SH-wave Green tensor for homogeneous transversely isotropic media by higher-order approximations in asymptotic ray theory

Seismic moment tensors of acoustic emissions recorded during laboratory rock deformation experiments: sensitivity to attenuation and anisotropy

“…The problem is simplified if we assume elliptic, viscoelastic, anisotropic media, when the slowness surface is spheroidal (Helbig 1994) and the medium is described by two viscoelastic parameters a 11 and a 33 . The stationary slowness vector p 0 , energy velocity vector v, and the Gaussian curvature of the slowness surface K can be expressed as follows (Vavryčuk & Yomogida 1996):…”

Properties ofSwaves near a kiss singularity: a comparison of exact and ray solutions

“…We shall show that zeroth‐order ray theory yields distorted results near the kiss singularity. If we consider the first‐order ray approximation, calculated by Vavryčuk & Yomogida (1996) and by Vavryčuk (1997), however, we obtain a satisfactory result. The first‐order ray approximation has a simple analytical form and its properties will be discussed in detail.…”

“…(2) in directions far from the kiss singularity, and by another formula in directions close to the kiss singularity. From these zeroth‐order terms, we can then construct the whole ray series (see Vavryčuk & Yomogida 1996). Thus the waves will be described by two different ray expansions with different and limited regions of applicability.…”

“…(2) can be expressed analytically. For the SH ‐wave Green tensor, we obtain a simple analytical formula (Vavryčuk & Yomogida 1996; eq. 25).…”

“…This term is composed of additional as well as principal components of the SV ‐ and SH ‐wave first‐order approximations. It has the following form (Vavryčuk & Yomogida 1996; eq. 28; Vavryčuk 1997; eqs 23a, 24a):…”