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Consider a uniform mesh on the space axis and a continuum on the time axis.
A simple dip destruction filter operating in (*t*,*x*)-space is
.Convolving this two-pulse filter on any (*t*,*x*)-data plane
destroys the *p*_{1} dip component in that plane.
(Of course if wavelengths are less than ,more than only the dip *p*_{1} will be destroyed.)
The operator that destroys two dips is a product in Fourier space
or a convolution in (*t*,*x*)-space.
The convolution is

| |
(3) |

The problem of estimating the filter in (3)
is dreadfully non-linear,
though a global 2-D search might work.
But
(3)
suggests the 2D filter
`
a v
b w
1 c x
d y
e z
`

After finding the coefficients,
this filter can be applied on a mesh with both *t* and *x* interleaved.
We are somewhat at the mercy of the regression procedure
that determines all the coefficients in the filter.
We have not imposed the constraint that the filter be a dip filter,
so maybe it will be something undesirable in addition to being a dip filter.
If the dip spectrum has nonzero bandwidth,
the filter can't be exactly right,
but it may perform adequately.
We should try it.
Perhaps it will work the way it is
or perhaps we need to find some way to limit
the number of free parameters in the differencing star
to force it to fit the mold of a narrow banded dip filter.

** Next:** Nonlinear least squares
** Up:** INTERPOLATION WITH SPATIAL PREDICTORS
** Previous:** Refining both t and
Stanford Exploration Project

1/13/1998