Path effects for seismic wave propagation within three-dimensional (3-D) basin structures are analyzed using a reciprocal source experiment. In this experiment, a numerical simulation is performed in which a point source is excited at a given location and then the wave field is propagated and recorded throughout a 3-D grid of points. Using the principle of reciprocity, source and receiver locations are reversed. This allows the modeling of path effects into a particular observation site for all possible source locations using only one simulation. The numerical technique is based on the use of paraxial extrapolators and currently tracks only acoustic waves. However, the method is capable of handling arbitrary media variations; thus, effects due to focusing, diffraction, and the generation of multiple reflections and refractions are modeled quite well.
The application of this technique to model path effects for local earthquakes recorded at stations in the Los Angeles area of southern California indicates the strong influence of the 3-D crustal basins of this region on the propagation of seismic energy. The modeling results show that the Los Angeles, San Fernando, and San Gabriel basins create strong patterns of focusing and defocusing for paths into these stations from various source locations. These simulations correlate well with earthquake data recorded at both stations. By comparing these calculations with earthquake data, we can begin to evaluate the importance of these basin effects on observed patterns of strong ground motions.