Analytical algorithms of Jacobian matrix in one-dimensional Occam inversion of central loop transient electromagnetism based on all-time apparent ressivivity
Song-Wei GUO1, Xiao-Pan LIU2, Kai ZHENG3, Lei ZHANG4
1. School of Earth Sciences and Resources, China University of Geosciences (Beijing) , Beijing 100083, China 2. Institute of Geology and Mineral Resources Exploration of Zhejiang Province, Hangzhou 310000, China 3. College of Geophysics and Petroleum Resources, Yangtze University, Wuhan 430100, China 4. Inner Mongolia Land Resources Exploration and Development Co., Ltd., Hohhot 010020, China
In the current engineering application, one-dimensional inversion result of TEM sounding is still an important basis for geological interpretation. In order to improve the computational efficiency and accuracy of one-dimensional inversion, it is necessary to analytically derive Jacobian matrix of one-dimensional forward. In this paper, the analytical formulas of Jacobian matrix in one-dimensional forward of central loop transient electromagnetic based on all-time resisitivity are derived in detail. It is proved that the formulas are correct and worth adopting, as shown by testing one-dimensional Occam inversion of theoretical model and measured data.
郭嵩巍, 刘小畔, 郑凯, 张磊. 基于全区视电阻率的瞬变电磁一维Occam反演中雅克比矩阵的解析算法[J]. 物探与化探, 2020, 44(3): 559-567.
Song-Wei GUO, Xiao-Pan LIU, Kai ZHENG, Lei ZHANG. Analytical algorithms of Jacobian matrix in one-dimensional Occam inversion of central loop transient electromagnetism based on all-time apparent ressivivity. Geophysical and Geochemical Exploration, 2020, 44(3): 559-567.
Yang Y J, He Z X, Wang X B. A discussion of the inversion of combined vertical electrical sounding and central-loop TEM data[J]. Geophysical and Geochemical Exploration, 2008,32(4):442-444.
[7]
Constable S C, Parker R L, Catherine G. Constable Occam’ sinversion: apractical algorithm for generating smooth models from electromagnetic sounding data[J]. Geophysics, 1987,52(3):289-300.
Chen X B, Zhao G Z, Tang J, et al. An adaptive regularized inversion algorithm for magnetotelluric data[J]. Chinese Journal of Geophysics, 2005,48(4):937-946.
Li G, Pan H P, Wang Z, et al. One-dimensional inversion for loop source transient electromagnetic method[J]. Coal Geology & Exploration, 2017,45(5):161-166,172.
[14]
白登海, Maxwell A Meju, 卢健, 等. 时间域瞬变电磁法中心回线方式全程视电阻率的数值计算[J]. 地球物理学报, 2003,46(5):698-704.
[14]
Bai D H, Maxwell A Meju, Lu J, et al. Numerical calculation of all-time apparent resistivity for the central loop transient electromagnetic method[J]. Chinese journal of geophysics, 2003,46(5):698-704.
Guo S W, Wang X B. Study on numerical calculation methods of transient electromagnetic all-time apparent resistivity[J]. Computing Technique for Geophysical and Geochemical Exploration, 2010,32(5):500-507,455.
[16]
内蒙古地质矿产局. 内蒙古自治区岩石地层[M]. 武汉: 中国地质大学出版社, 1996.
[16]
Inner Mongolia Bureau of Geology and Mineral Resources. Lithostratigraphic of Inner Mongolia. Wuhan: China University of Geosciences Press, 1996.
Ren A L. Outstanding achievements in the pre Feasibility Exploration Project of geothermal resources in Daihai area, Liangcheng County[J]. Westen Resource, 2014(3):32.