Fig. 7

Results of many numerical simulations with various friction parameters \(S_{\text{H}}\) and \(D_{\text{c}}\). Circles indicate that a rupture propagated successfully. Triangles indicate that a rupture was initiated but terminated shortly. Crosses indicate that no rupture was initiated. A rupture started spontaneously from the high ΔCFS regions on the Hinagu fault without the artificial shear stress increase in the cases indicated by the solid symbols. Among these cases, the blue and light blue symbols indicate that the high ΔCFS triggered ruptures not only at the hypocenter of the main shock but also at a shallow part of the Hinagu fault. In the other cases, a rupture was forced to be initiated by artificially increasing shear stress. In the cases shown by the light red and light blue symbols, the cohesive zone may not be resolved. For small \(S_{\text{H}}\) values indicated by gray, \(\mu_{\text{s}}\) is smaller than \(\mu^{\text{r}} = {{\tau^{\text{r}} } \mathord{\left/ {\vphantom {{\tau^{\text{r}} } {\sigma_{\text{n}}^{\text{r}} }}} \right. \kern-0pt} {\sigma_{\text{n}}^{\text{r}} }}\) in junction elements. Contours show the fracture energy \(G_{\text{c}}\) integrated on the whole fault plane (unit is \(10^{15} \;{\text{Nm}}\)), calculated by using \(\sigma_{\text{n}}^{0}\) values. In the computations, a non-planar fault is in the infinite medium (i.e., without a free surface). \(\sigma_{1}\) is 100 MPa and \(\sigma_{3}\) is a 50 MPa (case A) and b 70 MPa (case B), \(\sigma_{1}\) is 300 MPa and \(\sigma_{3}\) is c 160 MPa (case C) and d 260 MPa (case D), and \(\sigma_{1}\) is 500 MPa and \(\sigma_{3}\) is e 290 MPa (case E), f 400 MPa (case F), and g 460 MPa (case G)