Inversion of refraction data by wave field continuation

Abstract

The process of wave equation continuation (migration) is adapted for refraction data in order to produce velocity‐depth models directly from the recorded data. The procedure consists of two linear transformations: a slant stack of the data produces a wave field in the p — τ plane which is then downward continued using τ = 0 as the imaging condition. The result is that the data wave field is linearly transformed from the time‐distance domain into the slowness‐depth domain, where the velocity profile can be picked directly. No traveltime picking is involved, and all the data are present throughout the inversion. The method is iterative because it is necessary to specify a velocity function for the continuation. The solution produced by a given iteration is used as the continuation velocity function for the next step. Convergence is determined when the output wave field images the same velocity‐depth function as was input to the continuation. The method obviates the problems associated with determining the envelope of solutions that are consistent with the observations, since the time resolution in the data is transformed into a depth resolution in the slowness‐depth domain. The method is illustrated with several synthetic examples, and with a refraction line recorded in the Imperial Valley, California.