Deep generative models for accelerated Bayesian posterior inference of microseismic events

We present a series of generative models for fast emulation of noiseless isotropic microseismic traces from source coordinates, given a 3D heterogeneous velocity and density model. The surrogate models can accelerate Bayesian source inversion by emulating the forward modelling of the seismograms, thus replacing the expensive solution of the elastic wave equation at each likelihood evaluation. Our generative models, based on deep learning algorithms, are trained using only 2000 synthetic seismic traces forward modelled with a pseudospectral method. We evaluate the performance of our methods on a testing set and compare them against state-of-the-art algorithms applied to the same data, showing that all of our models provide more accurate predictions and up to a $\mathcal{O}(10^2)$ speed-up factor during their training and evaluation. We finally apply our generative models to a posterior inference analysis of a simulated microseismic event. We show that constraints three times tighter can be obtained $\sim 40$ times faster than with existing methods. The speed, accuracy and scalability of our proposed models pave the way for extensions of these emulators to more complicated source mechanisms and applications to real data.