Trans-dimensional Mt. Etna P-wave anisotropic seismic imaging

Trans-dimensional inference identifies a class of methods for inverse problems where the number of free parameters is not fixed. In seismic imaging these methods are applied to let the data, and any prior information, decide the complexity of the models and how the inferred fields partition the inversion domains. Monte Carlo trans-dimensional inference is performed implementing the reversible-jump Markov chain Monte Carlo (rjMcMC) algorithm; the nature of Monte Carlo exploration allows the algorithm to be completely non-linear, to explore multiple possibilities among models with different dimensions and meshes and to extensively investigate the under-determined nature of the tomographic problems, showing quantitative evidence for the limitations in the data-sets used. Implementations of this method overcome the main limitations of traditional linearized solvers: the arbitrariness in the selection of the regularization parameters, the linearized iterative approach and in general the collapse of the information behind the solution into a unique inferred model.

We present applications of the rjMcMC algorithm to anisotropic seismic imaging of Mt. Etna with P-waves. Mt. Etna is one of the most active and monitored volcanoes in the world, typically investigated under the assumption of isotropic seismic speeds. However, since body waves manifest strong sensitivity to seismic anisotropy, we parametrize a multi-fields inversion to account for the directional dependence in the seismic velocities. Anisotropy increases the ill-condition of the tomographic problem and the consequences of the under-determination become more relevant. When multiple seismic fields are investigated, such as seismic speeds and anisotropy, the data-sets used may not be able to independently resolve them, resulting in non-independent estimates and corresponding trade-offs. Monte Carlo exploration allows for the evaluation of the robustness of seismic anomalies and anisotropic patterns, as well as the trade-offs between isotropic and anisotropic perturbations, key features for the interpretation of tomographic models in volcanic environments. The approach is completely non-linear, free of any explicit regularization and it keeps the computational time feasible, even for large data-sets.