鲁凯亮^1,2,,
李貅^1,2,,,
戚志鹏^1,2,
樊亚楠^1,2,
周建美^1,2,
李文翰³,
李贺^1,2,
张明晶⁴,
王扬州⁵
1. 长安大学地质工程与测绘学院, 西安 710054
2. 长安大学地球物理场多参数综合模拟实验室(中国地球物理学会重点实验室), 西安 710054
3. 山东大学齐鲁交通学院, 济南 250061
4. 山东省交通规划设计院, 济南 250031
5. 北京探创资源科技有限公司, 北京 100071

基金项目: 国家自然科学基金"多辐射源、多分辨地空瞬变电磁深部探测偏移成像理论与方法研究"项目(41830101)，面上项目(42074168)，国家自然科学基金(41704108)联合资助


详细信息

作者简介: 鲁凯亮, 男, 1992年生, 博士研究生, 主要从事瞬变电磁场的理论与应用方面的研究.E-mail: chdlkl@163.com

通讯作者: 李貅, 男, 1958年生, 教授, 博士生导师, 主要从事瞬变电磁场的理论与应用方面的研究.E-mail: lixiu@chd.edu.cn

中图分类号: P631

收稿日期:2020-11-24
修回日期:2021-03-02
上线日期:2021-09-10

A precise integration transform algorithm for transformation from the transient electromagnetic diffusion field into the pseudo wave field

LU KaiLiang^1,2,,
LI Xiu^1,2,,,
QI ZhiPeng^1,2,
FAN YaNan^1,2,
ZHOU JianMei^1,2,
LI WenHan³,
LI He^1,2,
ZHANG MingJing⁴,
WANG YangZhou⁵
1. College of Geology Engineering and Geomatics, Chang'an University, Xi'an 710054, China
2. Integrated Geophysical Simulation Lab of Chang'an University(Key Laboratory of Chinese Geophysical Society), Xi'an 710054, China
3. School Qilu Transportation, Shangdong University, Jinan 250061, China
4. Shandong Provincial Transportation Planning and Design Institute, Jinan 250031, China
5. Beijing Tanchuang Resources Technology Co., Ltd, Beijing 100071, China


More Information

Corresponding author: LI Xiu,E-mail:lixiu@chd.edu.cn

MSC: P631

--> Received Date: 24 November 2020
Revised Date: 02 March 2021
Available Online: 10 September 2021


摘要
摘要:现有的瞬变电磁解释与反演方法主要对电阻率参数进行解释，较难给出准确的地质构造信息.为了能够较多获得地质构造信息，可将瞬变电磁扩散场信号转换为虚拟波场信号，提高瞬变电磁法的分辨率.本文采用精细积分法，实现了瞬变电磁扩散场到虚拟波场的转换.将一个高度病态的线性方程组转换成求积分的过程，大大降低了解决病态问题的难度.积分步长以2的指数增加，在保证精度的前提下，具有极高的计算效率；设置合理的终止迭代条件，进一步提高本文方法的适用性.对典型地电模型的计算，表明本文方法具有较高的精度；减小两个波峰之间的距离，证明了本文方法具有较好的分辨能力；对含有噪声信号的扩散场进行波场反变换，证明了本文方法具有较好的抗噪性.最后计算三维模型和实测数据的虚拟波场，可以很好地反映出三维地质体的界面信息，证明本文方法稳定、可靠，可以对地下地质目标体的界面进行有效识别.本文方法相比预条件正则化共轭梯度法(PRCG)，在计算效率方面提升了4倍左右；本文方法的相对误差在5%以内，而PRCG的最大相对误差可达40%~50%，精度最高可提升10倍；在分辨率与稳定性方面，也表现出较好的效果.
关键词: 瞬变电磁/
虚拟波场/
精细积分

Abstract:The existing transient electromagnetic interpretation and inversion methods focus on the resistivity parameters, which are difficult to give accurate geological structure information. To solve this problem, the transient electromagnetic diffusion field signal can be transformed into a virtual wave field signal to improve the resolution of the transient electromagnetic method. In this paper, a precise integration method is proposed to realize the conversion of the transient electromagnetic diffusion field to the virtual wave field. It is found that by converting a highly ill-conditioned system of linear equations into an integration process, the difficulties related to solving ill-conditioned problems are greatly reduced. Besides, based on the premise of ensuring high accuracy results, the integration step lengths are exponentially increased by 2, and high computational efficiency is achieved. The applicability of the method proposed in this study is further improved by setting reasonable iteration stopping conditions. The calculations of the typical geoelectric models show that this method has high precision. Then, by reducing the distances between two wave peaks, it was proven that the method introduced in this study had better resolution. Furthermore, through the wavefield inverse transformations of diffusion fields containing noise, it is confirmed that the proposed method also has better noise-resistant capability. Finally, calculations of the pseudo wave fields of 3D models and field data permit to identify well the interfaces of 3D geological bodies, which further demonstrates that the method proposed in this study is stable and reliable. Compared with the preconditioned regularization method, the efficiency of the proposed method is improved by about 4 times. The relative error of the method in this work is within 5%, while the maximum relative error of PRCG can reach 40%~50%, and the accuracy can be improved by 10 times. In terms of resolution and stability, this method also shows better performance.
Key words:Transient electromagnetics/
Virtual wave-fields/
Precise integration



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