Scattering of horizontally-polarized shear waves by surface irregularities

Summary. The problem of the scattering of harmonic SH waves by an arbitrary surface irregularity in an otherwise semi-infinite elastic, homogeneous, isotropic two-dimensional half-space is examined in this study in order to ascertain the effect of topography on this type of seismic ground motion and to develop a useful scheme which can realistically handle arbitrary two-dimensional topography. Three geometric models are considered: a semicircular hill which is of academic interest; a mountain with a Gaussian shape which utilizes realistic dimensions and the combination of a ridge and a depression that models a region in Sylmar, California.
A singular Fredholm integral equation of the second kind for the displacement at the free surface is developed and solved numerically. In the case of the semicircular hill, horizontal ground motion can be more than twice that occurring in the case of smooth topography. The mountain simulated by a Gaussian profile experiences at its crest amplifications for certain angles of incidence and de-amplifications for other angles of incidence, as well as displacements whose amplitudes vary slowly with frequency on the side of the mountain which is in the same direction as the incident waves. The ridge-depression combination which is approximated by a sixth-order polynomial actually experienced shattered earth at its ridge crest during the San Fernando, California earthquake of 1971. This amplification is also exhibited by the results of the analysis which, predicts amplifications of over 75 per cent at the top of the ridge for waves arriving on the same side as the ridge.