INTERPOLATION WITH P.D.E. DIP FILTERS

For difference representations of partial differential operators, mesh refinement is straightforward because expressions for the differencing star include $\Delta t$ and $\Delta x$ which can simply be halved. The star for $\partial_x-p\partial_t$is unchanged if $\Delta t$ and $\Delta x$ are simultaneously halved. If a dipping wavefield u(x-p₁t) is input to this operator the output vanishes if p=p₁, 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.