Rapid sampling of model space using genetic algorithms: examples from seismic waveform inversion

摘要: SUMMARY The seismic waveform inversion problem is usually cast into the framework of Bayesian statistics in which prior information on model parameters combined with data and physics forward to estimate a posteriori probability density (PPD) space. The PPD function an objective or fitness computed from observed synthetic data. In general, multimodal its shape unknown. Global optimization methods such as simulated annealing (SA) genetic algorithms (GA) do not require that be known. this paper, we investigate GA rapidly sample most significant portion portions PPD, when very little available. First, use simple three operator (selection, crossover mutation) acting randomly chosen finite population haploid binary coded models. We plane wave transformed normalized cross-correlation [E(m)] frequency domain function. A moderate value probability, low mutation high update proper size are required reach close global maximum Next, attempt accelerate convergence show concepts can used stretching function, i.e., exp [E(m)/T] rather than E(m) where T control parameter analogous temperature annealing. By schemata analysis, at temperatures, above average values reproduced large numbers causing much more rapid algorithm. assigns nearly equal selection thus retains diversity among members population. Thus step type cooling schedule (very beginning followed by temperature) improves performance dramatically: obtained using only half many models would conventional GA. Similar could also achieved first then decreasing value, while retaining same throughout. We address ‘genetic drift’ causes GAs converge one peak other algorithm applied highly several peaks height. parallel based concept ‘punctuated equilibria’ implemented circumvent problem. run each subpopulation collect good these runs. These grasp portion(s) compute weighted mean derived uncertainty parameters.