To prove that the familiar 15, 45, etc. wave extrapolators
are not frequency-dispersive, recall from chapter that
the dispersion relations all have the
form , where *f* is
a semicircle approximation, say, 15 or 45.No dispersion relation of this form can be frequency-dispersive.
Performing the derivatives required by (29), you see that while the
(*x*,*t*)-coordinates of a wavefront depend on the dip angle
through the parameter , they
do not depend explicitly on .So any frequency dispersion observed in practice does
not arise from a 15 or 45 approximation.

10/31/1997