To estimate the ground motion in two-dimensional (2D), laterally heterogeneous, anelastic media, a hybrid technique has been developed that combines modal summation and the finite-difference method. In the calculation of the local wave field owing to a seismic event, both for small and large epicentral distances, it is possible to take into account the source, path, and local soil effects.
As a practical application, we have simulated the ground motion in Mexico City caused by the Michoacan earthquake of September 19, 1985. By studying the one-dimensional (1D) response of the two sedimentary layers present in Mexico City, it is possible to explain the difference in amplitudes observed between records for receivers inside and outside the lake-bed zone. These simple models show that the sedimentary cover produces the concentration of high-frequency waves (0.2 to 0.5 Hz) on the horizontal components of motion. The large amplitude coda of ground motion observed inside the lake-bed zone and the spectral ratios between signals observed inside and outside the lake-bed zone can only be explained by 2D models of the sedimentary basin. In such models, the ground motion is mainly controlled by the response of the uppermost clay layer. The synthetic signals explain the major characteristics (relative amplitudes, spectral ratios, and frequency content) of the observed ground motion. The large amplitude coda of the ground motion observed in the lake-bed zone can be explained as resonance effects and the excitation of local surface waves in the laterally heterogeneous clay layer. Also, for the 1985 Michoacan event, the energy contributions of the three subevents are important to explain the observed durations.