Diffracted waves and displacement field over two‐dimensional elevated topographies

Abstract

The Aki‐Larner technique is used to perform, in both the time and frequency domains, an analysis of the effects of two‐dimensional elevated topography on ground motion. Incident plane SH‐, SV‐ and P‐waves are considered and the respective influences of surface geometry, elastic parameters and the incident wave characteristics, as long as they remain within the limits of applicability of the A‐L technique, are investigated in some detail. Besides the well‐known amplification/deamplfication effect related to the surface curvature, wave scattering phenomena on the convex parts of the surface are shown to contribute significantly to the disturbances in the displacement field around the topographic structure. These scattered waves are SH in the case of incident SH‐waves, and mainly Rayleigh waves in the P case, while both Rayleigh and horizontal P‐waves, sometimes of large amplitude, develop in the SV case. The frequency dependence of this scattering, though complex, seems to be mainly controlled by the horizontal scale of the topographic structure. The parameter study points out the regular and intuitive behaviour of this wave scattering in both SH and P cases, while it exhibits a puzzling complexity for incident SV‐waves, which is interpreted as resulting from the importance of the S‐P reflections on mountain slopes in that case. As to the ground motion, some general features may be pointed out. The amplification on mountain tops, which is systematically greater for incident S‐waves than for P‐waves, generally decreases as the average slope decreases or as the angle of incidence increases. Mountain slopes undergo either amplification or deamplification depending on site location, frequency and incidence angle, but they always undergo strong differential motion due to the lateral propagation of the scattered waves and their interference with the primary wave. Finally, all these effects may be greatly enhanced in the case of complex topographies, which moreover give rise to a significant prolongation of ground motion because of the large number of scattered waves. Copyright © 1982, Wiley Blackwell. All rights reserved