横向各向同性介质中的计算波形(第二部分:水平点力)

COMPUTED WAVEFORMS IN TRANSVERSELY ISOTROPIC MEDIA (Ⅱ. HORIZONTAL POINT FORCE )

美国科罗拉多矿业学院地球物理系

用数字付里叶反演方法计算了点力垂直作用于对称轴上所产生并向横向各向同性介质中扩散的瞬时位移。波至时间与已经发表的群速度表达式相一致,其中包括多次波的出现时间及准SV波的尖点。对于象石膏一土壤薄层这类强各向异性介质,准SV波的最大振幅出现在尖点附近。在尖点之间,准SV波的波形是时变力的希尔伯特变换。关于奥斯汀白垩与石膏一土壤,其SH波的振幅随方向而变化。本文是已发表的同一标题文章的续篇。

Transient displacements radiated into a transversely isotropic medium from a point force acting perpendicular to the axis of symmetry have been computed by numerical Fourier inversion. Arrival times agree with published expressions for group velocity, including the occurrence of multiple arrivals and cusps for the quasi-SV-wave. For the severely anisotropic gypsum-soil laminated medium, the largest amplitude of the q-SV-wave is near the cusps. Between the cusps, the waveform of the q-SV-wave is the Hilbert transform of the force time-dependence. For Austin chalk and gypsum-soil, the amplitude of the SH-wave varies with direction. The present paper complements an earlier paper on the same subject.