Transdimensional 2D Full-Waveform Inversion and Uncertainty Estimation

Abstract

Full-Waveform Inversion (FWI) has now become a widely accepted tool to obtain high-resolution velocity models from seismic data. Typically, the velocity model in its discrete form is represented on a rectangular grid, and we solve for the elastic properties at these grid points. FWI is mostly solved employing a local optimization method, where one obtains a velocity update by minimizing the misfit between the observed and the calculated seismograms. Note also that FWI is a highly non-linear problem which is known to be prone to non-uniqueness. The convergence to a globally optimum solution is not guaranteed; it depends on the choice of the starting model. Thus, a Bayesian formulation of the inverse problem with subsequent sampling of the posterior distribution is a preferred choice, since it enables uncertainty quantification. However, with the increase in the dimension of a model, sampling search space becomes computationally expensive. We employ a recently developed trans-dimensional sampling method called Reversible Jump Hamiltonian Monte Carlo (RJHMC), to the 2D full waveform inversion problem. We represent our velocity model using Voronoi cells, determined from the distribution of certain nuclei points in the model space. This method offers two advantages. First, it solves for a variable dimensional velocity updates by using a trans-dimensional reversible jump Markov Chain Monte Carlo (RJMCMC) step and thus tries to achieve an optimum number of nuclei to represent the model and minimize the misfit. A smaller number of parameters helps in an efficient sampling of the model search space. Second, it applies the gradient-based Hamiltonian Monte Carlo (HMC) step, which further improves the sampling by allowing the algorithm to take a large step guided by the gradient. This two-step algorithm proves to be a useful tool for model exploration and uncertainty quantification in FWI.