(1) JAMSTEC,
Yokosuka, Japan
(2) Department of Geology and
Geophysics and Minnesota Supercomputing
Institute, University of Minnesota, MN USA
(3) Department of Geophysics,
Faculty of Mathematics and Physics, Charles University, Prague, Czech
Republic
(4) Dept.
Physique, University of Montreal, Montreal, Quebec, Canada
The recent use of multi-dimensional wavelets has shown greatly the ability for capturing distinct features at different scales. In particular, two-dimensional wavelet analysis of non-hydrostatic geoid anomalies has revealed the strong anomalies at plate margins for both oceanic and continental plate boundaries, using a degree 90 geoid. In this study we have extended the previous geoid analysis by wavelets to degree 360 (Le Moine et al., 1996). The convergence of the earlier wavelet solutions is demonstrated clearly by comparing the various wavelet truncation levels up to degree 256. We have also compared these results with a nonlinear band-pass filter in the spectral domain where a Gaussian filter with the logarithm of the degree l acting as the argument has been employed. There are two parameters in this filter, the peak of the logarithm in the degree log2(lc) and the width w describing the spread in the Gaussian filter in log2(l) space. By using the spatial correlation function between the wavelet geoid solution and the filtered geoid, we are able to estimate the optimal parameters in the width and shift in the peak of log2(lc) for providing an excellent visual fit between the two types of solutions. This has been conducted for both global and local wavelet solutions, up to degree 256. However, the width of the optimal solution is extremely broad. A wavelet solution, with a length-scale corresponding to degree 256, would need a filter with over 300 spherical harmonics centering around lc=157 for an optimal spatial fit. For length-scales corresponding to degree 128 and 64, the respective filters because of the logarithmic nature of the argument in the Gaussian filter must also have the same 300 spherical harmonics but with lc centering respectively at 78 and 40. Thus the computational effort with the band-pass filter exceeds greatly those associated with wavelets.
Not available.
References
[1] Lemoine, F.G. et al., in Gravity,Geoid and Marine Geodesy ,ed.by I.
Segawa, H.Fujimoto and S.Okubo, pp.461-469, Springer Verlag, Berlin,1996.