A fast interpretation of self-potential data using the depth from extreme points method

We used a fast method to interpret self-potential data: the depth from extreme points (DEXP) method. This is an imaging method transforming self-potential data, or their derivatives, into a quantity proportional to the source distribution. It is based on upward continuing of the field to a number of altitudes and then multiplying the continued data with a scaling law of those altitudes. The scaling law is in the form of a power law of the altitudes, with an exponent equal to half of the structural index, a source parameter related to the type of source. The method is autoconsistent because the structural index is basically determined by analyzing the scaling function, which is defined as the derivative of the logarithm of the self-potential (or of its pth derivative) with respect to the logarithm of the altitudes. So, the DEXP method does not need a priori information on the self-potential sources and yields effective information about their depth and shape/typology. Important features of the DEXP method are its high-resolution power and stability, resulting from the combined effect of a stable operator (upward continuation) and a high-order differentiation operator. We tested how to estimate the depth to the source in two ways: (1) at the positions of the extreme points in the DEXP transformed map and (2) at the intersection of the lines of the absolute values of the potential or of its derivative (geometrical method). The method was demonstrated using synthetic data of isolated sources and using a multisource model. The method is particularly suited to handle noisy data, because it is stable even using high-order derivatives of the self-potential. We discussed some real data sets: Malachite Mine, Colorado (USA), the Sariyer area (Turkey), and the Bender area (India). The estimated depths and structural indices agree well with the known information.