Multiresolution Analysis of Geopotential and Gravity Data

Recent advances in the field of signal analysis have provided researchers with new tools for exploring and examining the Earth's crust and upper mantle. Traditional analysis tools employ global basis functions when characterizing measured data. Newer methods provide the opportunity to localize features and signal characteristics. These are exemplified by the use of wavelets for multiresolution analysis. Using symmetric wavelets of arbitrary scale applied to recent models of the geoid, the Earth's crust and upper mantle are examined to identify features that characterize their geological make-up. Two Fourier-based methods are employed in the analysis: filtering on standard rectangular grids, and filtering on the sphere. The results using various datasets and operators are compared in terms of resolution capability, and cost of analysis. With the availability of enormous satellite altimetry and gravity observations from several space missions, the development of new computational tools aims at extracting useful geophysical information from the datasets. Preliminary recommendations are included and ongoing investigations are described.