苏扬^1,,
殷长春^1,,,
刘云鹤¹,
任秀艳¹,
张博¹,
邱长凯²,
熊彬³
1. 吉林大学地球探测科学与技术学院, 长春 130026
2. 中国地质调查局发展研究中心, 北京 100037
3. 桂林理工大学地球科学学院, 桂林 541006

基金项目: 国家自然科学基金项目（41774125, 41530320, 41804098）, 中国科学院先导专项（XDA14020102）, 国家重点研发计划（2017YFC0601900, 2016YFC0303100）联合资助


详细信息

作者简介: 苏扬, 男, 1994年生, 博士, 主要从事大地电磁反演和航空电磁数据处理方法技术研究.E-mail:suyangjlu@163.com

通讯作者: 殷长春, 男, 1965年生, 教授, 国家特聘专家, 从事电磁法勘探理论模拟和应用技术研究.E-mail:yinchangchun@jlu.edu.cn

中图分类号: P631

收稿日期:2020-01-21
修回日期:2020-09-07
上线日期:2021-01-10

2D magnetotelluric sparse regularization inversion based on curvelet transform

SU Yang^1,,
YIN ChangChun^1,,,
LIU YunHe¹,
REN XiuYan¹,
ZHANG Bo¹,
QIU ChangKai²,
XIONG Bin³
1. College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China
2. Development and Research Center, China Geological Survey, Beijing 100037, China
3. College of Earth Sciences, Guilin University of Technology, Guilin 541006, China


More Information

Corresponding author: YIN ChangChun,E-mail:yinchangchun@jlu.edu.cn

MSC: P631

--> Received Date: 21 January 2020
Revised Date: 07 September 2020
Available Online: 10 January 2021


摘要
摘要:为了提高二维大地电磁反演对异常体边界的刻画能力, 我们引入曲波变换建立一种新的稀疏正则化反演方法.与传统的在空间域中对模型电阻率参数求解的方式不同, 我们借助曲波变换将二维电阻率模型转换为曲波系数, 并采用L1范数约束以保证系数的稀疏性.曲波变换是一种多尺度分析方法, 其系数分为粗尺度系数和精细尺度系数, 粗尺度的系数代表电阻率模型的整体概貌, 而精细尺度中较大系数代表目标体的边缘细节.此外, 曲波变换的窗函数满足各向异性尺度关系, 并具有多方向性, 因此曲波变换可以近似最佳地提取目标体的边缘特征信息, 这为我们在反演中恢复边界提供有利条件.通过对大地电磁的理论模型合成数据和实测数据反演, 验证了基于曲波变换稀疏正则化反演对异常体边界的刻画能力优于常规的L2范数和L1范数反演方法.
关键词: 大地电磁/
二维反演/
曲波变换/
稀疏正则化

Abstract:In order to improve the ability to describe the boundary of anomalous body of 2D magnetotelluric (MT) inversions, we introduce the curvelet transform to construct a sparse regularization inversion algorithm. This is different from the conventional methods that apply constraints on the model in the space domain. We convert the 2D resistivity model to curvelet coefficients via a curvelet transform and the L1-norm measure is applied to keep the sparsity of the coefficients. Curvelet transform is a multi-scale analysis, its coefficients contain both coarse- and fine-scale information of the model. The coefficients of the coarse scale represent the overview of the resistivity model, while the large coefficients of the rest scales represent the detailed edges of the targets. Furthermore, the window function of the curvelet transform satisfies the anisotropic scale relationship and has the characteristic of arbitrary directionality. Thus, the curvelet transform can extract the boundary features of the target objects in an approximately optimally way, which provides favorable conditions to recover the boundary in the inversion. We test our inversion methods both on synthetic and field MT data and illustrate the sparse regularization inversion based on curvelet transform is superior to the conventional L2- and L1-norm inversions for describing the boundary of the anomalous body.
Key words:Magnetotelluric (MT)/
2D inversion/
Curvelet transform/
Sparsity regularization



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