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Hi Sergey, Matt, and Sean,
Here are my latest speculations, plans:
The 3-D Lomoplan resembles a gradient, one field in, two or three out.
Lomoplan times its adjoint is like a generalized laplacian.
Factorizing it yields a lomoplan generalization of the helix derivative,
i.e. a one-to-one operator with the same spectral charactoristic
as the original lomoplan.
It will probably not come out to be a juxtaposition of planes,
will be more cube like.
The advantage of being one-to-one is
that it can be used as a preconditioner.
The application, naturally enough,
is estimating things with a prescribed dip spectrum.
Things like missing data and velocities.
Why use multiplanar lomoplan estimates if they will then be
converted by this complicated process into a cube?
Why not estimate the cube directly? Maybe to impose
the ``pancake" model instead of the noodle model of covariance.
Maybe to reduce the number of coefficients to estimate.
I haven't figured out yet how to convert this speculation
into an example leading to some figures.
If you like the idea, feel free to beat me to it :)

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Stanford Exploration Project

4/27/2004