Reversible-Jump, Markov-Chain Monte Carlo seismic tomographic inversion for anisotropic structure in subduction zones

The implementation of stochastic methods in seismic tomography arises as a response to the limitations introduced by traditional non-linear optimization solvers. Since tomographic problems are generally ill-conditioned, additional constraints on the model are set in the misfit function, and the weight given to each minimization term has a level of arbitrariness; different solutions are obtained with different choices for the damping/smoothing factors. Non-linear optimization solvers are based on a perturbative approach which linearizes the forward modelling locally around a reference model, updated at each iteration until convergence. These methods need the evaluation of the derivatives of the predictions with respect to the parameters of the model, which is not always an easy task, and they generally do not provide the uncertainties associated with the solution model.
The Reversible-Jump Markov-Chain Monte Carlo is a stochastic method which performs a random walk in the model space sampling the posterior probability distribution associated with the model in the light of the observations. This method is a trans-dimensional Metropolis-Hastings where the number of parameters used to represent the continuous fields (as interpolation nodes) is treated as a parameter itself of the inversion, as the positions of the nodes. Using statistical estimators on the ensemble of models produced by the algorithm it is possible to extract a reference model, typically as an average of the ensemble. With this method no regularization is needed, and uncertainty can be estimated using the ensemble of models sampled. The limitations of non-linear optimization solvers are overcome at the cost of an increase in the computational time required.

The presented applications of this method involve seismic tomography in subduction zones, where the anisotropic component of the seismic velocity field is relevant, and the inversion of seismological data could provide an interesting insight into the dynamics of these regions.