陈轻蕊1,2,,,
李昆1,2,
凌嘉宣1,2
1. 中南大学地球科学与信息物理学院, 长沙 410083
2. 中南大学有色金属成矿预测与地质环境监测教育部重点实验室, 长沙 410083
基金项目: 国家自然科学基金项目（41574127），国家科技重大专项（2018YFC0603602）和中南大学研究生自主创新项目（2018zzts200，2018zzts203）联合赞助
详细信息
作者简介: 戴世坤, 男, 1963年生, 教授, 博士生导师, 研究方向为重、磁、电、震三维正反演理论与方法及其实用化软件开发.E-mail:dskgmes@csu.edu.cn
通讯作者: 陈轻蕊, 女, 1992年生, 在读博士研究生, 研究方向为重、磁、电数值模拟与反演成像方法及并行化算法研究.E-mail:1532550316@qq.com
中图分类号: P631收稿日期:2018-10-08
修回日期:2019-05-10
上线日期:2020-05-05
Three-dimensional numerical simulation of the gravity anomaly field in the space-wave number mixed domain
DAI ShiKun1,2,,CHEN QingRui1,2,,,
LI Kun1,2,
LING JiaXuan1,2
1. School of Geosciences and Info-Physics of Central South University, Changsha 410083, China
2. key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring of Ministry of Education, Central South University, Changsha 410083, China
More Information
Corresponding author: CHEN QingRui,E-mail:1532550316@qq.com
MSC: P631--> Received Date: 08 October 2018
Revised Date: 10 May 2019
Available Online: 05 May 2020
摘要
摘要:重力勘探中复杂条件下的三维正演计算量大存储要求高，使得这种条件下重力勘探高效、精细正反演变得困难.针对这一问题，提出一种空间-波数混合域数值模拟方法，该方法将空间域引力位积分进行水平方向二维傅里叶变换，将三维空间域卷积问题转换为多个不同波数之间相互独立的空间垂向一维积分问题，一维积分垂向可离散为多个单元积分之和，每个单元采用二次形函数表征密度变化，可得出单元积分的解析表达式.该方法计算量和存储需求少，算法高度并行；保留垂向为空间域，优势之一在于可根据实际情况合理调整单元疏密程度，准确模拟任意复杂地形和密度异常体的重力异常，兼顾计算精度与计算效率；优势之二在于用形函数拟合求得积分的解析解，计算精度和效率高；充分利用一维形函数积分的高效和高精度，不同波数之间一维积分高度并行性及快速傅里叶变换的高效性，实现重力异常场三维数值模拟.设计棱柱体模型，通过数值解和解析解对比验证了该方法的正确性、适用性和高效性.针对任意复杂地形条件下的重力场及其张量的模拟问题，提出一种快速算法，对其有效性进行了验证.探究标准FFT法的截断效应对计算精度的影响，对比分析Gauss-FFT法和标准FFT扩边法两种方法的计算精度和效率，总结了二者的选取策略，结果表明选用标准FFT扩边法计算效率更高.实际地形的数值模拟表明本文算法适用于任意复杂地形的高效计算.
关键词: 重力数值模拟/
空间-波数混合域/
傅里叶变换/
形函数积分
Abstract:In gravity exploration, the three-dimensional forward calculation under complex conditions requires a large amount of storage, which makes it difficult to conduct highly efficient and fine forward modeling and inversion of gravity exploration under such conditions. To solve this problem, a numerical simulation method of the space-wave number mixed domain is proposed. This method transforms the convolution problem of gravitational potential integral in the three-dimensional space domain into several non-convolution problems by using two-dimensional Fourier transforms in the horizontal direction. For the problem of spatial vertical one-dimensional integration with independent wavenumber, the vertical integration of one-dimensional integration is discretized into the sum of multiple unit integrals. Quadratic function is used to characterize the density change of each unit, and the analytical expression of unit integral is derived. This method has less computation and storage requirements, and its algorithm is highly parallel, and the vertical integration is preserved in the spatial domain. One of its advantages is that it can be adjusted reasonably according to the actual situation. Integral element density can accurately simulate gravity anomalies of arbitrary complex terrain and density anomalies, taking into account both calculation accuracy and calculation efficiency. The other advantage is that the analytical solution of integration can be obtained by fitting shape function, with high calculation accuracy and efficiency. The high efficiency and accuracy of integration of one-dimensional shape function can be fully utilized, and the high parallelism of one-dimensional integration between different wavenumbers and the high efficiency of fast Fourier transform can be fully utilized. The correctness, applicability and efficiency of this method are verified by comparing numerical and analytical solutions. A fast algorithm is proposed to simulate the gravity field and its tensors under arbitrary complex terrain conditions. The validity of the algorithm is verified. The truncation effect of the standard FFT method is explored. The calculation accuracy and efficiency of Gauss-FFT method and standard FFT method are compared and analyzed. The selection strategies of the two methods are summarized. The results show that the standard FFT method is more efficient. The numerical simulation of real terrain shows that the proposed method is suitable for the efficient calculation of arbitrary complex terrain.
Key words:Gravity anomaly field numerical simulation/
Space-wave number mixing domain/
Fourier transform/
Shape function integral
PDF全文下载地址:
http://www.geophy.cn/data/article/export-pdf?id=dqwlxb_15470
