Construction of Wavelets on the Sphere for Global Data Representation and Efficient Solution of Inverse Problems
Abstract
Dimensional reduction through a sparse wavelet representation can be valuable, particularly so in difficult inversion problems. However, the topology of the sphere obstructs the straightforward application of traditional wavelets to spherical data. Recently a new family of wavelets on the sphere has been introduced. These new wavelets are particularly well suited for sparse representation of and numerical computation with data on the sphere via the so-called cubed sphere model, which has been applied in numerical simulations in fields as diverse as geophysics, atmosphere science, and general relativity.
Understanding the construction of these wavelets and their theoretical justification could broaden its use in scientific applications. This study elucidates their creation and design, implements the wavelet transform in software, and illustrates the effectiveness of these wavelets in efficiently and sparsely representing physical data on the sphere. The associated wavelet transform significantly reduced the dimensionality of complex physical models with minimal loss of fidelity. It is expected this will make tractable, heretofore too-large inverse problems and other problems of high order computational complexity. The transform can be combined with wavelet processing in the radial direction to represent a thick shell such as the earth's mantle or atmosphere, or the universe outside of a black hole.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2018
- Bibcode:
- 2018AGUFMDI31B0005V
- Keywords:
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- 0545 Modeling;
- COMPUTATIONAL GEOPHYSICSDE: 0560 Numerical solutions;
- COMPUTATIONAL GEOPHYSICSDE: 1932 High-performance computing;
- INFORMATICSDE: 3260 Inverse theory;
- MATHEMATICAL GEOPHYSICS