The Parkfield, California, earthquake of 1966 produced the first recording of ground motion in the immediate vicinity of an earthquake fault. The simplicity of displacement pulse observed at station 2 aroused great interest among seismologists working in the area of earthquake source mechanism. Since then, numerous theoretical works on simulating strong motion have been carried out, starting with the use of a simple kinematic model assuming a uniform slip over a fault plane. The assumption of uniform slip had to be modified to explain the strong motion observed during the Parkfield earthquake of 1966, the Borrego Mountain earthquake of 1968, the San Fernando earthquake of 1971, the Imperial Valley earthquake of 1979, the El Asnam earthquake of 1980, and others.

Through these studies, the simulation technique has been advanced to include a more realistic medium. In the beginning, most methods used Green's function for an unbounded homogeneous medium. Then, the free surface effect, the effect of a sedimentary layer as well as laterally heterogeneous basin structure have been included in the simulation.

The above simulation studies were, however, restricted to relatively low-frequency waves represented in a displacement or velocity seismogram. In order to predict an acceleration seismogram dominated by high-frequency waves, hybrid models have been proposed in which gross features of rupture propagation are specified deterministically, but the details of the process are described by a stochastic model specified by a small number of parameters. The application of these models to several California earthquakes revealed encouraging results that some of the key parameters of the model are stable among earthquakes.

Mathematical modeling techniques will play an important role in the prediction of strong motion for a great earthquake in California as well as for major earthquakes outside California, based on the records of moderate earthquakes already acquired in California.

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