Imaging of fault-slip distributions using a trans-dimensional geodetic slip inversion approach

Estimation of fault-slip distributions from geodetic data is generally performed by employing least squares methods with a spatial smoothing constraint whose weight is optimized based on ABIC or L-curve. However, the conventional methods have various problems: unsuitabilities for strictly estimating non-negative solutions, estimating unknowns following non-Gaussian distributions, estimating spatially non-uniform slip distributions, and optimization of many hyper-parameters. To overcome these problems, we have developed a trans-dimensional geodetic slip inversion method using reversible-jump MCMC (rj-MCMC) technique [Green, 1995]. Based on the approach of Bodin & Sambridge [2009], we parameterized a fault domain by using the Voronoi partition and optimized the Voronoi partition and the slip amounts through the rj-MCMC sampling. When we optimize the Voronoi partition, a spatial smoothing constraint is no longer necessary. Moreover, we also estimated the optimum scaling factors for observational errors. We prepared 2000 replicas and calculated their ensemble to avoid local minimum and influence of initial values. The total number of samples are 5✕ 10⁶ . We applied the method to the synthetic data assuming a subduction zone and the actual geodetic observation data associated with the 2011 Tohoku-oki earthquake. We calculated synthetic data as responses to assumed fault-slips in an elastic media [Okada, 1992]. As a result, the method successfully reproduced the target fault-slips assuming both of smooth and sharp distributions; i.e., a spatially non-uniform fault-slip distribution can be imaged. Furthermore, the method provided posterior probability distributions of the unknowns, which show non-Gaussian distribution such as large slip with low probability near the trench. Besides, we figured out that the scaling factors for the observational errors were properly estimated. Meanwhile, it is difficult to consider sensitivity of the given observational data from a sequence of the rj-MCMC samples, we performed checkerboard resolution tests and confirmed utility of the tests. We concluded that the developed method is a useful technique to solve the problems on the conventional inversion method and to flexibly estimate slip distributions considering the complicate uncertainties.