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物探与化探  2021, Vol. 45 Issue (2): 458-465    DOI: 10.11720/wtyht.2021.1280
  方法研究·信息处理·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
大地电磁交错采样有限差分二维正反演研究
周武1(), 罗威2,3(), 蓝星3, 简兴祥2
1.甘肃省交通规划勘察设计院股份有限公司,甘肃 兰州 730030
2.成都理工大学 地球物理学院,四川 成都 610000
3.四川省冶勘设计集团有限公司,四川 成都 610000
Two-dimensional magnetotelluric forward and inverse analysis of the finite-difference method with staggered sampling
ZHOU Wu1(), LUO Wei2,3(), LAN Xing3, JIAN Xing-Xiang2
1. Gansu Provincial Transportation Planning, Survey & Design Institute Co., Ltd., Lanzhou 730030, China
2. School of Geophysics,Chengdu University of Technology, Chengdu 610000, China
3. Sichuan Metallurgical Geological Survey and Design Group Co., Ltd., Chengdu 610000, China
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摘要 

交错采样网格能自动保证电磁场分布遵守能量守恒定律。本文基于交错采样网格,推导了大地电磁二维有限差分正演过程,实现了二维正演程序;通过与一维解析解对比,验证了算法的正确性且具有较高的计算精度。随后利用有限内存拟牛顿最优化算法,实现了交错采样有限差分二维反演;通过理论模型反演,验证了反演算法的稳定性,揭示有限内存拟牛顿反演计算效率明显优于非线性共轭梯度法。最后,通过对宕昌县官鹅沟大地电磁资料反演解释,查明了测区深部构造特征,表明算法具有较强实用性。

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关键词 大地电磁交错采样二维正演有限内存拟牛顿    
Abstract

The staggered sampling grid can automatically ensure that the electromagnetic field distribution obeys the law of energy conservation. Based on the staggered sampling grid, the authors deduced the two-dimensional finite difference forward process of magnetotelluric survey, and realized the two-dimensional forward program. Compared with one-dimensional analytical solution, the algorithm is proved to be correct and has high accuracy. Then, using the finite memory quasi Newton optimization algorithm, the authors realized the staggered sampling grid finite difference two-dimensional inversion. The correctness of the inversion algorithm was verified by theoretical model inversion, which shows that the efficiency of quasi Newton inversion with finite memory is better than that of nonlinear conjugate gradient. Finally, the deep structure of the survey area was found through the inversion and interpretation of the magnetotelluric data from Guanegou in Dangchang County, which shows that the algorithm has strong practicability.

Key wordsmagnetotelluric    interleaved sampling    two-dimensional forward modeling    LBFGS
收稿日期: 2020-06-01      修回日期: 2020-08-10      出版日期: 2021-04-20
ZTFLH:  P319.1+9  
基金资助:国家重点研发计划(2017YFC0601504)
通讯作者: 罗威
作者简介: 周武(1987-),男,硕士,工程师,主要从事工程物探研究工作。Email: 532954771@qq.com
引用本文:   
周武, 罗威, 蓝星, 简兴祥. 大地电磁交错采样有限差分二维正反演研究[J]. 物探与化探, 2021, 45(2): 458-465.
ZHOU Wu, LUO Wei, LAN Xing, JIAN Xing-Xiang. Two-dimensional magnetotelluric forward and inverse analysis of the finite-difference method with staggered sampling. Geophysical and Geochemical Exploration, 2021, 45(2): 458-465.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2021.1280      或      https://www.wutanyuhuatan.com/CN/Y2021/V45/I2/458
Fig.1  MT二维交错网格有限差分离散示意
模式
位置
顶边界
(z=zmin)
底边界
(z=zmax)
侧边界
(y=ymin|ymax)
TE模式 Ey=1 ?Ey?z=iωμEyZbottom ?Ey?x=0
TM模式 Hy=1 ?Hy?zHyZbottom ?Hy?x=0
Table 1  边界条件形式
Fig.2  层状模型二维正演中心测点视电阻率和阻抗相位
Fig.3  异常体模型
Fig.4  异常体模型正演拟断面
Fig.5  异常体模型二维反演步长和拟合差曲线
Fig.6  异常体模型二维反演
模式  迭代10次耗时/s NLCGLBFGS  拟合差<1的耗时/s NLCGLBFGS
TE 75 59 175 125
TM 57 45 92 73
TE+TM 133 88 506 371
Table 2  LBFGS和NLCG反演效率对比
Fig.7  MT测线分布
Fig.8  MT反演结果
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