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Article Dans Une Revue Geophysical Journal International Année : 2016

Stochastic seismic tomography by interacting Markov chains

Alexandrine Gesret
Thomas Romary
Mark S. Noble
Christophe Maisons
  • Fonction : Auteur

Résumé

Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches, they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high-dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case, the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on importance resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non-linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper, the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a simulated annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet-based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.

Dates et versions

hal-01410415 , version 1 (06-12-2016)

Identifiants

Citer

Alexis Bottero, Alexandrine Gesret, Thomas Romary, Mark S. Noble, Christophe Maisons. Stochastic seismic tomography by interacting Markov chains. Geophysical Journal International, 2016, 207 (1), pp.374-392. ⟨10.1093/gji/ggw272⟩. ⟨hal-01410415⟩
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