Real‐coded multi‐scale genetic algorithm for pre‐stack waveform inversion

Abstract

Due to strong non‐linearity of the seismic waveform inversion problem global optimization methods such as very fast simulated annealing (VFSA) and genetic algorithms (GA) have been employed to estimate model parameters from pre‐stack gathers. In this paper we revisit three fundamental issues, namely, the computation speed, layer parameterization, and efficient and accurate computation of posterior probability density (PPD) function. We demonstrate that given a model parameterization, we attain a substantial speed up in computation and obtain accurate estimates of model parameters using ‘real coding’ unlike conventional ‘binary coding’. Although one can apply full scale over‐parameterization together with smoothing to avoid the problem of layer definition, such an approach is computationally expensive. To address this, we employ a multi‐scale GA in which several GAs (each with different scale or layer thickness) are run in parallel. At each generation chromosomes from different scales are swapped using an up‐scaling or down‐scaling, as appropriate. We pick models in each generation from a proposal distribution that ensures smoothness and physical constraints. Such a multi‐scale GA is proven to converge to a stationary distribution, the PPD, and thus our algorithm is an efficient alternative to Monte Carlo Markov chain (MCMC) based on Metropolis‐Hastings algorithm or a Gibb's sampler. We demonstrate the feasibility and usefulness of our algorithm with application to data generated from well logs. A real coded GA shows a superior performance compared to a binary‐coded GA and multi‐scale GAs do help in identifying layer boundaries.