Bayesian estimation of fault slip distributions based on ensemble modeling of the underground structure uncertainty

Abstract:

In fault slip estimation using geodetic or seismic waveform data, the prediction errors originated from the underground structure uncertainty is often a major contributor to the errors associated with the estimation. However, most studies on slip inversions neglected the model prediction errors or did not distinguish it from observation errors. In the past decade, several methods that incorporate the model prediction errors explicitly in slip estimation were proposed. These methods commonly assume Gaussian distribution for the stochastic property of the prediction errors to simplify the formulation.

Here, we develop a flexible Bayesian estimation method for estimating fault slips that can accurately incorporate non-Gaussian prediction errors. The method considers the uncertainty of the underground structure, including fault geometry based on the ensemble modeling of the uncertainty of Green’s 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. The method also estimated a posterior PDF of the dip angle that has a strong peak near the true angle. The distribution shapes of the prediction errors for the representative model parameters in certain observation points are significantly asymmetric with large absolute values of skewness, for which Gaussian approximation is not usually applied.