Directionally dependent attenuation in transversely isotropic (TI) media can influence significantly the body-wave amplitudes and distort the results of the AVO (amplitude variation with offset) analysis. Here, we develop a consistent analytic treatment of plane-wave properties for TI media with attenuation anisotropy. We use the concept of homogeneous wave propagation, assuming that in weakly attenuative media the real and imaginary parts of the wave vector are parallel to one another. The anisotropic quality factor can be described by matrix elements Q ij , defined as the ratios of the real and imaginary parts of the corresponding stiffness coefficients. To characterize TI attenuation, we follow the idea of the Thomsen notation for velocity anisotropy and replace the components Q ij by two reference isotropic quantities and three dimensionless anisotropy parameters Q , δ Q , and γ Q. The parameters Q and γ Q quantify the difference between the horizontal-and vertical-attenuation coefficients of P-and SH-waves, respectively, while δ Q is defined through the second derivative of the P-wave attenuation coefficient in the symmetry direction. Although the definitions of Q , δ Q , and γ Q are similar to those for the corresponding Thomsen parameters, the expression for δ Q reflects the coupling between the attenuation and velocity anisotropy. Assuming weak attenuation as well as weak velocity and attenuation anisotropy allows us to obtain simple attenuation coefficients linearized in the Thomsen-style parameters. The normalized attenuation coefficients for P-and SV-waves have the same form as the corresponding approximate phase-velocity functions, but both δ Q and the effective SV-wave attenuation-anisotropy parameter σ Q depend on the velocity-anisotropy parameters in addition to the elements Q ij. The linearized approximations not only provide valuable analytic insight, but they also remain accurate for the practically important range of small and moderate anisotropy parameters-in particular, for nearvertical and near-horizontal propagation directions.

Anisotropic attenuation can provide sensitive attributes for fracture detection and lithology discrimination. This paper analyzes measurements of the P-wave attenuation coefficient in a transversely isotropic sample made of phenolic material. Using the spectral-ratio method, we estimate the group (effective) attenuation coefficient of P-waves transmitted through the sample for a wide range of propagation angles (from [Formula: see text] to [Formula: see text]) with the symmetry axis. Correction for the difference between the group and phase angles and for the angular velocity variation help us to obtain the normalized phase attenuation coefficient [Formula: see text] governed by the Thomsen-style attenuation-anisotropy parameters [Formula: see text] and [Formula: see text]. Whereas the symmetry axis of the angle-dependent coefficient [Formula: see text] practically coincides with that of the velocity function, the magnitude of the attenuation anisotropy far exceeds that of the velocity anisotropy. The quality factor [Formula: see text] increases more than tenfold from the symmetry axis (slow direction) to the isotropy plane (fast direction). Inversion of the coefficient [Formula: see text] using the Christoffel equation yields large negative values of the parameters [Formula: see text] and [Formula: see text]. The robustness of our results critically depends on several factors, such as the availability of an accurate anisotropic velocity model and adequacy of the homogeneous concept of wave propagation, as well as the choice of the frequency band. The methodology discussed here can be extended to field measurements of anisotropic attenuation needed for AVO (amplitude-variation-with-offset) analysis, amplitude-preserving migration, and seismic fracture detection.

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Unconventional resources such as shale gas are becoming increasingly important exploration and production targets. To understand the geophysical responses of shale-gas plays, we use a rock physics relationship, which is constrained with geology and formation-evaluation analysis, to calculate effective properties such as impedance and [Formula: see text]. Numerical studies suggest that in-situ rock para-meters such as mineral composition (e.g., clay, quartz, and calcite) and TOC, as well as the interaction among them, can significantly influence the geophysical responses of the organic-rich rocks, thus providing the basis for the geophysical characterization of shale-gas plays.

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Orthorhombic velocity and attenuation models are needed in the interpretation of the azimuthal variation of seismic signatures recorded over fractured reservoirs. Here, we develop an analytic framework for describing the attenuation coefficients in orthorhombic media with orthorhombic attenuation (i.e., the symmetry of both the real and imaginary parts of the stiffness tensor is orthorhombic). The analogous form of the Christoffel equation in the symmetry planes of orthorhombic and VTI (transversely isotropic with a vertical symmetry axis) media helps to obtain the symmetry-plane attenuation coefficients by adapting the existing VTI equations. To take full advantage of this equivalence with transverse isotropy, we introduce a set of attenuation-anisotropy parameters similar to the VTI parameters Q , δ Q , and γ Q. This notation, based on the same principle as Tsvankin's velocity-anisotropy parameters for orthorhombic media, leads to simple linearized equations for the symmetry-plane attenuation coefficients of all three modes (P, S 1 , and S 2). The attenuation-anisotropy parameters also allow us to simplify the P-wave attenuation coefficient A P outside the symmetry planes under the assumption of weak attenuation and weak velocity and attenuation anisotropy. The approximate A P has the same form as the linearized phase-velocity function, with Tsvankin's velocity parameters (1,2) and δ (1,2,3) replaced by the attenuation parameters (1,2) Q and δ (1,2,3) Q. The exact attenuation coefficient A P , however, also depends on the velocity-anisotropy parameters, while the body-wave velocities are almost unperturbed by the presence of attenuation. The reduction in the number of parameters responsible for the P-wave attenuation and the simple approximation for the coefficient A P provide a basis for inverting P-wave attenuation measurements from orthorhombic media. The attenuation processing has to be preceded by anisotropic velocity analysis that can be performed (in the absence of pronounced velocity dispersion) using existing algorithms for nonattenuative media.

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