Higher-order terms in the generalized seismic reflection moveout equation are usually neglected, resulting in the familiar second-order, or hyperbolic, moveout equation. Modeling studies show that the higher-order terms are often significant, and their neglect produces sizable traveltime residuals after correction for moveout in such cases as kinked-ray models. Taner and Koehler (1969) introduced velocity spectra for estimating stacking velocity defined on the basis of second-order moveout. Through the use of orthogonal polynomials, an iterative procedure is defined that permits computation of fourth-order moveout spectra while simultaneously upgrading the previously computed, second-order spectra. Emphasis is placed on the fourth-order term, but the procedure is general and can be expanded to higher orders. When used with synthetic and field recorded common-midpoint (CMP) trace data, this technique produces significant improvements in moveout determination affecting three areas: (1) resolution and interpretability of moveout spectra, (2) quality of CMP stacked sections, and (3) computation of velocity and depth for inverse modeling.

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