PP-wave reflection coefficients in weakly anisotropic elastic media

Citation
V. Vavrycuk et I. Psencik, PP-wave reflection coefficients in weakly anisotropic elastic media, GEOPHYSICS, 63(6), 1998, pp. 2129-2141
Citations number
21
Categorie Soggetti
Earth Sciences
Journal title
GEOPHYSICS
ISSN journal
00168033 → ACNP
Volume
63
Issue
6
Year of publication
1998
Pages
2129 - 2141
Database
ISI
SICI code
0016-8033(199811/12)63:6<2129:PRCIWA>2.0.ZU;2-K
Abstract
Approximate PP-wave reflection coefficients for weak contrast interfaces se parating elastic, weakly transversely isotropic media have been derived rec ently by several authors. Application of these coefficients is limited beca use the axis of symmetry of transversely isotropic media must be either per pendicular or parallel to the reflector. In this paper, we remove this limi tation by deriving a formula for the PP-wave reflection coefficient for wea k contrast interfaces separating two weakly but arbitrarily anisotropic med ia. The formula is obtained by applying the first-order perturbation theory . The approximate coefficient consists of a sum of the PP-wave reflection c oefficient for a weak contrast interface separating two background isotropi c half-spaces and a perturbation attributable to the deviation of anisotrop ic half-spaces from their isotropic backgrounds. The coefficient depends li nearly on differences of weak anisotropy parameters across the interface. T his simplifies studies of sensitivity of such coefficients to the parameter s of the surrounding structure, which represent a basic part of the amplitu de-versus-offset (AVO) or amplitude-versus-azimuth (AVA) analysis. The refl ection coefficient is reciprocal. In the same way, the formula for the PP-w ave transmission coefficient can be derived. The generalization of the proc edure presented for the derivation of coefficients of converted waves is al so possible although slightly more complicated. Dependence of the reflectio n coefficient on the angle of incidence is expressed in terms of three fact ors, as in isotropic media. The first factor alone describes normal inciden ce reflection. The second yields the low-order anular variations. All three factors describe the coefficient in the whole region, in which the approxi mate formula is valid. In symmetry planes of weakly anisotropic media of hi gher symmetry, the approximate formula reduces to the formulas presented by other authors. The accuracy of the approximate formula for the PP reflecti on coefficient is illustrated on the model with an interface separating an isotropic half-space from a half-space filled by a transversely isotropic m aterial with a horizontal axis of symmetry. The results show a very good fi t with results of the exact formula, even in cases of strong anisotropy and strong velocity contrast.