Summary
In the last few decades, the spectral analysis approach has been successfully applied for depth estimation of gravity and magnetic anomaly sources by analyzing the signal power distribution as a function of spatial frequencies. In the present work, application of high-resolution spectral methods is proposed for inversion of self-potential (SP) data. In particular, Periodogram Method (PM), Maximum Entropy Method (MEM) and Multi Taper Method (MTM) are used to invert synthetic SP data generated by cylinder and sheet sources. From analysis, MEM was found to be better in providing more accurate estimates of the source depth as compared to PM and MTM. Finally, the application of the proposed methods to field data is presented and the estimated depths are compared with those obtained by other numerical methods.
Introduction
Several graphical and numerical methods have been proposed for a quantitative interpretation of SP data. As concerns the numerical based approach, different methods have been developed for detecting source parameters (shape and/or depth), such as derivative and gradient analysis (Abdelrahman et al., 1997, 1998, 2003), Fourier transform analysis (Asfahani et al., 2003; Das and Agarwal, 2012), Enhanced Local wavenumber technique (Srivastava and Agarwal, 2009), extended Euler deconvolution (Agarwal and Srivastava, 2009). Some of these methods need a priori information on the anomalous body shape, others require the computation of the second order derivatives, which are very sensitive to noise.
Electric as well as gravity and magnetic fields are potential fields, and, therefore, satisfy Laplace's or Poisson's equations and their properties can be described in the Fourier domain. For this reason, features of the sources (depth to the interface) of potential field data can be determined by using methods of spectral analysis. Recently, high resolution spectral methods have been applied for interpreting magnetic and gravity data (Ghil et al., 2002; Bansal et al., 2006). In this work, three different methods of spectral analysis, i.e. Periodogram Method (PM), Maximum Entropy Method (MEM) and Multi Taper Method (MTM) are used for depth estimation of selfpotential (SP) anomaly sources. Once power spectrum is computed, the top depth of the anomalous body is estimated as half of the slope of straight line fitted to the log of power spectrum, P(k), versus the wavenumber, k, by following the approach of Spector and Grant (1970). If more than one straight line can be fitted in the log P - k plot, the slopes of subsequent line fits will give the shallower depths for higher wavenumbers (Spector and Grant, 1970).
