Estimation of the heterogeneity of stress fields using misfit angles in focal mechanisms

Abstract

The stress field of the Earth's crust is spatially heterogeneous on various scales. The focal mechanism of an earthquake provides important information associated with the stress state at the seismogenic depths. These focal mechanisms are affected by the pore fluid pressure and/or friction coefficient. In this study, we focused on misfit angles, particularly the difference in the angle between the slip direction in an observed focal mechanism and the resolved shear stress direction that can be obtained using the directions of the principal stress axes and the stress ratio of a reference stress field. Resolved shear stress does not depend on the fault friction or pore fluid pressure, allowing us to use misfit angles to evaluate the heterogeneity of stress fields if the effect of an error in a focal mechanism has been properly removed. By statistically evaluating the error in focal mechanisms using a Bayesian approach, we evaluated the misfit angles of the aftershocks of the 2000 Western Tottori Earthquake, in which numerous focal mechanisms could be precisely determined using dense seismic observation. The spatial distribution of the misfit angles of the aftershocks suggested that the stress field in the aftershock region, particularly in the southern portion of the region, was in a heterogeneous state. We also demonstrated that this spatial variability cannot be explained solely by errors in the focal mechanisms. If we assume a uniform stress field before the mainshock, the observed cumulative curve of misfit angles can be explained by coseismic stress changes and the background stress field's depth gradient of differential stress of 3.2 MPa/km.