*Gravity Anomaly and Basement Estimation Using Spectral Analysis DOI: http://dx.doi.org/10.5772/intechopen.99536*

content. Naturally, high-frequency anomalies are due to shallow anomalous sources whereas the low-frequency anomalies are due to anomalous sources that are at greater depths. The average power spectrum of potential field data usually shows a decaying curve with increasing frequency [21]. Spector and Grant [21] method has become an important technique for top depth estimation of anomalous sources in frequency/wavenumber domain [23]. Their concept is based on an ensemble of prisms of frequency-independent randomly and uncorrelated distribution of sources equivalent to white noise distribution. According to Spector and Grant [21] method, the logarithm of the power spectrum generated from horizontal distribution of sources is always directly proportional to ð Þ �**2***dw* , where *d* is the depth to top of sources and *w* is the radial wavenumber. The depth of the anomalous sources can therefore be estimated directly from the slope of the logarithmic plot of the power spectrum against the wavenumber. The power spectrum of sources could suggest the presence of various horizontal distributions of anomalous sources in the crust pending on the number of segments defined from the power spectrum. The power spectrum is usually not straight, due to the randomly and uncorrelated distribution of anomalous sources assumed in the Spector and Grant [21] method. The random and uncorrelated distribution was assumed due to lack or little knowledge about the depth distribution of the sources. The statistical ensemble of anomalous sources is therefore determined using the following equation

$$\ln\left[P(\boldsymbol{w})\right] = \ln\left[\mathbf{C}\right] - 2\mathbf{d}\mathbf{w} = \ln\left[\mathbf{C}\right] - 4\mathbf{n}df \tag{1}$$

### **Figure 4.**

*Residual component of the complete Bouguer gravity anomaly map. Central block (B01, B02, … , B17) of 55 km x 55 km with 50% overlap are shown for the sedimentary basement estimation. Gboko as well as the basement outcrops east of Ogoja are shown. Intrusions and locations of the anticline and syncline are superimposed.*

This equation is analogous to equation of straight line as follows

$$y = m\mathbf{x} + \mathbf{C} \tag{2}$$

Comparing the two equations, it can be shown that, the slope ð Þ *m* power spectrum is given as

$$m = -2d = -4\text{nd} \tag{3}$$

$$\text{for depth}, d = -\frac{m}{2} = -\frac{m}{4\text{n}}\tag{4}$$

**Figure 4** shown, is the residual gravity anomaly map showing the central 55 km x 55 km blocks used for the estimation of sedimentary basement. Seventeen (17)

**Figure 5.** *Power spectra of blocks (B01, B02, … , B06), showing the depths (D1 & D2) estimated.*

*Gravity Anomaly and Basement Estimation Using Spectral Analysis DOI: http://dx.doi.org/10.5772/intechopen.99536*

**Figure 6.** *Power spectra of blocks (B07, B02, … , B12), showing the depths (D1 & D2) estimated.*

blocks labeled B1, B2, … , B17 for estimations with 50% overlapping are shown. The approach of spectral analysis for the estimation of sedimentary thickness has been done. **Figures 5**–**7**, showed the seventeen power spectra generated from the gravity anomaly. In the area, basement depth between 2.01 km and 3.73 k is calculated and interpreted the sedimentary basement and shallow sources interpreted in term of depth to top of intrusions in the area between the depths of 0.45 km and 0.76 km (**Figure 8**).

**Figure 7.** *Power spectra of blocks (B13, B02, … , B17), showing the depths (D1 & D2) estimated.*
