DeepGEM-egf: A Bayesian strategy for joint estimates of Source time functions and Empirical Green's functions

Théa Ragon, Angela F. Gao, & Zachary E. Ross

Published September 8, 2024, SCEC Contribution #13992, 2024 SCEC Annual Meeting Poster #054

An earthquake record is the convolution of source radiations, path propagation and site effects, and instrument response. Isolating the source component requires solving an ill-posed inverse problem. Whether the inferred instability of source parameters arises from varying properties of the source, or from approximations we introduce in the problem, remains an open question. Such approximations often derive from limited knowledge of the forward problem. The Empirical Green’s functions (EGF) approach, which consists of assuming the records of a small event represent the forward response of a larger one, is only a partial remedy. Indeed, 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 and STF using one or a few small events as prior EGF. Our approach is based on DeepGEM, an unsupervised Generalized Expectation-Maximization framework for blind inversion (Gao et al., 2021). We demonstrate with toy models, and an application to a Californian swarm, the potential of DeepGEM-egf to bring STFs characterization to a new level of detail, and to deepen our understanding of the variability of the source of earthquakes.

References :
Angela F. Gao, Jorge C. Castellanos, Yisong Yue, Zachary E. Ross, and Katherine L. Bouman (2021). "DeepGEM: Generalized Expectation-Maximization for Blind Inversion." Neural Information Processing Systems, 2021.

Citation
Ragon, T., Gao, A. F., & Ross, Z. E. (2024, 09). DeepGEM-egf: A Bayesian strategy for joint estimates of Source time functions and Empirical Green's functions. Poster Presentation at 2024 SCEC Annual Meeting.

Related Projects & Working Groups
Seismology