Using convolutional neural networks to expedite the Hamiltonian Monte Carlo inversion of Rayleigh wave dispersion curves

The inversion of Rayleigh wave dispersion curves is a non-linear problem in which a numerical sampling of the posterior probability density function (pdf) is needed for accurate uncertainty appraisals. Hamiltonian Monte Carlo (HMC) algorithm is a very promising sampling method that guarantees rapid convergence toward the stationary regime while maintaining high acceptance ratios and independence between the sampled models. The main downside of HMC is that several forward evaluations per iteration are needed to compute the derivative information of the target pdf. This makes this approach inapplicable to problems with expensive forward calculations and many unknown parameters. Here, we replace the semi-analytical evaluation of the forward problem (i.e. the Haskell-Thomson method) with a convolutional neural network that, once trained, can be evaluated extremely fast. This introduces a modelings error that can also be reliably propagated into the posterior model. We validate our approach on synthetic inversions in which the observed dispersion curves have been extracted from seismic gathers computed on a schematic subsurface model. Our tests demonstrate that this strategy guarantees accurate model estimations and uncertainty evaluations while ensuring a very efficient sampling that is order of magnitude less computationally expensive than a standard HMC based on the Haskell-Thomson method