AVAZ inversion for anisotropy parameters of a fractured medium: A physical modeling study

Faranak Mahmoudian, Gary F. Margrave, Joe Wong and Brian Russell

ABSTRACT

This report presents an amplitude inversion of PP data, collected through physical modelling, for the Thomsen anisotropy parameters (ε, δ, and γ) of an orthorhombic medium. Orthorhombic symmetry with three mutually perpendicular directions each with different velocity is the most general symmetry that can describe the vertical fractures in horizontal fine layering. Assuming the natural coordinate system along with the fracture orientation, 3D PP data with several azimuths over a phenolic layer have been acquired using the physical modeling facility in CREWES. The phenolic material has been shown to possess orthorhombic symmetry; however it is approximately transversely isotropic with two independent directions. The PP amplitudes picked from the reflection off an isotropic layer and the phenolic layer contrast at several azimuths were used as the data for the inversion. Deterministic amplitude corrections, similar to those used for the real-world acquisition were applied to the physical model amplitudes prior to inversion to scale them to represent the reflectivity. We also applied an additional source-receiver directivity correction specific to the piezoelectric transducers used in the physical modeling. A linearized PP reflection coefficient approximation for an orthorhombic media is used to facilitate the inversion. Some constraints on the vertical velocities and density were also incorporated in the inversion process. Large offset data are required for the azimuthal amplitude inversion of the phenolic layer, as the material shows only slight azimuthal amplitude variations. The results for all three anisotropy parameters from AVAZ inversion compare very favourably to those obtained previously by a traveltime inversion. This result makes it possible to compute the splitting parameter, γ, (historically determined from shear-wave data) from a quantitative analysis of the PP data.

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