Three-component broadband waveforms of two small earthquakes near Upland, California, recorded on the Pasadena broadband, high dynamic range instrument, were modeled to obtain useful Green's functions for this path and to examine the sensitivity of the synthetic seismograms to perturbations of the crustal model. We assumed that the source of each event was both simple and known, as determined from the Caltech-USGS array first motions. A trapezoidal time function was chosen to fit the width of the direct S wave. Generalized rays, reflectivity, and finite-difference techniques were used to compute the synthetic seismograms.
We found that a simple layer over a half-space model is an adequate approximation of the upper crust along this profile. In particular, the waveforms are controlled by a relatively slow, 4-km-thick surficial layer (α = 4.5km-s−1, β = 2.6 km-s−1) over a faster layer (α = 5.9 km-s−1, β = 3.5 km-s−1). The relative amplitudes of direct and multiple S indicate that the main shock occurred at a depth of 6 km, while the aftershock occurred at a depth of 8 to 9 km. Sensitivity analyses indicate that for distances less than 50 km and for periods longer than 1 sec, the synthetic seismograms are not very sensitive to perturbations of the deep crustal structure. Analysis of upper crustal model perturbations revealed that the surficial layer is between 3 to 5 km thick. In addition, the contact between this layer and the underlying material can be smoothed with a 2-km-wide velocity gradient without adversely affecting the fit to the data. Two-dimensional finite-difference calculations show that a ridge structure beneath the recorder acts as a lowpass filter (the lower frequency phases are largely unaffected). Other two-dimensional models with ridges between the source and receiver clearly did not fit the data. Synthetic seismograms computed for the best fitting model were used to estimate a long-period moment of (6 ± 2) × 1022 dyne-cm (ML = 4.6) and 1 × 1022 dyne-cm (ML = 3.7) with identical triangular source-time durations of 0.3 sec. Assuming the same fault dimension of 0.4 km from standard scaling laws, stress drop estimates of 410 and 70 bars are obtained for the two events, respectively. Generally, we found that it is possible to reproduce local waveforms at frequencies up to 1 Hz without a complete knowledge of fine structural detail. Resulting Green's functions can be useful in studying historic events, and in simulations of large events from a given source region.