Filters for GRACE data analysis

Author: M. Fang, Rui M. Ponte, C. Wunsch and B.H. Hager
December 1, 2004
AGU Fall Meeting, San Francisco

Fang, M., R.M. Ponte, C. Wunsch, and B.H. Hager, 2004. Filters for GRACE data analysis, AGU Fall Meeting, San Francisco, December 2004.

Conversion from differential GRACE geoid to near surface mass variation is an unbounded high-pass filter generated by a singular spherical cap with a divergent harmonic spectrum. Low-pass smoothing windows have to be used for control of error amplification due to the spectral divergence of this so-called inverse geoid filter (IGF) We present the criteria for under-smoothing and over-smoothing. A properly smoothed IGF is characterized by a nearly symmetric dome-shaped harmonic spectrum. Ascending from the lower end of the spectrum preserves the high-pass nature of IGF, while descending from the peak of the spectrum controls the error. Smoothed IGF with dome-shaped spectrum represents a class of wiggled spherical caps that are no longer positive definite over the surface. We demonstrate that a properly smoothed IGF that is also robust in resolving the geometry of sub-surface mass sheets should have zero-mean over the surface. The zero-mean nature makes the smoothed IGF a mother wavelet of proper scale. We propose a reversed process for the design of smoothing windows, starting from an effective spherical wavelet with an arbitrary multiplier as the end-result IGF. The low-pass smoothing window is recovered from the end-result IGF by modulating it with the exact IGF, and the multiplier can be determined by scaling the amplitude of the smoothing window against mass conservation. We developed a new smoothing window from an effective analytical spherical wavelet based upon the new procedure. Comparative studies are conducted with the new IGF on GRACE data and predicted ocean bottom pressure series over several oceanic and Ocean-land mixed regions.