There are two fundamentally different ways to invert seismic data for subsurface properties. One is to perform nonlinear optimization and end up with an estimation of the full stiffness matrix at each medium location. Another way is to parameterize the data in a way that allows an estimation of a few parameters which describe the data reasonably well. If the problem is transformed into the frequency domain, the exact dispersion relation is not solved for, but a sparse estimate is attempted. The single elliptic paraxial approximation, developed by Dellinger and Muir (1985), was recently extended to a double elliptic paraxial form, which approximates a two-dimensional dispersion relation.