THE INSENSITIVITY OF REFLECTED SH WAVES TO ANISOTROPY IN AN UNDERLYING LAYERED MEDIUM¹

Propagation in the plane of mirror symmetry of a monoclinic medium, with displacement normal to the plane, is the most general circumstance in anisotropic media for which pure shear‐wave propagation can occur at all angles. Because the pure shear mode is uncoupled from the other two modes, its slowness surface in the plane is an ellipse. When the mirror symmetry plane is vertical the pure shear waves in this plane are SH waves and the elliptical SH sheet of the slowness surface is, in general, tilted with respect to the vertical axis. Consider a half‐space of such a monoclinic medium, called medium M, overlain by a half‐space of isotropic medium I with plane SH waves incident on medium M propagating in the vertical symmetry plane of M. Contrary to the appearance of a lack of symmetry about the vertical axis due to the tilt of the SH‐wave slowness ellipse, the reflection and transmission coefficients are symmetrical functions of the angle of incidence, and further, there exists an isotropic medium E with uniquely determined density and shear speed which gives exactly the same reflection and transmission coefficients underlying medium J as does monoclinic medium M. This means that the underlying monoclinic medium M can be replaced by isotropic medium E without changing the reflection and transmission coefficients for all values of the angle of incidence. Thus no set of SH seismic experiments performed in the isotropic medium in the symmetry plane of the underlying half‐space can reveal anything about the monoclinic anisotropy of that underlying half‐space. Moreover, even when the underlying monoclinic half‐space is stratified, there exists a stratified isotropic half‐space that gives the identical reflection coefficient as the stratified monoclinic half‐space for all angles of incidence and all frequencies.