INTRODUCTION
Mapping faults within a sedimentary basin is critical to an exploration program for oil, gas, petroleum, groundwater and solid minerals. Even where the basement is highly fractured, the overlying sediments hide them from view. However, these fractures are reactivated at later times during, or after, deposition of the sedimentary section and create structures and/or sedimentary facies that become oil and gas traps and reservoirs.
Pierce et al. (1998) showed that fluid flow along vertically aligned fractures is an important factor controlling the deposition of minerals in sedimentary sections. The working hypothesis is that fluids scavenge metals from the basement rocks and these fluids move regionally updip along fractures of opportunity. When the metalsrich fluid reach a reducing environment such as shale or a hydrocarbon charged zone, a variety of iron rich minerals are precipitated. Similarly, groundwater movement and accumulation in rocks is facilitated by the increased secondary porosity and permeability resulting from a network of fractures and faults.
On potential field maps, fractures and faults mark zones where there are changes
in the density or magnetic susceptibility of the rock mass. In particular, gravity
data in sedimentary basins are sensitive to vertical offsets across highangle
faults, where rocks with different densities are juxtaposed. Therefore, faults
can be identified on gravity anomaly maps using any of the available schemes
for mapping contacts such as the calculation of derived fields: The horizontal
gradient magnitude, the analytic signal and the local wavenumber or their enhanced
equivalents, such as the enhanced analytic signal amplitude and the enhanced
local wavenumber.
The method used to map faults in this study was described by Zeng et al (1994). It is based on the calculation of the Cross Correlation Function (CCF) between the gravity anomaly of an area and the gravity anomaly due to a model fault. The main restriction here is that the displacement on the fault is vertical as in normal or reverse faults so that the structure can be represented by a step.
THEORY OF THE METHOD
Let g_{o}(n), n = 1, 2, 1………M, represent the observed Bouguer anomaly
values at M points along a profile and g_{f}(n'), n' = N,Y,0,YYN are
the calculated anomalies along a profile perpendicular to the strike of a step
fault. Since we are interested in shallow faults, the observed and the calculated
gravity values may be replaced by their second vertical derivative functions
g_{o}” (n) and g_{f}” (n), respectively. Then, the Cross Correlation
Function (CCF) between g_{o}”(n) and g_{f}”(n’) at point x
on the profile is given by:
Where x = N+1, N+2,………………,M  N. The discrete
form of the second vertical derivative of the gravity anomaly due to a step
is given by
where I = N, …,1,0,1,2,……N, Δx is the station spacing,
G is the gravitational constant, ρ is the density contrast of the step,
h_{1} and h_{2} are the depths to the top and bottom of the
step, respectively.
Since the gravity anomaly g_{o}(n) includes the effects of faults that
may exit in the area, then the moving window CCF expressed in Eq.
1 produces a maximum at each point x along the profile where there is a
fault. The CCF method has an additional advantage which is not provided by the
application of derived fields mentioned earlier. This relates to the polarity
of the fault with respect to the location of the downthrown/upthrown side of
the step. Where the polarity of the detected faults is the same as that of the
model step, the CCF is a maximum. If the polarity of the fault is opposite that
of the model step, the CCF is a minimum. Furthermore, because the faults will
generally have different strike directions, it is necessary to perform the cross
correlation analysis along two orthogonal directions, namely along profiles
in the eastwest and northsouth directions of the grid in order to map all
faults. Consequently, two maps of the CCF are required for fault mapping in
a given area.
The study area: The study was conducted on a 12, 100 km^{2}
area bounded by latitudes 7°30' and 8°30' and longitudes 8°30' and
9°30' and located in the Benue trough, Nigeria. The northeast trending trough
is about 800 km long and 80 to 150 km wide and is filled with Cretaceous rocks
whose age range from middle Albian to Maastrichtian. It is bounded on either
side by granite and gneisses of probably Palaeozoic age, which make up the crystalline
basement. Structures in the area include two major anticlines, the Keana anticline,
which trends some 64 km in a northeasterly direction from east of Keana and
another which runs with ENE trending axis immediately north of Awe Cratchley
and Jones (1965). Faulting is significant in the area and the en echelon arrangement
of some of the folds axes suggest sinistral movement along NNE shear faults
(Benkhelil, 1982).
PROCESSING AND ANALYSIS OF GRAVITY DATA
The gravity data used in this study was taken from the Bouguer anomaly map of the Benue valley (Fig. 1) prepared by Cratchley and Jones (1965). The contour map was digitized and interpolated unto a square grid with a spacing of 1.0 km. A contour map of the gravity field is shown in Fig. 2a. The major trend of the contours is southwestnortheast, parallel to the trend of the trough. In the central and southeastern portions, the trend of the contours is mainly eastwest. The magnitude of the gravity field increases from the northwestern corner to the east and to the south. A prominent closure of gravity low occurs near the center of the study area.
Since we are interested in shallow faults, a Second Vertical Derivative (SVD)
map was produced to highlight the short wavelength anomalies and suppress the
long wavelength anomalies associated with deep structures. This was achieved
using the FFT technique, thus necessitating that the grid be preconditioned
by detrending and tilting to make the southeast and northwest corners equal.

Fig. 1: 
Generalized geological map of Nigeria showing the Benue trough
and the study area 

Fig. 2: 
(a) Bouguer anomaly map of the study area and its (b) second
vertical derivative field 
This was followed by extrapolating the data in the north and east directions
using a cosine taper to make the opposite sides of the data wrap smoothly in
both directions. This preconditioning significantly minimizes the distortion
of the high frequency and axial regions of the spectra, characteristic of the
discrete transform (Cordell and Grauch, 1982). Furthermore, because of the amplification
of noise in second derivative computation, the SVD data was subjected to a lowpass
filter to suppress the high frequency noise components. The resulting SVD map
is shown in Fig. 2b.
RESULTS AND DISCUSSION
The CCF maps for the eastwest and northsouth directions are shown in Fig.
3.

Fig. 3: 
Maps showing the normalised cross correlation functions for
(a) eastwest and (b) northsouth directions 
Faults can be interpreted on these maps by drawing lines along the long axis
of elongated closures defining maxima or minima in the contour pattern as described
by Zeng et al (1992). A different and less subjective approach was used
to mark out maxima and minima in this study. This involved the use of the computer
program BOUNDARY described by Phillips (1992), which automatically identifies
points of maxima on the CCF grid. In order to use the same program to identify
points of minima, the values on the CCF grid were multiplied by 1 before the
search for maxima which actually are minima. In effect, two maps showing maxima
(Fig. 4) and minima (Fig. 5), respectively
were produced for each CCF map. On these maps, a fault will be taken to consist
of points which are contiguous and display unambiguous continuity.

Fig. 4: 
Maps showing the maxima of the cross correlation functions
for (a) eastwest and (b) northsouth directions 

Fig. 5: 
Maps showing the minima of the cross correlation functions
for (a) eastwest and (b) northsouth directions 
Based on this criterion, faults interpreted from the maxima and minima of
the CCF for the study area are shown in Fig. 6 and 7,
respectively.
At present, there is no field data to corroborate the mapped faults. However,
one can rely on both direct and indirect evidence. The former derives from the
regional structural map of Nigeria prepared by the Geological Survey, Nigeria
(1985). Some of the faults interpreted from the CCF maps coincide with fractures
on the structural map particularly when the short aligned segments in the former
are joined together to form continuous and longer features (Fig.
8). Indirect evidence of these faults is sourced from the occurrence of
leadzinc mineralization in the area. These are restricted to Albian and Cenomanian
strata and are better defined on lobes located in steeplydipping fracturefilled
veins striking mainly northsouth and grouped in NESW zones generally associated
with the axes of the major anticlines (Cratchley and Jones, 1965). Some of the
northsouth trending faults are normal faults resulting from the major strikeslip
movements associated with the formation of the trough (Benkhelil).

Fig. 6: 
Maps showing the faults deduced from the maxima of the cross
correlation functions for (a) eastwest and (b) northsouth directions 

Fig. 7: 
Maps showing the faults deduced from the minima of the cross
correlation functions for (a) eastwest and (b) northsouth directions 

Fig. 8: 
Structural map of the study area showing major fractures and
folds (after Geological Survey of Nigeria, 1985) 
CONCLUSIONS
The anomalies observed on a typical Bouguer anomaly map represent the integrated effects of lateral variations in rock density due to faults, intrusive bodies, shear zones, etc. Faults of the normal or reverse type can be identified easily on gravity anomaly profiles. Using the same method to identify faults on maps can be tedious and time consuming particularly for large areas. However, the use of the cross correlation function technique, as demonstrated in this study, is efficient and rapid. When data on a gravity anomaly map is correlated with the gravity effect of a model step, maximum positive correlation occurs at points where the observed anomaly has the same polarity as that of the model fault while a minimum occurs where they have opposite polarities. Application of the method to part of the Benue trough, Nigeria facilitated the identification of known faults and others which have not been mapped previously.