Bicubic Spline Interpolation as a Method for Treatment of Potential Field Data
Bicubic Spline Interpolation as a Method for Treatment of Potential Field Data
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DOI：
10.1190/1.1440019
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发表时间：
1969-06
期刊：
影响因子：
3.3
通讯作者：
B. Bhattacharyya
中科院分区：
文献类型：
--
作者：
B. Bhattacharyya
本文提出了一种双三次样条函数的生成方法。从这种方法中可以明显看出，这些函数通过在整个观测区域保持变量及其斜率和曲率的连续性，在准确和可靠地表示二维数据方面获得了潜在的优势。通过计算模型和现场数据的水平和垂直导数所获得的结果说明了样条函数所达到的异常精度。利用空间解析表示观测数据的分段三次多项式函数估计磁异常的振幅谱和相位谱。在相对较长的波长下，由此计算的振幅谱显示出与真实谱的显著相似性，并且被发现上级用二维傅里叶级数展开获得的振幅谱。本文还提出了一种三次样条方法，用于计算观测变量在沿着两个正交方向等距点上的值。
A method for the generation of bicubic spline functions is presented in this paper. From this method it becomes apparent that these functions derive their potential strength in accurate and reliable representation of two‐dimensional data by maintaining continuity of the variable and its slope and curvature throughout the area of observation. The results obtained by computing horizontal and vertical derivatives with model and field data illustrate the exceptional accuracy achieved with spline functions. The piecewise cubic polynomial functions expressing observed data analytically in space are used to estimate amplitude and phase spectra of magnetic anomalies. At relatively long wavelengths the amplitude spectrum thus calculated displays remarkable similarity with the true spectrum and is found to be superior to that obtained with two‐dimensional Fourier series expansion. A cubic spline method is also presented for computing values of an observed variable at equispaced points along two orthogonal direction...