Scattering of plane sh waves by a semi‐cylindrical canyon

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Abstract
The two‐dimensional scattering and diffraction of plane SH waves by a semi‐cylindrical canyon is analysed for a general angle of wave incidence. The closed‐form solution of the problem shows that the surface topography can have prominent effects on incident waves only when the wavelengths of incident motion are short compared to the radius of a canyon. The surface amplification of displacement amplitudes around and in the canyon changes rapidly from one point to another, but the amplification is always less than 2. The over‐all trends of amplification pattern are determined by two principal parameters: (1) γ, the angle of incidence of plane SH waves, and (2) η, the ratio of radius of the canyon to one‐half wave length of incident waves. The higher η leads to greater complexity of the pattern of surface displacement amplitudes characterized by more abrupt changes of amplification from one point to another, while γ mainly determines the over‐all trends of displacement amplitudes. For grazing and nearly grazing incidences, for example, a strong shadow zone is developed behind the canyon.The qualitative analysis of the topographic effects on the Pacoima Dam accelerogram,1 based on the semi‐cylindrical canyon, suggests that this strong‐motion record was not seriously affected by surface topography of the recording site.

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