An analytical method to interpret self-potential anomalies caused by 2-D inclined sheets

The first-order horizontal and vertical derivatives of the self-potential (SP) anomalies caused by a 2-D inclined sheet of infinite horizontal extent are analysed to obtain the depth h, the half width a, the inclination alpha, and the constant term containing the resistivity rho and the current density I of the surrounding medium. The vertical derivative of the SP anomaly is obtained from the horizontal derivative via the Hilbert transform, which is also redefined to yield a modified version, a 270 degrees phase shift of the original function. The point of intersection of these two Hilbert transforms corresponds to the origin. The amplitudes constitute a similar case. The practicability of the method is tested on a theoretical example as well as on field data from the Surda area of Rakha mines, Singhbhum belt, Bihar, India. The results agree well with those of other methods in use. Since the procedure is based on a simple mathematical expression involving the real roots of the derivatives, it can easily be automated.