A method integrating a non-stationary random field for constrained inversion of CSAMT data

Authors

DAI Qianwei, School of Geosciences and Info-physics, Central South University, Changsha 410083, China; Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, Changsha 410083, ChinaFollow
GUO Luyao, School of Geosciences and Info-physics, Central South University, Changsha 410083, China; Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, Changsha 410083, China
WU Yun, School of Geosciences and Info-physics, Central South University, Changsha 410083, China; Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, Changsha 410083, ChinaFollow
XIONG Zhexian, School of Geosciences and Info-physics, Central South University, Changsha 410083, China; Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Central South University, Changsha 410083, China
DUAN Dan, School of Geosciences and Info-physics, Central South University, Changsha 410083, China; Zhengyuan International Mining Co., Ltd., Beijing 101399, China
BAO Zhonglin, Altay Zhengyuan International Mining Co., Ltd., Altai 836700, China
WU Hongfei, Altay Zhengyuan International Mining Co., Ltd., Altai 836700, China
HAO Fengyun, Altay Zhengyuan International Mining Co., Ltd., Altai 836700, China

Abstract

Objective The inversion of controlled-source audio-frequency magnetotelluric (CSAMT) data remains challenging due to two key issues: computational efficiency and resolution. To tackle these two issues, especially the over-smoothing effect caused by traditional regularization methods in estimating complex geological structures, this study proposed an improved regularization inversion method to reflect the spatial distribution characteristics of subsurface physical property parameters more accurately. Methods The proposed method was developed using the method for establishing the stochastic partial differential equation (SPDE) based on the Matérn covariance function. By introducing vector fields and the shape parameters of a range ellipse, this method fully considered both variations in the inclination of strata and the non-stationary nature of physical property distribution. Accordingly, this study developed a model covariance matrix meeting the non-stationary assumption. Then, inversion was conducted using the model covariance matrix as the regularization constraint. From the perspective of inversion results, residuals, relative residuals of apparent resistivity, and uncertainty, this study compared the proposed method with traditional maximum smoothness-constrained inversion and covariance-constrained inversion based on the stationary assumption. In addition, the proposed method was applied to measured data from the exploration of the Ye’erkeman-Jinba gold deposit in Habahe County, Xinjiang to validate its practical application effects. Results The results from the theoretical model indicate that the four experiments with the non-stationary constraint yielded residuals ranging from 20.47% to 21.29%, which were lower than those of experiments with the stationary constraint (21.25% and 22.83%) and those of experiments using traditional maximum smoothness-constrained inversion (32.46%). Furthermore, the proposed method could characterize geological structures more accurately and delineate geological boundaries more distinctly. The results from measured data show that the covariance-constrained CSAMT inversion based on the non-stationary assumption delivered significantly higher imaging performance than the conventional Occam-type (smoothness constrained) inversion, achieving a 51.47% reduction in data fitting residuals. The proposed method exhibited a remarkably enhanced capacity to identify complex geological structures and reduced the uncertainty in the inversion results of deep areas, thereby effectively improving the overall reliability of inversion results. Conclusions The non-stationary assumption-based inversion method with the Matérn covariance function as the regularization constraint provides a novel technical solution for addressing the issues of the insufficient computational efficiency and resolution of CSAMT inversion. This method holds great significance for advancing geophysical inversion technology.

Keywords

controlled-source audio-frequency magnetotelluric method (CSAMT), non-stationary assumption, Matérn covariance function, stochastic partial differential equation (SPDE), vector field

DOI

10.12363/issn.1001-1986.25.01.0003

Recommended Citation

DAI Qianwei, GUO Luyao, WU Yun, et al. (2025) "A method integrating a non-stationary random field for constrained inversion of CSAMT data," Coal Geology & Exploration: Vol. 53: Iss. 6, Article 21.
DOI: 10.12363/issn.1001-1986.25.01.0003
Available at: https://cge.researchcommons.org/journal/vol53/iss6/21

Reference

[1] 汤井田，何继善. 可控源音频大地电磁法及其应用[M]. 长沙：中南大学出版社，2005.

[2] 冯兵，李建国，赵斌，等. 音频大地电磁法在南岭于都–赣县矿集区银坑示范区深部矿产资源探测中的应用[J]. 地质学报，2014，88(4)：669−675.

FENG Bing，LI Jianguo，ZHAO Bin，et al. The application of audio magnetotelluric method (AMT) in Nanling Yudu–Gan County ore–concentrated area Yinkeng demonstration plot to survey deep mineral resources[J]. Acta Geologica Sinica，2014，88(4)：669−675.

[3] 牛兴国，许志河，孙丰月，等. 胶东招平断裂南段山后金矿区深部地球物理特征及找矿效果[J]. 黄金，2022，43(6)：12−16.

NIU Xingguo，XU Zhihe，SUN Fengyue，et al. Geophysical characteristics and prospecting effect deep in Shanhou Gold District，south part of Zhaoping Fault，Jiaodong Peninsula[J]. Gold，2022，43(6)：12−16.

[4] STREICH R. Controlled–source electromagnetic approaches for hydrocarbon exploration and monitoring on land[J]. Surveys in Geophysics，2016，37(1)：47−80.

[5] 高敬语，谭嘉言，朱占升，等. 音频大地电磁法在地下水质评价中的应用[J]. 物探与化探，2013，37(5)：895−898.

GAO Jingyu，TAN Jiayan，ZHU Zhansheng，et al. The application of the audio magnetotelluric method to the assessment of underground water quality[J]. Geophysical and Geochemical Exploration，2013，37(5)：895−898.

[6] SCHAMPER C，REJIBA F，TABBAGH A，et al. Theoretical analysis of long offset time–lapse frequency domain controlled source electromagnetic signals using the method of moments：Application to the monitoring of a land oil reservoir[J]. Journal of Geophysical Research：Solid Earth，2011，116：B03101.

[7] 赵虎，王玲辉，李瑞，等. 大地电磁测深法在高原特长隧道勘查中应用研究[J]. 地球物理学进展，2014，29(5)：2472−2478.

ZHAO Hu，WANG Linghui，LI Rui，et al. Application of geophysical prospecting technology in survey of deeply–buried long tunnels on the plateau[J]. Progress in Geophysics，2014，29(5)：2472−2478.

[8] WANG Meng，DENG Ming，ZHAO Qingxian，et al. Two types of marine controlled source electromagnetic transmitters[J]. Geophysical Prospecting，2015，63(6)：1403−1419.

[9] YAN Liangjun. Advancements in controlled source electromagnetic methods for prospecting unconventional hydrocarbon resources in China[J]. Surveys in Geophysics，2024，45(1)：239−276.

[10] 朱满怀，王运，刘凯，等. 激电测深法在南秦岭苏岭沟金矿区的勘查应用[J]. 地质与勘探，2024，60(2)：294−310.

ZHU Manhuai，WANG Yun，LIU Kai，et al. Application of IP sounding method to the exploration of the Sulinggou gold mining area in south Qinling Mountains[J]. Geology and Exploration，2024，60(2)：294−310.

[11] 张继伟，谭慧. 可控源音频大地电磁和微动资料的拟二维联合反演[J]. 物探与化探，2024，48(4)：1094−1102.

ZHANG Jiwei，TAN Hui. Quasi–two–dimensional joint inversion of the data from the controlled source audio–frequency magnetotellurics and the microtremor survey[J]. Geophysical and Geochemical Exploration，2024，48(4)：1094−1102.

[12] COMMER M，NEWMAN G A. New advances in three–dimensional controlled–source electromagnetic inversion[J]. Geophysical Journal International，2008，172(2)：513−535.

[13] STREICH R，BECKEN M. Sensitivity of controlled–source electromagnetic fields in planarly layered media[J]. Geophysical Journal International，2011，187(2)：705−728.

[14] 林昌洪，谭捍东，舒晴，等. 可控源音频大地电磁三维共轭梯度反演研究[J]. 地球物理学报，2012，55(11)：3829−3838.

LIN Changhong，TAN Handong，SHU Qing，et al. Three–dimensional conjugate gradient inversion of CSAMT data[J]. Chinese Journal of Geophysics，2012，55(11)：3829−3838.

[15] EGBERT G D，KELBERT A. Computational recipes for electromagnetic inverse problems[J]. Geophysical Journal International，2012，189(1)：251−267.

[16] 栾文贵. 地球物理中的反问题与不适定问题[J]. 地球物理学报，1988，31(1)：108−117.

LUAN Wengui. Inverse problems and ill–posed problems in geophysics[J]. Chinese Journal of Geophysics，1988，31(1)：108−117.

[17] CONSTABLE S C，PARKER R L，CONSTABLE C G. Occam’s inversion;a practical algorithm for generating smooth models from electromagnetic sounding data[J]. Geophysics，1987，52(3)：289−300.

[18] GÜNTHER T，RÜCKER C，SPITZER K. Three–dimensional modelling and inversion of DC resistivity data incorporating topography–II. Inversion[J]. Geophysical Journal International，2006，166(2)：506−517.

[19] MAURER H，HOLLIGER K，BOERNER D E. Stochastic regularization：Smoothness or similarity?[J]. Geophysical Research Letters，1998，25(15)：2889−2892.

[20] LINDE N，BINLEY A，TRYGGVASON A，et al. Improved hydrogeophysical characterization using joint inversion of cross–hole electrical resistance and ground–penetrating radar traveltime data[J]. Water Resources Research，2006，42(12)：W12404.

[21] LIU Changsheng，REN Zhengyong，TANG Jingtian，et al. Three–dimensional magnetotellurics modeling using edge–based finite–element unstructured meshes[J]. Applied Geophysics，2008，5(3)：170−180.

[22] HERMANS T，VANDENBOHEDE A，LEBBE L，et al. Imaging artificial salt water infiltration using electrical resistivity tomography constrained by geostatistical data[J]. Journal of Hydrology，2012，438：168−180.

[23] PHILLIPS W S，FEHLER M C. Traveltime tomography;a comparison of popular methods[J]. Geophysics，1991，56(10)：1639−1649.

[24] STEIN M L. Interpolation of spatial data：Some theory for kriging[M]. New York：Springer New York，1999.

[25] AUNE E，EIDSVIK J，URSIN B. Three-dimensional non-stationary and non-linear isotropic AVA inversion[J]. Geophysical Journal International，2013，194(2)：787−803.

[26] LINDGREN F，RUE H，LINDSTRÖM J. An explicit link between Gaussian fields and Gaussian Markov random fields：The stochastic partial differential equation approach[J]. Journal of the Royal Statistical Society Series B：Statistical Methodology，2011，73：423−498.

[27] FUGLSTAD G A，LINDGREN F，SIMPSON D，et al. Exploring a new class of non–stationary spatial Gaussian random fields with varying local anisotropy[J]. Statistica Sinica，2015，25(1)：115−133.

[28] KEY K. MARE2DEM：A 2–D inversion code for controlled–source electromagnetic and magnetotelluric data[J]. Geophysical Journal International，2016，207(1)：571−588.

[29] HANDCOCK M S，STEIN M L. A Bayesian analysis of kriging[J]. Technometrics，1993，35(4)：403−410.

[30] WHITTLE P. On stationary processes in the plane[J]. Biometrika，1954，41(3/4)：434−449.

[31] JORDI C，DOETSCH J，GÜNTHER T，et al. Geostatistical regularization operators for geophysical inverse problems on irregular meshes[J]. Geophysical Journal International，2018，213(2)：1374−1386.

[32] DAI Qianwei，WU Yun，YUE Jianhua. 2. 5D transient electromagnetic inversion based on the unstructured quadrilateral finite–element method and a geologic statistics–driven Bayesian framework[J]. Geophysics，2024，90(3)：WA1–WA16.