A new asymptotic method for the modeling of near-field accelerograms

We study high-frequency radiation from a dislocation model of rupture propagation at the earthquake source. We demonstrate that in this case all the radiation emanates from the rupture front and, by a change of variables, that at any instant of time the high-frequency waves reaching an observer come from a line on the fault plane that we call isochrone. An asymptotic approximation to near-source velocity and acceleration is obtained that involves a simple integration along the isochrones for every time step. It is shown that wave front discontinuities (critical or stopping phases) are radiated every time an isochrone becomes tangent to a barrier. This leads to what we call the critical ray approximation which is given in a closed form. The previous results are compared with discrete wavenumber synthetics obtained by Bouchon (1982) for the Gilroy 6 recording of the Coyote Lake earthquake of 1980. The fit between the asymptotic and full numerical method is extremely good. The critical ray approximation permits the identification of different phases in Bouchon's synthetics and the prediction of the behavior of the signal in the vicinity of their arrival time.