Transverse isotropy with a vertical axis of symmetry is a common form of anisotropy in sedimentary basins, and it has a significant influence on the seismic amplitude variation with offset. Although exact solutions and approximations of the PP‐wave reflection coefficient for the transversely isotropic media with vertical axis of symmetry have been explicitly studied, it is difficult to apply these equations to amplitude inversion, because more than three parameters need to be estimated, and such an inverse problem is highly ill‐posed. In this paper, we propose a seismic amplitude inversion method for the transversely isotropic media with a vertical axis of symmetry based on a modified approximation of the reflection coefficient. This new approximation consists of only three model parameters: attribute A, the impedance (vertical phase velocity multiplied by bulk density); attribute B, shear modulus proportional to an anellipticity parameter (Thomsen's parameter ε−δ); and attribute C, the approximate horizontal P‐wave phase velocity, which can be well estimated by using a Bayesian‐framework‐based inversion method. Using numerical tests we show that the derived approximation has similar accuracy to the existing linear approximation and much higher accuracy than isotropic approximations, especially at large angles of incidence and for strong anisotropy. The new inversion method is validated by using both synthetic data and field seismic data. We show that the inverted attributes are robust for shale‐gas reservoir characterization: the shale formation can be discriminated from surrounding formations by using the crossplot of the attributes A and C, and then the gas‐bearing shale can be identified through the combination of the attributes A and B. We then propose a rock‐physics‐based method and a stepwise‐inversion‐based method to estimate the P‐wave anisotropy parameter (Thomsen's parameter ε). The latter is more suitable when subsurface media are strongly heterogeneous. The stepwise inversion produces a stable and accurate Thomsen's parameter ε, which is proved by using both synthetic and field data.

A rock physics model is a very effective tool to describe the anisotropy and mechanical properties of rock from a seismology perspective. Compared to

Part 1 of this paper presented an improved shale rock physics model to enable the prediction of anisotropy parameters from both vertical and horizonta

Conventional elastic impedances are derived as scalars by means of the integration of reflectivity. In this sense, they are attributes of the seismic reflection but not the intrinsic physical property of the subsurface media. The derivation of these expressions shares the same assumptions as the reflectivity approximations, such as weak impedance contrast, small angle of incidence, or weak anisotropic media, and thus it limits the accuracy and interpretation capability. The exact P/SV impedance matrices relating the stress and strain represent the mechanical property of the subsurface media and yield reflection coefficients at an arbitrary angle of incidence. We have extended the impedance matrices to a transversely isotropic medium. The resulting elastic impedances (stress/velocity ratios) can be used to characterize those unconventional reservoir formations with strong seismic anisotropy, such as shale-gas and coal-bed methane. Our numerical analyses determined their variations with the phase angle and anisotropy parameters. The exact expressions of the P- and S-wave elastic impedances are used to model the seismic reflection coefficients, and thus they can be inverted simultaneously if all of the types of reflection waves are available. We then derive approximations of quasi-P-wave elastic impedances for seismic inversion of anisotropy parameters and further interpretation. Our applications on real logs and seismic data for a turbidite fan reservoir and a shale-gas reservoir determined the robust interpretation capability of derived elastic impedances in lithology characterizations.

A well log penetrating the Lower Silurian shale in the south of Sichuan Basin shows that this organic-rich shale formation presents strong vertically transverse isotropy properties. The magnitude of the anisotropy is determined by clay content and the volume of clay-bound water, but kerogen content is found to have a negative correlation with seismic anisotropy. Core sample analysis reveals an extremely high level of maturity. This overmature shale includes a large volume of randomly distributed organic matter and developed pores of free water and gas; both phases reduce anisotropy. We propose a modified rock physics model based on the result of analysis, and this model can successfully describe the elastic behaviour of this overmature organic-rich shale. The intrinsic anisotropy is modelled from varied laminated clay minerals, and the clay-related pore space by using effective medium theories, while kerogen is considered as an isolated inclusion embedded with clay platelets. This model is applied to anisotropy parameter prediction from well log data. The clay-related pore geometry and a lamination parameter are inverted from C₃₃ and C₄₄ in a borehole. The end result is supported by agreement between prediction and borehole measurement of C₆₆ and Thomsen's anisotropy parameter, γ. Besides, the anisotropic synthetic angle gather generated using the predicted logs shows a better seismic well tie than the isotropic synthetic angle gather. Therefore, this method can provide reliable anisotropy parameters for anisotropic seismic inversion and interpretation, and thus is useful for reservoir characterization.