FASTDASH: an implementation of 3-D earthquake cycle simulation on complex fault systems using the boundary element method accelerated by H-matrices

Major fault systems are inherently complex, including geometric features such as multiple interacting fault segments and variations in strike, dip, and depth. Fault geometries can be effectively reconstructed through field observations and seismic monitoring. Many studies have demonstrated that this geometric complexity plays an important role in controlling the initiation, arrest, and recurrence of both seismic and aseismic slip. In particular, 3D variations in fault geometry cannot be neglected.

However, the vast majority of slip-dynamics models are conducted on planar faults due to algorithmic limitations. To overcome this restriction, we develop a 3D quasi-dynamic slip-dynamics model capable of simulating arbitrarily complex fault geometries. In boundary-element methods, the elastic response to fault slip is computed through the multiplication of a dense matrix with a slip rate vector, which are computationally expensive. We accelerate these calculations using hierarchical matrices (H-matrices), reducing the computational complexity from O(N^2) to O(NlogN), where N is the number of elements. The H-matrix parameters provide explicit control over the trade-off between computational efficiency and accuracy.

In our framework, fault geometry is fully arbitrary and discretized using triangular elements. Fault slip is governed by rate-and-state friction laws and loaded by either stressing rates or plate rate. This approach enables efficient simulation of the spatiotemporal evolution of slip and stress on complex fault systems over multiple earthquake cycles.

We validate the model against analytical solutions for static cracks and through a numerical benchmark (SCEC SEAS BP4). Finally, we apply the method to a realistic fault system with complex geometry that was reactivated during the 2023 Kahramanmaraş–Türkiye earthquake doublet. The results highlight the model’s ability to generate complex earthquake sequences driven solely by fault geometry, without including additional complexities such as rheological, frictional, or fluid-interaction effects.