45207-AC8
Attenuation Analysis for Azimuthally Anisotropic Media
Reflection coefficients in attenuative anisotropic media
Such reservoir rocks 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. We evaluated the influence of attenuation on PP- and PS-wave reflection coefficients for anisotropic media with the main emphasis on models with VTI (transversely isotropic with a vertical symmetry axis) symmetry.
Concise analytic solutions obtained by linearizing exact plane-wave reflection coefficients were 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 absorbing media, it is also necessary to take attenuation anisotropy into account if the magnitude of the Thomsen-style attenuation-anisotropy parameters is relatively large. However, the sensitivity of reflection coefficients to attenuation anisotropy is weaker than that to velocity anisotropy.
Our formalism also helps to estimate the influence of the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector) on the reflection coefficient. A nonzero inhomogeneity angle of the incident wave introduces additional terms into the PP- and PS-wave reflection coefficients, which makes 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 PS-wave at normal incidence, even if both halfspaces have a horizontal symmetry plane. The developed linearized solutions can be efficiently used in AVO inversion for strongly attenuative reservoirs.
Role of the inhomogeneity angle in attenuation analysis
The inhomogeneity angle is seldom taken into account in estimating attenuation coefficients from seismic data. However, wave propagation through layered media may result in relatively large inhomogeneity angles x, especially for models with significant attenuation contrasts across layer boundaries. We studied the influence of the angle x on phase and group attenuation in transversely isotropic (TI) media using the first-order perturbation theory verified by exact numerical modeling.
Application of the spectral-ratio method to transmitted or reflected waves yields the normalized group attenuation coefficient AG, which is responsible for the amplitude decay along seismic rays. Our analytic solutions linearized in the anisotropy parameters show that AG is close to the normalized phase attenuation coefficient A computed for a zero inhomogeneity angle. The coefficient A (x=0) can then be inverted for the attenuation-anisotropy parameters using the existing formalism developed by Zhu and Tsvankin (2006). In other words, no knowledge of the inhomogeneity angle is required for attenuation analysis of seismic data in TI media. This conclusion remains valid even for uncommonly high attenuation with the quality factor Q less than 10 and strong velocity and attenuation anisotropy.
We also demonstrated that the velocity function remains practically independent of attenuation for arbitrary values of x, while the angle variation of the attenuation coefficients is controlled primarily by the attenuation-anisotropy parameters. The influence of velocity anisotropy on attenuation becomes non-negligible only for strongly attenuative media (Q<5) and large inhomogeneity angles (x >70o). In principle, estimation of the attenuation-anisotropy parameters from the coefficient A requires computation of the phase angle, which depends on the anisotropic velocity field. However, for moderately anisotropic models the difference between the phase and group directions does not significantly distort the results of attenuation analysis.
