Physics – Geophysics
Scientific paper
Dec 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001agufmng41a..02y&link_type=abstract
American Geophysical Union, Fall Meeting 2001, abstract #NG41A-02
Physics
Geophysics
3200 Mathematical Geophysics, 3299 General Or Miscellaneous, 8124 Earth'S Interior: Composition And State (Old 8105)
Scientific paper
Today we are facing a severe crisis of being flooded with huge amounts of data being generated by higher-resolution numerical simulations , laboratory instrumentions and satellite observations. Since there is no way one can visualize the full data set, we must extract essential features from the data-set. One way of addressing this problem is to use mathematical filters , such as multidimensional wavelets. We present imaging results in the geosciences based on using multidimensional Gaussian wavelets as a filter. This approach has been applied to a wide-range of problems, which span from the nanoscale in mineral surfaces imaged by atomic force microscopy to hundreds of kilometers in geoidal undulations determined from satellite orbits or small-scale plumes in high Rayleigh number convection. Besides decomposing the field under consideration into various scales , called a scalogram, we have also constructed two-dimensional maps, delineating the spatial distributions of the maximum of the wavelet transformed quantity E-max and the associated local wave-number. We have generalized the application of multidimensional wavelets to quantify in terms of a two-dimensional map the correlation C for two multidimensional fields A and B. We will show a simple 2D isotropic wavelet-like transform for a spherical surface. We have analyzed the transformed geoid data with a band-pass filter in the spherical harmonic domain and have shown the equivalency of the two representations. This spherical wavelet-like filter can be applied also to problems in planetary science, such as the surface topography and geoid of other planetary bodies, like Mars.
Kido Manabu
Vincent Alain P.
Yuen Dave A.
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