Interpolation using a generalized Green's function for a spherical surface spline in tension
Interpolation using a generalized Green's function for a spherical surface spline in tension
复制标题
使用广义格林函数对受拉球面样条进行插值
DOI：
10.1111/j.1365-246x.2008.03829.x
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发表时间：
2008
影响因子：
2.8
通讯作者：
J. Becker
中科院分区：
文献类型：
--
作者：
P. Wessel;J. Becker
发明内容存在多种方法用于在称为网格化的过程中将笛卡尔或球面数据插值到等距点阵上。基于格林函数的方法实现起来特别简单。在此类方法中，网格算子的格林函数被确定，并且所得的网格解决方案由每个数据约束的贡献的叠加组成，并由针对所有输出-输入点分离评估的格林函数加权。格林函数方法具有相当大的灵活性，例如完全自由地指定评估解决方案的位置（不必在晶格上）以及包含表面高度和表面梯度作为数据约束的能力。 1、2 和 3 维空间中笛卡尔数据的格林函数解是众所周知的，球面上最小曲率样条的二对数解也是众所周知的。在这里，球面情况被扩展为包括张力，并导出了新的广义格林函数。结果表明，新函数在零张力极限下可简化为二对数解。检查了新函数的属性，并在 Matlab R 中实现了新的网格化方法，并在三个地球物理数据集上进行了演示。
SUMMARY A variety of methods exist for interpolating Cartesian or spherical surface data onto an equidistant lattice in a procedure known as gridding. Methods based on Green’s functions are particularly simple to implement. In such methods, the Green’s function for the gridding operator is determined and the resulting gridding solution is composed of the superposition of contributions from each data constraint, weighted by the Green’s function evaluated for all output–input point separations. The Green’s function method allows for considerable flexibility, such as complete freedom in specifying where the solution will be evaluated (it does not have to be on a lattice) and the ability to include both surface heights and surface gradients as data constraints. Green’s function solutions for Cartesian data in 1-, 2- and 3-D spaces are well known, as is the dilogarithm solution for minimum curvature spline on a spherical surface. Here, the spherical surface case is extended to include tension and the new generalized Green’s function is derived. It is shown that the new function reduces to the dilogarithm solution in the limit of zero tension. Properties of the new function are examined and the new gridding method is implemented in Matlab R � and demonstrated on three geophysical data sets.