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

The recent applications of multidimensional wavelets in solid-earth geophysics have received great impetus from the fast wavelet transform technique developed by Bergeron et al. (1999). We have employed this method to three problems in geophysics: (1) geoid anomalies (2) mixing of passive heterogeneities (3) high Rayleigh mantle convection in an axisymmetric spherical-shell domain . Besides decomposing the field into various distinct length-scales, we have also constructed the field describing the spatial distributions of the maximum of the wavelet-transformed norm E-max (x,z) and its corresponding local wavenumber k-max(x,z), where x and z are the coordinates of the real space. For geoid anomalies, using wavelets up to a resolution of 2 degree, we can discern the outlines of convergent and divergent zones and can conduct a quantitative comparison of the short-wavelength gravitational anomalies at those wavelengths between two different geographical locations, such as a comparison between the Andes and the Himalayan region. Strongest signal for degree 90 comes from the Antiplano area in the Andes. We can also detect the boundaries of old sutured zones on continents in Australia and North America. From wavelets we can discern that mixing of chemical heterogeneities behaves differently for different length scales by looking at different scales and also in the E-max and k-max distributions. In mantle convection, up to Ra of ten billion ,we have analyzed the fluid dyanmics at different scales , down to a resolution of 0.005 of the depth of the convecting layer. A transition in the style of convection at a Ra between one and ten billion is found, in which a tendency toward a subadiabatic mantle with quasi-layered convection consisting small scales at both top and bottom boundary layers is found at the extremely high Rayleigh number.

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References
[1] Bergeron, S.Y., Vincent, A.P., Yuen, D.A., Tranchant, B.J.S. and C. Tchong, Viewing seismic velocity anomalies with 3-D Continuous Gaussian wavelets, Geophys.Res.Lett., Vol.26., No.15, pp. 2311-2314, 1999.