Reflection coefficients in attenuative anisotropic media

Abstract

Reservoir rocks such as heavy oils are characterized by significant attenuation and, in some cases, attenuation anisotropy. Most existing attenuation studies are focused on plane-wave attenuation coefficients, which determine the amplitude decay along the raypath of seismic waves. Here, we discuss the influence of attenuation on PP-and PS-wave reflection coefficients for anisotropic media with main emphasis on models with VTI (transversely isotropic with a vertical symmetry axis) symmetry. Concise analytic solutions obtained by linearizing the exact plane-wave reflection coefficients are verified by numerical modeling. To make a substantial contribution to reflection coefficients, attenuation has to be strong, with the quality factor Q not exceeding 10. For such highly attenuative media, it is also necessary to take attenuation anisotropy into account if the magnitude of the Thomsen-style attenuation-anisotropy parameters is relatively large. In general, the linearized reflection coefficients in attenuative media include velocity-anisotropy parameters but have almost "isotropic" dependence on attenuation. Our formalism also helps to evaluate the influence of the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector) on the reflection coefficients. A nonzero inhomogeneity angle of the incident wave introduces additional terms into the PP-and PS-wave reflection coefficients, making conventional AVO (amplitude-variation-with-offset) analysis inadequate for strongly attenuative media. It is interesting that an incident P-wave with a nonzero inhomogeneity angle generates a mode-converted PSwave at normal incidence, even if both halfspaces have a horizontal symmetry plane. This phenomenon can provide an alternative explanation for substantial PS-wave energy at zero offset observed on field data. The linearized solutions developed here can be used in AVO inversion for highly attenuative (e.g., gassand and heavy-oil) reservoirs.

Anisotropic permeability in fractured reservoirs from frequency‐dependent seismic Amplitude Versus Angle and Azimuth data

“…Behura and Tsvankin () also analysed PP‐ and PS‐wave reflection coefficients in attenuative anisotropic media using linearized approximations verified by exact numerical modelling. They concluded that for an incident P‐wave with zero inhomogeneity angle, the form of linearized PP‐ and PS‐wave reflection coefficients is the same as that in purely elastic media but all terms become complex.…”

“…This assumption raises questions as real seismic data mostly involve inhomogenous waves rather than homogenous waves but Behura and Tsvankin (2009a) showed that no knowledge of the inhomogeneity angle is required for attenuation analysis. Behura and Tsvankin (2009b) also analysed PP-and PSwave reflection coefficients in attenuative anisotropic media using linearized approximations verified by exact numerical C 2013 European Association of Geoscientists & Engineers, Geophysical Prospecting, 62, Anisotropic permeability in fractured reservoirs 309…”

Kirchhoff modeling for attenuative anisotropic media using Gaussian beams

“…Although the reflection coefficient and slowness vector also become complex in attenuative media, we compute these quantities for the reference elastic medium. Unless attenuation is anomalously high, plane-wave reflection coefficients are not significantly distorted in attenuative media (Behura and Tsvankin, 2009b). Although the complex-valued slowness vectors at the reflector can somewhat change the weighting function defined in equation 2, they do not significantly contribute to the displacement computed from equation 3 because attenuation is a propagation phenomenon.…”

AVO theory for large contrast elastic and anelastic targets in pre-critical regimes

“…A potentially important second order influence on seismic AVO is target anelasticity, which, though far from a new idea (e.g., White, 1965;Kjartansson, 1979), has grown in interest in recent years (e.g., Stovas and Ursin, 2001;Chapman et al, 2006;Odebeatu et al, 2006;Lines et al, 2008;Behura and Tsvankin, 2009). Although fundamental questions remain about correctly formulating anelastic reflection coefficients (Krebes and Daley, 2007), the problem is on relatively solid theoretical footing (Borcherdt, 2009), and with simple alterations of the Zoeppritz equations, displacement reflection coefficients can be calculated for an elastic incidence medium overlying an anelastic target medium obeying a nearly-constant Q model.…”