Spherical Wavelet Bases for Storing, Representing and Analyzing Terrestrial and Extraterrestrial Planetary Data
Abstract
Sensors on satellites and space probes have observed the planets and some of the moons in our solar system, collecting measurements such as altimetry, gravitational potential, magnetic, optical and spectrographic data in the visible and infrared spectrum.
It is customary to refer to these measurements' position by its distance above some point on the surface, and the latitude and longitude of that point of the moon or planet being observed. Familiar and simple, latitude and longitude can be straightforwardly plotted in 2D, however with distortion that becomes infinite at the poles. This infinite distortion is inevitable because the topology of the sphere is different from the topology of the plane. Therefore there is no 1-to-1 mapping of the sphere to the plane that is continuous in both directions. Thus any map between sphere and plane that is 1-to-1 must fail to be continuous in one or both directions. And any map between sphere and plane that is continous in both directions must fail to be 1-to-1. Are there alternatives to latitude/longitude coordinates in representing, visualizing and analyzing spherical data? A number of schemes have been put forth as alternatives. Spherical harmonics, being solutions to Laplace's equation, are convenient for representing electromagnetic and gravitational fields, but less convenient for representing localized phenomena. To address this shortcoming, the Slepian functions were crafted from spherical harmonics for representing localized data. Other constructions are based on subdivisions of the icosahedron or the cube, and have their own advantages and disadvantages. A spherical wavelet basis can be used to represent spherical data electronically. It enables significant data compression ratios with minimal distortion. It also enables more efficient storage and transmission of spherical data. This study explores these spherical wavelets and their usefulness in analyses of planetary data. They may have advantages in identifying subtle patterns at multiple scales.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.T52C..04V
- Keywords:
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- 0545 Modeling;
- COMPUTATIONAL GEOPHYSICS;
- 0560 Numerical solutions;
- COMPUTATIONAL GEOPHYSICS;
- 1932 High-performance computing;
- INFORMATICS;
- 3275 Uncertainty quantification;
- MATHEMATICAL GEOPHYSICS