Abstract It is well known from asymptotic ray theory that the complex wave amplitude along a ray undergoes a phase shift every time the ray touches a caustic surface. If the slowness surface associated with the propagation of this ray is not convex, which is possible for quasi-shear waves in anisotropic elastic media, the phase shift may be opposite in sign from the isotropic case. We present a simple explanation for this phenomenon based on the relation between slowness surfaces and the delay time function. We demonstrate that both the approaching and the receding wavefronts are convex toward the caustic in the anomalous case. This is exactly the opposite of the more familiar isotropic case. Since the magnitude of the phase shift is π/2 in both cases, neglecting the possibility of an anomalous phase shift may introduce a phase error of ±π in the calculated wavefield. Nonconvex quasi-S slowness surfaces frequently arise in naturally occurring anisotropy, and curved reflecting boundaries and other heterogeneities lead to a profusion of caustics. Therefore, encountering this problem is quite likely in practical exploration geophysics using shear-wave imaging.
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Anisotropy 2000: Fractures, Converted Waves, and Case Studies
“This volume contains 25 papers that represent most of the best work in seismic anisotropy in 1998 and 1999. Fracture characterizations and processing of converted waves are the two main topics covered in this volume. They are addressed from both theoretical and practical viewpoints. Also included are papers describing the historical roots of seismic anisotropy.”