Sommerfeld 積分を使った離散化波数境界積分方程式法による三次元弾性波動場の数値計算法

Abstract

The author proposes a formulation of the discrete wavenumber—boundary integral equation method for three dimensional problem, using Green's function for homogeneous half-space calculated by the Sommerfeld integral, based on the consideration about the orthogonality of the horizontal wave function. This orthogonality gives a relation between Green's function for each point source and the total wave field. A wavenumber component of the total wave field is composed only of the wavenumber components radiated by each point source, which correspond to the same wavenumber. For the total wave field, it can be said easily that it is sufficient to evaluate the integral over wavenumber up to that a little superior to the wavenumber corresponding to the fundamental mode of the Rayleigh wave. Then, it is found that the integral over wavenumber to obtain Green's function for each point source can be truncated at the same wavenumber. This may not be exact, mathematically, but it is reasonable in term of the wave theory. The calculation for some simple problems with axi-symmetrical surface irregularity, gives the stable and reasonable wave forms. It is expected that this strategy can be applied not only to axi-symmetrical surface irregularity but also to arbitrary shape of irregularity of surface and of interface.