Smooth Slip Is All You Need: Strain Energy at the Himalayan Range Front

Throughout the earthquake cycle, spatially heterogeneous slip occurs on non-planar fault surfaces. Here, we describe an implementation of an analytic approach to calculating displacements and stresses resulting from fault slip in a linear elastic medium. This approach is based on the idea that fault slip is both spatially continuous and smoothly differentiable to first-order. Compared with the classical constant-slip Green's function boundary element models, the continuous slip approach eliminates stress singularities at the element boundaries, enabling greater mechanical interpretability. We describe the construction and application of continuous slip boundary element models in two-dimensions applied to the inferred geometry of the Himalayan Range Front (HRF) faults in Nepal and show that strain energy accumulates at $5.6\times 10^{13}$ Pa-m/meter of convergence for the greater HRF region and grows quadratically with convergence amount. The strain energy released by the 2015 $\MW=7.8$ 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 $6$ 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.