Analysis of dispersive waves by wave field transformation

Abstract

The dispersive waves in a common‐shot wave field can be transformed into images of the dispersion curves of each mode in the data. The procedure consists of two linear transformations: a slant stack of the data produces a wave field in the phase slowness‐time intercept (p — τ) plane in which phase velocities are separated. The spectral peak of the one‐dimensional (1-D) Fourier transform of the p — τ wave field then gives the frequency associated with each phase velocity. Thus, the data wave field is linearly transformed from the time‐distance domain into the slowness‐frequency (p — ω) domain, where dispersion curves are imaged. All the data are present throughout the transformations. Dispersion curves for the mode overtones as well as the fundamental are directly observed in the transformed wave field. In the p — ω domain, each mode is separated from the others even when its presence is not visually detectable in the untransformed data. The resolution achieved in the result is indicated in the p — ω wave field by the width and coherence of the image. The method is applied to both synthetic and real data sets.