DeepGEM-EGF: A Bayesian strategy for joint estimates of source-time functions and empirical Green's functions

An earthquake record is the convolution of source radiation, path propagation and site effects, and instrument response. Isolating the source component requires solving an ill-posed inverse problem. Whether the instability of inferred source parameters arises from varying properties of the source, or from approximations we introduce in solving the problem, remains an open question. 
Such approximations often derive from limited knowledge of the forward problem. The Empirical Green’s function (EGF) approach offers a partial remedy, by approximating the forward response of large events using the records of smaller events. The choice of the « best » small event drastically influences the properties estimated for the larger earthquake. Discriminating variability in source properties from epistemic uncertainties, stemming from the forward problem or other modeling assumptions, requires us to reliably account for, and propagate, any bias or trade-off introduced in the problem. 
We propose a Bayesian inversion framework that aims at providing reliable and probabilistic estimates of source parameters (here, for the source-time function or STF), and their posterior uncertainty, in the time domain. We jointly solve for the best EGF using one or a few small events as prior EGF. Our approach expands on DeepGEM, an unsupervised generalized expectation-maximization framework for tomography (Gao et al., 2021). We demonstrate, with toy models and various applications to mainshocks of Mw ranging from ~4 to 6.3, the potential of DeepGEM-EGF to disentangle the variability of the seismic source from biases introduced by modeling assumptions.