivity
structure.
To further investigate the conductivity substructure of, first, the
Otjiwarongo region, and in an effort to find a single strike angle that
fits the Otjiwarongo data, the data were rotated to user-defined
strike directions in increments of 10°, with the aim of observing
changes in GB-errors with rotation. The interesting result was that
for all rotations the GB-errors at each individual site remained ap-
proximately equal (Figure 9shows the constant GB-errors for 0°,
20°, 40°, 60°, and 80°). GB-errors calculated for the rotation of site
ELG005s data from 0° to 90° showed the largest variation, with a
standard deviation of 0.43. At all the other sites, a standard devia-
tion of 0.26 or lower was derived. It was concluded that the small
change in errors indicate that each site contains, for most of the
available frequencies, data with associated GB-errors that remain
largely unchanged by rotation (approximately 1D). The problem
of finding a strike angle for the Otjiwarongo region is now reduced
Figure 6. The dense 1977 magnetometer array (dots) relative to
regional geology in Namibia [(a), Otjiwarongo study region indi-
cated], and the proposed conductor, determined with the 1972
and 1977 arrays and Schlumberger sounding data (see text), cross-
ing mainly Namibia and Botswana, in relation to a simplified Bou-
guer anomaly map [(b), the Otjiwarongo and Katima Mulilo study
regions are indicated] (van Zijl and de Beer, 1983).
Figure 7. (a) The DMB sandwiched between the Kalahari and
Congo cratons in Namibia and the 1998–1999 MT profile (x–y,Rit-
ter et al., 2003) crossing the conductive belt. Post-Karoo alkaline
igneous complexes are indicated in dark gray, and (b) 2D MT in-
version results showing the highly conductive middle crust in the
central part of the profile and the resistive upper crust. AF denotes
the Autseib Fault and WF/OL denotes the Waterberg Fault/Omaruru
Lineament (Ritter et al., 2003).
B156 Share et al.
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to identifying the frequencies at each site that have higher dimen-
sional characteristics and calculating an average strike angle using
only the identified higher dimensional data.
In the Otjiwarongo region, data from each site were analyzed de-
cade-by-decade, by assigning strike angles from 0° to 90° to each
decade independently and observing the associated change in GB-
errors with the changes in angle. Only the decades characterized by
GB-errors that remain greater than two for most angles and then
drop below the tolerance level of two within some angle range were
selected for further strike analysis. In total, 62 frequency decades
from the 13 Otjiwarongo sites were analyzed and only nine decades
from eight sites passed the criterion for higher dimensionality. Due
to the consistently poor impedance estimates in the AMT dead
band, the decade 10,000–1000 Hz was not considered for further
analysis, even if it appeared to have 2D characteristics. The eight
sites, their frequency decades that were determined to be higher di-
mensional, and the strike angles computed using strike are listed in
Table 1and depicted graphically in Figure 10a. Only one frequency
decade (100–10 Hz, ELG002m in Table 1) has a GB-error greater
than two. Thus, as before, it can be concluded that the data predomi-
nantly sense 1D and 2D subsurface structures and the continued
analyses of data using 2D modeling tools is justified. After exam-
ining the eight groups of frequencies, it was determined that there
exists no overlapping frequency or Niblett-Bostick depth (NB-
depth, Niblett and Sayn-Wittgenstein, 1960;Bostick, 1977;Jones,
1983a) range among them. Subsequently, strike could not be used,
in multisite mode, to compute a common strike angle for the eight
sites. Consequently, a single strike angle was obtained by calculat-
ing a simple arithmetic average of the eight strike estimates. Aver-
aging the eight strike angles computed produced a value of 82°, and
the corresponding average GB-error for all 13 Otjiwarongo sites in
the resultant strike direction was 1.86.
The single site strike analysis of the Katima Mulilo data demon-
strated that there is a high degree of one-dimensionality in the re-
gion. Therefore, upon rotation of the data, the consistency in GB-
errors, similar to the Otjiwarongo data, was expected. Subsequently,
the same decade-for-decade analysis applied in the Otjiwarongo re-
gion was used to analyze the Katima Mulilo data to extract minor
parts of higher dimensional data from the predominantly 1D data. In
total, 65 frequency decades (from 14 Katima Mulilo sites) were an-
alyzed and only 12 from seven sites passed the criterion for higher
dimensionality. The seven sites, their frequency decades that were
determined to be higher dimensional, and the strike angles com-
puted using strike, are listed in Table 1and depicted graphically
in Figure 10b. At all but one of the sites a GB-error less than
two is achieved (ELZ102m, Table 1). Again, no common frequency
or NB-depth range could be established and an arithmetic average
of the seven values was calculated to obtain a representative strike
angle for the Katima Mulilo region. The resultant average was 54°,
and the corresponding average GB-error for all 14 Katima Mulilo
sites in the resultant strike direction was 1.12.
2D inversions of Otjiwarongo and Katima Mulilo data
In the current study, all 2D conductivity models were derived
from inversions of the Otjiwarongo and Katima Mulilo data using
the algorithm by Rodi and Mackie (2001), as implemented in the
WinGLink software package. The algorithm minimizes a function
that includes a data misfit and a regularization term, usually taken to
be a smoothing term. In WinGLink, the main user-definable vari-
able, which controls the amount of regularization (smoothing), is
denoted by τ. In addition, the regularization can be alternated be-
tween minimization of the Laplacian and minimization of the gra-
dient of the model. It is also possible to specify either a uniform grid
or standard grid Laplacian regularization to be applied on the cre-
ated meshes.
In the Otjiwarongo and Katima Mulilo regions, the acquisition of
data in a semiarray format lead to 2D inversion profiles (orientated
perpendicularly to obtained strike angles) being placed in regions
where the site density was highest. The Otjiwarongo sites nearest to
the chosen profile, and included in the inversion process, were
ELG007m, ELG005, ELG004, ELG002m, ELG012, ELG009,
ELG001m, and ELG008 (Figure 11a). The sites included in the Ka-
tima Mulilo 2D inversion were RAK054, ELZ294, RAK053,
ELZ102m, CPV029, ELZ002, ELZ555, and ELZ001 (Figure 11b).
In both cases, if two sites, after projection took place, located at the
Figure 8. Strike angles computed for each individual MT site in the
(a) Otjiwarongo (Otji. denotes Otjiwarongo) and (b) Katima Mulilo
regions (Kat. denotes Katima Mulilo) over all the available frequen-
cies. The colors of the boxes indicate the GB-errors (root mean
square —rms) for each calculation of strike and the arrow lengths
depict the phase differences between TE and TM modes at each site.
The northeast-trending line is a prominent intra-DMB magnetic fea-
ture and represents the dominant structural trend in the area.
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same point on the profile then the farthest one from the profile was
excluded during inversion.
For the construction of meshes for the two inversions the follow-
ing general guidelines were followed:
1) The first horizontal gridline was placed approximately half the
smallest EM skin depth of all the sites from the surface. A hori-
zontal line represented the surface, as no significant elevation
changes were observed in either the Otjiwarongo or Katima
Mulilo area.
2) In accordance with the loss in resolution with increasing depth
as EM energy diffuses into the earth, each successive horizontal
gridline was separated from the previous one by a distance that
gradually increased with depth.
3) The array format of sites meant that intersite spacing was irregu-
lar after projection of sites onto a profile. Subsequently, the den-
sity of vertical gridlines was made highest around site locations
(on the profile) and less dense in between, and away from, sites,
in accordance with the fact that resolution decreases laterally
away from an observation point with decreasing frequency.
4) All horizontal and vertical gridlines assigned to a 2D plane were
done such that the aspect ratios (length-to-width ratio) of the
rectangular cells remained reasonable. A reasonable aspect ra-
tio, in this case, is one that is not less than 0.025 and not greater
than 40.
For all inversions, uniform 100 Ωm half-spaces were used as
starting models. Also, minimization of the Laplacian (default op-
tion) was selected because, although minimizing the gradient pro-
duces a smoother model, the same smoothness can be obtained by
selecting the default option and varying the other regularization
parameters. A regularization trade-off curve (Hansen, 1992), which
is optimally L-shaped, was used to obtain the most appropriate
smoothing operator τfor each set of inversions. Similar approaches
have been used in seismology (Boschi et al., 2006) and MT (Schwa-
lenberg et al., 2002). Trade-off curves were constructed for the Ot-
jiwarongo and Katima Mulilo data by gradually decreasing τfrom
100 to 1, running a smooth 2D inversion for each of the τvalues,
and plotting the resultant rms errors versus τvalues. TE and TM
modes were inverted for, and, by assigning much larger error floors
to the apparent resistivities than the phases, emphasis on fit was
placed predominantly on phase (phase values are not affected by
static shifts). Uniform grid and standard grid Laplacian options,
with the default αand βselected, were used to construct the
trade-off curves. As an example, the curve for
the uniform grid Laplacian inversions of the Ot-
jiwarongo data is shown in Figure 12, and the
point (τ¼20) indicative of the optimal regulari-
zation value for these inversions is highlighted.
Similarly, after analyses of the remaining curves,
aτvalue of seven was selected for all subsequent
standard grid Laplacian inversions of the Otji-
warongo data, and a τvalue of 10 was used
for all inversions of the Katima Mulilo data.
The optimal αand βvalues to use in the stan-
dard grid Laplacian inversions of the two data
sets were selected by noting how the rms errors
of inversions varied as different pairs of weight-
ing parameters were used, and selecting the pair
that gave the smallest rms error (Table 2). TE and
TM modes (with equal error floors) as well as
apparent resistivities and phases were inverted
for. During inversions to determine the appropri-
ate αand βvalues, and all inversions mentioned
henceforth, phase data are inverted for first, by,
as before, assigning larger error floors to the ap-
parent resistivity estimates than the phase data.
Thus, the effect of static shifts on initial inver-
sions is effectively zero. During succeeding
inversion runs, the apparent resistivity error
floors are lowered, and the initial models are
modified by the additional constraint of requiring
a minimal misfit to the apparent resistivity data as
well. As the apparent resistivity error floors are
lowered, the option to invert for static shifts is
selected (zero summation of the natural loga-
rithm of all computed static shift factors is re-
quired at each iteration, de Groot-Hedlin,
1991). Such a sequence of inversions, results
in models that are least biased by static shifts.
For both standard grid Laplacian inversions of
the Otjiwarongo and Katima Mulilo data αand
Figure 9. GB-errors (rms) and phase differences computed after assigning strike angles
of 0°, 20°, 40°, 60°, and 80° to data from the Otjiwarongo region.
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βvalues of one and three, respectively, produced the lowest rms
errors and were subsequently used in all further standard grid Lap-
lacian inversions (Table 2). Owing to the equal weighting assigned
to all cells when using uniform grid Laplacian regularization, αand
βvalues were kept at the default values of one and one, respectively,
and Hand Vremained 0 and 0 m, respectively.
To observe the unique information given by the TE and TM
modes in the Otjiwarongo and Katima Mulilo regions, respectively,
the two modes were initially independently inverted (Figures 13 and
14). The variations in penetration depths for each mode were also
calculated (Figures 13 and 14). In each case, the error floors as-
signed to the apparent resistivities and phases of the two modes
were 8% and 3%, respectively, and static shifts were inverted
for. Earlier studies indicated that the TM mode is generally more
robust to the effects of surficial 3D bodies than the TE mode (Jones,
1983b;Wannamaker et al., 1984). More recent studies show that the
greater robustness of the TM mode mostly applies to conductive 3D
features (Berdichevsky, 1999). In addition, Berdichevsky (1999)
also points out that for resistive 3D features both modes are equally
robust, whereas in some geologic models, such as a 3D resistive
horst, it is even possible that the TE mode is the more robust
component.
The standard grid Laplacian inversions of the Otjiwarongo data
gave much larger rms errors fitting the TE mode responses rather
than the TM mode ones (Figure 13). It is, therefore, concluded that
the TE mode is more affected by surface 3D features, and in par-
ticular conductive 3D features. In contrast, the uniform grid Lap-
lacian inversion of the TM mode responses gives a larger rms
error than the TE mode inversion (Figure 13). The smoothness
constraints placed on the inversion using uniform grid Laplacian
regularization counteracts the unique information provided by
the TM mode, thus the higher TM rms error is ascribed to regulari-
zation. The equal TE and TM rms errors of the standard grid Lap-
lacian inversions of the Katima Mulilo data (Figure 14) show that
either the modes are unaffected by 3D features or both are affected
by, and are equally robust to, resistive 3D features present. Again,
selecting uniform grid Laplacian regularization resulted in the TM
mode inversion of the Katima Mulilo data having a higher rms error
than the TE mode inversion (Figure 14). It should also be noted that
structures appearing below the penetration depth of each site (NB-
depths in Figures 13 and 14) are not sensed by the data and are, in
fact, regularization effects and were subsequently removed from
further models (Figure 15 onwards).
During joint inversion of the TE and TM modes of the Otjiwar-
ongo data, and using standard grid Laplacian regularization, error
floors of 10% and 5% as well as 8% and 3% were selected for the
TE apparent resistivities and phases and TM apparent resistivities
Table 1. The eight selected Otjiwarongo and seven selected
Katima Mulilo sites (see text), their frequency decades
determined to be higher dimensional, the strike angles
computed for the identified decades and the GB-errors (rms)
associated with each computation.
Frequencies (Hz) Strike (°) GB-error
Otjiwarongo sites
ELG001m 1–0.1 80.02 0.89
ELG002m 100–10 43.66 2.57
ELG003 10–1 53.14 1.64
ELG005 10–1 75.77 0.71
ELG007m 10–1 73.49 0.44
ELG009 10–1 94.77 0.88
ELG013m 100–10 109.42 0.54
ELG014m 10–0.1 93.32 1.44
Katima Mulilo sites
CPV028 1–0.001 57.51 1.92
ELZ101m 1–0.1 54.87 1.50
ELZ102m 1–0.01 48.69 2.53
ELZ201m 1–0.1 92.57 1.10
ELZ294 0.1–0.01 57.81 0.34
RAK053 0.1–0.001 51.45 1.47
RAK054 1–0.01 54.72 0.35
Figure 10. Strike angles (arrow directions in boxes), GB-errors
(rms, box colors), and phase differences (arrow lengths in boxes)
for the eight Otjiwarongo (a) and seven Katima Mulilo (b) sites,
which passed the higher dimensional criterion, computed over
the limited number of frequencies that have higher dimensional
characteristics. The frequency ranges of each site are indicated
as well (e.g., 1–0.1 means 1–0.1 Hz).
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and phases, respectively (Figure 15). The selection of larger TE
mode error floors ensures the preferential minimization of misfit
between model and TM mode data, which are less sensitive to
3D surficial structures, during each iteration. To improve the rms
error of the joint TE and TM mode inversion, when using uniform
grid Laplacian regularization, error floors of 8% and 3% as well as
10% and 5% were assigned to the TE apparent resistivities and
phases and TM apparent resistivities and phases, respectively
(Figure 15). Using the same error floors, a uniform grid Laplacian
inversion with τset to seven was also completed with the purpose of
comparing standard grid and uniform grid Laplacian joint inver-
sions of the Otjiwarongo data where equal smoothing factors are
used (Figure 15). The equal rms errors of the individual TE and
TM mode standard grid Laplacian inversions (Figure 14) of the
Katima Mulilo data resulted in the apparent resistivities and phases
of both the modes being assigned equal error floors of 8% and
3%, respectively, during joint inversion (Figure 16). Error floors
of 8% and 3% as well as 10% and 5% were assigned to the
TE and TM apparent resistivities and phases, respectively, of the
Katima Mulilo data during joint uniform grid Laplacian inversion
(Figure 16). For all inversions, except for the standard grid Lapla-
cian inversion of the Katima Mulilo data, the order in which the TE
and TM components were added to the inversion that resulted in the
lowest possible rms was TE phase, TM phase, TE apparent resis-
tivity, and TM apparent resistivity; for the standard grid Katima
Mulilo inversion the TM phases were added before TE phases.
Therefore, phase first inversions, and the inversion for static shift
when the apparent resistivity data are added, simultaneously give
the lowest rms errors and guarantee models that are least biased
by static shifting.
Figure 11. Two-dimensional inversion profiles created perpendicular
to the 82° and 54° average strike directions in the Otjiwarongo (a)
and Katima Mulilo (b) regions, respectively. The eight sites in-
cluded in the 2D inversion of each region are indicated.
Figure 12. Regularization trade-off curve (plot of rms misfit versus
log [τ]) for the uniform grid Laplacian inversions of the Otjiwar-
ongo data. The optimal τvalue of 20 is indicated.
Table 2. The rms errors for inversions of the Otjiwarongo
and Katima Mulilo data using standard grid Laplacian
regularization and varying weighting parameters αand β.
The Hand Vwere both kept at the default value of 500 m.
The absence of entries for some Katima Mulilo inversions
indicates that there was no convergence of the inversion
algorithm for the αand βvalues shown.
β¼1β¼2β¼3
Otjiwarongo
4.10 3.39 2.96 α¼1
4.36 3.69 3.55 α¼2
4.81 3.84 3.57 α¼3
Katima Mulilo
4.99 3.76 2.52 α¼1
4.74 ––α¼2
–––α¼3
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SENSITIVITY TESTING
A comparison of the two uniform grid Laplacian inversions with
τ¼20 (Figure 15b) and τ¼7(Figure 15c) shows that in general
the same conductive and resistive structures are present, but that the
resistivities of the structures differ between models. Owing to the
stated similarities and to better compare uniform and standard grid
Laplacian inversions of the Otjiwarongo data, where model
differences are not due to different τ-values, the uniform grid Lap-
lacian inversion with τ¼7is used in further analysis. A site-for-site
misfit comparison between the two Otjiwarongo inversions in
Figure 13. Standard grid (top) and uniform grid (bottom) Laplacian inversions for the individual TM (left) and TE (right) modes of the
Otjiwarongo data. The standard grid Laplacian weighting factors were α¼1,β¼3,H¼500 m, and V¼500 m and the uniform grid
Laplacian weighting factors were; α¼1,β¼1,H¼0m, and V¼0m. Also shown are the NB-depth estimates for the TE and TM modes.
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Figure 15a and 15c shows that sites ELG012, ELG009, and
ELG001m have large misfits, where large in this instance is defined
as a misfit that is greater than the average rms error of the entire
model, for the standard grid and uniform grid Laplacian inversions.
Site ELG009 contains poor data estimates at several frequencies,
explaining why it has the largest misfit, whereas the data from
sites ELG001m and ELG012 probably still suffer from the effects
of surficial conductive 3D structures. Interestingly, in terms of
Figure 14. Standard grid (top) and uniform grid (bottom) Laplacian inversions for the individual TM (left) and TE (right) modes of the Katima
Mulilo data. The standard grid Laplacian weighting factors were; α¼1,β¼3,H¼500 m, and V¼500 m and the uniform grid Laplacian
weighting factors were; α¼1,β¼1,H¼0m, and V¼0m. Also shown are the NB-depth estimates for the TE and TM modes.
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conductivity structure, the two models differ the most around sites
ELG004 and ELG002m, which correlates well with site ELG004
having a large rms error in Figure 15a and a small error in Fig-
ure 15c, whereas the opposite applies for site ELG002m. The model
differences, and subsequent differences in rms
misfit, owe their origin to the standard grid
and uniform grid Laplacian operators attempting
to fit data that are biased by random noise
(ELG002A and ELG004B had no remote sites
and were locally processed) differently. This fact
is also clear in the large discrepancy between the
inverted static shift factors of, for example, site
ELG004 (standard grid TM‐SS ¼8.39 and
TE‐SS ¼2.41 versus uniform grid TM‐SS ¼
3.41 and TE‐SS ¼1.08, Figure 15). Due to it
being smoother (minimizing the risk of over in-
terpreting a model) and fitting the data better
(rms of 2.19 compared with 2.49), the uniform
grid Laplacian inversion model with τ¼7was
selected for further analysis instead of the stan-
dard grid Laplacian inversion model.
The chosen Otjiwarongo model has several in-
teresting features, but there are two prominent
ones to highlight. The first is a highly resistive
upper crustal structure reaching a maximum
depth of approximately 8 km between sites
ELG012 and ELG009 that is interrupted by more
conductive material beneath sites ELG005 and
ELG004 (Figure 15). The second is a highly con-
ductive midcrustal conductor that appears to be
connected with the conductive material interrupt-
ing the shallow-resistive layer (Figure 15).
The robustness of the midcrustal conductor
was tested first by replacing all resistivities in-
cluded in the conductive region with 100 Ωm,
running the inversion again (with the same regu-
larization settings), and noting whether the con-
ductor reappeared. The conductor did reappear
and was similar in location and appearance to
the original one and the inversion produced
the same rms error (Figure 17). Second, the ro-
bustness of the conductor was tested by replacing
all resistivities included in the conductive region
by 100 Ωm, locking the altered cells, running
the inversion again and forcing other parts of
the model to change to try to produce the same
rms error. The resultant inversion showed that
there were no changes that could be made to
the variable parts of the model to produce the pre-
vious rms error of 2.19, and instead a larger rms
error of 4.55 was obtained (Figure 17). As was
intuitively expected, sites ELG005, ELG004, and
ELG002m contributed most to the increased
average misfit, where their rms errors increased
to 6.65, 5.10, and 6.72, respectively, compared
with the errors in Figure 15c. The same two
robustness tests were applied on the shallow-
resistive layer with similar results. When the re-
sistor was removed, it reappeared unaltered after
inversion (rms error of 2.24), and when it was removed and the al-
tered cells locked, no major changes were observed after inversion
for the rest of the model, while the rms error increased to 14.71
(misfit for all sites increased to larger than 10).
Figure 15. Standard grid (a) and uniform grid (b and c) Laplacian joint inversions of the
TM and TE modes of the Otjiwarongo data. The standard grid Laplacian weighting
factors were α¼1,β¼3,H¼500 m,V¼500 m, and τ¼7. The uniform grid Lap-
lacian weighting factors were; α¼1,β¼1,H¼0m,V¼0m,τ¼20, and τ¼7for
the middle and bottom results, respectively. Static shift inversion results for the TE (TE-
SS) and TM (TM-SS) modes and individual rms errors for each of the eight sites are
shown. Also shown are the NB-depth estimates for the TE and TM modes.
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NB-depth estimates for the Otjiwarongo sites (Figure 15c)
showed that deep structure has been added by regularization that
is not required by the data. To emphasize the role of regularization,
most of the midcrustal conductor was removed and still, after for-
ward modeling, the rms error of the altered model remained 2.19
(Figure 18, left). In view of the fact that with MT the base of a
conductor is not well resolved, and because of regularization, an
attempt was made to reduce the effects of regularization by locking
parts of the conductor that the data are sensitive to, and running
the inversion again (Figure 18). The resultant inversion model
(Figure 18, right) required less structure to be added to the conduc-
tor and its base is shallower than in the original model (Figure 15),
and subsequently it was used in further analysis.
The uniform grid Laplacian inversion of the Katima Mulilo data
is smoother and has a smaller rms error than the standard grid Lap-
lacian inversion (Figure 16), and was, therefore, selected for further
analysis. The most prominent feature in the chosen model is a shal-
low-conductive layer that is detected by all sites and reaches a maxi-
mum depth of approximately 6 km (Figure 16).
The robustness of the shallow-conductive layer
was tested, in a similar manner to the Otjiwar-
ongo conductor, by first replacing all resistivities
in the shallow subsurface with 100 Ωm, running
the inversion again (with the same regularization
settings) and seeing if the conductive layer reap-
peared. The conductive layer did reappear and
was identical to the original and the rms error re-
mained the same (Figure 19). Second, the shal-
low subsurface was given a value of 100 Ωm, the
altered cells were locked, and the inversion was
restarted. The second test result shows that
although subtle changes were made to the rest
of the model, the original rms error of 1.08 could
not be achieved, and instead, the rms error in-
creased to 15.03 (Figure 19). All sites contrib-
uted to the increased average misfit, with site
ELZ102m (rms ¼8.30) being the only site with
an increased error less than 10.
The NB-depths of the TE and TM modes of
the Katima Mulilo data (Figure 16) indicate that
there is much greater depth sensitivity when
compared with the Otjiwarongo data (Figure 15).
However, because the spacing between some
sites is large compared with the depth of the
conductive layer, parts of the layer can still be
removed keeping the rms error the same (Fig-
ure 20, left). To quantify the effects of regulari-
zation on the thickness and depth of the layer,
only the parts of the model that the data are sen-
sitive to were locked, similar to the Otjiwarongo
conductor, and the inversion was run again
(Figure 20). Unlike the Otjiwarongo inversion,
the inversion result after locking the appropriate
parts of the Katima Mulilo conductive layer was
not different from the original inversion (com-
pare Figures 16 and 20, right).
DISCUSSION
Placement of earth electrodes
The successful placement of an HVDC earth
electrode depends on the conductivity of rock
volumes near the surface and in close proximity
to the electrode (Thunehed et al., 2007;J.H.de
Beer, personal communication, 2009). There-
fore, thorough evaluations of conductivity varia-
tions in the shallow subsurface associated with
the Otjiwarongo and Katima Mulilo regions,
Figure 16. Standard grid (a) and uniform grid (b) Laplacian joint inversions of the TM
and TE modes of the Katima Mulilo data. The standard grid Laplacian weighting factors
were α¼1,β¼3,H¼500 m,V¼500 m, and τ¼10. The uniform grid Laplacian
weighting factors were α¼1,β¼1,H¼0m,V¼0m, and τ¼10. Static shift in-
version results for the TE (TE-SS) and TM (TM-SS) modes and individual rms errors for
each of the eight sites are shown. Also shown are the NB-depth estimates for the TE and
TM modes.
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especially where AMT data are available, need to be completed
before a decision on electrode placement is made.
It is clear from the two Otjiwarongo inversions (Figure 15),
which are in agreement, that of all sites included in the inversions,
the shallow subsurface is most conductive below sites ELG005 and
ELG004. Despite similar structures surrounding sites ELG005 and
ELG004 in the two models, the uniform grid Laplacian inversion is
used for further testing because although in the standard grid
Figure 17. Sensitivity tests done on the Otjiwarongo inversion by first removing the midcrustal conductor, leaving all cells free to vary, and
inverting again (top); and second, removing the conductor, leaving only cells outside the conductive region free, and inverting again (bottom).
Figure 18. Locking only the parts of the midcrustal conductor that the Otjiwarongo data are sensitive to, and the inversion result with the
appropriate cells locked (right).
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Laplacian model greater emphasis is placed on resolving shallow
structures, and the TM mode responses (providing information
about conductivity boundaries) are not weighted down during in-
version, sites ELG005 and ELG004 also have higher misfits (com-
pared with neighboring sites) in the latter model. The robustness of
the high conductivity beneath sites ELG005 and ELG004 in
Figure 15c was tested by assigning 5000 Ωm resistivities to all cells
greater than 5 km depth and running the inversion again (using the
same inversion settings) (Figure 21a). The resulting model shows
that across the profile the conductivity remains the highest beneath
sites ELG005 and ELG004 (Figure 21a).
According to the currently available geologic information in the
Otjiwarongo region, site ELG004 is situated on an undifferentiated
Damara sequence (NDA in Figure 4), whereas site ELG005 is lo-
cated on Nosib group rocks, consisting of quartzite, arkose with
conglomerate, and ironstone (NNS in Figure 4). It is unclear what
the cause of the high conductivity beneath site ELG004 is, whereas
prior studies have determined that the several dome structures
Figure 19. Sensitivity tests done on the Katima Mulilo inversion by first removing the shallow-conductive layer, leaving all cells free to vary,
and inverting again (top); and second, removing the conductive layer, leaving only cells below the layer free to vary, and inverting again
(bottom).
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located southwest of Otjiwarongo, and underlying site ELG005,
carry in excess of 4% graphite (Miller, 2008,p.13–31). Therefore,
site ELG005, rather than site ELG004, is proposed as an optimal
location to place the HVDC earth electrode in the Otjiwarongo
region.
Similar to the Otjiwarongo region, the robustness of all conduc-
tive structures present in the Katima Mulilo uniform grid inversion
model was tested by substituting all resistivities in the shallow sub-
surface (up to 1 km) with a thin 5000-Ωm layer and inverting again
(using the same inversion settings) (Figure 21b). The resulting in-
version model is similar to the original and both show that beneath
sites RAK054, ELZ294, RAK053, ELZ102m, and CPV029 the
conductivity is highest (Figure 21b).
Owing to the lack of detailed geologic information in the Katima
Mulilo region, attributed to the vast Kalahari sediment cover
(Moore and Larkin, 2001;Singletary et al., 2003), geology cannot
be used to facilitate the choice of an appropriate electrode location.
A choice based solely on the conductivity information gathered
from the MT data must be made. Due to the approximate 1D behav-
ior of data in the AMT frequency range (Figure 8b), 1D inversion
tools can be used to observe conductivity variations with depth be-
low each site. The 1D behavior is especially prevalent in the upper-
most subsurfaces (only low frequencies in Table 1show higher
dimensional characteristics), which correlates well with the ex-
pected layered sedimentary environment (Kalahari sediments and
Karoo sediments and basalts). Subsequently, NB resistivities (Ni-
blett and Sayn-Wittgenstein, 1960;Bostick, 1977) were computed
for the AMT sites at depths of 100, 200, 500, 900, and 1000 m
(Figure 22). The 1D inversion results show that the conductivities
of regions including sites ELZ102m and ELZ103 are consistently
high at all depths calculated (Figure 22). Other sites also have
highly conductive subsurfaces (as expected), but the conductivities
are not consistently high at all depths. In addition, at the shallowest
modeled depth (i.e., 100 m), the conductivity beneath site ELZ103
is highest.
The shallow subsurface beneath ELZ102m was also indicated as
highly conductive in the 2D inversion model. Its neighboring site in
the model RAK053, which had a similar high conductivity subsur-
face, is situated, in plan view (Figure 11b), between it and site
ELZ103. In light of the similarities between 1D and 2D inversions
of the Katima Mulilo data, regarding the high conductivity shallow
subsurfaces beneath sites ELZ102m, RAK053, and ELZ103, the
region enclosing the three sites is deemed most appropriate for earth
electrode placement.
Interpretation of 2D inversion results
The Otjiwarongo area is characterized by large volumes of meta-
morphic rocks and sparse intrusive igneous complexes (Figure 4).
By combining knowledge of geology and the factors controlling
conductivity, it can be concluded that resistive shallow rocks, as
measured, are unfractured (not fluid-filled, van Zijl and de Beer,
1983), and do not contain interconnected highly conductive mate-
rials. The same metamorphic rocks exposed at the surface continue
to midcrustal depths (Gray et al., 2006), but, in contrast, the con-
ductivity, along most of the 2D profile (Figure 15), increases sig-
nificantly. The temperature at midcrustal depths is too low for the
conductivity to be increased by semiconduction, and the presence of
large quantities of fluid can be ruled out due to high pressures.
Although there has been volcanic activity in the past (attested by
the presence of igneous intrusions, Figure 7a) there is none at
present. Thus, the presence of partial melt can also be ruled out
as a possible cause of the high conductivity.
A comparison of localities of the Otjiwarongo array and the con-
ductive belt in northern Namibia and Botswana indicates that most
of the array overlies the belt (Figure 6b). The Otjiwarongo conduc-
tor is also situated at the same midcrustal depth range characteristic
of the conductive belt. Therefore, it can be confidently concluded
that the conductive belt exists below the Otjiwarongo area and the
MT data have substantiated its existence. The materials suggested to
Figure 20. Locking only the parts of the conductive layer that the Katima Mulilo data are sensitive to, and the inversion result with the
appropriate cells locked (right).
Audio-magnetotellurics in north Namibia B167
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be the cause of high conductivities observed in the belt, were mag-
netite (produced by serpentinization of the DMB rocks, van Zijl and
de Beer, 1983) and graphite, correlated with marble units present in
shear zones (Ritter et al., 2003). In the Otjiwarongo region, marble
units (NSWm in Figure 4) are also present, and are contained in
undifferentiated Swakop group rocks associated with the regional
shear zone traversing the study area. The shear zone manifests itself,
on the surface, as the Othohorongo thrust, which is the southwest
extension of the same shear zone, which intersected the MT profile
of Ritter et al. (2003), namely the Autseib Fault (Figure 7a). Hence,
it is concluded that interconnected graphite is also associated with
marble units in the Otjiwarongo region, and it is the cause of the
high conductivity of the midcrustal conductor.
High conductivities at the uppermost subsurface of the Katima
Mulilo area (Figure 16) are attributed to porous sediments of the
Kalahari group. However, Kalahari sediments in the area have a
maximum thickness of 100–200 m (Thomas and Shaw, 1990),
and therefore, there exists an alternate reason for the high conduc-
tivities observed deeper down. A cause similar to the one respon-
sible for the DMB conductive belt appears unlikely because the
Katima Mulilo area does not coincide with any region covered
by the conductive belt (Figure 6b), and the Katima Mulilo conduc-
tive layer is confined to the upper crust, whereas the belt is a mid-
crustal phenomenon. Near horizontal shear zones could be present,
and the materials found within the shear zones could be causing the
anomaly. Due to the high grades of metamorphism present in the
DMB (which also increases to the northwest; Singletary et al.,
2003), it can be deduced that horizontal shear zones are implausible
and near vertical ones more realistic.
Clastic and carbonate rocks of the Ghanzi group, existing within
the Northwest Botswana rift, directly underlie the Kalahari sedi-
ments (Figure 5). It is possible that the clastic and carbonate rocks
are fractured and fluid-filled at upper crustal depths, but in Namibia
the shallow DMB rocks have been found to be unfractured (van Zijl
and de Beer, 1983;Ritter et al., 2003), and the depositional and
deformational histories of DMB rocks in Namibia and Botswana
are alike. The Ghanzi group is, in part, an extension of the Nosib
group, which contains localized ironstone (Tankard et al., 1982,
Figure 21. (a) Uniform grid Laplacian inversion result (right) after placing a 5-km-thick resistive layer at the top of the original Otjiwarongo
inversion model (left) and (b) uniform grid Laplacian inversion result (right) after placing a thin 1-km resistive layer at the top of the original
Katima Mulilo inversion model (left).
B168 Share et al.
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p. 317) and in some instances large amounts of graphite (southwest
of Otjiwarongo, Miller, 2008, pp. 13–31). Ironstone has also been
discovered in the mobile belts in Botswana (Hutchins and Reeves,
1980;Kampunzu et al., 2000). The hypothesis is, therefore, formu-
lated that ironstone and/or graphite is present in the Ghanzi group
rocks forming the basement beneath the Katima Mulilo area, and it
is the cause of the observed high conductivity at upper crustal
depths (not including the shallowest depths). The conductive layer
can, in part, also be due to conductive materials located within the
Karoo basin sediments. This could explain the 1D layered nature of
the conductive feature in the Katima Mulilo region. To determine
which possibility is more plausible, drilling will be needed in
the area.
CONCLUSION
Inversions models have been derived from MT data of the Otji-
warongo and Katima Mulilo regions, Namibia. Analyses of the sur-
ficial conductivities of the Otjiwarongo and Katima Mulilo areas
show that areas around site ELG005, close to Otjiwarongo, and sites
ELZ102m, RAK053, and ELZ103, close to Katima Mulilo, are op-
timal locations for HVDC earth electrode placement. At greater
crustal depth, the most prominent feature of the Otjiwarongo
2D models, a midcrustal conductor, was deduced to be caused
by graphite associated with marble units in a local shear zone.
The Katima Mulilo 2D inversion detected an upper crustal high-
conductivity layer. The uppermost 200 m of the layer, and its related
high conductivity, is attributed to the thick sedi-
mentary Kalahari cover in the area (porous and
fluid-filled), whereas the cause of the conduc-
tivity deeper down (to a depth of 6–7 km) re-
mains enigmatic. It is possible that ironstone
or graphite present in the basement rocks could
be the cause, due to the discovery of such ele-
ments in similar rock types in other parts of
the DMB. However, such a hypothesis needs
to be tested, preferably by drilling.
ACKNOWLEDGMENTS
The first author’s research was sponsored by
Council for Scientific and Industrial Research,
South Africa. We would like to acknowledge
the entire SAMTEX team for their hard work
and assistance throughout the entire length of
the project. Also, the authors would like to ex-
press their gratitude to H. Thunehed and J. de
Beer for informative discussions on the content
of the paper. Last, the authors acknowledge
and thank three anonymous reviewers of the pa-
per and the associate editor for very insightful
comments and suggestions.
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