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

Abstract

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 highresolution 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.

An efficient regularized inversion approach for self-potential data interpretation of ore exploration using a mix of logarithmic and non-logarithmic model parameters

“…The SP anomaly (V ) due to a semi-infinite vertical cylinder, infinitely long horizontal cylinder, or sphere ( Figure 1) at a point P (x) along a profile has a closed-form solution, and is given by Abdelrahman et al, 2004;El-Araby, 2004;Essa et al, 2008;Monteiro Santos, 2010;Fedi and Abbas, 2013)…”

“…Gokturkler and Balkaya (2012) described three global optimization approaches based on stochastic algorithms (genetic algorithm (GA), simulated annealing (SA), and particle swarm optimization (PSO)) to invert SP anomalies by some polarized bodies of simple geometries, and concluded that the inverse parameters recovered by the GA, SA and PSO are in good agreement. Fedi and Abbas (2013) developed a fast imaging technique (the so called depth from extreme points (DEXP) method) based on the upward continuation to interpret SP anomalies.…”

Improving the local wavenumber method by automatic DEXP transformation

“…To circumvent this effect, we present a new multiscale method, which is highly stable vs. high wavenumber noise. In particular, we will consider the DEXP transformation (Fedi, 2007;Fedi and Abbas, 2013) of the LWN and will derive a simple scaling-law, which is specific for this function.…”

Depth from extreme points method for gravity gradient tensor data

“…Many of these methods have been improved in order to be applied in gradient tensor data interpretation, such as the migration method (Zhdanov et al 2011(Zhdanov et al , 2012 and the correlation (probability) method (Guo et al 2009). Fedi and Abbas (2013) demonstrated that it also is a reliable method to interpret self-potential data. It has shown many advantages over other methods due to its flexible form of depth weighting.…”