Non‐linear inversion of resistivity profiling data for some regular geometrical bodies¹

Abstract

The inversion of resistivity profiling data involves estimation of the spatial distribution of resistivities and thicknesses of rock layers from the apparent resistivity data values measured in the field as a function of electrode separation. The drawbacks of using traditional curve-matching techniques to solve this inverse problem have been overcome by iterative linear techniques but these require good starting models even if the shape of the causative body is asssumed known. In spite of the recent developments in inversion techniques, no robust method exists for the inversion of resistivity profiling data for the simple model of dikes and spheres which are the classical models of geophysical prospecting.We apply three different non-linear inversion schemes to invert synthetic resistivity profiling data for the classical models embedded in a uniform matrix of contrasting resistivity. The three non-linear algorithms used are called the Metropolis simulated annealing (SA), very fast simulated annealing (VFSA) and a genetic algorithm (GA). \7e compare the performance of the three algorithms using synthetic data for an outcropping vertical dike model. Although all three methods were successful in obtaining optimal solutions for arbitrary starting models, VFSA proved to be computationally the most efficient.

Hybrid optimization methods for geophysical inversion

“…-1-1-1 1 I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 I I 1 close to the global minimum and the CG algorithm helped in accelerating the convergence. This also confirms the notion that VFSA reduces the misfit rapidly in the initial iterations and requires a large number of model evaluations to further reduce the misfit as discussed in Chunduru et al (1995). This study suggests that the cost effectiveness of the hybrid algorithm can best be improved by applying the CG algorithm only at the most appropriate points on the error surface.…”

“…Detailed derivations of equations governing the CG method are given in Young (1971) and a detailed description of the Monte Carlo methods are given by various researchers (Metropolis et al, 1953;Kirkpatrick et al, 1983: Rothman, 1985: Sen and Stoffa, 1995. Chunduru et al (1995) and Sen and Stoffa (1995) compared various global algorithms in the inversion of resistivity profiling data and found VFSA to be computationally the most efficient. VFSA as described in Ingber (1989) is a variant of simulated annealing that allows for narrowing the search range with iteration and results in rapid convergence.…”

“…Comparison of hybrid algorithms with other optimization algorithms Sen and Stoffa (1995) compared variants of simulated annealing (heat bath, SA, VFSA) and genetic algorithms [GA, evolutionary programming (EP)] using the 1-D resistivity sounding data from the above examples. A comparison of these algorithms was done by finding the number of model evaluations required to find a good model by allowing the same search range for all the model parameters.…”

“…The data consist of 19 observation points. The same data set was analyzed by Sen et al (1993) using heat bath SA and by Sen and Stoffa (1995) using a suite of global optimization algorithms.…”

Object-based model verification by a genetic algorithm approach: Application in archeological targets

“…Some genetic algorithms that use a 1D conceptual model for the interpretation of vertical electrical sounding data have been described by Başokur et al (2007), Fernández Alvarez et al (2008), Jha et al (2008) and Sen and Stoffa (1995). Chunduru et al (1995) compared global methods for the interpretation of apparent resistivity profiling data by using some regular geometrical bodies, such as a dike and a sphere. Some other variants of the genetic algorithm employed for the 2D interpretation of magnetotelluric data can be found in Everett and Schultz (1993) and Perez-Flores and Schultz (2002).…”