基于曲波压缩的重磁异常三维反演及其应用  

Three⁃dimensional inversion of gravity/magnetic anomalies based on curvelet compression and its applications

作　　者：张恒磊 耿美霞[3] 胡祥云 ZHANG Henglei;GENG Meixia;HU Xiangyun(Key Laboratory of Geological Survey and Evaluation of Ministry of Education,China University of Geosciences(Wuhan),Wuhan,Hubei 430074,China;School of Geophysics and Geomatics,China University of Geosciences(Wuhan),Wuhan,Hubei 430074,China;Khalifa University of Science and Technology,Abu Dhabi 127788,United Arab Emirates)

机构地区：[1]中国地质大学(武汉)地质探测与评估教育部重点实验室,湖北武汉430074 [2]中国地质大学(武汉)地球物理与空间信息学院,湖北武汉430074 [3]哈利法科学技术大学,阿联酋阿布扎比127788

出　　处：《石油地球物理勘探》2023年第4期993-1001,共9页Oil Geophysical Prospecting

基　　金：地质探测与评估教育部重点实验室主任基金和中央高校基本科研业务费项目“水下隐蔽物磁场探测前沿研究”(GLAB2022ZR08);国家重点研发计划项目“海洋电磁场传感器研发与电磁探测应用示范”(2022YFC3104000);国家自然科学基金重点项目“华南地块东部岩石圈属性及其动力学过程研究”(41630317)联合资助。

摘　　要：重磁异常三维反演在构建地下三维空间精细结构研究中作用显著,然而反演核函数矩阵规模较大,对计算机内存需求高,限制了三维反演的广泛应用。为了减小核函数的内存需求,提出了基于曲波压缩的重磁异常三维反演方法,即通过曲波变换,核矩阵的能量主要保留在小部分稀疏的曲波系数中,可实现高效的压缩反演。相比小波变换,曲波变换具有更优越的信号稀疏表征能力,因此在相同压缩率条件下曲波变换可以获得更高的压缩精度。文中对比研究了小波压缩与曲波压缩在重磁异常三维反演中的应用效果。考虑相同计算精度,曲波压缩可以将核函数压缩率提高100%,降低50%的内存需求。理论模型试验中反演核函数大小为(100×100)×(100×100×50)(双精度存储量约37 GB),利用文中方法仅需4%的压缩比(即核函数的内存需求仅为1.48 GB),即可实现与传统小波压缩10%的压缩比类似的反演效果。将文中方法应用于中国西部尕林格矿区的磁异常三维反演,曲波压缩反演得到的三维磁化强度模型较清晰地揭示了矿体的埋藏深度、空间分布、磁性强弱等特征,为后期钻探验证、储量评估、盲矿探测等提供了可靠依据。The three‑dimensional(3D)inversion of gravity/magnetic anomalies plays an important role in constructing the 3D fine structure of underground space.However,the matrix of the kernel function in 3D inversion is large,and it requires huge computer memory,which limits its wide application.In order to reduce the memory required by the kernel function,a 3D inversion method of gravity/magnetic anomalies based on curvelet compression is proposed in this paper.In other words,through curvelet transform,the energy of the kernel matrix is mainly retained in a small part of sparse curvelet coefficients,which can achieve efficient compression inversion.Compared with wavelet transform,curvelet transform has superior signal sparse representation ability,so it can obtain higher compression accuracy under the same compression rate.In this paper,the application effects of wavelet compression and curvelet compression in the 3D inversion of gravity/magnetic anomalies are compared.Under the same calculation accuracy,curvelet compression can improve the kernel compression rate by 100%and reduce the memory requirement by 50%.In the model test,the kernel function has a size of(100×100)×(100×100×50),with a storage capacity of 37 GB in double precision,and the proposed method adopting a compression ratio of 4%(the kernel’s memory is only 1.48 GB)obtains the inversion results similar to the wavelet compression adopting a compression ratio of 10%.The proposed method is applied to the 3D inversion of magnetic anomalies in the Galinge mining area in western China,in which the 3D magnetization model obtained from compression and inversion reveals the buried depth,spatial distribution,and magnetic strength of the ore body,which provides a reliable basis for later drilling verification,reserve evaluation,and concealed ore detection.

关 键 词：重力异常 磁异常 三维反演 压缩 曲波变换 

分 类 号：P631[天文地球—地质矿产勘探]