Two distinct types of errors are made in wave migration. Of greater practical importance is frequency dispersion, which occurs when different frequencies propagate at different speeds. This may be reduced by improving the accuracy of finite-difference approximations to differentials. Its cure is refinement of the differencing mesh.
Of secondary importance, and the subject of this section, is
anisotropy dispersion.
Anisotropic wave propagation is waves going different directions
with different speeds.
In principle, anisotropic dispersion
is remedied by the Muir square-root expansion.
In practice, the expansion is generally truncated at either
the 15
or 45 term, creating anisotropy error in data processing.
The reasons often given for truncating the series and causing the error are
(1) the cost of processing and (2) the
larger size of other errors in the overall
data collection and processing activity.
Anisotropy error
should be studied in order to (1)
recognize the problem when it occurs and (2)
understand the basic trade-off between cost and accuracy.
Anisotropy is often associated with the propagation of light in crystals. In reflection seismology, anisotropy is occasionally invoked to explain small discrepancies between borehole velocity measurements (vertical propagation) and velocity determined by normal moveout (horizontal propagation). These fundamental, physical anisotropies and the subject of this section, anisotropy in data processing, share a common mathematical and conceptual basis.