We consider a case where a 3D depth migration has been performed in the local angle domain (LAD) using rich-azimuth seismic data (e.g., conventional land surveys). The subsurface geologic model is characterized by considerable azimuthally anisotropic velocity variations. The background velocity field used for the migration can consist of azimuthally independent, e.g., vertical transverse isotropy, and/or azimuthally dependent (e.g., orthorhombic), velocity layers. The resulting 3D full-azimuth reflection angle gathers generated by the LAD migration represent in situ high-resolution amplitude preserved reflectivities associated with opening angles between incident and reflected slowness vectors in the specular directions. Residual moveouts (RMOs) automatically picked on these 3D image gathers along major horizons can indicate considerable residual periodic azimuthal variations. This situation is typical in depth imaging applied to unconventional shale plays, where the background velocity model doesn’t yet account for the aligned stress/fracture systems that exist in some of the target layers. We use the azimuthally dependent, phase-angle RMOs to update the interval parameters of the background model, accounting for the azimuthal anisotropy effect. Until now, this problem was mainly treated in the unmigrated time-offset domain, which is limited in describing the actual in situ changes of the velocity field with azimuths. The subsurface full-azimuth phase-angle domain RMOs provide better physical parameters to analyze the in situ azimuthal variations of the anisotropic media. Our method is grounded in a newly derived generalized Dix-based theory, where locally the background and updated models are assumed to be 1D anisotropic velocity models. At each lateral location, the orthorhombic axis x3 points in the vertical direction across all layers, but the azimuthal orientations of the orthorhombic layers change from layer to layer. An effective model for such a layered structure (background or updated) is represented by a single layer with a vertical time identical to that of the whole package, effective fast and slow normal moveout (NMO) velocities, and an effective azimuthal orientation of the slow NMO velocity. Our approach begins with computation of these effective parameters for the background model and conversion of the high-resolution RMOs into a dense set of updated, effective, azimuthally dependent NMO velocities, which are then converted into three effective parameters of the updated model. Next, we apply a generalized Dix-based inversion approach to estimate the local NMO parameters for each updated layer. Finally, we convert the local parameters into interval azimuthally varying anisotropic model parameters (e.g., TTI, orthorhombic, or tilted orthorhombic) within each layer. The 1D Dix-based approach presented in this work should not be considered an alternative to more accurate 3D global inversion approaches, such as global anisotropic tomography. However, the proposed method can be effectively used for moderately laterally varying models, and some of the principal physical rules derived for the 1D model can be further used to improve the formulation and geophysical constraints applied to 3D global inversion methods.

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