[SSS12-P13] Analytical solution of near-field term, intermediate term, far-filed term, and quasi-static displacement due to rectangular fault in a homogeneous whole space
Keywords:near-field term, quasi-static displacement, forward directivity, analytical solution, rectangular fault
We consider the fault model which is same as Sato (1975). Rupture front looks like line, whose rupture velocities along strike and dip are constant. Slip time function is ramp function, whose risetime is constant. Here we integrated over strike direction displacement field by point source, near-field term, intermediate term, far-filed term, and quasi-static displacements (e.g. Aki & Richards, 2002).
Fig.1 shows an example of fault model. Numerical calculation setting is P-wave velocity:6.0 km/s, S-wave velocity:3.5 km/s, Length of fault:60 km, Width of fault:15 km, slip amount:2.0m, risetime:2.5 s, slip angle:0°(strike-slip fault), rupture velocity:2.5 km/s. We consider two cases about the direction of rupture as examples. One of cases (a) is that rupture propagates forward to strike-direction, the other (b) is that rupture propagates upward obliquely. Calculation results are doubled due to the effect of free surface.
Fig.2 shows displacement, near-filed terms, far-field terms and quasi-static displacement in case (a). In case (a), at stations in direction of rupture far-field terms mainly contributes to ground motion in FN component. This shows forward directivity. Near-field terms are not influenced by forward directivity. In case (b), the contribution of far-field terms is nearly equal to that of near-field terms because that of far-field terms becomes smaller than case (a). Quasi-static displacement is different from Near-field terms. In FP component, near-field terms mainly contribute to ground motion in both (a) and (b). Quasi-static displacement is similar to near-field terms compared with FN component and behaviors like ground motion because far-field terms little contributes to ground motion.