The Upper Mantle Seismic Velocity Structure of South-Central Africa and the Seismic Architecture of Precambrian Lithosphere Beneath the Congo Basin - Geology and Resource Potential of the Congo Basin - page 7

The ensemble of group velocity measurements at each
period was inverted using a linear 2-D tomographic inver-
sion to obtain maps of Rayleigh wave group velocities. The
inversion was performed over a grid of 1

information, invert for a one dimensional shear wave velo-
city profile for grid nodes every 0.5 , and apply a Gaussian
weighted smoothing parameter across the one-dimensional
models to create a quasi 1 cells and the

slowness for each cell was calculated using a conjugate
gradient method (Paige and Saunders 1982 ). Damping and
smoothing were used to stabilize the inversion. Changing the
damping parameter did not significantly affect the results,
and therefore a low damping of 0.1 was used. A smoothing
value of 3,000 was used for all periods based on tradeoff
curves between smoothing and travel time misfit (Fig. 1.7 ).
Values of misfits in velocity, as defined by the expression
P dis tan ce

three-dimensional shear wave

velocity model.
To compute shear wave velocity profiles at each node, we
follow the inversion methodology described by Juli ` et al.
( 2000 ). This method uses an iterative damped generalized
linear least-squares approach that inverts the data with model
smoothness and weighting parameters to solve for changes to
a starting velocity model. The method was designed to jointly
invert dispersion and receiver function data, and so to apply
this joint inversion method, we designate the weight assigned
to receiver function data to be equal to zero.
The starting model used for the inversions is the IASP91
(Kennett and Engdahl 1991 ) model. The model parameter-
ization includes 21 layers with a 37-km thick continental
crust. Within the crust, the top ten layers are each 1 km thick,
the next three layers are each 2 km thick, and the bottom four
layers are each 5 km thick. Ten km thick layers are used in
the mantle to a depth of 700 km. In the inversion, velocities
below 200 km depth are fixed to IASP91 (Kennett and
Engdahl 1991 ) values. We include a 1 km thick layer
above and below the Moho with no vertical smoothing to
constrain the Moho depths, yet still allow large variation in
velocity across the Moho. A linear smoothing parameter is
used to prevent large and unrealistic contrasts in velocity
between adjacent layers, which Rayleigh waves are not
sensitive to. For the ocean basins, the model parameter-
ization is similar to the continent but with the Moho fixed
at a depth of 7 km.
A continental crustal thickness of 37 km was used every-
where because a recent study that compared crustal structure
in eastern Africa to southern and central Africa using
receiver functions found little variability in the thickness of
Precambrian crust, which comprises most of the study region
(Tugume et al. 2012 ). The average crustal thickness for most
terrains varies between 35 and 40 km, and therefore we used
a mid-range value of 37 km. Because there are no seismic
estimates of crustal thickness for the Congo Basin, we used
our group velocities between periods of 20 and 50 s to see if
there was any evidence for substantial thinning of the crust
under the basin, as argued for by Kadima et al. ( 2011b ).
Figure 1.10 shows a plot of the average group velocity curve
for the regions of the basin where Kadima et al. ( 2011b )
show crustal thickness on the order of 25-30 km, and syn-
thetic dispersion curves calculated using a model that
contains low velocity sediments in the top 5 km of the
crust, an average crustal Vs of 3.7 km/s and a Moho ranging
from 20 to 40 km depth. The best fit to the data is obtained
for models with a Moho at 35 to 40 km depth. This result
justifies using a crustal thickness beneath the basin that is

t

2

1 1

predicted traveltime observed traveltime

number of dispersion curves

are used as approximations for uncertainty in velocity and
were found to be between 0.06 and 0.48 km/s.
Checkerboard tests were performed to estimate the model
resolution. The velocity of the input checkers was 9%of

the initial model velocity, and synthetic velocities were
calculated from the actual ray paths and then inverted
using the procedure described above. From the recovered
models, it was determined that 4 checkers were the smallest
size that could be resolved over the Congo Basin (Fig. 1.8 ).
Regions of limited resolution were excluded from further
analyses, which include all regions north of 7 north latitude
where there is a substantial amount of smearing between
many of the checkers.
Figure 1.9 shows the maps of Rayleigh wave group
velocities for periods of 20, 40, 60, 80 and 100 s. At periods
greater than 100 s, the resolution degrades considerably
because of limited ray path coverage, and therefore we do
not use group velocities for periods greater than 100 s. At
shorter periods (20 and 40 s), the most prominent features
are lower velocity regions associated with the Congo and
Kalahari Basins. At these periods, the Rayleigh waves still
have sufficient sensitivity to the low velocity sediments to
make the basin locations stand out. At periods of 60 s and
higher, regions of expected thick lithosphere begin to
emerge as regions of faster velocity (i.e. the Tanzania,
Congo, Kaapvaal and Zimbabwe cratons) separated by
slower regions.

1.4.2 Shear Wave Velocity Model

We follow the method of Park et al. ( 2008 ) for inverting the
group velocity observations to obtain a quasi-three dimen-
sional shear wave velocity model for the upper mantle. In
this method, we constrain crustal structure based on a priori