The two-dimensional scattering and diffraction of SH waves of arbitrary angle of incidence from irregular, canyon-shaped topography is formulated in terms of an integral equation. Taking advantage of the simple boundary conditions of SH-wave problems, the method of images is applied to reduce the integral equation to one with a finite integral, which can readily be solved numerically by available methods.
The method is first applied to the analytically solved case of a cylindrical canyon to verify its accuracy, and then to two idealized cross sections based upon Pacoima Canyon to investigate the effects of topography in a more realistic case. The results of the harmonic analysis include wave amplification patterns and transfer functions for different wavelengths and for different angles of incidence. The study also includes analysis of transient motions. With the N76°W component of the Pacoima Dam accelerogram specified to occur at one point in the cross section, the effects of different angles of incidence upon the required input motion and upon the motion at several other points in the cross section were examined by calculating accelerograms and response spectra.
The effects of canyon-shaped topography are seen most prominently in the amplification patterns and transfer functions for harmonic response, wherein shielding and focusing can cause variations up to a factor of six for wavelengths comparable to, or shorter than, the canyon width. In the case of transient motions, the accelerograms at different points show significant differences, but not as large as seen in the harmonic analysis. The response spectra show the smallest differences; significant effects are confined to the higher frequencies.