This study investigates different methods for generating non-uniform support acceleration at actual topographic sites. The factors affecting the non-uniform excitation of a topographic site include the time delay between the arrival times of incident waves at different soil depths, causing a phase difference, and the coherence function. The existing coherence models are based on data recorded on flat surfaces and are not suitable for surfaces with topographic features. Therefore, in the present study, models of a canyon site subjected to Ricker waves with different predominant frequencies, shear wave velocities, and shape ratios have been developed, and the results of boundary element analyses in the time domain (using the BEMSA code) have been obtained at different elevations on the canyon surface. Then, by conducting a statistical analysis employing the symbolic regression method on the results of numerous presumed cases, the relationships for calculating the time delay between the support responses and the coherence function of V-shaped canyons were obtained. To verify the accuracy of the proposed relationships, the results were compared with the records from the Pacoima Dam site during two different earthquakes and a good agreement was obtained between the results. Eventually, by implementing the proposed relationships in the random vibration method, the non-uniform acceleration of the site was simulated. The results indicate that the proposed relationships have an appropriate level of accuracy for calculating the time delay and the spectral coherence function of V-shaped canyons.
