Bayesian framework for inversion of second-order stress glut moments: application to the 2020 M_w 7.7 Caribbean Earthquake

Abstract

We present a fully Bayesian inverse scheme to determine second moments of the stress glut using teleseismic earthquake seismograms. The second moments form a low-dimensional, physically-motivated representation of the rupture process that captures its spatial extent, source duration, and directivity effects. We determine an ensemble of second moment solutions by employing Hamiltonian Monte Carlo and automatic differentiation to efficiently approximate the posterior. Our method explicitly constrains the parameter space to be symmetric positive definite, ensuring the derived source properties have physically meaningful values. The framework accounts for the autocorrelation structure of the errors and incorporates hyperpriors on the uncertainty. We validate the methodology using a synthetic test and subsequently apply it to the 2020 M_w 7.7 Caribbean earthquake. The second moments determined for this event indicate the rupture was nearly unilateral and relatively compact along-strike. The solutions from this inverse framework can resolve ambiguities between slip distributions with minimal a priori assumptions on the rupture process.

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