SH Waves in a Transversely Isotropic Medium-I

Abstract

Summary In a transversely isotropic medium plane SH waves, polarized parallel to the plane of isotropy, are propagated with phase velocity (normal to the wave front) I/ = (v,,~ cos2c+ v,’ sin2e), where V, and V, are shear wave velocities perpendicular and parallel to the plane of isotropy, and e is the angle of incidence on that plane. The direction of energy propagation, on the other hand, is in general not normal to the wave front but in the direction of the radius vector from the origin to the wave surface, which is the envelope, at time t = 1, of plane waves which all passed through the origin at time t = 0. The velocity of energy propagation, which is here the group velocity, has magnitude u = (vV4 cos2e+ v,,~ sin2e)f/V. Expressions for I/ and U in terms of ray direction are derived, and also the modified form of Snell’s Law for refraction. We show that when the seismic velocity is calculated from travel times and hypocentral distances it is U, not V, which is obtained.