New methods for shape and depth determinations from SP data

Abstract

We have extended our earlier derivative analysis method to higher derivatives to estimate the depth and shape (shape factor) of a buried structure from selfpotential (SP) data. We show that numerical second, third, and fourth horizontal-derivative anomalies obtained from SP data using filters of successive window lengths can be used to simultaneously determine the depth and the shape of a buried structure. The depths and shapes obtained from the higher derivatives anomaly values can be used to determine simultaneously the actual depth and shape of the buried structure and the optimum order of the regional SP anomaly along the profile. The method is semi-automatic and it can be applied to residuals as well as to observed SP data.We have also developed a method (based on a leastsquares minimization approach) to determine, successively, the depth and the shape of a buried structure from the residual SP anomaly profile. By defining the zero anomaly distance and the anomaly value at the origin, the problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of form f (z) = 0. Knowing the depth and applying the least-squares method, the shape factor is determined using a simple linear equation.Finally, we apply these methods to theoretical data with and without random noise and on a known field example from Germany. In all cases, the depth and shape solutions obtained are in good agreement with the actual ones.

A Best-Estimate Approach for Determining Self-potential Parameters Related to Simple Geometric Shaped Structures

“…5. Using derivative analysis techniques, these methods were developed by ABDELRAHMAN et al (1998ABDELRAHMAN et al ( , 2003, and necessitate higher derivative anomaly. 6.…”

Evaluation of the streaming potential effect of piping phenomena using a finite cylinder model

“…This is so because a low data density with respect to the depth of a body can give uncertain estimations of the required characteristic points. These are the reasons that a derivative analysis of SP anomalies (Abdelrahman et al, 1998;Abdelrahman et al, 2003) cannot be applied in most of the SP fields recorded at dams. The finite cylinder formula can be added to the existing analytical expressions for the bodies of simple geometrical forms.…”

“…Recently, Abdelrahman et al (2003), published an interpretation method based on this formula. The favourable results obtained from such an approach can be understood if the fields generated by both models are analysed.…”

A new method for complete quantitative interpretation of self-potential anomalies

“…Here, the model parameters that give a best fit are derived using an initial presumption, as well as characteristic points and distances from the measured anomaly curve. Examples of these methods are of Abdelrahman and Sharafeldin (1997), Abdelrahman et al (1997bAbdelrahman et al ( , 2003.…”