Plane waves in three dimensions

3-D SPECTRAL FACTORIZATION

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 :)

Plane waves in three dimensions