Conversely from gradient-based deterministic approaches, stochastic optimization methods, like Genetic Algorithms (GA), search for the global minimum of the misfit function within a given parameter range not requiring any calculation of gradients of error surfaces. But, more importantly, they collect a series of models and associated likelihoods that can be used to estimate the posterior probability density distribution (PPD). However, it is demonstrated that GA do not honour the principle of the importance sampling. Therefore, a biased estimation of the PPD is produced if it is directly computed from the collected models and their associated likelihoods. On the other hand applying Markov Chain Monte Carlo methods (MCMC), such as Metropolis-Hastings and Gibbs sampler, can provide accurate PPD but at considerable computational cost. In this work we use a hybrid method, which combines the speed of GA, to find an optimal solution, with the accuracy of a subsequent Gibbs sampling (GS), to obtain a reliable estimation of the PPD. We apply this method on a 1D elastic Full Waveform Inversion (FWI) on synthetic and actual data. It turns out that GA, if appropriately implemented, yield PPD estimations that, although with an underestimated variance, can be very close to the correct ones.
1D Elastic FWI and Uncertainty Estimation by Means of a Hybrid Genetic Algorithm-Gibbs Sampler Approach.
ALEARDI, MATTIA;MAZZOTTI, ALFREDO
2014-01-01
Abstract
Conversely from gradient-based deterministic approaches, stochastic optimization methods, like Genetic Algorithms (GA), search for the global minimum of the misfit function within a given parameter range not requiring any calculation of gradients of error surfaces. But, more importantly, they collect a series of models and associated likelihoods that can be used to estimate the posterior probability density distribution (PPD). However, it is demonstrated that GA do not honour the principle of the importance sampling. Therefore, a biased estimation of the PPD is produced if it is directly computed from the collected models and their associated likelihoods. On the other hand applying Markov Chain Monte Carlo methods (MCMC), such as Metropolis-Hastings and Gibbs sampler, can provide accurate PPD but at considerable computational cost. In this work we use a hybrid method, which combines the speed of GA, to find an optimal solution, with the accuracy of a subsequent Gibbs sampling (GS), to obtain a reliable estimation of the PPD. We apply this method on a 1D elastic Full Waveform Inversion (FWI) on synthetic and actual data. It turns out that GA, if appropriately implemented, yield PPD estimations that, although with an underestimated variance, can be very close to the correct ones.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
