位场的footprint分析及footprint-FFT快速正演方法  

Footprint analysis and footprint-FFT-based fast forward modeling of potential fields

作　　者：孙思源 高秀鹤 曹学峰 SUN Si-Yuan;GAO Xiu-He;CAO Xue-Feng(China Aero Geophysical Survey and Remote Sensing Center for Natural Resources,Beijing 100083,China)

机构地区：[1]中国自然资源航空物探遥感中心,北京100083

出　　处：《物探与化探》2025年第1期63-72,共10页Geophysical and Geochemical Exploration

基　　金：国家深地重大专项(20242D1002806);国家重点研发计划项目(2021YFB3900205);国家自然科学基金青年基金项目(42004125)。

摘　　要：传统大规模重磁位场数据正反演对计算机性能要求较高,同时计算效率较低。针对这一问题,本文定义了位场footprint判定方法,分析其影响因素,并首次提出了一种footprint-FFT位场正演策略。该算法从3个方面改善这一过程:①基于位场衍生性质计算核矩阵,大幅精简位场核矩阵大小;②引入并定义适用于位场的footprint概念,实现数据规模和核矩阵大小的“脱钩”,改善核矩阵计算效率和硬件成本;③在前两者基础上对计算区域划分子空间,首次提出footprint-FFT策略,实现子空间的位场批量计算,加速正演计算过程。该方法降低了核矩阵计算量和存储量,在大幅提高运算速度的同时,保证了计算精度。基于本文提出的方法,在笔记本电脑上实现了10多亿网格的位场快速正演,并在数分钟内完成计算。理论算例表明该方法效率高,同时对计算机的配置要求不高,在大规模位场数据正反演上潜力巨大。Conventional inversion and forward modeling of large-scale potential field data from gravity and magnetic exploration,demanding high computer performance,exhibit low efficiency.Hence,this study defined a footprint determination method for potential fields,analyzed the influencing factors,and innovatively proposed a footprint-FFT strategy for forward modeling of potential fields.The footprint-FFT algorithm improved the forward modeling process from three aspects:(1)Kernel matrices were calculated based on the potential field-derived properties,significantly reducing their size;(2)A footprint concept for potential fields was introduced and defined,decoupling data scales from kernel matrix sizes,thus improving the kernel matrix computing efficiency and reducing the hardware cost;(3)Based on the above,the computing area was divided into subspaces,and the footprint-FFT strategy was first proposed for the batch computing of potential fields in subspaces,accelerating the forward modeling process.By reducing the computational complexity and storage of the kernel matrix,the method proposed in this study significantly improved the operational speed while ensuring computational accuracy.This method enabled the fast forward modeling of potential fields with more than 1 billion grids on a laptop computer within a few minutes.Theoretical examples demonstrate that this method has high efficiency and moderate requirements for computer configuration,manifesting considerable potential in the forward modeling and inversion of large-scale potential field data.

关 键 词：核矩阵 FOOTPRINT FFT 位场 正演 

分 类 号：P631[天文地球—地质矿产勘探]