Non-linear multiparameter inversion using a hybrid global search algorithm: applications in reflection seismology

Abstract

SUMMARY Many interesting inverse problems in geophysics are non-linear and multimodal. Parametrization of these problems leads to an objective function, or measure of agreement between data and model predictions, that has a complex topography with many local minima. Optimization algorithms that rely on local gradients in the objective function or that search the model space locally may become trapped in these local minima. By combining simulated annealing with the downhill simplex method, a hybrid global search algorithm is presented in this paper for non-linear, multimodal, inverse problems. The hybrid algorithm shares the advantages of both local search methods that perform well if the local model is suitable, and global methods that are able to explore efficiently the full model space. The hybrid algorithm also utilizes a larger and more complex memory to store information on the objective function than simulated annealing algorithms. The effectiveness of this new scheme is evaluated in three problems: minimization of the multidimensional Rosenbrock function, non-linear, 1 -D, acoustic waveform inversion, and residual statics. The performance of the hybrid algorithm is compared with simulated annealing and genetic algorithms and is shown to converge more rapidly and to have a higher success rate of locating the global minimum for the cases investigated.