| Abstrakt: |
Abstract: Consider a plane homogeneous harmonic SH wave incident upon an interface between two anelastic half-spaces. Computing the plane wave displacement and energy-flux-based reflection and transmission coefficients correctly requires determining the proper signs of the vertical slowness components of all the reflected and transmitted waves, i.e., determining which of the two values of the square root for a given vertical slowness should be chosen. For anelastic media, this can be problematic, as unphysical results can arise. Previous research has led to a specific recommendation on how to choose the signs. However, when this recommendation is employed, it is found via numerical experimentation that for certain values of the medium parameters, the energy-flux-based transmission coefficient T can be negative for certain supercritical values of the incidence angle, whereas physical reasoning suggests it should be zero. To investigate this seemingly unphysical result, an analytical determination of the mathematical conditions under which it occurs would be useful. Such a determination is performed in this article. Letting V 1 and V 2 be the wave speeds of homogeneous SH plane waves in the incidence and transmission media respectively, and Q 1 and Q 2 be the corresponding quality factors, with Q 1, Q 2 ≫ 1, it is found that if V 1 < V 2 and Q 1 < Q 2 (a common situation in the Earth), then T will be negative for part of the supercritical incidence angle range if 1 < Q 2/Q 1 ≤ 2 − (V 1/V 2)2 and for all of it if 2 (V 1/V 2)2 < Q 2/Q 1. |
