Theoretical comparisons of linear and nonlinear seismic responses of two-dimensional (2D) alluvial basins show that in general the character of the seismic wave propagation is similar in both cases, but important differences exist regarding both the time history and the response spectra. The nonlinear model, based on yielding elements arranged into a 2D finite-difference mesh, tends to distribute the total seismic energy over longer time durations, resulting in lower peak accelerations and lower response spectra than those produced by the linear model. On the other hand, the Fourier spectra in each comparison are similar; particularly the peak amplitudes occur at about the same frequencies in both cases. However, resonant peaks, obtained with both models for weak input amplitudes, do not appear when the input amplitude is increased 10-fold in the nonlinear case, due to greater damping determined by its assumed stress-strain relationship, which restricts the buildup of resonances.
The examples presented in this study correspond to a trapezoidal sedimentary basin embedded in an elastic half-space. The P- and S-wave velocities of the sediments are chosen to be constant in one case, and linearly varying with depth in the other. The input motion is obtained from the bedrock at the Castaic Old Ridge Route Station, during the 1971 San Fernando earthquake, scaled to provide a “weak” motion, with peak acceleration 0.04 g, and a “strong motion” with peak acceleration 0.4 g. In the linear case, suitable values of Q are chosen to yield the same average damping as that by the nonlinear case, for both inputs.