We have simulated 2-Hz-wave propagation in a three-dimensional model of the upper Borrego Valley, southern California, for a M 4.9 earthquake with epicenter 5 km north of the valley. A 4th-order staggered-grid finite-difference method was used to calculate viscoelastic ground motion in a basin model (9 km by 5 km by 0.4 km) consisting of heterogeneous sediments surrounded by bedrock. We simulated the earthquake as a double-couple point source and computed the ground motions in the valley separately for the parts of the source incident from below and from the North. The earthquake was recorded by a surface array as well as a deep downhole array (0–238 m depth) in the center of the valley, all equipped with digital three-component seismic instruments. The simulation reproduces the overall pattern of ground motions at basin and borehole sites and shows a good correlation of observed to synthetic waveforms. In particular, the 3D simulation reproduces the recorded peak motions, cumulative kinetic energies, and Fourier spectral amplitudes within a factor of 2 for most components at the individual sites. The correlation between data and simulation allows us to identify the secondary arrivals in the records as Love and Rayleigh waves generated at the edges of the valley and the troughs of the basin. The peak velocities for the waves incident into the valley from below are generally more than an order of magnitude larger than those for the waves incident from the North. The success of the prediction requires the inclusion of anelastic attenuation in the simulation with Q values for P and S waves in the alluvium of about 30.
We also used a profile of the 3D model and the soil parameters at the deep borehole to examine the ability of 2.5D and 1D model approximations to predict the data. The maximum peak velocities and total cumulative kinetic energies are reproduced at the recording sites within a factor of 2 for both 2.5D and 1D model approximations, but are underpredicted by up to an order of magnitude at some depths for individual components. In particular, the 2.5D and 1D simulations tend to underpredict the duration.