Bayesian inversion for tectonic stress level using topography and rupture models

Stress loading controls the energy release of earthquakes, which is of fundamental importance for understanding the earthquake hazard. However, stress at the seismogenic depth can only be estimated indirectly through seismic observations. One strategy of stress estimation is to use the co-seismic slip model of large earthquakes to estimate the back-ground stress level. By assuming stresses on the fault plane is a combination of back-ground and topographic stresses, the slip-direction on the fault plane can be influenced by the topography changes. For earthquakes ruptured through significant topographic changes, the topographic stresses may introduce observable slip direction changes on the fault plane. Thus, slip direction changes revealed by finite fault rupture models, provides a probe to investigate the back-ground stress level. Due to the non-linearity of this inversion problem, we use a Bayesian inversion strategy so that the uncertainty of the results can be estimated. The posterior probability distribution is yielded by the Markov chain Monte Carlo (MCMC) sampling method.

To validate the efficiency of this inversion scheme, we conducted synthetic tests using point stress loading on the ground and slip model on a rectangular fault plane to explore the effect of topography on the slip directions. The influence of topographic stress depends on the geometry and relative location of the fault. As the dip angle increase, the sense of motion on the fault plane changes from reverse left-lateral to normal left-lateral when the topography is located on the hanging wall; and changes from normal left-lateral to reverse right-lateral if topography loading on the footwall. We also invert for the tectonic stress fields using the Bayesian MCMC method based on synthetic slip data produced by tectonic stress tensors with different magnitudes. The larger the real tectonic stress, the smaller the constraint of topographic stress on it in the inversion process. Even the tectonic stress is larger than the topographic stress by 3 magnitudes, we can still recover the input tectonic stress tensor, indicating the high effectiveness and stability of the Bayesian MCMC approach.