AN ANALYTICAL METHOD TO INTERPRET SELF-POTENTIAL ANOMALIES CAUSED BY 2-D INCLINED SHEETS

The first-order horizontal and vertical derivatives of the self-potent ial (SP) anomalies caused by a 2-D inclined sheet of infinite horizont al extent are analysed to obtain the depth h, the half width a, the in clination alpha, and the constant term containing the resistivity rho and the current density I of the surrounding medium. The vertical deri vative of the SP anomaly is obtained from the horizontal derivative vi a the Hilbert transform, which is also redefined to yield a modified v ersion, a 270 degrees phase shift of the original function. The point of intersection of these two Hilbert transforms corresponds to the ori gin. The amplitudes constitute a similar case. The practicability of t he 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 proce dure is based on a simple mathematical expression involving the real r oots of the derivatives, it can easily be automated.