Simulation of spontaneous rupture based on a combined boundary integral equation method and finite element method approach: SH and P-SV cases

Abstract

S U M M A R YWe present a hybrid approach for solving the dynamic rupture problem in an anelastic medium. It combines the advantages of the boundary integral equation method (BIEM), which is capable of representing accurately the solution near a crack tip, with those of the domain finite element method (FEM), which can handle conveniently heterogeneous materials, as well as the traction-free condition on a free surface and the continuity of traction across interfaces. When applied jointly, the proposed BIEM and the FEM can be used to solve efficiently spontaneous rupture problems in heterogeneous media, provided the rupture surface is contained within a homogeneous portion of the domain. The proposed method, BIEM-FEM approach (BDM, for Boundary/Domain Method), is verified for several antiplane (SH) and in-plane (P-SV ) 2-D cases, in which the slip is prescribed along the fault (kinematic rupture). For spontaneous rupture, we examine the performance of the BDM by computing its convergence rate for an example in a homogeneous half-space with a slip-weakening friction law on the fault. By including the boundary integral representation on the fault, without using any refinement near the crack tips, the solution converges with the same rate as problems that do not exhibit any stress concentrations; that is, for the piecewise linear elements used here, the rms of the slip-rate distribution and of the traction distribution on the fault converge as O( x), whereas the slip distribution converges as O( x 2 ), in which x is the mesh size of the finite element mesh. Additional 2-D spontaneous rupture simulations are performed for an inclined fault in a half-space for different values of the dip angle and for a folded layer system in a half-space, focusing only the P-SV case. The results show that the waves generated at the free surface and within the layers contribute to the propagation of the fault rupture and have a visible and sometimes strong effect on the ensuing ground motion.

Dynamic rupture simulation of the 2011 off the Pacific coast of Tohoku Earthquake: Multi-event generation within dozens of seconds

“…Most of the methods are categorized as either domain-based methods (e.g., FDM and FEM), or boundarybased methods (e.g., BIEM). Goto et al (2010) proposed an alternative hybrid approach: viz., the boundary-domain method (BDM). In this method, instantaneous traction change is represented by the combination of a direct term calculated by a boundary-based method for a homogeneous full space, and a residual term calculated from the differences between two solutions for a target heterogeneity model and for a homogeneous full space model by a domain-based method.…”

“…The detail scheme in time progress is identical to the BDM introduced by Goto et al (2010). In the following section, we show some numerical tests such as the representation of the perturbation T D1 − T D2 , and the small size of spontaneous rupture simulation.…”

“…The boundary integral equation method (BIEM) (Tada and Yamashita, 1997;Goto et al, 2010) is applied as the boundary-based method, and the finite-difference method (FDM) (Levander, 1988) is applied as the domain-based method in pBDM. The velocity models for BIEM are set to be 7.34 km/s for V p and 4.20 km/s for V s , which are the average values on the deeper side of the fault.…”

Three-dimensional elastic wave numerical modelling in the presence of surface topography by a collocated-grid finite-difference method on curvilinear grids

“…Since each method has its own advantages and disadvantages, hybrid methods are proposed to combine the advantages of different methods (e.g. Moczo et al 1997; Galis et al 2008; Goto et al 2010; Liu et al 2011).…”

Delayed Subevents During the MW6.2 First Shock of the 2016 Kumamoto, Japan, Earthquake

“…Journal of Geophysical Research: Solid Earth surface (e.g., Fukuyama & Hok, 2015;Goto et al, 2010;Kaneko & Lapusta, 2010;Oglesby et al, 2000). On the other hand, our results for the Kumamoto earthquake suggest another episode that the second energy release (rupture) causes the dynamic triggering, as summarized in Figure 6.…”