Smooth slip is all you need: A singularity-free boundary element method for fault slip problems

Abstract

Fault slip during the earthquake cycle is often spatially heterogeneous and occurs on non-planar fault surfaces. In this study, we present an analytical method for calculating displacements and stresses resulting from spatially variable fault slip on faults with arbitrary geometry in a linear elastic medium. This method enforces that fault slip is spatially continuous and differentiable, in contrast to classical constant-slip Green’s function boundary element models which suffer from stress singularities at element boundaries. By eliminating these stress singularities, our approach improves mechanical interpretability and accuracy in strain energy calculations. We demonstrate the construction and application of continuous slip boundary element models in two dimensions for the Himalayan Range Front (HRF) faults in Nepal, and show that strain energy accumulates at $5.6\times 10^{13}$ Pa-m/m of convergence for the greater HRF region and grows quadratically with convergence amount. The strain energy released by the 2015 $M_W=7.8$ Gorkha earthquake was $\sim 10^{15}$ Pa-m, equivalent to the complete release of strain energy from only $\sim 4$ m of convergence as compared to nearly uniform 6–7 m of slip estimated geodetically. The discrepancy between coseismic slip and the equivalent convergence represents a roughly 30% increase in the total strain energy in the volume over the considered interval of the earthquake cycle.