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 Mw 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.