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

该项目将开发、形式化和改进一套用于地球物理学研究和教育的代码的文档和功能，但在其他领域也有潜在的应用。该项目将继续使用小波、矢量球面谐波和Slepian函数进行地球物理分析的算法开发和软件文档。例如：在地球动力学中，描述地球内部和内部的变形；地磁中，岩石圈磁场；在大地测量学中，地球和行星引力模型；以及在其他科学和工程领域中任何本质上是矢量的定向球形过程。这些代码支持（或将支持）场分解、谐波分析、功率谱估计、反演参数化、矢量场分析和卫星数据。该项目还将开发用于分析探地雷达数据的软件。这项工作将涉及两个非常不同的机构之间的学生和课程工作，包括持续使用、测试和对代码开发的投入。矢量球面谐波的分析已经很好地建立起来了，但是到目前为止只有遗留代码，主要是用Fortran编写的。Matlab或Octave软件档案是非常需要的，特别是考虑到现代数学方法，这些方法包括将矢量谐波的优化线性组合形成带宽有限的、地理上局部化的函数：所谓的Slepian基。以健壮和可复制的方式设计算法并对其进行编程，这是一项要求很高的工作，但通常不被视为科学目标本身。当所有的研究级和教育级代码都有完整的文档和可用性，可供新手或专家使用时，整个社会和科学界都能得到最好的服务。Matlab和Octave是可移植的低门槛脚本语言，混合了低水平的灵活性，中等复杂性和高性能。

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.