Optimization strategies for Markov chain Monte Carlo inversion of seismic tomographic data
Probabilistic approach to inverse problem by means of Monte Carlo simulation is a computationally intensive approach whose feasibility has shown to be directly connected with the availability of computational resources and optimization. This study aims to introduce at first some fundamental theoretical aspects and to focus on the issue of optimization of McMC algorithms. We developed a transdimensional inversion scheme in the framework offered by the established deterministic inversion code simulr16. The issues of optimization and performance improvement were tackled by means of parallel independent realizations of the sampling process in addition to a staggered grid approach. The inverse model parametrization of the simulr16 code in conjunction with transdimensional McMC sampling, provided an affordable and reliable inversion strategy able to offer naturally smooth solutions equipped with a quantitative uncertainty estimation. Our probabilistic inversion method was tested on synthetic data and then applied on the inversion of a field data set from the Salzach valley (Austria). The structures recovered with our approach are compatible with those obtained with other well established methods. Metropolis-Hastings-based McMC algorithms require a careful tuning in order for the model space to be optimally sampled. Sub-optimal scaling of the size of random walk steps for Markov samplers leads to less efficient chains that require longer runtimes. We proposed a multivariate updating scheme that, using information carried by the model resolution matrix, proved to improve the performances of the classical M-H proposal. Trade-off relations between model parameters were obtained from the model resolution matrix and implemented in our updating scheme. McMC and non-stochastic tests revealed an improvement in performance in terms of increased acceptance rate and enhanced mixing properties.
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