Determination of depth and the half-width of an inclined plate selfpotential anomaly using a second moving average window curves method

Self-potential (SP) prospecting is one of the oldest geoelectrical methods, and it is stillused in many fields of applied geophysics. The SP measurements refer to that part of thenatural electric field which is stationary in time, or nearly so, and whose current sourcesystem is generated and sustained by phenomena occurring underground withingeological structures. From the physical point of view, the common aspect of the manysource models is an electrical charge polarization is setup, which is responsible forelectrical current circulation in conductive rocks. Hence, the detected SP anomalies aresimply the surface evidence of a more or less steady state of electrical polarization (Abdelrahman et al., 1999). The two-dimensional inclined sheet model can be useful inquantitative interpretation of SP data measured in a small area over a buried structure.Estimating the depth upper edges and the dip of a two-dimensional inclined sheet fromself-potential anomalies measured perpendicular to the strike of the structures has drawnconsiderable attention. The advantages of the fixed geometrical methods over the 2-D and3-D continuous modeling are that they require no current density, and the resistivity andrough estimation on depth and the interpretation of isolated SP anomalies is fast andaccurate. Many of the geological structures in mineral exploration can be classified intofour categories: spheres, vertical cylinders, horizontal cylinders and inclined sheets. Thesefour simple geometric forms are convenient approximations of common geologicalstructures often encountered in the interpretation of SP data. The models may not beentirely geologically realistic, but the approximate equivalence is usually sufficient todetermine whether the form and magnitude of calculated SP effects are close enough tothose observed to make the geologic interpretation reasonable. Evaluation of the depthand the width of a 2D plate from self-potential (SP) anomalies measured perpendicular tothe strike of the structure has attracted considerable attention. Several methods have been proposed and discussed by many researchers to interpret the self-potential anomalies caused by 2D inclined plates, including, for example, logarithmic curve matching(Murthy and Haricharan, 1985) and the analysis in the frequency domain using theFourier transform (Rao et al., 1982). In this paper, a new method has been developed toestimate the depth and the half-width of a 2D inclined plate with a self-potential anomaly.This method is the second- moving average for successive window lengths to determinethe depth and half-width of two-dimensional inclined plate. For a fixed window length,the depth is determined iteratively using the solution of a nonlinear equation with theiterative Newton Raphson method for each half-width value (Stanley, 1977). Thecomputed depths are plotted against the half-width values representing a continuouswindow curve. This method can be used for two model and synthetic data with andwithout random noise. After adding 10% random error in the synthetic data, themaximum error in model parameters is less than 3%. The problem of determining theplate parameters from self-potential data of short profile length can be solved using thesecond-moving average method. The method of window curves has been extended usingthe second-moving average self-potential anomaly to determine the depth and half-widthof an inclined plate.