We developed a flexible finite-fault inversion method for teleseismic P waveforms to obtain a detailed rupture process of a complex multiple-fault earthquake. We estimate the distribution of potency-rate density tensors on an assumed model plane to clarify rupture evolution processes, including variations of fault geometry. We applied our method to the 23 January 2018 Gulf of Alaska earthquake by representing slip on a projected horizontal model plane at a depth of 33.6 km to fit the distribution of aftershocks occurring within one week of the mainshock. The obtained source model, which successfully explained the complex teleseismic P waveforms, shows that the 2018 earthquake ruptured a conjugate system of N-S and E-W faults. The spatiotemporal rupture evolution indicates irregular rupture behavior involving a multiple-shock sequence, which is likely associated with discontinuities in the fault geometry that originated from E-W sea-floor fracture zones and N-S plate-bending faults.

Geodetic fault slip inversions have been generally performed by employing a least squares method with a spatial smoothing constraint. However, this conventional method has various problems: difficulty in strictly estimating non-negative solutions, assumption that unknowns follow the Gaussian distributions, unsuitability for expressing spatially non-uniform slip distributions, and high calculation cost for optimizing many hyper-parameters. Here, we have developed a trans-dimensional geodetic slip inversion method using the reversible-jump Markov chain Monte Carlo (rj-MCMC) technique to overcome the problems. Because sub-fault locations were parameterized by the Voronoi partition and were optimized in our approach, we can estimate a slip distribution without the spatial smoothing constraint. Moreover, we introduced scaling factors for observational errors. We applied the method to the synthetic data and the actual geodetic observational data associated with the 2011 Tohoku-oki earthquake and found that the method successfully reproduced the target slip distributions including a spatially non-uniform slip distribution. The method provided posterior probability distributions with the unknowns, which can express a non-Gaussian distribution such as large slip with low probability. The estimated scaling factors properly adjusted the initial observational errors and provided a reasonable slip distribution. Additionally, we found that checkerboard resolution tests were useful to consider sensitivity of the observational data for performing the rj-MCMC method. It is concluded that the developed method is a powerful technique to solve the problems of the conventional inversion method and to flexibly express fault-slip distributions considering the complicated uncertainties.

We consider a Bayesian multi-model fault slip estimation (BMMFSE), in which many candidates of the underground-structure model characterized by a prior probability density function (PDF) are retained for a fully Bayesian estimation of fault slip distribution to manage model uncertainty properly. We performed geodetic data inversions to estimate slip distribution in long-term slow slip events (L-SSEs) that occurred beneath the Bungo Channel, southwest Japan, in around 2010 and 2018, focusing on the two advantages of BMMFSE: First, it allows for estimating slip distribution without introducing strong prior information such as smoothing constraints, handling an ill-posed inverse problem by combining a full Bayesian inference and accurate consideration of model uncertainty to avoid overfitting; second, the posterior PDF for the underground structure is also obtained through a fault slip estimation, which enables the estimation of sequential events by reducing the model uncertainty. The estimated slip distribution obtained using BMMFSE agreed better with the distribution of deep tectonic tremors at the down-dip side of the main rupture area than those obtained based on strong prior constraints in terms of the spatial distribution of the Coulomb failure stress change. This finding suggests a mechanical relationship between the L-SSE and the synchronized tremors. The use of the posterior PDF for the underground structure updated by the estimation for the 2010 L-SSE as an input of the analysis for the one in 2018 resulted in a more preferable Bayesian inference, indicated by a smaller value of an information criterion.