An analytical solution of the elastodynamic equations along the axis of a circular fault

Abstract

The seismic radiation generated by a kinematic model of a circular fault with a shear dislocation is computed analytically for a homogeneous elastic medium and an observation point located on the axis of the circular fault. The far-field, intermediate-field and near-field terms are computed for a uniform dislocation starting from the centre, growing radially at a constant rupture velocity and stopping abruptly at the periphery of the disk. The local slip history of the dislocation is given by a ramp function of finite duration. Our analytical solution is compared with a numerical estimate computed for an intermediate-size earthquake simulated by a circular fault of radius 10 km, a shear dislocation of 1 m and a slip rate of 1 m s−1. A detailed analysis of the different terms involved in the analytical solution gives us some insight into the properties of the displacement field when the source is approached. We show, in particular, that, in addition to the static offset remaining after the arrival time of the far-field S pulse, there is a significant negative slope in the seismic motion between the P and S arrivals which is clearly observable at distances of a few source dimensions.