Bayesian Self‐Adapting Fault Slip Inversion With Green's Functions Uncertainty and Application on the 2016 M w 7.1 Kumamoto Earthquake

Kinematic finite‐extent models of earthquake sources can be determined by inverse modeling of observed waveforms and/or geodetic data. Such models are subject to significant uncertainty as a result of inaccurate observations and imperfect physical description of the complex properties of the Earth's crust. For slip inversions of large earthquakes, the major source of uncertainty is related to the uncertainty of Green's functions due to the imperfect description of the crustal model and selected parameterization of the source model. To account for both, we introduce an effective nonlinear Bayesian slip inversion with transdimensional source parameterization, including analytical representation of uncertainties of Green's functions. Our nonlinear slip inversion method relies on a self‐adapting spatial parametrization of the slip distribution by means of a varying number of spline control points on the assumed fault. For the temporal parameterization, it utilizes the regularized Yoffe function with spatially varying rise time and rupture velocity. Rake angle is also treated as an unknown spatially dependent parameter. The Green's function uncertainties are included using full covariance matrices. The posterior probability density function is sampled by the transdimensional Markov chain Monte Carlo algorithm with parallel tempering. The performance of our slip inversion method is demonstrated on a synthetic test from the Source Inversion Validation project and real‐data inversion of the 2016 M w 7.1 Kumamoto earthquake. In the latter test, we infer an ensemble of ~7,300,000 possible rupture models, representing samples of the posterior probability density, and inspect which features of these models are reliable and which are rather artifacts.