Finite Element Models for Near-Fault Stress Rotations and the Distribution of Lower Crustal Strain

Lynch, John C.; Richards, Mark A.; Department of Geology and Geophysics, University of California at Berkeley; Berkeley, California 94720-4767,

The relationship between the state of stress in California and the San Andreas fault is poorly understood. While the maximum principal compressive stress is nearly perpendicular to the fault throughout the state, the cumulative moment release over the past 150 years is dominated by almost purely strike-slip earthquakes. Reconciling these two observations is one of the more important topics facing modelers of crustal deformation. Additionally, little is known about the distribution of strain in the lower crust. While both distributed and localized deformation models have been used successfully to model post-seismic and strain accumulation data, it has been shown that such geodetic data alone cannot distinguish between the two extremes. Addressing these issues, we present here finite element models of earthquakes in an elastic layer overlying a finite width viscoelastic shear zone in the lower crust.

The overall dimensions of the model are 300 km wide, 400 km long, and 50 km deep, with three geometries for the lower crustal shear zone considered: 1) a viscoelastic half-space approximation, with a shear zone that extends to the model boundaries (300 km in width); 2) a wide shear zone model (70 km in width); and 3) a narrow shear zone model (10 km in width). Earthquakes are simulated with a momentarily frictionless fault plane centered above the shear zone, extending to a depth of 15 km and running the length of the mesh. Far field plate velocity boundary conditions are enforced at the edges and fault stresses evolve naturally. A Coulomb-type failure criterion is set such that the earthquake cycle is $\sim 250$ years. The models are run until a limit cycle is reached and transient stresses have died out.

We focus on the maximum changes in the stress field during the earthquake cycle by examining stresses immediately before and after each earthquake. We present results in the form of maximum principal stress orientations and beach ball diagrams that facilitate visualizing the full tensor. We find that shear stresses are concentrated in the upper crust where it overlies the viscoelastic shear zone. Thus, the maximum principal stress in the far-field is rotated toward higher angles with respect to the fault strike when compared to its orientation above the shear zone. Our results suggest that an examination of stress orientations in the upper crust from focal mechanisms and bore hole breakouts may provide insight as to the distribution of strain in the lower crust, and may eventually allow us to distinguish between localized and distributed deformation models. Additionally, this model provides an alternative interpretation for recent observations of maximum principal stress rotations near major strike slip faults.