Small-angle AVO response of PS-waves in tilted transversely isotropic media

Abstract

Field records for small source-receiver offsets often contain intensive converted PS-waves that may be caused by the influence of anisotropy on either side of the reflector. Here, we study the small-angle reflection coefficients of the split converted [Formula: see text]- and [Formula: see text]-waves ([Formula: see text] and [Formula: see text]) for a horizontal interface separating two transversely isotropic (TI) media with arbitrary orientations of the symmetry axis. The normal-incidence reflection coefficients [Formula: see text] and [Formula: see text] vanish when both half-spaces have a horizontal symmetry plane, which happens if the symmetry axis is vertical or horizontal (i.e., if the medium is VTI or HTI). For a tilted symmetry axis in either medium, however, the magnitude of the reflection coefficients can reach substantial values that exceed 0.1, even if the anisotropy strength is moderate. To study the influence exerted by the orientation of the symmetry axis and the anisotropy parameters, we develop concise weak-contrast, weak-anisotropyapproximations for the PS-wave reflection coefficients and com-pare them with exact numerical results. In particular, the analytic solutions show that the contributions made by the Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-axis tilt [Formula: see text] to the coefficients [Formula: see text] and [Formula: see text] can be expressed through the first derivative of the P-wave phase velocity at normal incidence. If the symmetry-axis orientation and anisotropy parameters do not change across the interface, the normal-incidence reflection coefficients are insignificant, regardless of the strength of the velocity and density contrast. The AVO (amplitude variation with offset) gradients of the PS-waves are influenced primarily by the anisotropy of the incidence medium that causes shear-wave splitting and determines the partitioning of energy between the [Formula: see text] and [Formula: see text] modes. Because of their substantial amplitude, small-angle PS reflections in TI media contain valuable information for anisotropic AVO inversion of multicomponent data. Our analytic solutions provide a foundation for linear AVO-inversion algorithms and can be used to guide nonlinear inversion that is based on the exact reflection coefficients.

Seismic anisotropy in the crystalline upper crust: observations and modelling from the Outokumpu scientific borehole, Finland

“…Ruger 1998;Grechka & Tsvankin 1999;Perez et al 1999;Behura & Tsvankin 2006;Landro & Tsvankin 2007). Ruger 1998;Grechka & Tsvankin 1999;Perez et al 1999;Behura & Tsvankin 2006;Landro & Tsvankin 2007).…”

“…In sedimentary environments, seismic reflection methods have long been used to constrain anisotropy; almost always under somewhat restrictive assumptions regarding orientation of the rock mass symmetry (e.g. Ruger 1998;Grechka & Tsvankin 1999;Perez et al 1999;Behura & Tsvankin 2006;Landro & Tsvankin 2007).…”

3-D mapping of permeable structures affecting a deep granite basement using isotropic 3C VSP data

“…In addition to the fluid content, the anisotropy induced by the fractures in the damage zones of the faults could be of importance in the reflection coefficients (see among others Zillmer et al 1997). Some computations have been carried out by Behura & Tsvankin (2006) and Cai & Chen (2009) showing in a simple case study that the P – S reflection coefficient may attain a value of ∼0.065 for a incidence value of 60°. Nevertheless, no value is computed regarding the P – P reflection coefficient.…”

Joint PP‐ and PSV‐wave amplitudes versus offset and azimuth inversion for fracture compliances in horizontal transversely isotropic media

“…Rüger's equation is widely used in anisotropy parameter estimation from PP-wave seismic data (Nelson 2001;Bachrach et al 2009;Liu and Martinez 2012;Downton and Roure 2015). Behura and Tsvankin (2006) presented small-angle AVO response of PS waves in tilted transversely isotropic media. Behura and Tsvankin (2006) presented small-angle AVO response of PS waves in tilted transversely isotropic media.…”

“…Jílek (2002a, b) derived PS-wave reflection coefficients at a planar weak-contrast interface separating two arbitrarily anisotropic media. Behura and Tsvankin (2006) presented small-angle AVO response of PS waves in tilted transversely isotropic media. Much work has been done to utilise PSV-wave data to detect fractures (Li 1998;Grechka, Theophanisz and Tsvankin 1999;Tsvankin and Larner 2004;Tang, Zhang and Li 2008;.…”