[S-CG45] Science of slow-to-fast earthquakes

[SCG45-P40] Inconsistency of a single-point evaluation of traction and improved methods for a fault discretized with triangular dislocations

*Hiroyuki Noda¹ (1.Kyoto University, Disaster Prevention Research Institute)

Keywords:BIEM, Triangular element, Fault, Discretization

Triangular dislocation is typically used to discretize a fault because of its flexibility in expressing nonplanar surfaces; however, its consistency, convergence of the numerical solution to the analytic solution with decreasing element size Δx, for the traction on the fault was not mathematically proven. In this study, it was shown that a trivial problem of the linear distribution of the displacement gap on a planar infinite fault resulted in numerical inconsistency for the simple uniform triangular mesh with single-point evaluation within the element when not under special circumstances. The numerical oscillatory error, with its amplitude proportional to the gap gradient, does not smear out with decreasing Δx. Several new methods have been proposed to resolve this problem and compared with a classical circular shear crack model and a smooth problem. The conventional centroid evaluation “CTR” was inconsistent and was corrected by subtracting the estimation of the oscillation from the local gap gradient in “CTRC.” The oscillation was canceled out by multiple-point evaluation in “M244” and “M236.” These two methods were combined with optimization to yield the hybrid method “HYB.” Convergence analyses with equilateral and isosceles right triangle meshes show that the numerical errors of the newly proposed methods typically decrease as Δx^(-1) except near the singularity at the crack tip. If the number of elements is smaller than approximately 100, CTRC yields the smallest numerical error, but such low-resolution calculations may not be important these days. For a greater number of elements, HYB is the best method. Further investigations on better selection of evaluation points, mathematical proof of consistency, and similar issues expected in more general problems with nonplanar faults deserve future study.