We address the following two questions. Can a microearthquake's ground motions be modeled by incident P and S waves that excite a site transfer-function that is a smooth function of incidence angle? Given recorded ground motions from a set of earthquakes having known locations and mechanisms, can we derive such a site transfer-function and use it to obtain the ground motions that would result from an earthquake source occurring somewhere in the same volume but having a location and mechanism that are different from the recorded events? Although many factors will cause two distinct microearthquake sources to have different seismograms at a common station, in this paper we concentrate only upon the differences caused by source mechanisms, P- and S-wave travel-time variations and by variations in the site transfer-function. We specifically exclude the effects of waves scattered from heterogeneities in the geologic structure away from the seismic site. We express the site transfer-function as a sum of several terms having simple dependences upon incidence angle and azimuth. Each term is an independent function of time. Given a set of seismograms observed at the site, we solve a linear system of equations for the time dependences of each term. These time series may be used to calculate the seismograms that would have resulted from an earthquake having arbitrary mechanism and location. This step is an interpolation. We have applied this technique to seismograms after aftershocks of the 1986 North Palm Springs earthquake. Our interpolation technique works fairly well within the volume occupied by the recorded events, but the method is not very successful at providing accurate seismograms for sources located outside the aftershock volume. The primary causes of the inaccuracy are the inadequacy of our chosen angular functions to model the site response fully and the likely scattering of seismic waves by geological heterogeneities (in this case, the Banning and Mission Creek faults) near the seismic stations. Our methods could be used to determine the effects of single scattering from lateral heterogeneities in geologic structure.
