Seismic amplitude inversion for the transversely isotropic media with vertical axis of symmetry

Abstract

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 in vertical transverse isotropy media and its application to Eagle Ford shale

“…To estimate effective properties of clays as well as shales, a mixture of different rock physics models and workflows have been used. Differential effective medium (DEM), self‐consistent approximation (SCA) and Backus averaging are the main combined models for these purposes (Zhang et al., 2019). However, the model presented here can handle all at once.…”

Direct pre-stack inversion of elastic modulus using the exact Zoeppritz equation and the application in shale reservoir

“…Elastic parameters can be recovered by using pre-stack amplitude variation with offset (AVO) inversion in oil and gas exploration (Minato and Ghose, 2016;Xu et al, 2016;Zhang et al, 2019). Due to the strongly non-linear inverse problems based on the exact Zoeppritz equation, several approximate Zoeppritz equations have been proposed and used in practice.…”

Sequential Seismic Anisotropic Inversion for VTI Media with Simulated Annealing Algorithm Aided by Adaptive Setting of Optimization Parameters

“…Then, under the assumption of weak anisotropy, Rüger [25,26] derived a simplified expression for the reflection coefficient as a function of the three Thomsen's parameters. Due to the simple and linear forms, the Rüger approximation and its modified forms have become the widely used reflection coefficient expressions for AVO/AVA inversion of VTI media [27][28][29][30][31]. However, these approximations have lower accuracy at large incidence angles and are restricted to the assumptions of weak anisotropy and weak impedance contrasts, which limit the accuracy and applicability of the corresponding inversions [32,33].…”