Ground motions around a semicircular canyon with a dipping edge under SH plane wave incidence

In order to explore the spatial distribution and temporal variation of ground motions near a semicircular canyon with a dipping edge, a simplified mathematical model is constructed. Based on the region-matching technique, a Fourier-Bessel series solution for the plane SH-wave excitation is derived and then applied to theoretically simulate the seismic response of the canyon. The use of the adequate wavefunctions and a newly derived Graf’s addition formula can solve the unknown expansion coefficients. Parametric analyses with respect to the frequency of input motion, angle of incidence, and canyon geometry are illustrated. Both frequency- and time-domain computations are presented. The canonical case, a completed semicircular canyon, which has the exact analytical solution, and the horizontally truncated case analyzed in previous works are considered as particular cases of the proposed general model. Comparisons with boundary-element solutions show good agreement. Steady-state results show that the phenomenon of wave focusing tends to be significant when the incident angle bends toward the horizontal ground surface. Propagation and attenuation of scattered waves that originated from the surficial anomaly are exhibited in transient-state simulations.