Madagascar satellite data: an inversion test case

Jesse Lomask

lomask@sep.Stanford.EDU

ABSTRACT

The Madagascar satellite data set provides images of a spreading ridge off the coast of Madagascar. This data set has two regions: the southern half is densely sampled and the northern half is sparsely sampled. This data set is an excellent test case for inversion methods. It presents several challenges that geophysicists face in generating seismic maps in general. The data is acquired in swaths that follow irregular paths(tracks), similar in some respects to irregular 3D acquisition geometries. Inversion allows us to combine these different data paths into one image. Shifts between tracks are removed by taking the derivative along the tracks in the inversion fitting goals. By looking at the residual in data-space, we were able to see errors in the weighting operator. The sparsely sampled region presents a missing data problem. In the future, we intend to estimate 2D prediction error filters (PEFs) on these sparse tracks and use them to fill in the missing data. I have tested one method on a simple 1D model, in which I estimate a PEF and missing data simultaneously while throwing out fitting equations where the leading 1 coefficient of the PEF lands on unknown data. Thus, this data will give us an opportunity to test different methods of estimating PEFs on sparse and irregular data. Also, preconditioning on the helix greatly speeds convergence.