The seismic wave field is considerably influenced by local structures close to the source and to the receiver. This applies to sources and receivers situated close to localized inhomogeneities, to structural interfaces, to the Earth's surface, etc. In this paper we concentrate our attention mainly to the ray-theoretical radiation patterns of point sources situated close to the structural interfaces and to the Earth's surface. In numerical modeling of high-frequency seismic wave fields by the ray method, the interaction of the source with the Earth's surface has not usually been taken into account. This has, however, introduced great inaccuracies into the numerical modelling.
The procedure of the computations is based on the hybrid ray-reflectivity method, see Cerveny (1989). The method allows to compute the radiation patterns of point sources situated close to structural interfaces, to thin transition layers situated inside the medium, and to thin surficial layers. The thin layer need not be homogeneous; it may include an arbitrary inner layering (transition layers, laminas, etc.). The only requirement is that the layer is thin. Roughly speaking, we require that its thickness is less than one quarter of the prevailing wavelength. The hybrid ray-reflectivity method describes well even certain non-ray effects (tunnelling, pseudospherical waves, S* waves, etc.). Explicit analytical expressions for radiation patterns for all above listed radiation patterns are found.
Numerical examples of radiation patterns of P and S waves of point sources situated close to the Earth's surface and to a thin low-velocity surficial layer are presented and discussed. The point sources of explosive type, and the vertical and horizontal single forces are considered. It has been found that the radiation patterns of point sources depend drastically on the depth of the source below the surface even if the depths vary within one quarter of the prevailing wavelength.
Jilek, P. & Cerveny, V.: Radiation patterns of point sources situated close to structural interfaces and to the Earth's surface. PAGEOPH, 148 (1996), 175-225.