SEISMIC-WAVES IN A LATERALLY INHOMOGENEOUS LAYERED MEDIUM .1. THEORY

Seismic waves in a layered half-space with lateral inhomogeneities, ge nerated by a buried seismic dislocation source, are investigated in th ese two consecutive papers. In the first paper, the problem is formula ted and a corresponding approach to solve the problem is provided. Spe cifically, the elastic parameters in the laterally inhomogeneous layer , such as P and S wave speeds and density are separated by the mean an d the deviation parts. The mean part is constant while the deviation p arr, which is much smaller compared to the mean part, is a function of lateral coordinates. Using the first-order perturbation approach, it is shown that tile total wave field may be obtained as a superposition of the the mean wave field and the scattered wave field. The mean wav efield is obtainable as a response solution for a perfectly layered ha lfspace (without lateral inhomogeneities) subjected to a buried seismi c dislocation source. The scattered wave field is obtained as a respon se solution for the same layered half-space as used in the mean wave f ield, but is subjected to the equivalent fictitious distributed body f orces that mathematically replace the lateral inhomogeneities. These f ictitious body forces have the same effects as the existence of latera l inhomogeneities and can be evaluated as a function of the inhomogene ity parameters and the mean wavefield. The explicit expressions for th e responses in both the mean and the scattered wave fields are derived with the aid of the integral transform approach and wave propagation analysis.