The CPD can provide an approximation to the depth to the bottom of the magnetised crust that defines the depth to which ferromagnetic minerals lose their magnetisation. This depends on the magnetic mineralogy of the crust which is usually magnetite which has a Curie temperature of ~580?C (Ross et al., 2006; Spector & Grant, 1970). However, this value changes depending on the magnetic mineral composition within the rocks (Chiozzi et al., 2005).
Spectral methods have been intensively used in the determination of the depth to the Curie isotherm. These methods are best in determining the regional CPD by examining the spectral properties of the magnetic anomalies over relatively large regions (Blakely, 1988; Hussein et al., 2013; Shuey et al., 1977). As pointed out by (Hussein et al., 2013), the main problem with this method is that small scale variations in the CPDs and depth to the bottom of the magnetic source (DBMS) are difficult to determine. The area to be analysed to determine the depth to the bottom of a magnetic source must be at least three to four times the depth to that source (Bouligand et al., 2009; Hussein et al., 2013).
To estimate the depth to the base of magnetic source, a 2D power spectrum analysis approach by (Tanaka et al., 1999) was used, which was originally developed by (Okubo et al., 1985) based on the technique of (Spector & Grant, 1970). The radial average of the power density spectra of a magnetic anomaly is written as;
, 1
Where A is a constant related to the dimensions of the magnetic source, magnetization direction and geomagnetic field direction; Zt is the depth to the top of the magnetic source; Zb is the depth to the bottom of the magnetic source; and Z0 is the depth to the centre of the magnetic source. For wavelengths less than about twice the thickness of the magnetic source, eq. (1) can be approximated as;
Where B is a constant. From eq. (2), it is possible to estimate the depth to the top of the magnetic source by the slope of the power spectrum of the total field anomaly. On the other hand, eq. (1) can be rearranged as;
Where C is a constant. At long wavelengths, eq. (3) could also be written as;
, 4
where 2d is the thickness of the magnetic source. From eq. (4), it is possible to write an equation as follows:
Where D is a constant.
The depth to the top of the magnetic source could be estimated by fitting a straight lie through the medium to highest wavenumber portions of the radially averaged spectrum of ranging from 0.05 to 0.1 rad/km. On the other hand, the depth to the centroid is determined by fitting a straight line throught the lower wavumber number parts of the radially averaged spectrum of ranging between 0.008 and 0.04 rad/km as suggested by (Chiozzi et al., 2005; Hussein et al., 2013). The selection of the most suitable wavenumber band is very crucial for calculating the centroid and the top of the deepest anomalous magnetic sources (Bansal et al., 2011). The above wavenumber bands were selected because the power spectra show a clear linear segment that can be fitted (fig. required).
Finally, the depths to the bottom of the bodies were calculated using the equation . 6
In summary, as pointed out by (Dolmaz et al., 2005) the CPD estimates involves three stages as follows:
1) Division into overlapping square sub-regions,
2) Calculation of radially averaged log power spectrum for sub-regions,
3) Estimation of the CPD from the centroid and the top depth estimated from the magnetic source for each sub-region.
Due to the narrow width of continental rifts (30 – 50 km in the case of Rukwa Rift Basin), a 55 × 55 km window size was used in order to provide reliable estimates of the CPDs of less than 15 km. A 55 km window size is selected due the fact that a window size greater than 55 km will incorporate anomalies from the neighbouring geological provinces, a contamination that affects the estimation of basal depth within the region (Ross et al., 2006). As suggested by (Tanaka et al., 1999), a 50% overlap were used to obtain a better lateral coverage and to minimize the ringing artefacts (fading signal) near the edges. The power spectrum of each block is computed using the fast Fourier transform (FFT) implemented in MAGMAP extension in Oasis montaj software (Geosoft Inc., 2015). A first-order trend is removed from each block, and grids are expanded by 10% using the maximum entropy method to make the edges continuous.
The statistical error was calculated using the Linest Function in Excel based on the least squares best fit method (Chiozzi et al., 2005; Mousa et al., 2017). The error of the power spectrum from the linear fit was then calculated from the ratio between the standard deviation and the range of radial frequency used in the determination of Zt and Z0 based on the methods of Okubo et al. (2003).