Development of a Trans-Dimensional Fault Slip Inversion for Geodetic Data

Geodetic fault slip inversions have generally been performed by employing a least squares method with a spatially uniform 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 these 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 need for spatially uniform smoothing constraints. 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.