Collaborative Research: Reproducible research and educational software for geoscience data analysis in spherical and planar geometry

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This project will develop, formalize, and improve documentation and functionality for a set of codesused for research and education in geophysics but of potential application in other fields. The projectwill continue algorithmic development and documentation of software for geophysical analysis usingwavelets, vector spherical harmonics and Slepian functions. Examples are: in geodynamics, the description of deformation in and of the Earth; in geomagnetics, the lithospheric magnetic field; in geodesy, models of terrestrial and planetary gravity; and any directional spherical processes that are vectorial in nature in other fields of science and engineering. The codes support (or will support) decomposition of fields, harmonic analysis, power spectral estimation, inversion parameterization, vectorfield analysis, and satellite data. The project will also develop software for analysis of Ground PenetratingRadar data. The work will involve students and course work between two very different institutions incontinual use, testing, and input to the development of the codes. Analyses in vector-spherical harmonics are well established, but only legacy code, mostly in Fortran, exists to date. Matlab or Octave software archives are much needed, especially in the light of modern-day mathematical methods which consist in forming optimized linear combinations of vector harmonics into bandlimited, geographically localized functions: the so-called Slepian basis. Designing algorithms, and programming them well, in a robust and reproducible manner, is demanding but not often considered a scientific objective per se. The society at large, and the scientific community, are best served when all research-grade and educational code is fully documented and available, ready to run by novice or expert alike. Matlab and Octave are portable, low-threshold scripting languages that blend low-level flexibility, intermediate complexity and high-performance.