Global optimization methods for multimodal inverse problems

Abstract

Global optimization methods such as simulated annealing and genetic algorithms are potentially useful in attacking the multimodal search calculations which arise in a number of geophysical inverse problems. In the one-dimensional waveform inversion problem considered here, the optimization method must find a one-dimensional earth structure which produces a seismogram that agrees with an observed seismogram. Both simulated annealing and genetic algorithms provide satisfactory performance when the earth structure has only 15 free parameters. As this number is increased to 22, and then 30 parameters both techniques become more costly. Genetic algorithms, however, still yielded accurate solutions for problems with 30 free parameters, a point at which simulated annealing was only marginally useful. The superior performance of genetic algorithms may reflect the nonproximate search methods used by them or, possibly, the more complex and capacious memory available to a genetic algorithm for storing its accumulated experience.