Comparison of 3-D Fourier forward algorithms for gravity modelling of prismatic bodies with polynomial density distribution
Comparison of 3-D Fourier forward algorithms for gravity modelling of prismatic bodies with polynomial density distribution
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具有多项式密度分布的棱柱体重力建模的 3-D 傅立叶前向算法比较
DOI：
10.1093/gji/ggy379
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发表时间：
2018-09
影响因子：
2.8
通讯作者：
Wu Leyuan
中科院分区：
文献类型：
--
作者：
Wu Leyuan
我们提出了一个比较研究不同的傅立叶域算法的3-D模拟的重力场所造成的一个直角棱镜一般多项式密度分布。首先，我们推导出重力位及其一阶导数的傅立叶域表达式。重新发现并强调了傅里叶域表达式中的张量积结构，它可以用来显著地加速傅里叶域算法。然后研究了傅立叶域和空间域的不同采样策略。在傅立叶域中，三种不同的采样技术，包括混合矩形高斯采样计算的高斯-FFT算法，球形采样计算的非均匀快速傅立叶变换（NUFFT）算法，和两者的组合，通过分裂连续傅立叶积分成两个部分，使用正则化函数，进行了研究和比较的数值精度和效率。在空间或物理域中，重力正演值在三维规则网格上或在一组任意位置处建模。所有的傅里叶正演算法进行了数值检查的空间域解析解。数值试验表明，对于重力位，在傅立叶域采用非均匀球面采样，自然地解决了波矢零点处的奇异性，比Gauss-FFT采样具有更好的数值精度。两者的结合实现了最佳的精度和效率。对于重力矢量分量，Gauss-FFT算法为在3-D规则网格上建模提供了良好的精度和效率。然而，如果需要在一组任意点的重力场，组合算法再次实现最佳的数值性能。虽然本文的数值试验仅限于矩形棱柱体模型，但联合算法所采用的改进傅立叶域采样策略也可用于其他重力正演模型，如多面体模型、地形模型和一般的三维棱柱体叠加模型。
We present a comparative study of different Fourier-domain algorithms for the 3-D modelling of gravity fields caused by a rectangular prism with general polynomial density distributions. First we derive Fourier-domain expressions of the gravity potential and its first order derivatives. The tensor product structures embedded in the Fourier-domain expressions are rediscovered and emphasized, which can be used to accelerate Fourier domain algorithms significantly. Then different sampling strategies both in the Fourier domain and in the space domain are studied. In the Fourier domain, three different sampling techniques, including a hybrid rectangle-Gaussian sampling computed by the Gauss-FFT algorithm, a spherical sampling computed by the nonuniform fast Fourier transform (NUFFT) algorithm, and a combination of the two by splitting the continuous Fourier integral into two parts using a regularization function, are investigated and compared in terms of numerical accuracy and efficiency. In the space or physical domain, gravity forward values are modelled on a 3-D regular grid, or at a set of arbitrary positions. All Fourier forward algorithms are numerically checked by space-domain analytical solutions. Numerical tests show that for the gravity potential, a nonuniform spherical sampling in the Fourier domain solves the singularity at the zero wave vector naturally and offers better numerical accuracy than the Gauss-FFT sampling. A combination of the two achieves the best accuracy and efficiency. For gravity vector components, the Gauss-FFT algorithm offers good accuracy and efficiency for modelling on a 3-D regular grid. However, if gravity fields are needed at a set of arbitrary points, the combined algorithm again achieves the best numerical performance. Although numerical tests are restricted to rectangular prism models in this study, the improved Fourier-domain sampling strategy applied by the combined algorithm may also be useful in other gravity forward models, such as polyhedral models, topographic models and general 3-D prism-stacked models.
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影响因子：
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作者：
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通讯作者：
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DOI：
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