Ryoichiro Agata, Amato Kasahara, Yuji Yagi

The prediction errors that originate from the uncertainty of underground structure is often a major contributor of the errors between the data and the model predictions in fault slip estimation using geodetic or seismic waveform data. However, most studies on slip inversions either neglect the model prediction errors or do not distinguish them from observation errors. Several methods that explicitly incorporated the model prediction errors in slip estimation, which has been proposed in the past decade, commonly assumed a Gaussian distribution for the stochastic property of the prediction errors to simplify the formulation. Moreover, the information on slip distribution and the underground structure is expected to be successfully extracted from the data by accurately incorporating the stochastic property of the prediction errors.
In this study, we develop a novel flexible Bayesian inference method for estimating fault slips that can accurately incorporate non-Gaussian prediction errors. This method considers the uncertainty of the underground structure, including fault geometry based on the ensemble modeling of the uncertainty of Greens function. Furthermore, the framework allows the estimation of the posterior probability density function (PDF) of the parameters of the underground structure, by calculating the likelihood of each sample in the ensemble.
To validate the advantage of the proposed method, we performed simple numerical experiments for estimating the slip deficit rate (SDR) distribution on a 2D thrust fault using synthetic data of surface displacement rates. In the experiments, the dip angle of the fault plane was the parameter used to characterize the underground structure. The proposed method succeeded in estimating a posterior PDF of SDR that is consistent with the true one, despite the uncertain and inaccurate information of the dip angle. In addition, the method could estimate a posterior PDF of the dip angle that has a strong peak near the true angle. In contrast, the estimation results obtained using a conventional approach, which introduces regularization based on smoothing constraints and does not explicitly distinguish the prediction and observation errors, included a significant amount of bias, which was not noticed in the results obtained using the proposed method. The experiments with different settings of the parameters suggested that inaccurate prior information of the underground structure with a small variance possibly results in significant bias in the estimation results, particularly the posterior PDFs for SDR, those for the underground structure, and the posterior predicted PDF of the displacement rates. The distribution shapes of the prediction errors for the representative model parameters in certain observation points are significantly asymmetric with large absolute values of the sample skewness, for which Gaussian approximation is not usually applied.