Analysis of Dispersive Waves by Wave-Field Transformation
, by George A. McMechan and Mathew J. Yedlin
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 fieldin the phase slowness-time intercept
(p-tao) plane, in which phase velocities are separated; the spectral
peal of the one-dimensional Fourier transform of the p-tao 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-omega) 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-omega domain,
each mode is separated from the others even when its presence is not
visually detectable n the unstransformed data. The resolution achieved
in the result is indicated in the p-omega wave field by the width and
coherence of the image. The method is applied to both synthetic and
real datasets.
STANFORD