The most commonly used method for obtaining interval velocities from seismic data requires a prior estimate of the root-mean-square (rms) velocity function. A reduction to interval velocity uses the Dix equation, where the interval velocity in a layer emerges as a sensitive function of the rms velocity picks above and below the layer. Approximations implicit in this method are quite appropriate for deep data, and they do not contribute significantly to errors in the interval velocity estimate. However, when the data are from a shallow depth (vertical two-way traveltime being less than direct arrival to the farthest geophone), the assumption within the rms approximation that propagation angles are small requires that much of the reflection energy be muted, along with, of course, all the refraction energy.By means of a simple data transformation to the ray parameter domain via the slanted plane-wave stack, three types of arrivals from any given interface (subcritical and supercritical reflections and critical refractions) become organized into a single elliptical trajectory. Such a trajectory replaces the composite hyperbolic and linear moveouts in the offset domain (for reflections and critical refractions, respectively). In a layered medium, the trajectory of all but the first event becomes distorted from a true ellipse into a pseudo-ellipse. However, by a computationally simple layer stripping operation involving p-dependent time shifts, the interval velocity in each layer can be estimated in turn and its distorting effect removed from underlying layers, permitting a direct estimation of interval velocities for all layers. Enhanced resolution and estimation accuracy are achieved because previously neglected wide-angle arrivals, which do not conform to the rms approximation, make a substantial contribution in the estimation procedure.

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