This paper describes a new method for recovering velocity profiles utilizing both phase and amplitude information including wide-angle arrivals, post- and pre-critical reflections.This method is based on a double spatial transformation with a minimization procedure. The first transformation is slant stacking of the observed wave field (seismogram). The second is projecting the slant stacked wave field into the domain of horizontal slowness p and depth z. In this domain the inverse problem is reduced to finding the critical path p = V (super -1) (z) where V(z) is the true velocity of the compressional waves. A numerical algorithm based on a minimization technique is used to find the critical path, which is equivalent to the set of turning points of the critically reflected rays. When this path is found, then the following criteria are satisfied:(1) most of the energy is concentrated away from the precritical region;(2) the computed reflection coefficients reach their maximum on this path; and(3) for horizontally stratified media or CMP data, the reflectors are aligned in the p-z domain.In tests, this method has been shown to recover the velocity profile from both synthetic and real data. It is shown that the method is able to recover accurately velocity profiles even if only part of the data are given. For example, only part of the data are available when low- and high-frequency components are missing or when the data are truncated in lateral extent due to the finite length of the recording system. Moreover, the method is able to handle virtually any vertical velocity gradients in a medium; therefore, it can be applied to complicated geologic structures. The method does not require elimination of multiples, but it is not applicable to the case of a medium with a large lateral velocity gradient. It can be used even for an elastic medium when the mode-converted energy is not small.

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