Hamiltonian Monte Carlo inversion of surface wave dispersion curves: preliminary results

Rayleigh wave measurements are highly sensitive to the S-wave velocity (Vs) and for this reason they are attractive for geotechnical characterization or seismic site response studies (Socco and Strobbia 2004). Over the last years, the full-waveform inversion of surface waves is getting growing attention thanks to the increased computational power of modern parallel architectures (Gross et al. 2017). Well-established methods rely on dispersion curve inversion under the assumption of a 1D subsurface structure. The dispersion curve inversion is a highly non-linear and ill-conditioned problem. For these reasons, it is crucial adopting inversion approaches that efficiently converge toward the global minimum. In this context, local inversion methods exhibit fast convergence rates but limited capability to explore the model parameter space, resulting in a final solution highly dependent on the initial model. Global search algorithms (genetic algorithms, simulated annealing) exhaustively explore the model space but they usually require a considerable computational effort ( Cercato, 2011). Markov Chain Monte Carlo (MCMC) algorithms exhibit global convergence capabilities and honour the importance sampling principle, but they usually rely on specific MCMC recipes in order to maintain the computational cost affordable. More specifically, MCMC methods are primarily affected by low acceptance rates and show strong correlations between the sampled models. Hamiltonian Monte Carlo (MC) algorithm was designed to circumvent these two critical issues of MCMC algorithms. HMC treats a model as the mechanical analogue of a particle that moves from its current position (current model) to a new position (proposed model) along a given trajectory. The geometry of the trajectory is controlled by the misfit function, which is interpreted as potential energy (U), and by the kinetic energy (K) and the mass of the particle. After the so-called burn-in period, the ensemble of HMC sampled models can be used to numerically derive the so-called posterior probability density (PPD) function in the model space. In this work we apply an HMC algorithm for inverting Rayleigh waves dispersion curves on synthetic and experimental tests. We inverted for Vs, Vp/Vs ratio and layer thicknesses, whereas the density is kept fixed during the inversion at a constant value. The implemented HMC algorithm requires the number of layers be defined as input to the inversion. However, the limited computational cost of the HMC inversion allows us to perform different inversions with different model space parameterizations. Then, standard statistical tools (such as χ2 probability or the Bayesian information criterion “BIC”) can be used to define the most appropriate model parameterization to use.