We have used a 3D finite-difference method to model 0.2 to 1.2 Hz elastodynamic site amplification in the Salt Lake Valley, Utah. The valley is underlain by a sedimentary basin, which in our model has dimensions of 48 by 25 by 1.3 km. Simulations are carried out for a P wave propagating vertically from below and for P waves propagating horizontally to the north, south, east, and west in a two-layer model consisting of semi-consolidated sediments surrounded by bedrock.

Results show that in general, sites with the largest particle velocities, cumulative kinetic energies, duration times of motion, and spectral magnitudes overlie the deepest parts of the basin. The maximum values of these parameters are generally found above steeply dipping parts of the basin walls. The largest vector particle velocities are associated with P or SV waves that come from within 10° of the source azimuth. Low-energy S and surface waves follow the strongest arrivals. The largest peak particle velocities, cumulative kinetic energies, signal durations, and spectral magnitudes in the simulations are, respectively, 2.9, 15.9, 40.0, and 3.5 times greater than the values at a rock site measured on the component parallel to the propagation direction of the incident P wave. Scattering and/or mode conversions at the basin boundaries contribute significantly to the signal duration times.

As a check on the validity of our simulations, we compared our 3D synthetic seismograms for the vertically incident plane P wave to seismograms of nearly vertically incident teleseismic P waves recorded at an alluvium site in the valley and at a nearby rock site. The 3D synthetics for the alluvium site overestimate the relatively small amplification of the initial P wave and underestimate the large amplification of the coda. Using 2D simulations, we find that most of the discrepancies between the 3D synthetic and observed records can be explained by an apparently incorrect total sediment thickness, omission from the model of the near-surface low-velocity unconsolidated sediments and of attenuation, and the inexact modeling of the incidence angle of the teleseism. The records from a 2D simulation in which these deficiencies are remedied (with Q = 65), and which also includes topography and a near-surface velocity gradient in the bedrock, provide a better match to the teleseismic data than the records from the simple two-layer 3D simulation.

Our results suggest that for steeply incident P waves, the impedance decrease and resonance effects associated with the deeper basin structure control the amplification of the initial P-wave arrival, whereas reverberations in the near-surface unconsolidated sediments generate the large-amplitude coda. These reverberations are caused mainly by P-to-S converted waves, and their strength is therefore highly sensitive to the incidence angle of the source.

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