Developing a Dynamic Stress Inversion Method to Study Coseismic Stress Evolution of Earthquakes

Abstract:

Kinematic slip inversions of earthquakes have been the primary tool for seismologists to infer what happens during an earthquake, including temporal and spatial evolutions of slip and final slip distribution on the fault. From final slip distribution, one may also calculate stress changes around the fault, which has been used routinely to calculate Coulomb stress changes on nearby faults to assess potential risks of nearby faults after a major earthquake.

Recently, Xie and Cai (2018) develop an earthquake stress model and apply it to the 2011 Mw 9.0 Tohoku earthquake. In this model, deformation in the medium is considered as the results of stress changes on the fault directly. Using this model, they invert both shear and normal stress changes on the fault due to the 2011 Tohoku earthquake directly from GPS data. The zero shear stress change contour precisely delineates the rupture area on the fault, which is much clearer than that from kinematic slip inversions. Fault normal stress becomes more compressive on the down-dip portion and less compressive on the up-dip portions from the hypocenter, respectively. These changes in fault normal stress may be difficult to infer from kinematic slip inversions.

In this work, we develop a dynamic stress inversion method based on the earthquake stress model to study coseismic stress evolution on the fault. In this method, numerical Green’s functions at selected stations are calculated by an explicit finite element method for a unit change of shear or normal stress change on a sub-fault patch. These forward calculations for real cases with low velocity layers at shallow depth are computationally demanding and need high-performance computing. In the inversion, we apply several constraints, including zero normal slip (i.e., no separation or penetration of the fault), non-negative shear slip (i.e., positive or zero shear slip), and moment constraints. Tests on a checkerboard model, a synthetic data set and real data set, based on the 2016 Mw5.0 Cushing (Oklahoma) earthquake show that the method works well with stable solutions. The spatial resolutions depend on station coverage and frequency contents in seismic recordings. We expect that the method will improve seismic source inversions significantly from a dynamic point of view.