Earthquake cycle simulations with rate-and-state friction and nonlinear Maxwell rheology

Kali L. Allison, & Eric M. Dunham

Submitted May 19, 2017, SCEC Contribution #7272

We present a numerical method for simulating earthquake cycles with rate-and-state fault friction and an off-fault nonlinear Maxwell viscoelastic rheology. This is done for the classic 2D antiplane shear geometry of a vertical, strike-slip plate boundary fault. We investigate the interaction between fault slip and bulk viscous flow with parameters motivated by the well-studied Mojave Desert region in Southern California. Experimentally-based flow laws for quartz-diorite and olivine are used for crust and upper mantle, respectively. We consider a suite of three linear geotherms, having $dT/dz = 20$, 25, and 30 K/km. These simulations produce different deformation styles in the lower crust and upper mantle, ranging from significant interseismic fault creep to purely bulk viscous flow. Despite the differences in deformation style, the simulations have almost identical earthquake recurrence interval, nucleation depth, down-dip coseismic slip limit, and total coseismic surface slip. This indicates that bulk viscous flow and interseismic fault creep load the brittle portion of the crust similarly, even though viscous flow is distributed over a region that is several kilometers wide. Despite these similarities, the predicted postseismic surface deformation varies between the simulations, in a manner that might permit discrimination of the deformation mechanism at depth using geodetic observations. In general, frictional afterslip is significant over a shorter time period following an earthquake, and significant displacements are observed closer to the fault, than when deformation at depth occurs via bulk viscous flow. Additionally, the simulations make different predictions regarding stress within the lithosphere throughout the interseismic period. In the 25 and 30~K/km simulations, the upper crust drags the low crust and mantle; the 20~K/km simulation predicts this as well, except within 10~km of the fault, where the reverse occurs. However, basal tractions play a minor role in the overall force balance of the lithosphere. As a result, the integrated stress on the fault and its deep extension it is balanced mainly by shear stresses on vertical planes parallel to the fault. Because the region below the fault experiences higher strain rates than the region far from the fault, stresses are higher below the fault than far from it at the same depth. This means that the upper crust far from the fault has to bear a substantial part of the load, resulting in unrealistically high stresses. We speculate that in the real Earth, this might lead to the formation of subparallel strike-slip faults as part of the plate boundary.

Key Words
earthquake cycle, viscoelastic flow, power law rheology, strike-slip, brittle-ductile transition, rate and state friction, summation-by-parts operators

Allison, K. L., & Dunham, E. M. (2017). Earthquake cycle simulations with rate-and-state friction and nonlinear Maxwell rheology. Tectonophysics, (submitted).