RADIATION-PATTERNS OF POINT SOURCES SITUATED CLOSE TO STRUCTURAL INTERFACES AND TO THE EARTHS SURFACE

The seismic wave field is considerably influenced by local structures close to the source and to the receiver. This applies to sources and r eceivers situated close to localized inhomogeneities, to structural in terfaces, to the earth's surface, etc. In this paper we concentrate ou r 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 surf ace has not usually been taken into account. The proposed procedure of the computation of the radiation patterns of point sources situated d irectly on structural interfaces and on the earth's surface is based o n the zero-order approximation of the ray method, assuming that the le ngth of the ray between the source and the receiver is long. The deriv ed equations are extended to point sources located close to structural interface, to the earth's surface and to thin transition layers using the hybrid ray-reflectivity method, see CERVENY (1989). The thin laye r need not be homogeneous; it may include an arbitrary inner layering (transition layers, laminas, etc.) The only requirement is for the lay er to be thin. Roughly speaking, we require its thickness to be less t han one quarter of the prevailing wavelength. The hybrid ray-reflectiv ity method describes well even certain non-ray effects (tunnelling, S waves, etc.). Explicit analytical expressions for radiation patterns for all above listed point sources are found. These expressions have a local character and may be easily implemented into computer codes des igned for the routine computation of ray amplitudes and synthetic ray seismograms in 2-D and 3-D, laterally varying isotropic layered and bl ock structures by the ray method.Numerical examples of radiation patte rns of P and S waves of point sources situated close to the earth's su rface and to a thin low-velocity surface layer are presented and discu ssed. The explosive point source (center of dilatation) and the Vertic al and horizontal single force point sources are considered. It has be en ascertained that the radiation patterns of point sources depend dra stically on the depth of the source below the surface even if the dept hs vary within one quarter of the prevailing wavelength.