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Reflection traveltimes (moveout) provide the most reliable information for building velocity models using surface seismic data, in both isotropic and anisotropic media. If the medium is anisotropic, an attempt to fit the traveltime-offset relationship using a purely isotropic velocity field may lead to misstacking of reflection events and distortions in seismic images (see examples in chapters 6–8). Hence, understanding of the influence of anisotropy on the kinematics of reflected waves is of primary importance in seismic velocity analysis and processing.

Moveout of pure (nonconverted) modes on common-midpoint (CMP) gathers is conventionally approximated by the Taylor series expansion near the vertical (e.g., Taner and Koehler, 1969):

where x is the source-receiver offset, and the coefficients are given by

t0 is the two-way zero-offset traveltime. Equation (3.1) does not include odd powers of x because CMP moveout of pure modes is symmetric with respect to zero offset (i.e., it remains the same when one interchanges the source and receiver). Later on we will replace the Taylor series (3.1) with a more accurate approximation that still includes the moveout coefficients A0, A2, and A4.

The moveout parameter of most practical significance in exploration is the normal-moveout (NMO) velocity Vnmo, responsible for the hyperbolic moveout on conventional-length spreads that do not exceed the distance between the CMP and the reflector:

If the traveltime is plotted in the t2x2 coordinates, the factor 1/Vnmo2 determines the initial slope of the moveout curve. With increasing offset, the t2(x2) curve deviates from a straight line due to

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