最小二乘配置在磁力异常数据网格化中的应用

doi:10.11720/wtyht.2025.1286

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摘要

为了解决传统网格化方法在处理不规则分布的磁力异常数据时难以同时兼顾计算精度与计算效率的问题,本文将大地测量学领域经典的最小二乘配置法应用于地面磁力异常数据的网格化处理中。仿真数据和煤田实测数据的测试与分析结果表明:最小二乘配置网格化方法的计算精度取决于离散观测数据的误差估计、协方差函数的选取与拟合,误差估计越准确插值计算精度越高;采用多项式函数作为磁力异常数据处理的经验协方差函数是简单、有效的;相较于克里金法、最小曲率法和径向基函数法,最小二乘配置法在网格化处理时对噪声具有更好的压制能力。应用最小二乘配置方法进行磁力异常数据的网格化处理,能够提高数据处理的精度与计算效率。

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	高小伟
	李雄伟
	庞少东
	李文刚
	姚伟华
	杜劲松

关键词 ：最小二乘配置, 磁力异常, 网格化, 插值, 协方差函数

Abstract：

Traditional gridding methods struggle to balance computational accuracy and efficiency when processing irregularly distributed magnetic anomaly data. To address this issue, this study applied the classic least-squares collocation method from geodesy to the gridding of ground-based magnetic anomaly data. This application was verified through the test and analysis of the simulation data and the actual coalfield data. The results indicate that the computational accuracy of gridding based on least-squares collocation is dictated by the error estimation of discrete observational data and the selection and fitting of the covariance function. More accurate error estimation contributes to higher-accuracy interpolation. A polynomial function is a simple and effective empirical covariance function for processing magnetic anomaly data. The least-squares collocation method demonstrates more effective noise suppression compared to the Kriging, minimum curvature, and radial basis function methods. Overall, applying the least-squares collocation to the gridding of magnetic anomaly data can enhance the accuracy and efficiency of data processing.

Key words： least-squares collocation magnetic anomaly gridding interpolation covariance function

收稿日期: 2024-07-10 修回日期: 2024-12-25 出版日期: 2025-04-20

ZTFLH:

P631

基金资助:中煤科工西安研究院(集团)有限公司科技创新基金项目(2022XAYJS06);陕西省自然科学基金重点研发计划项目(2022SF-046);国家自然科学基金面上项目(42174090)

通讯作者: 杜劲松(1985-),男,副教授,长期从事地磁场与磁法勘探方面的教学与研究工作。Email: jinsongdu@cug.edu.cn

作者简介: 高小伟(1977-),男,高级工程师,主要从事煤田水文物探方面的研究工作。Email: 26930319@qq.com

引用本文:

高小伟, 李雄伟, 庞少东, 李文刚, 姚伟华, 杜劲松. 最小二乘配置在磁力异常数据网格化中的应用[J]. 物探与化探, 2025, 49(2): 422-432.
GAO Xiao-Wei, LI Xiong-Wei, PANG Shao-Dong, LI Wen-Gang, YAO Wei-Hua, DU Jin-Song. Application of least-squares collocation to the gridding of magnetic anomaly data. Geophysical and Geochemical Exploration, 2025, 49(2): 422-432.

链接本文:

https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2025.1286 或 https://www.wutanyuhuatan.com/CN/Y2025/V49/I2/422

Fig.1 仿真模拟的理论数据(a)与仿真模拟的观测数据(b)

Fig.2 计算的观测协方差值及拟合曲线

Fig.3 待插点预测数据(a)与插值误差(b)

Fig.4 仿真模拟的理论数据(a)、仿真模拟的噪声数据(b)与仿真模拟的观测数据(c)
(图中黑点表示模拟的观测点位置)

Table 1 不同噪声标准差设置情况下的计算精度统计参数

Fig.5 不同插值方法的计算结果

Fig.6 不同插值方法计算结果与理论值的偏差

Table 2 4种插值方法的计算精度统计参数

Fig.7 不同插值方法计算的残差数据的柱状统计

Fig.8 不同插值方法在不同噪声水平情况下的残差标准差

Fig.9 磁力测点高程(a)、原始ΔT磁力异常数据(b)与剔除干扰之后的ΔT磁力异常数据(c)

Fig.10 由实测数据计算的协方差以及拟合的协方差函数曲线

Fig.11 采用不同插值方法计算的网格化结果

Fig.12 不同网格化方法计算结果与实测数据之间的偏差

Table 3 4种网格化方法的计算误差统计参数

Fig.13 不同网格化方法计算误差的柱状统计

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