A High‐Order Accurate Summation‐By‐Parts Finite Difference Method for Fully‐Dynamic Earthquake Sequence Simulations Within Sedimentary Basins

Abstract

We present an efficient numerical method for earthquake sequences in 2D antiplane shear that incorporates wave propagation. A vertical strike‐slip fault governed by rate‐and‐state friction is embedded in a heterogeneous elastic half‐space discretized using a high‐order accurate Summation‐by‐Parts finite difference method. Adaptive time‐stepping is applied during the interseismic periods; during coseismic rupture we apply a non‐stiff method, enabling a variety of explicit time stepping methods. We consider a shallow sedimentary basin and explore sensitivity to spatial resolution and the switching criteria used to transition between solvers. For sufficient grid resolution and switching thresholds, simulations results remain robust over long time scales. We explore the effects of full dynamics and basin depth and stiffness, making comparisons with quasi‐dynamic counterparts. Fully‐dynamic ruptures generate higher stresses, faster slip rates and rupture speeds, producing seismic scattering in the bulk. Because single‐event dynamic simulations penetrate further into sediments compared to the quasi‐dynamic simulations, we hypothesize that the incorporation of inertial effects would produce sequences of only surface‐rupturing events. However, we find that subbasin ruptures can still emerge with elastodynamics, for sufficiently compliant basins. We also find that full dynamics can increase the frequency of surface‐rupturing events, depending on basin depth and stiffness. These results suggest that an earthquake's potential to penetrate into shallow sediments should be viewed through the lens of the earthquake sequence, as it depends on basin properties and wave‐mediated effects, but also on self‐consistent initial conditions obtained from seismogenic cycling.

Earthquake Cycle Mechanics During Caldera Collapse: Simulating the 2018 Kı̄lauea Eruption

“…We use an implicit backward differentiation formula, which takes time steps much longer than the Courant-Friedrichs-Lewy condition when the solution is evolving slowly. This avoids the efficiency limitations of explicit time-stepping (Erickson & Nordström, 2014) and the difficulties of switching methods between coseismic and interseismic intervals (Harvey et al, 2023). We chose error tolerances and mesh sizes (Figure 2) based on convergence testing.…”