One of the main challenges in anisotropic velocity analysis and imaging is simultaneous estimation of velocity gradients and anisotropic parameters from reflection data. Approximating the subsurface by a factorized VTI (transversely isotropic with a vertical symmetry axis) medium provides a convenient way of building vertically and laterally heterogeneous anisotropic models for prestack depth migration.

The algorithm for P-wave migration velocity analysis (MVA) introduced here is designed for models composed of factorized VTI layers or blocks with constant vertical and lateral gradients in the vertical velocity VP0. The anisotropic MVA method is implemented as an iterative two-step procedure that includes prestack depth migration (imaging step) followed by an update of the medium parameters (velocity-analysis step). The residual moveout of the migrated events, which is minimized during the parameter updates, is described by a nonhyperbolic equation whose coefficients are determined by 2D semblance scanning.

For piecewise-factorized VTI media without significant dips in the overburden, the residual moveout of P-wave events in image gathers is governed by four effective quantities in each block: (1) the normal-moveout velocity Vnmo at a certain point within the block, (2) the vertical velocity gradient kz, (3) the combination k^x=kx1+2δ of the lateral velocity gradient kx and the anisotropic parameter δ, and (4) the anellipticity parameter η. We show that all four parameters can be estimated from the residual moveout for at least two reflectors within a block sufficiently separated in depth. Inversion for the parameter η also requires using either long-spread data (with the maximum offset-to-depth ratio no less than two) from horizontal interfaces or reflections from dipping interfaces.

To find the depth scale of the section and build a model for prestack depth migration using the MVA results, the vertical velocity VP0 needs to be specified for at least a single point in each block. When no borehole information about VP0 is available, a well-focused image can often be obtained by assuming that the vertical-velocity field is continuous across layer boundaries. A synthetic test for a three-layer model with a syncline structure confirms the accuracy of our MVA algorithm in estimating the interval parameters Vnmo, kz, k^x, and η and illustrates the influence of errors in the vertical velocity on the image quality.

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