Data and code for "Modified Parker's method for gravity forward modeling of general polyhedral models"

We propose a new modified Parker's method for the efficient forward modeling of gravity fields caused by general polyhedral sources with either constant or arbitrarily variable density distributions. The method is implemented first by reducing the 3D Newtonian volume integral into summation of 2D surface integrals over the polyhedron's boundary facets, or by decomposing the polyhedron into a tetrahedron mesh, depending on whether the polyhedron is of constant or variable density. Then an irregularly distributed mass point model is obtained by applying either 2D or 3D Gaussian quadrature to each triangular surface or tetrahedron element. Finally the mass point model is evaluated efficiently using a combination of Non-Uniform Fast Fourier Transform (NUFFT) and Gauss-FFT algorithms. Optimal orders for the Gaussian quadratures and parameters for the hybrid spectral sampling are determined empirically to guarantee a predefined relative error of 0.01%. The method is demonstrated using both synthetic and real polyhedral models, including a sphere model approximated by a polyhedron, two asteroids, and a digital elevation model in the Himalaya region. The numerical results show that the modified Parker's method can improve the computational efficiency by several orders of magnitude while obtaining almost the same simulation results as the analytical solution of the polyhedron in the space domain. The new method is suitable for the fast computation of the gravity potential, the gravity vector, and the gravity gradient tensor due to polyhedral models such as geological abnormal bodies, asteroids, and single or multilayer density interface models with triangulated surfaces. <br>

本文提出一种新型改进帕克（Parker）方法，用于高效正演模拟由具有恒定密度或任意可变密度分布的一般多面体源产生的重力场。该方法可通过两种路径实现：当多面体为恒定密度时，将三维牛顿体积积分约化为多面体边界面元上的二维表面积分之和；当多面体为可变密度时，则将多面体分解为四面体网格。随后，通过对每个三角形曲面或四面体单元分别施加二维或三维高斯求积，得到非均匀分布的质点模型。最终，通过结合非均匀快速傅里叶变换（Non-Uniform Fast Fourier Transform, NUFFT）与高斯快速傅里叶变换算法，可高效求解该质点模型。通过经验确定高斯求积的最优阶数与混合光谱采样的相关参数，可将相对误差预先控制在0.01%以内。本文采用合成与实测多面体模型对所提方法进行验证，包括多面体近似的球体模型、两颗小行星以及喜马拉雅地区的数字高程模型（Digital Elevation Model, DEM）。数值实验结果表明，改进后的帕克方法可将计算效率提升数个数量级，同时在空间域中可获得与多面体解析解近乎一致的模拟结果。该新方法适用于快速计算由多面体模型（如地质异常体、小行星，以及采用三角剖分曲面的单层或多层密度界面模型）产生的重力位、重力矢量与重力梯度张量。