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

该项目将开发、正式化和改进一套代码的文件和功能，这些代码用于地球物理研究和教育，但可能在其他领域应用。该项目将继续使用小波、矢量球谐函数和Slepian函数进行地球物理分析软件的算法开发和文件编制。例如：在地球动力学中，描述地球内部和地球上的变形；在地磁学中，描述岩石圈磁场；在大地测量学中，描述地球和行星重力模型；以及在其他科学和工程领域中，任何在性质上是矢量的定向球状过程。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、矢量场分析和卫星数据。该项目还将开发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，以及对代码开发的持续使用、测试和投入。矢量球谐函数的分析已经建立得很好了，但到目前为止，只有遗留代码(主要是Fortran语言)存在。我们非常需要MatLab或Octave软件档案，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、地理上局部的函数：即所谓的Slepian基。以健壮和可重复的方式设计算法，并对其进行良好的编程，要求很高，但通常不会被认为本身就是一个科学目标。当所有研究级别和教育代码都完全记录在案并可供新手或专家运行时，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、低门槛的脚本语言，融合了低级别的灵活性、中等的复杂性和高性能。

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.