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For difference representations of partial differential operators,
mesh refinement is straightforward
because expressions for the differencing star include
and which can simply be halved.
The star for is *unchanged* if and are simultaneously halved.
If a dipping wavefield *u*(*x*-*p*_{1}t) is input to this operator
the output vanishes if *p*=*p*_{1},
so this operator deserves the name ``dip filter''
or ``dip rejection filter''
or ``plane-wave destruction filter''.
As deconvolution offers well-known opportunities
with narrow-banded frequency spectra,
the possibility of destroying a perfect plane wave
with only two seismograms offers similar opportunities.

** Next:** Spatial interpolation with
** Up:** Nonlinear problems
** Previous:** DIP FILTER DEFINITION
Stanford Exploration Project

1/13/1998