Bayesian Elastic Full‐Waveform Inversion Using Hamiltonian Monte Carlo
Lars Gebraad, Christian Boehm, Andreas Fichtner
Abstract
Abstract We present a proof of concept for Bayesian elastic full‐waveform inversion in 2‐D. This is based on (1) Hamiltonian Monte Carlo sampling of the posterior distribution, (2) the computation of misfit derivatives using adjoint techniques, and (3) a mass matrix tuning of the Hamiltonian Monte Carlo algorithm that accounts for the different sensitivities of seismic velocities and density. We apply our method to two synthetic end‐member scenarios with different dimension that are particularly relevant in the context of full‐waveform inversion: low‐dimensional models ( ) with potentially large variations in material parameters and high‐dimensional models ( > 30,000) describing smaller‐scale variations of lower amplitude relative to some background. For both end members, the Hamiltonian Monte Carlo sampling reliably recovers important aspects of the posterior, including means, covariances, skewness, and 1‐D and 2‐D marginals. Depending on the strength of material variations, the posterior can be significantly non‐Gaussian. This suggests to replace local methods for uncertainty quantification based on Gaussian assumptions by proper sampling of the posterior. In addition to P wave and S wave velocity, the sampling provides constraints on density structure that are free from subjective regularization artifacts.