Extraction of structure-based geoelectric models by hybrid genetic algorithms

Abstract

A major difficulty in electrical resistivity imaging is the identification of the lithologic units, especially in the sedimentary environments. The geologic interpretation generally is realized by visual inspection of the final resistivity section. Although sharp boundary inversion techniques based on a local linearization could allow the delineation of interfaces between geologic units, these techniques will succeed only if an initial model already close to the best solution is available. Stochastic algorithms might localize a point around the global minimum of the misfit function; however, they are not efficient at finding the precise solution. For this reason, our previously published hybrid genetic algorithms, derived from evolution theories, are used to verify structure-based models. The geometric parameters are defined by thickness values of the lithologic units at control points distributed along the horizontal axis. A zero thickness value indicates the nonexistence of a certain unit at the corresponding con-trol point. An unstructured grid composed of irregular triangles is constructed by the application of Delaunay triangulations to represent complicated structural boundaries. In addition, the computation time for the calculation of model response is reduced greatly by this strategy. Because the suggested parameterization reduces the number of unknown parameters to a few tens and the computation time for the model responses is reduced by the Delaunay triangulation, the implementation of hybrid genetic algorithms for 2D problems becomes possible. A huge number of models are generated randomly in the first generation (a population of parameters) and then updated in subsequent generations by the simulation of biological processes. The suggested algorithms consist of two computational phases. In the first stage, the physical property of each subsurface layer is represented by a distinct resistivity value. After some succeeding genera-tions, laterally varying resistivities within the same lithologic unit are permitted to simulate lateral changes in geologic conditions.