Two dimensional wavelet analysis applied to geoid anomalies, mixing and high Rayleigh number mantle convection

(1) Department of Geophysics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
(2) Department of Geology and Geophysics and Minnesota Supercomputing Institute, University of Minnesota, MN USA

Abstract

Wavelets have been around for over 15 years. The first applications were in seismology (1983). It has found use in many applications, such as a signal analysis, image processing, theoretical physics and numerical mathematics. There are many places where 1-D wavelets have been applied. In geophysics, work by Simons and Hager (1997) in looking at one-dimensional tracks of gravity data over Larurentide. Gibert et al. (1998) used the so-called Moreau wavelets for work on the Chandler Wobble. Our primary concern is the use of multidimensional wavelets (2-D and 3-D), which means a lot more computations then 1-D wavelets. However, the real world is multi-dimensional and should be studied with multidimensional wavelets and not just many one dimensional tracks, and we need to see the periphery of an object by doing the multidimensional wavelet analysis.

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References
[1] Simons, M. and B.H. Hager, Localization of the gravity field and the signature of glacial rebound, Nature, Vol. 390, pp. 500-504, 1997.
[2] Gibert, D., Holschneider, M. and J.L. Le Mouel, Wavelet analysis of the Chandler Wobble, J. Geophys. Res. Sol. Ea., Vol. 103, No. B11, pp. 27,069-27,089, 1998.