The Madagascar seasat sea level dataset is a collection of two passes (ascending and descending) of the GEOSAT satellite over a region of the Southwest Indian Ridge in the Indian Ocean. There is a densely-acquired region of the dataset in the south, which ranges from 40 to 70 degrees (E) longitude and 30 to 40 degrees (S) latitude, while the latitude of the sparsely-acquired data ranges from 20 to 40 degrees (S) latitude.
The satellite tracks are much like feathered marine geophone cables, sail lines, or shot lines in a 3D seismic survey. Any method that hopes to succeed on 3D seismic data should be able to deal with this toy problem.
There are several issues to account for when dealing with this data. The crossing tracks of the dataset result in single locations with multivalued data, which can be substantially different due to tidal variations, weather patterns, and currents. In addition, there is spiky noise throughout the dataset, which is infamous for its effect on least-squares based methods Claerbout and Muir (1973); Guitton and Symes (2003). Finally, the only tracks in the northern half of the survey area have a very wide spacing, so an interpolation problem also arises.
Previous work on this dataset at SEP Ecker and Berlioux (1995); Lomask (1998, 2002) has mainly dealt with the systematic errors present in the dense dataset Ecker and Berlioux (1995), or with ways in which to use information in the dense portion of the data to regularize the missing bins in the northern, sparse portion of the data Lomask (1998, 2002).
Some previous methods of dealing with sparse data rely on creating proxy data, either by an initial guess of a prediction-error filter (PEF) Claerbout (1999) or by using coarser scales of the data Curry (2002). I propose a method where we solve the interpolation problem in the data space coordinate system. The model space is warped to fit the data location and two different approaches are applied. In the first approach te data are preprocessed so that they are single valued. In the second, two sets of co-located tracks are used to create a map.