Hamiltonian Monte Carlo Inversion of Surface Wave Dispersion to Evaluate their Potential to Constrain the Density Distribution in the Earth.

We present a probabilistic approach to constrain the density distribution in the Earth based on surface wave dispersion. Despite its outstanding importance in studies of the Earth's thermo-chemical state and dynamics, 3D density variations remain poorly known, thereby posing one of the major challenges in geophysics.Since the sensitivity of most seismic data to density is small compared to sensitivity with respect to seismic velocities, regularisation in traditional deterministic inversion tends to bias the recovered density image significantly. To avoid this issue, we propose to solve a regularisation-free Bayesian inference problem using the Hamiltonian Monte Carlo Markov Chain algorithm.In the interest of simplicity, we consider anisotropic stratified media, where dispersion curves and corresponding sensitivity kernels can be computed semi-analytically. Exploiting derivative information for efficient sampling, Hamiltonian Monte Carlo approximates the posterior probability density of all model parameters, namely the P-wave velocities vPV and vPH, the S-wave velocities vSV and vSH, the anisotropy parameter , and, of course, density .The proposed method forms the foundation of an open-source tool box that can be used to assess the unbiased ability of surface wave dispersion data, characterised in terms of frequency and modal content, to constrain density variations and their trade-offs with other Earth model parameters.