An Automatic Geophysical Inversion Procedure Using a Genetic Algorithm

Abstract

One of the most interesting challenges of the last twenty years in geophysics is the determination of the structure of the underground from data from geophysical prospection. The goal of the inverse problem in seismic reflection is to identify the velocity distribution in the underground from recorded reflection profiles of acoustic waves. This identification problem can be turned into an optimization problem whose the objective function is quite irregular. Indeed, it is highly nonlinear, exhibits several local minima and can be globally discontinuous. An efficient way to find a global optimum (or a good local optimum) for such a problem is to use stochastic algorithms like Genetic Algorithms. The work presented in this paper relies on the use of an hybrid GA, based on a variable-length piecewise-constant representation built on Voronoi diagrams. The choice of a reliable fitness function is also a crucial step for the success of the inversion method. The classic least square error (LSE) can be successfully used for the inversion of simple models in reasonable computing times. However, when dealing with more complex models that are greedier in terms of computing time, the LSE criterion alone is not sufficient, and had to be coupled with the Semblance, a more geophysical criterion, introduced by Taner and Koehler (1969), in which the adaptability of a model is derived from the flatness of imaged events in the migrated cube. Numerical results on 2D simulated data illustrate the effectiveness of the proposed approach, and enlighten some weaknesses of each criterion (LSE or Semblance) considered alone.KeywordsGenetic AlgorithmVoronoi DiagramVoronoi CellSalt DomeLess Square ErrorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.