Geophysical Application of Global Optimization Methods

Model based inversion methods as applied to geophysical problems Involve finding the global minimum of an objective function (given by a suitably chosen norm) that corresponds to an earth model which best explains the observed geophysical data. It has long been realized that geophysical inverse problems are nonlinear and the objective functions are multimodal. Traditionally such problems have been solved using iterative linear methods which require a good starting solution. We describe the application of two global optimization methods, namely, simulated annealing (SA) and genetic algorithm (GA) to a variety of geophysical problems such as I-D seismic waveform inversion, 2-D migration velocity estimation and 2-D resistivity inversion. For all these applications the GA and a variant of SA called very fast simulated annealing (VFSA) perform significantly better than a pure Monte Carlo search or an iterative linear inversion scheme. The GA 1-D seismic waveform inversion results applied to large offset marine CMP data compare very well with other independent inversion' results. For both 2-D seismic migration velocity analysis and 2-D resistivity problems, we prefer parameterizing the models by splines. This reduces the number of model parameters greatly and naturally applies smoothing over the model parameters resulting in a stable and computationally efficient algorithm. For both these applications VFSA was found to be superior than other inversion algorithms.