DiffractedP, SV, andSHwaves and their shadow boundary shifts

Abstract

Diffraction of plane body waves caused by a cylindrical cavity in an otherwise homogeneous, elastic, and infinite medium has been studied in the neighborhood of the shadow boundary for wave periods up to 100 seconds. Poisson's summation formula is used in formulating the theory, followed by an asymptotic expansion to isolate the diffracted energy that arrives in the correct time window. A numerical study is also conducted to examine in detail the behavior of the diffracted amplitudes near the shadow boundary. It is found that the transitional zone between the illuminated and the shadow regions broadens, together with a shadow-boundary shift, as frequency decreases. With a scatterer of stress-free boundary condition, the shadow boundary shifts toward the illuminated region in both P- and SV-wave cases, with the amount of shift in the SV-wave case being appreciably larger. These results have confirmed earlier observations in an ultrasonic model study. In contrast, with the same boundary condition, the SH-wave shadow boundary shifts toward the shadow region instead, with large SH amplitudes extending deep into the shadow zone. Implications of these findings are discussed with reference to the amplitudes of teleseismic body waves and the definition and location of the seismic shadow boundary.