Seismic Amplitude Inversion for Orthorhombic Media Based on a Modified Reflection Coefficient Approximation

• Published in: Surveys in geophysics Vol. 43; no. 5; pp. 1395 - 1433
• Main Authors: Cheng, Jiwei, Zhang, Feng, Li, Xiangyang
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2022; Springer Nature B.V
• Subjects: Accuracy; Acoustic impedance; Amplitude; Amplitudes; Anisotropy; Approximation; Astronomy; Bayesian analysis; Coefficients; Earth and Environmental Science; Earth Sciences; Fractures; Geophysics/Geodesy; Impedance; Isotropy; Mathematical models; Methods; Modelling; Observations and Techniques; P waves; Parameters; Phase velocity; Probability theory; Reflectance; Reflection; Reservoirs; Review Paper; Sedimentary rocks; Seismic activity; Seismic data; Seismic response; Seismic stability; Seismic surveys; Seismic wave velocities; Seismological data; Shale; Shale gas; Shales; Shear modulus; Velocity; Wave phase; Wave reflection; Wave velocity; Orthorhombic medium; Fracture; Seismic inversion; Shale
• ISSN: 0169-3298; 1573-0956
• DOI: 10.1007/s10712-022-09718-z

Shales represent strongly intrinsic vertical transverse isotropy (VTI) property or polar anisotropy. The presence of vertically aligned fractures makes shale exhibit orthogonal anisotropy and the seismic responses have azimuthal variation. Conventional linearized PP-wave reflectivity expression for orthorhombic (ORT) media includes at least 8 parameters to be inverted, and the amplitude inversion based on such equations can be highly ill-posed. In this paper, we derive a modified PP-wave approximation of reflection coefficients in ORT media and propose a two-step strategy based on the Bayesian-framework inversion method. The new equation represents the seismic response of polar anisotropy and azimuthal anisotropy separately, and it consists of only 5 model parameters to be inverted. Three of these model parameters are azimuthal independent: A—acoustic impedance, B—anisotropic shear modulus and C—horizontal P-wave phase velocity (along the fracture strike), and two of them are azimuthal dependent: D—azimuthal anisotropic gradient and E—horizontal P-wave anisotropy parameter. Accuracy analysis demonstrates that the derived approximation has similar accuracy to the existing approximation. A stepwise inversion strategy is proposed to invert azimuthal-independent parameters and azimuthal-dependent parameters separately. Synthetic tests show that the proposed strategy is more stable and better conditioned than the existing multi-parameter simultaneous inversion. Field seismic data set of a fractured shale-gas reservoir is also used to demonstrate the stability and accuracy of the proposed inversion method. Article Highlights PP-wave reflection coefficient is derived in terms of only 5 model parameters for orthorhombic media. Three of them are azimuthal independent: A—acoustic impedance, B—anisotropic shear modulus, C—horizontal P-wave phase velocity (along the fracture strike), and the others are azimuthal dependent: D—azimuthal anisotropic gradient, and E—horizontal P-wave anisotropy parameter A stepwise inversion strategy for inverting azimuthal-independent parameters and azimuthal-dependent parameters is proposed Tests on synthetic and field seismic datasets imply that the proposed inversion method has the potential to generate reliable results of the model parameters for reservoir characterization