Geophys. J. Int. (1996) 127,635-650
Mechanisms of isostatic compensation of the Zimbabwe and
Kaapvaal cratons, the Limpopo Belt and the Mozambique basin
0.Gwavava,' C. J. Swain2 and F. Podmore'
'Department of Physics, University of Zimbabwe. PO Box MP167, Mount Pleasant, Harare, Zimbabwe
' Western Mining Corporation Limited, 55 McDonald Street, Kalgoorlie WA6430, Australia
Accepted 1996 July 16. Received 1996 June 17; in original form 1994 June 7
SUMMARY
The Bouguer gravity anomaly map of the Zimbabwe and Kaapvaal cratons, the
Limpopo Belt and the Mozambique basin shows a regional gravity high in the
southeast. Superimposed on this gravity high is a line of elongate gravity highs that is
coincident with the Lebombo-Nuanetsi-Sabi volcanics. Gwavava et al. ( 1992) argue
that the regional anomaly over this region is the effect of Mesozoic crustal thinning
and igneous activity during the breakup of Gondwana. Lithospheric extension resulted
in crustal thinning by at least 4 km beneath the central Limpopo Belt.
2-D Fourier transforms of Bouguer gravity and topography data have been used to
obtain the admittance and coherence throughout the region. Assuming a regionally
compensated isostatic model comprising two layers with statistically independent
surface and subsurface loading, the predicted coherence was compared to the observed
coherence to obtain the best estimate of the effective elastic thickness of the lithospheric
plate. This coherence analysis reveals that the Archaean cratons have a minimum
effective elastic thickness of about 56 km, whereas that of the area beneath the
Mozambique basin is only about 22 km, a value similar to that obtained in other East
African rift basins. Hence, the stable cratonic areas are more rigid than the area
beneath the Mozambique basin, which was subjected to Mesozoic crustal extension
and thinning.
An isostatic anomaly map has been computed by filtering the Bouguer gravity in
the wavenumber domain with the square root of the predicted coherence function of
the whole area generated from the best-fitting two-layer model with an effective elastic
thickness of 52 km. The isostatic anomaly map is characterized by ( 1 ) a zone of positive
isostatic anomalies over the Lebombo-Nuanetsi-Sabi area, which are partly due to
crustal thinning and partly to basic plutons emplaced in the upper crust, both resulting
from an extensional episode associated with Gondwana breakup, (2) positive isostatic
anomalies over the Southern Marginal Zone of the Limpopo Belt, which we interpret
as being due to dense granulites within the upper crust, (3) negative isostatic anomalies
over the Northern Marginal Zone of the Limpopo Belt, which may have resulted from
recent rapid erosion, and (4) negative isostatic anomalies over the Mozambique basin,
which are due to the gravity effect of low-density Cretaceous and Tertiary sediments.
Key words: crust, gravity anomalies, isostasy, lithosphere.
INTRODUCTION
The concept of isostasy requires that topography (surface loads)
above sea level be hydrostatically compensated by a deficit
of mass below sea level. In Airy's (1855) model, compensation
is achieved by variation of the crustal thickness such that
the crust-mantle interface (Moho) mirrors the topography,
whereas in Pratt's (1855) model hydrostatic equilibrium is
attained by lateral changes in the density of blocks of constant
0 1996 RAS
depth. Both models involve local compensation, in that the
compensating mass occurs directly below the surface load, and
loads have no effect on adjacent lithosphere.
The Airy and Pratt models imply that the crust has no
strength, an assumption that is not generally correct since the
crust can support surface loads regionally over a long geological timescale. To overcome this problem, a third type
of isostatic model, known as the flexure model, is used
that assumes an elastic lithosphere overlying a weak, fluid
635
636
0. Gwavava, C. J. Swain and F. Podmore
asthenosphere. The lithosphere responds to surface and subsurface loads by plate flexure, so the compensating masses are
distributed over a region around the surface load. Hence
compensation is regional. The flexural response of the lithosphere is governed by its flexural rigidity, which, for the thinplate model used here, is a function of its effective elastic
thickness. Moreover, as pointed out by Forsyth (1985), any
general regional isostatic model should also consider subsurface as well as surface loads.
The approach developed by Dorman & Lewis (1970) to
understand the isostatic compensation mechanism is to study
the linear relationship between the Bouguer gravity and topography in the wavenumber domain. This makes it possible to
distinguish, on the basis of wavelength, between topographic
features that are isostatically compensated and those that are
supported by the lithospheric plate. The 'isostatic response
function', or admittance, contains information on the isostatic
state of the lithosphere. Assuming a regional model of isostasy,
the admittance can be interpreted in terms of the flexural
rigidity of the lithosphere, e.g. McNutt & Menard (1982).
Another more robust function to compute is the coherence,
which is defined as the ratio of the square of the cross-spectrum
of Bouguer gravity and topography to the product of the
powers of gravity and topography at a given wavenumber. As
with the admittance, a predicted coherence can be computed
by assuming some isostatic model.
The admittance and coherence functions have been used to
study isostasy in other parts of the world such as North
America, Australia and East Africa. Since the flexural response
of the lithosphere to a load depends strongly on its effective
elastic thickness, T,, or its equivalent flexural rigidity, D, the
admittance and coherence have been used in this study to
estimate the effective elastic thickness of the lithosphere. Table 1
gives values of T, obtained by various authors for North
America, Australia and East Africa.
The results in Table 1 show that estimates of the continental flexural rigidity obtained from the admittance technique
( 1019-1022Nm) are biased towards low values compared
to those obtained from using the coherence technique
( lOZ3-lOz5 Nm). Values of the flexural rigidity obtained by the
coherence technique are in good agreement with estimates
from studying individual features ( 1023-1025Nm) such as
mountain ranges (Karner & Watts 1983; Stern & ten Brink
1989), sedimentary basins (Watts, Karner & Steckler 1982)
and lakes (Passey 1981; Nakiboglu & Lambeck 1983; Bills &
Table 1. Effective elastic thickness
May 1987). Forsyth (1985) and Bechtel et al. (1990) attribute
the bias towards low flexural rigidities using the admittance
technique to ( 1 ) assuming only surface loading when subsurface
loading could also be important, (2) the strong weighting of
provinces with large topographic relief and (3) averaging over
several different geological provinces with different flexural
rigidities.
At the time of undertaking the present study there were no
other isostatic studies of this region of southern Africa to
enable us to understand the thermomechanical evolution of its
lithosphere. The region is extremely interesting since it includes
a large area of very old rocks (3.5 to 2.6 Ga) forming the
Archaean cratons, the Limpopo Belt with some rocks as old
as those of the cratons but highly deformed and metamorphosed, and the Mesozoic Mozambique sedimentary basin
filled with recent sediments. The objectives of this study are to
use Bouguer gravity and topography data to:
(1) obtain the admittance and coherence to enable us
to distinguish topographic features that are isostatically
compensated from those that are uncompensated;
(2) estimate the flexural rigidity of the lithospheric plate
assuming a regional compensation model and investigate the
possibility of variation of the effective elastic thickness of the
plate beneath the Archaean cratons and the Mozambique
basin;
(3) investigate the relative importance of surface and
subsurface loading;
(4) obtain an isostatic anomaly map.
GEOLOGY
The Zimbabwe and Kaapvaal cratons (Fig. 1 ) are Archaean
low-grade granite-greenstone terrains, which have formed a
stable unit since about 2300 Ma (Piper, Briden & Lomax 1973;
McElhinny & McWilliams 1977), comprising greenstone belts
of different ages, various mafic and ultramafic intrusions,
together with a variety of granites and gneisses. The greenstone
belts are the folded remnants of volcanic-sedimentary piles
and, for the most part, have been metamorphosed to greenschist facies. The Archaean rocks of the Zimbabwe craton
range in age from about 3500 to 2600 Ma (Nisbet, Wilson &
Bickle 1981). The Great Dyke intruded the Zimbabwe craton
at about 2460Ma (Hamilton 1977); the Bushveld Igneous
T.for some continental areas.
Area
Tectonic region
Method
T.(km)
D (Nm)
Reference
Australia
Continental Australia
Continental Australia
Cratonic Australia
East coast Australia
Admittance
Admittance
Coherence
Coherence
<5
<1
130
15-35
< lo2'
<5 x 16'
2 x 1025
(3-38) x 10''
Cochran (1980)
McNutt & Parker (1978)
Zuber et al. (1989)
Zuber et al. (1989)
Continental USA
Continental USA
Precambrian Shield
Admittance
Admittance
Coherence
5-10
> 100
102'-102*
< 102'
< 1025
Banks et al. (1977)
Cochran (1980)
Bechtel et al. (1987)
Kenya
East African Rift
East African Rift
Coherence
Coherence
25-30
< 25
(1.4-2.4) 1023
1.4 x 1023
Forsyth (1985)
Bechtel et al. (1987)
East Africa
Stable cratonic regions
Rift Valley
Coherence
Coherence
64-90
21-36
>2.3 x 1025
(8.2-41.5) x loz2
Ebinger et al. (1989)
Ebinger et al. (1989)
N. America
<5
+
0 1996 RAS, GJI 127, 635-650
Mechanisms of isostatic compensation in Africa
27O
2B0E
20"
3F'
637
33'
32OE
Legend
International boundar)
----
El
Aeolian sands
Cretaceous sediments
Igneous complex
-
Karoo voicanics
Proterozoic sediments
Bushveld Complex
Great Dyke
Paragneiss
Gneiss
-
Greenstones
Granitk
AHA'
Gravity profiles
X++Y
Seismic traverse
fl-N
Reststtvity profile
0
210
2PE
29'
30°
31 O
32"E
330
50
100
150 k m
3 40
Figure 1. Geological map of the Limpopo Belt and surrounding areas. NMZ =Northern Marginal Zone of the Limpopo Belt; CZ = Central Zone
of the Limpopo Belt; SMZ = Southern Marginal Zone of the Limpopo Belt. A-A': gravity profiles (Gwavava 1990);X-Y seismic traverse (Stuart
& Zengeni 1987); M-N resistivity profile (Van Zijl 1978).
Complex, which intrudes the Kaapvaal craton, is dated at
about 2000 Ma (Hunter & Hamilton 1978).
The Limpopo Belt (Fig. 1) consists of Archaean rocks that
have undergone high-grade metamorphism and polyphase
deformation resulting in the formation of high-grade gneisses
and granulites. The rocks were subjected to a major episode of
metamorphism and deformation from about 2900 to 2500 Ma
(Van Breemen & Dodson 1972; Hickman & Wakefield 1975)
and a second event at about 2000 Ma (Van Breemen & Dodson
1972), which is shown only in mineral ages and palaeomagnetic
studies. The Belt can be subdivided on both structural (Cox
et al. 1965) and stratigraphic (Watkeys 1983) grounds into a
Northern Marginal Zone consisting of high-grade equivalents
of the Zimbabwe craton granite-greenstone terrains, a Central
Zone made up mainly of mylonites and amphibolite-facies
gneisses, and a Southern Marginal Zone of reworked Kaapvaal
craton granitegreenstone material forming high-grade
metamorphic rocks.
On the eastern side of the Limpopo Belt and overlying the
Karoo sediments are Karoo volcanics forming the LebomboNuanetsi-Sabi volcanics, dated between 160 and 200 Ma
0 1996 RAS, GJI 127, 635-650
(Hales 1960; Gough et al. 1964). The Karoo basalts in
Zimbabwe, which also include rhyolites in the south, have a
regional strike in an ENE direction and a gentle southerly dip
of 2" to 8" (Swift et al. 1953). The volcanics along the Lebombo
monocline comprise a lower basaltic group, a middle rhyolitic
group and a less-extensive upper basaltic group; they dip
eastwards beneath sediments of the Mozambique rift basin at
between 5" and 20", reaching a maximum value of 30" to 60"
before flattening out to the east (Du Toit 1929; White &
McKenzie 1989); they have a thickness that is thought to
increase eastwards and is estimated to be between 6 and 13 km
along the coast (Eales, Marsh & Cox 1984).
Associated with the extrusive rocks are intrusive complexes,
which include gabbros, granophyres, granites, syenites and
carbonatites. The Nuanetsi-Sabi area has a linear set of ring
complexes, dated between 190 and 200 Ma (Gough et al. 1964),
paralleling the ENE faulting trend of the Limpopo Belt.
The Mozambique basin in the eastern part of the study area
is bounded to the west by the Zimbabwe and Kaapvaal
cratons. It is an asymmetric, pericontinental rift basin that
developed along the East African margin and contains
638
0.Gwavava, C.J. Swain and F, Podmore
Mesozoic and Cenozoic sediments that thicken eastwards
(Coster, Lawrence & Fortes 1989). The post-Karoo section
consists of mid-Jurassic to Tertiary marine, continental and
deltaic sediments.
shows a regional gravity high, which has an amplitude of
about 1400gu in the southeast. Superimposed on this longwavelength feature, up to 350 km wide, are two lines of shortwavelength gravity highs coincident with the Lebombo and
Nuanetsi-Sabi volcanics. The Bouguer anomalies are generally
negative over the Mozambique sedimentary basin. Gwavava
et al. (1992) modelled three profiles crossing the Limpopo Belt
and one profile across the Mozambique basin. The crustal
models were controlled by surface geology, seismic refraction
results (Stuart & Zengeni 1987) and densities from outcrops.
The lower-crust and upper-mantle density values in the
Limpopo Belt were fixed at 2800 and 3400 kg m-3 using the
seismic refraction results. In Mozambique, borehole information was used to constrain the thickness of the sediments
to 3 km towards the southeastern end of profile B-B'. Gwavava
et al. (1992) interpreted the positive gravity anomaly over this
area largely in terms of Mesozoic crustal thinning associated
with the breakup of Gondwana. The 34 km thick crust beneath
the Zimbabwe craton and the Northern Marginal Zone of the
Limpopo Belt thins in a SSE direction by at least 4 km beneath
the central Limpopo Belt (see Fig. 6a), in accordance with the
results from the seismic refraction study (along line A-A in
Fig. 5) of Stuart & Zengeni (1987). Using the idea that lateral
changes in densities can occur from the interior of a continent
PREVIOUS GEOPHYSICAL STUDIES
From a resistivity profile crossing the Limpopo Belt between
the two cratons, Van Zijl (1978) suggested a horizontal Moho
at a depth of 40 km and a hydrated lower Frust at a depth of
25 to 40 km (Fig. 2). Stuart & Zengeni (1987) carried out a
seismic refraction study across the northern and central parts
of the Limpopo Belt in Zimbabwe. The Moho of the Northern
Marginal Zone, which had reverse coverage, was found to be
at a depth of 34km with a P-wave velocity of 8.4kms-'
(Fig. 3). In the Central Zone the Moho has a lower apparent
velocity of 7.8 km s-', which is due to the Moho dipping
northwards at about 6". This implies that within the Central
Zone the Moho rises from a depth of 34km to 29km.
Alternatively, this can be viewed as crustal thinning in a
southerly direction.
Gwavava et al. (1992) present results from a recent gravity
survey in the study area compiled with data from surrounding
countries (see Fig. 4). The Bouguer anomaly map (Fig. 5)
Kaapvaal,
Craton !
Limpopo B e l t
I
:
Zimbabwe
Craton
M
20
E
2
-5 40
fa
0
-
0.01
60 -
80
Zone 4
20
t'
- 0.05
- 30
1
I
Figure 2. Resistivity profile across the Limpopo Belt (Van Zijl 1978). Present-day crustal thickness is assumed to be 40 km. Zone 3 is at a depth
of 25 km beneath the Limpopo Belt.
_____
E
-r:
20
E
-
f
0
-
40
-I--
---5.7 k m l s
6.5 kmls
- - - - _ _ _ - _ _ _ _ _5_. 8 _km/_s-
6.4 k m l s
L
,@
"c5.
.?is
3
-____
_________'
-
-
__---_
-
,
-,<,-.7:.
:. :::
: : : : : .. .. : : : : : : : : : . . . . . . . . . . . . .
...........
: : .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . . .*
............................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 . 4 k m l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
................................................................
................................................................
-
Figure 3. Crustal model deduced from seismic studies (Stuart & Zengeni 1987). Note that the crustal thickness under Rutenga is about 34 km
and thins beneath the Central Zone to about 29 km.
0 1996 RAS, GJL 127, 635-650
Mechanisms of isostatic compensation in Africa
19a
S
190
200
20’
639
S
..
.....
Legend
Gravity s t a t i o n s
----
lnternatlonal boundary
210
210
2 20
220
23O
S
23O
240
240
25O
259
0
100
50
150km
S
Figure 4. Gravity-station distribution map of the study area. Reprinted from Gwavava et al. (1992) with kind permission of Elsevier ScienceNL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.
to its margin (Boillot 1981), Gwavava et al. (1992) argued
that it is possible that the upper-mantle density under the
Mozambique basin could be lower than that under the
Limpopo Belt. Thus they presented an alternative model to
Fig. 6(a) showing that the crust under the Mozambique basin
could be even more highly extended and attenuated to a
thickness of only about 22 km (see Fig. 6b). The latter model
would then be consistent with a tighter fit of Antarctica
against the Sabi and Lebombo monoclines if an anomalous
low-density upper mantle (3100 kg m-3) exists under the
Mozambique basin.
Heat-flow measurements of direct relevance to this study
were made by Ballard & Pollack (1987) in southern Africa
and Nyblade et al. (1990) in East and southern Africa. Both
studies show a general trend of increasing heat flow away from
the centres of Archaean cratons into surrounding younger
Proterozoic and Pan-African mobile belts. Nyblade et a/..
(1990) give a mean heat flow of 4 7 + 2 m W m - ’ for the
Archaean Kaapvaal and Zimbabwe cratons. They report a
single site in the northern margin of the Limpopo Belt with
a heat-flow value of 49mWm-’. At the time of writing
this paper there were no published heat-flow data for the
Mozambique sedimentary basin. Heat flow can be interpreted
directly in terms of lithospheric thickness (Chapman & Pollack
1977) and so is highly relevant.
0 1996 RAS, GJI 127, 635-650
D E F I N I T I O N S OF ISOSTATIC RESPONSE
A N D COHERENCE F U N C T I O N S
We use the Fourier amplitudes of Bouguer gravity, B(k), and
topography, H(k), in the wavenumber (k) domain to obtain
the power and cross-spectra of the two data sets and then use
them to define the admittance and coherence. Several authors
(e.g. Dorman & Lewis 1970; McKenzie & Bowin 1976; Forsyth
1985; Bechtel, Forsyth & Swain 1987; Lambeck 1988) give a
more detailed explanation of most of the expressions quoted
below.
Defining the following:
power of gravity
Eo = (B(k)B*(k))
power of topography
El= (H(k)H*(k)),
cross-spectrum
Co = (B(k)ff*(k))
9
(1)
3
where the angle brackets ( ) denote azimuthal averaging over
discrete wavenumber bands, the asterisk repesents a complex
conjugate, and the magnitude of the wavenumber k in the
horizontal x-y plane is
k = Ikl= (kz + kc)”’.
(2)
The isostatic response function is given by
Q(k)= Co/Ei >
(3)
0.Gwavava, C . f. Swain and F. Podmore
640
0
28OE
I
4
30°
290
I
1
I
I
31O
I
1
32OE
1
I
330
I
1
\
/I
1
19O
19"
5
5
Legend
----
International boundary
Balane
20-
Bouguer gravity contours a t
intervals o f 20 mGals.
Gravity profile
-.
200
2 00
A
210
210
+---I
A'
220
23O
23O
5
well
GD
Great Dyke
MG
Mberengwa greenstone belt
0
I
22"
-1
0
50
1
100
,
l5Okm
1
5
240
240
25"
25O
2
Figure 5. Bouguer anomaly map of the Limpopo Belt and surrounding areas. Reprinted from Gwavava et al. (1992) with kind permission of
and the observed coherence is
y; = C ; / E o E 1 .
(4)
An unbiased estimate of the observed coherence used in this
study is
Y2=(nY6-1)k-1),
(5)
where n is the number of independent Fourier coefficients
within a wavenumber band (Munk & Cartwright 1966). Unlike
the observed coherence, which is always positive, the unbiased
coherence can be negative if the product of n and y; is less
than unity. This happens when both n and yg are small. The
error in the observed coherence is
Ay2 = ( 1 - yi)( 2y$")1'2
(6)
(Bendat & Piersol 1980).
A theoretical isostatic model has an admittance that attains
a value of the Bouguer slab correction (-27cGp) at long
wavelengths and zero at short wavelengths (see Banks, Parker
& Huestis 1977; Ebinger et al. 1989). For a flexure model the
predicted coherence between Bouguer gravity and topography
(1) is unity for long-wavelength topography, implying that the
plate is too weak to support the loads and therefore surface
and subsurface loads are fully locally compensated; (2) is zero
for short-wavelength features, i.e. the loads are completely
supported by the strength of the plate and are therefore not
compensated; and (3) changes from unity to zero in the rolloff region, implying some regional compensation. The transition from high to low coherency depends to a large extent on
the flexural rigidity of the plate, to a small extent on the ratio
of bottom-to-top loading (for a two-layer model), and is almost
independent of the depth of bottom loading (Forsyth 1985; see
Fig. 10). The observed coherence can therefore be matched to
the predicted coherence to yield an estimate of the flexural
rigidity.
DATA SETS
The 6679 irregularly spaced gravity values (Gwavava 1990) in
the area from 27" to 34"E and 18" to 25"s (see Fig.4) were
interpolated using minimum curvature (Swain 1976) onto a
1/12O regular grid (9.2 km) to produce an 85 x 85 array. The
topography data were obtained by digitizing by hand the mean
elevations from 1 :250 000 relief maps on a 1/12" square grid
(Gwavava 1990). The topography has values of over 1000 m in
the northern and western parts of the area and gradually
decreases to about 50 m in the southeastern corner of the area
(see Fig. 7).
0 1996 RAS, G J I 127, 635-650
Mechanisms of isostatic compensation in Africa
I
20
40
0
Observad
x
Calculated G r a v i t y
641
Gravity
-40
d
m
c
rn
L
-60
-80
a,
3
7 -100
0
m
-120
-1 40
-160 I
0
I
50
I
100
I
I
I
I
I
I
200
250
300
Distance in k m
150
B
I
350
400
0
E
+
10
0"
30
.-c
f 20
a.
/
3600
Oensity model
40
20
.-c
-20
=E -40
m
m
-60
& -80
1
cn
m
-100
-120
-140
-160
I
0
1
1
1
50
100
150
I
200
250
300
, Distance in km
51
I
I
350
400
1
Density model
Figure 6. (a) A simple 2.5-D interpretation of profile B-B (Gwavava et al. 1992). The surface of the density model represents the topography.
Density in kg m-3. (b) Alternative model of profile B-B showing that the crust is highly extended and attenuated. Crustal thickness beneath B on
the craton is about 34 km, whereas that beneath B is about 22 km.
0 1996 RAS, G J I 127, 635-650
642
0. Gwavaua, C. J. Swain and F. Podmore
,
27E
28E
g
29E
I
3GE
I
31E
32E
I
I
33E
I
341
I
1.3:
1BS
19s
19s
20s
20s
21 s
21 s
22s
22s
23s
23s
24s
24s
25s
25s
I
L
I
I
I
I
I
I
!7E
28E
29E
30E
31 E
32E
33E
34E
-5
100 150
km
Figure 7. Topography map of the study area. Contour intervals at 50 m.
The gridded gravity and topography data were mirrored
along the northern and eastern boundary and then Fourier
transformed using the FORTRAN subroutines of Banks ( 1979),
which utilize a fast Fourier transform algorithm (Singleton
1969). Prior to Fourier transformation, the mean of each data
set was removed. To compute the admittance and coherence,
the cross and power spectra were estimated by taking azimuthal
averages in wavenumber bands chosen such that the midpoints of these bands were at approximately logarithmic
intervals. The mean wavenumber at which the admittance and
coherence were estimated was obtained by weighting each wavenumber within a wavenumber band with the product of the
power of the Bouguer gravity and the power of the topography
rather than taking the mid-point of a wavenumber band.
FLEXURAL MODEL A N D COHERENCE
TECHNIQUE
We used a two-layer elastic-plate model (with loads both at
the surface and at the Moho) for which we have calculated
the theoretical coherence, and hence estimated its effective
elastic thickness, using the theory outlined by Forsyth ( 1985).
Other authors who have based their interpretation on this
formulation include Bechtel et al. (1987), Ebinger et al. (1989)
and Zuber, Bechtel & Forsyth (1989). The coherence technique
is carried out in the wavenumber domain, in which the elasticplate equation has a very simple form. In summary, it involves
first downward continuing the gravity to find the Moho relief
( W ) ,then, for a given rigidity (5),solving for the initial surface
topography ( H I ) and Moho relief (WI),from which the components of relief on these interfaces due to loading at both top
and bottom can be found:
H=HT+HB
and
W=WT+WB,
(7)
where HT and H B are components of the surface topography
due to top and bottom loading respectively. WT and WB are
similarly defined with respect to the Moho relief.
Once WZ and H I are known, the ratio f of initial bottomto-top loading at every wavenumber k can be found from
Ap WI
f=-
PoHI ’
(8)
where A p is the density contrast between the mantle and crust,
of densities pm and p o respectively. The theoretical coherence
is then calculated, after upward continuing the Moho relief to
get its gravity effect at the surface, and compared to the
observed coherence at each wavenumber to get a root-meansquare misfit. This calculation is repeated for a range of D
values to find a best estimate in a least-squares sense of 5.
Note that load maps and components of relief are then
available for this 5 value leaving no isostatic anomalies. Note
also that there is no unique solution for H I and WI at the
longest wavelengths, for which the plate is weak and top and
bottom loading are indistinguishable. There is thus a locally
compensated long-wavelength component of topography HC.
0 1996 RAS, GJI 127, 635-650
Mechanisms of isostatic compensation in Africa
643
Effective elastic thickness from the coherence technique
RESULTS
Admittance
The admittance Q(k) (see Fig. 8) of the mirrored data shows a
response that is:
(1) mainly negative for topographic features with wavelengths
greater than 200 km; and
(2) close to zero for features with wavelengths less than
200 km.
Features with wavelengths greater than the unreflected size of
the data set (770 km) may not be present in the data. There
are large errors, especially in the fall-off region, which is an
indication of departures from the single isostatic model assumed
to represent the map area. These are most likely to be variations
in D or in the ratio of subsurface to surface loading (f),which
both strongly affect the admittance (Forsyth 1985).
Coherence
The observed coherence (Fig.9) falls from unity to zero
somewhere between wavelengths of 770 to 300 km, i.e. at
longer wavelengths than for the Kenya curve. According to
our flexural model the data imply that at wavelengths longer
than about 450-770 km the plate bends under loads, while
at wavelengths shorter than 300 km topography is supported
by the strength of the plate (lithosphere). A comparison of
Figs 9 and 10, to get an initial estimate of the effective elastic
thickness of the plate (T,), shows that T, lies in the range 35
to 55 km for a model with f = 1, ,z = 35 km, po = 2670 kg m-3
and A p = 600 kg m-3. A more reliable estimate of the elastic
thickness is described in the next section.
A computer program (Forsyth, personal communication) to
determine iteratively the effective elastic thickness and loads
for a two-layer model (summarized above) was used with data
for the whole area. The study area was then divided into two
tectonic areas (i.e. one block covering the cratons and another
the sediments in Mozambique), where we expect uniform T, in
each area. The effective elastic thickness of each subregion was
similarly determined for mirrored data. The size of each block
had to be made sufficiently large to observe coherence values
approaching unity at long wavelengths, as well as the transition
wavebands. Since the size of the area was only 770 x 770 km,
it was necessary to have the two subregions overlapping (see
Fig. 1). The model parameters used in the inversion program
are listed in Table 2 and the results in Table 3. Note that there
are no predicted coherences at the longest wavelengths, for
which the observed coherences approach unity as these wavebands are affected by the mirroring process. The authors tried
several bigger block sizes for both the cratonic area (up to
900 x 900 km) and the Mozambique sedimentary basin (up to
370 x 600 km) in order to obtain realistic error estimates of T,.
For the whole area, Fig. 11 shows that the coherence estimates have been made at more closely spaced wavenumbers
than in Fig. 9 in an attempt to constrain T, more tightly. The
range of T, values (50-57 km) implies a flexural rigidity of the
lithospheric plate of 1.11-1.65 x
Nm.
For the cratonic areas, a 5" square block (27" to 32"E by
19" to 24"s) consisting mainly of the Zimbabwe and Kaapvaal
cratons with part of the Limpopo Belt in between the cratons
was selected (see Fig. 1). A large portion of the area covered
by the Lebombo-Nuanetsi-Sabi volcanics was also included
on the eastern side to give a sufficiently large area. The
coherence for the cratonic area (Fig. 12) yields an effective elastic
I I I I I
-0.10
-0 .08
I
I
I
i
0.08
Wavenumber x 2
rad/km
Figure 8. Isostatic response function of the Bouguer gravity and topography. The response is generally negative for topographical features of
wavelengths greater than 200 km.
0 1996 RAS, GJI 127, 635-650
644
0. Gwavava, C. J. Swain and F. Podmore
Wavelength
1.10
1 .oo
I,I
1000
1 , I 1
I
1
1
,
I
i n km
100
I
llil
'
I
I
I
I
-
0.90-
0.80 0.70 -
0.60C
(u
L
0.50-
a,
LZ
8
0.40-
0.300 . 2 00.10
-
0.00I
I
1
1
1
1
1
I
1
I
I
1
1
1
0.01
Wavenumber x 2
1
1
0.1
rad/km
Figure 9. Observed coherence curve. Upper curve is for Kenya (Swain 1979) and lower curve is for this study.
Wavelength
a,
U
C
1 .oo
-
0.90
-
0.80
-
0.70
-
i n km
0.60 -
a,
L
a,
0.50
S
0
V
0.40 -
-
0.30 -
0.20
-
0.100.00-
V .
Wavenumber x
27T
1
rad/km
Figure 10. Theoretical coherence curves assuming a flexure model with a bottom-to-toploading ratio off = 1, effective elastic thickness T.= 5 to
100 km and depth to Moho of 35 km.
thickness in the range 52-62 km. The observed coherences for
wavelengths less than 200 km lie on the theoretical curve for
T,= 22 km (Fig. 13), indicating the possible influence of a
weaker plate, probably due to the inclusion of the LebomboNuanetsi-Sabi volcanics, an area of thinned crust (Gwavava
et al. 1992).
For the Mozambique sedimentary area a 3" square area was
chosen extending from 30.5" to about 34"E and 21" to 24.5"s.
The coherence technique gives an effective elastic thickness of
22 1 km. The negative coherence (Fig. 13) can be explained
by the lowest Bouguer anomalies in this area correlating with
the lowest elevation due to a large thickness of low-density
sediments. A bigger block of this area, which includes a sizeable
portion of the craton on the western part of the sedimentary
0 1996 RAS, GJI 127, 635-650
Mechanisms of isostatic compensation in Africa
Table 2. Two-layer model parameters for the inversion program.
Parameter
-m
Po
Pm
E
G
g
P
Isostatic anomalies
Definition
Value
Depth to Moho
Average crust density
Mantle density
Young’s modulus
Gravitational constant
Gravitational acceleration
Poisson’s ratio
34 km
2800 kg m-3
3400 kg IT-^
1.0 x 10” Nm-’
6.67 x lo-” m3 kg-ls-’
9.8 m s-’
0.25
The two-layer model assumed, although adequate for estimating
T, (Forsyth 1985), is certainly an oversimplification as it
explains the gravity anomalies having no topographic correlation in terms of Moho relief. This includes ones with relatively
short wavelengths like the Sabi-Nuanetsi-Lebombo anomalies,
which are at least partly due to upper-crustal intrusions
(Gwavava et a/. 1992). (It is worth noting here that the
downward continuation is stabilized at short wavelengths by
allowing ekz a maximum value of 5, i.e. a minimum wavelength of 133 km.) The load maps are misleading because these
intracrustal density contrasts have not been considered, and
are not presented here; instead, we give an isostatic anomaly
map.
In order to generate isostatic anomalies, a filter was designed
using the square root of the coherence (Banks & Swain 1978)
of the best-fitting elastic-plate model with a T, of 52 km. It is
easier to generate theoretical coherence curves using a constant
ratio f . Several values o f f were tried and it was found that
f = 1.5 best reproduced the observed coherence. This filter
gives an estimate of the attraction of the compensating masses,
which is subtracted from the Bouguer anomaly to obtain
isostatic anomalies.
The isostatic anomalies (Fig. 14) range from -600 to
+ 1000 gu (1 gu=O.l mGal). The Lebombo-Nuanetsi-Sabi
area has large positive isostatic anomalies. These positive
isostatic anomalies are a combination of the gravity effects
of the Moho shallowing rapidly southeastwards (and overcompensating the fall in elevation, which is gentle and occurs
further north) and uncompensated igneous intrusions. The
Great Dyke and the Bushveld Igneous Complex also exhibit
positive isostatic anomalies, and these represent the gravity
effect of uncompensated masses within the upper crust.
Table 3. Effective elastic thickness T,.
Area
T,(km)
T- (km) T,,, (km) rms
Whole area
Cratons
Mozambique (small block)
Mozambique (big block)
52
56
22
34
50
52
21
29
57
62
23
39
0.137
0.160
0.203
0.043
Note: (1) rms is the root mean square of the misfit between the
observed and predicted coherence. Tminand T,, are the minimum
and maximum elastic-plate thicknesses that fit the same number of
points in the fall-off region as the best-fitting model.
ET:
(2) Flexural rigidity D =
12(1 - p Z ) ’
~
basin, gave a T, estimate of 34 km. These T, values are similar
to the ones obtained using the coherence technique (21-44 km)
for the East African Rift zones (Bechtel et al. 1987; Ebinger
et aZ. 1989), for eastern Australia (Zuber et al. 1989) and for
Afar (Ebinger et a/. 1989). Ebinger (personal communication,
1993) has re-analysed the Afar area with more data, and the
results suggest a still-weaker lithosphere with T, less than
10 km.
W a v e l e n g t h i n km
1 10
1000
1111
I
I I
100
I
I
I
I
I
I
I
I
.-
I
~--PPeO~cteC
a oherence
o a s e r v s d cOnBrenCe
1.oo
0.90
0.80
0.70
0.60
I
c
al
0.50
L
al
.c
8
0.40
0.30
0.20
0.10
1
0.00
-0.10
1
1
I
1
I
J 1 1 1
0.001
I
1
-
1
I
I
I I
I
I
I
0.01
Wavenumber x 2
I
I
I
I
I
I
l-r
rad/km
Figure 11. Observed (solid line) and predicted (dashed line) coherence curves for the whole area. Best estimate of T, = 52 2 km.
0 1996 RAS, GJI 127, 635-650
645
646
0.Gwavava, C . J. Swain and F. Podrnore
w
t
venumber 2
T
rad/km
Figure 12. Observed (solid line) and predicted (dashed line) coherence curves for the cratonic areas including the Limpopo Belt. The perturbation
of the curve for wavelengths of less than 200 km is probably due to the inclusion of the Lebombo-Nuanetsi-Sabi volcanic area.
W a v e l e n g t h i n km
1000
o - - - P r e d i = t e e Caneience
m - o ~ s e r v e ac o n e ~ e n c e
0.90
0.00
0, 7 01
a,
0.60
U
C
al
L
@.I
c
0
u
0.50
-
0.40
-
0.30
-
0.20
-
0.10
-
0.00-0.10
I
I I I '
0.001
I
U
I
Wavenumber 2
I
l
l
l
l
~
C
d.01
rad/km
Figure 13. Observed (solid line) and predicted (dashed line) coherence curves for the Mozambique sedimentary area.
There are negative isostatic anomalies of up to - 300 gu
over the Mozambique basin. These are due to the gravity
effect of low-density Cretaceous and Tertiary sediments.
A large zone of negative anomalies extends NE from about
30.5"E, 20.5"s.This zone coincides with the southward downslope from the watershed (see Figs 15 and 16), which is
relatively recently eroded and probably has not yet had time
to adjust isostatically to this erosion.
0 1996 RAS, GJI 127,635-650
Mechanisms of isostatic compensation in Africa
27E
28E
29E
30E
31 E
32E
33E
I
I
I
I
I
I
647
34E
I
185
18s
195
19s
205
20s
215
21s
222
22s
232
235
242
24s
25s
255
I
I
I
I
I
I
I
27E
28E
29E
30E
31 E
32E
33E
50
I
34t
100 150
0
krn
Figure 14. Isostatic anomaly map of the study area obtained by filtering the gravity with the square root of the coherence. Contour intervals at
10 mGals. Note: 1 mGal = 10 gu.
la1
..1500
~
E
I
r"
Pm 500
I
I
5 so0
-
1
:
--
r
-500
Figure 15. N-S profiles showing components of the topography along
31"E. Note that h = h, ih, 4- hb.
The Southern Marginal Zone at about 29.5"E, 23.5"s has a
positive isostatic anomaly of more than 300 gu, which may be
due to dense upper-crustal rocks (granulites). Immediately
north of this high is a low reaching -200 gu. The steep linear
gradient between the two anomalies appears to mark the
Soutpansberg fault zone.
0 1996 RAS, GJI 127,635-650
18's
1
19"
2 o y
2lP-l 210
+
2c
25"s
Figure 16. N-S profiles showing components of the topography along
32"E. Note that h = h, + h, + hb.
Components of topography
Although we do not show the load maps, because our twolayer model attributes all the isostatic anomalies except the
shortest wavelengths to Moho relief, we think that the components of topography are instructive. Two N-S profiles
648
0. Gwavava, C . J . Swain and F. Podmore
(Figs 15 and 16), each 770 km long, illustrate the components
of topography due to surface and subsurface loading. The
present topography h is the sum of the locally compensated
topography h, and topography due to surface loading h, and
to subsurface loading hb. Both profiles show that a large
fraction of the present topography is locally compensated,
probably by density variations in the upper mantle. For these
profiles, surface and subsurface loadings seem to have about
equal importance in the development of the topography (i.e.
f z 1). In Fig. 15 the subsurface loading profile hb implies 2
to 3 km of crustal thinning, in rough agreement with the model
of Gwavava et al. (1992) along profile A-A.
DISCUSSION
A regional isostatic compensation model was used to study
isostatic compensation in the region. The model assumes that
the lithosphere behaves as an elastic plate, responding to
surface and subsurface loads by flexure. Using the coherence
between Bouguer gravity and topography it was found that
loads with wavelengths greater than about 500 km (Fig. 11)
are fully locally compensated, and for these wavelengths surface
and subsurface loads are thus indistinguishable; loads with
wavelengths in the range 300 to 500 km are partially regionally
compensated (i.e. partly supported by the plate) and loads
with wavelengths less than 300 km are uncompensated, i.e.
they are completely supported by the strength of the lithosphere. An effective elastic thickness (T,) of the lithospheric
plate of 52 + 5/-2 km was obtained for the model that best
fits the observed coherence. This gives a flexural rigidity D of
about 1.25 x
Nm.
The coherence technique when applied to two tectonically
different subregions, the cratons and the Mozambique basin,
yielded different elastic-plate thicknesses. The value of 56 km
for the cratonic area is felt to be a minimum value since it
includes the Limpopo Belt, for which T, is almost certainly
smaller than for the cratons. Bearing this in mind, we feel there
is no discrepancy with the values of 60 to >90 km obtained
for cratonic areas in Sudan, Zaire and Congo (Ebinger et al.
1989).
The Mozambique rift basin, containing Cretaceous and
Tertiary sediments, has an elastic-plate thickness in the range
21-39 km, which is significantly lower than the value obtained
for the cratonic area. Ebinger et al. (1989) found similar values
for rifted zones of East Africa (T,=21-36 km). Using 2.5-D
modelling, this area of Mozambique was shown by Gwavava
et al. (1992) to have a thinner crust than the cratons by 4 to
12 km (Figs 4a, b). Although T, does not relate directly to
crustal thickness, a thin elastic plate agrees with the idea that
the lithosphere under the Mozambique sedimentary area was
stretched and thinned during the breakup of Gondwana, and
we feel it offers support to the alternative 2.5-D gravity model
(Fig. 4b) involving greater crustal thinning and a low-density
(3100 kg m-3) uppermost mantle beneath the Mozambique
basin.
The difference in elastic-plate thickness for the cratonic area
and the Mozambique basin supports the contention that stable
cratons are underlain by relatively strong lithosphere compared
to younger rifted or stretched continental crust. The difference
in plate strength for the two subregions implies that there
exists a transitional region where the strength of the lithosphere
increases rapidly to the north and west: this transitional region
lies beneath the Lebombo-Nuanetsi-Sabi volcanics. We would
therefore expect a difference in thermal lithospheric structure
between the Archaean cratons and the Mozambique basin
i.e. low heat flow in the cratons and high heat flow in the
Mozambique basin.
The map of isostatic anomalies (Fig. 16) shows prominent
zones of positive and negative isostatic anomalies corresponding to areas with uncompensated masses either in the upper
crust, the lower crust or at the Moho. The area with thinned
crust and magmatic intrusions, the Lebombo-Nuanetsi-Sabi
area, stands out as a zone of positive isostatic anomalies on
the map (Fig. 15). It is interesting to note that the SMZ (Fig. 1)
is characterized by positive isostatic anomalies, whereas
negative isostatic anomalies occur over the NMZ. This difference is interpreted as being due to granulites of the SMZ being
significantly denser than granulites of the NMZ. Densities of
granulites in the NMZ were found by Gwavava (1990) to be
about 2690 kg m-3, which is close to that of granites on the
Zimbabwe craton (2670 kg m-’)). If this slight increase in
density (20 kg m-3) is assumed to apply to a layer 5.8 km
thick (Stuart & Zengeni 1987), the upper crust there would
give rise to a positive anomaly of only about 5Ogu. This is
very small compared to the isostatic anomalies of up to 400 gu
observed over the SMZ.
CONCLUSIONS
These results reveal that the lithosphere is relatively stronger
under the Archaean stable cratons than beneath the Mesozoic
Mozambique basin. This difference in elastic behaviour of the
lithosphere is linked to the separation of Antarctica from
Africa during the breakup of Gondwana, which started in the
Jurassic. The breakup of Gondwana resulted not only in
stretching and thinning of the lithosphere, but also in extensive
rifting and volcanism. Basins such as the Mozambique basin
developed during the Karoo rifting, and as the basins were
loaded with sediments the crust flexurally subsided.
The main conclusions from this paper are as follows.
(1) The Archaean cratons have an effective elastic thickness
of at least 56 km compared with values in the range 21-39 km
for the Mozambique basin.
(2) We deduce from the coherence function of the whole
area that for topographic features with wavelengths greater
than about 500 km the lithosphere behaves as though it were
weak, whereas features of wavelength less than 300 km are
completely supported; features of intermediate wavelength are
partially supported by the plate.
(3) The isostatic anomaly map is characterized by an outstanding zone of positive anomalies along the Lebombe
Nuanetsi-Sabi volcanics zone, which is due to a combination
of crustal thinning and basic intrusions emplaced in the upper
crust. This zone also marks the transition between the strong
lithosphere of the cratons and the weak lithosphere under the
Mozambique basin.
ACKNOWLEDGMENTS
A major part of this paper comes from a Doctor of Philosophy
study by OG. We thank the University of Zimbabwe Research
0 1996 RAS, GJI 127, 635-650
Mechanisms of isostatic compensation in Africa
Board for funding the study. We also thank the British Council
for financial assistance through the Universities of Zimbabwe
and Leeds link scheme which enabled OG to carry out some
of the interpretation at the University of Leeds.
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