Hamiltonian Monte Carlo Inversion of Seismic Sources in Complex Media

We present a probabilistic seismic point source inversion, taking into account 3-D heterogeneous Earth structure. Our method rests on (1) reciprocity and numerical wavefield simulations in complex media and (2) Hamiltonian Monte Carlo sampling that requires only a small amount of test models to provide reliable uncertainty information on the timing, location, and mechanism of the source. Using spectral element simulations of 3-D, viscoelastic, anisotropic wave propagation, we precompute receiver side strain tensors in time and space. This enables the fast computation of synthetic seismograms for any hypothetical source within the volume of interest, and thus a Bayesian solution of the inverse problem. To improve efficiency, we developed a variant of Hamiltonian Monte Carlo sampling. Taking advantage of easily computable derivatives, numerical examples indicate that Hamiltonian Monte Carlo can converge to the posterior probability density with orders of magnitude less samples than the derivative-free Metropolis-Hastings algorithm, which we use for benchmarking. Exact numbers depend on observational errors and the quality of the prior. We apply our method to the Japanese Islands region where we previously constrained 3-D structure of the crust and upper mantle using full-waveform inversion with a minimum period of 15 s.