Hamiltonian Monte Carlo inversion of Rayleigh wave dispersion curves: Preliminary results on synthetic data.

We present a Hamiltonian Monte Carlo (HMC) algorithm to infer S-wave velocity and layer thicknesses from the inversion of Rayleigh wave dispersion curves. The aim of this work is three-fold: derive a reliable uncertainty appraisal, implement an inversion method with global converge capabilities and fast-convergence rates. Differently from classical MC methods, HMC is a sampling algorithm that constructs an artificial Hamiltonian system in which a model is treated as a high-dimensional particle moving along a trajectory in an extended space. Using derivatives of the forward operator, HMC is able to make long-distance moves from the current towards a new independent model, thereby promoting model independence, while maintaining high acceptance ratios. To draw essential conclusions about the suitability of the HMC approach to dispersion curve inversion, we focus on synthetic data inversions and we limit to consider the fundamental mode, which is analytically computed from schematic 1D reference models. The combination of HMC algorithm with standard statistical tools (e.g. chi-squared value) is used to infer to most appropriate model parameterization. Our preliminary tests show that the HMC algorithm is a very promising approach for dispersion curve inversion that guarantees reliable uncertainty appraisals and accurate model predictions with an affordable computational effort.