Three-dimensional tensor controlled-source audio-frequency magnetotelluric inversion using LBFGS
Kunpeng Wang 1 Handong Tan 1 2 5 Changhong Lin 1 2 Jianlong Yuan 3 Cong Wang 3 Jing Tang 4
+ Author Affiliations
- Author Affiliations
1 School of Geophysics and Information Technology, China University of Geosciences (Beijing), Beijing 100083, China.
2 Key Laboratory of Geo-detection (China University of Geosciences), Ministry of Education, Beijing 100083, China.
3 College of Geophysics, Chengdu University of Technology, Chengdu 610059, China.
4 Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China.
5 Corresponding author. Email: thd@cugb.edu.cn
Exploration Geophysics 49(3) 268-284 https://doi.org/10.1071/EG16079
Submitted: 21 June 2016 Accepted: 6 April 2017 Published: 19 May 2017
Abstract
The controlled-source audio-frequency magnetotelluric (CSAMT) method has become an important method in geophysical electromagnetic exploration. However, traditional CSAMT only gathers a single set of orthogonal electric and magnetic data, which cannot describe the whole subsurface geological structure. Due to increasingly complex geological targets, the drawbacks of traditional CSAMT have gradually become more significant, promoting the need for tensor CSAMT. Tensor CSAMT can gather richer information, but the 3D forward and inversion models of this method have developed slowly since it was first proposed. The common method for inverting the data of the tensor CSAMT is still magnetotelluric (MT). This paper adopts a staggered-grid finite difference method to realise the 3D forward modelling of the tensor CSAMT. On this basis, we adopt a limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method to implement a 3D inversion with full impedance data. Through inverting synthetic and real data, we prove that: (1) directly using an MT method to invert the data of the tensor CSAMT will obtain an incorrect result, (2) the inversion result of tensor CSAMT is more reliable than that of the traditional CSAMT, and (3) LBFGS is more efficient than the nonlinear conjugate gradient (NLCG) for tensor CSAMT. Our research shows that 3D tensor CSAMT inversion with LBFGS is very useful and practical for electromagnetic exploration.
Key words: full impedance, LBFGS, NLCG, tensor CSAMT.
References
Boerner, D. E., Wright, J. A., Thurlow, J. G., and Reed, L. E., 1993, Tensor CSAMT studies at the Buchans Mine in Central Newfoundland: Geophysics, 58, 12–19| Tensor CSAMT studies at the Buchans Mine in Central Newfoundland:Crossref | GoogleScholarGoogle Scholar |
Caldwell, T. G., Bibby, H. M., and Brown, C., 2002, Controlled source apparent resistivity tensors and their relationship to the magnetotelluric impedance tensor: Geophysical Journal International, 151, 755–770
| Controlled source apparent resistivity tensors and their relationship to the magnetotelluric impedance tensor:Crossref | GoogleScholarGoogle Scholar |
Egbert, G. D., and Kelbert, A., 2012, Computational recipes for electromagnetic inverse problems: Geophysical Journal International, 189, 251–267
| Computational recipes for electromagnetic inverse problems:Crossref | GoogleScholarGoogle Scholar |
Freund, R. W., and Nachtigal, N. M., 1991, QMR: a quasi-minimal residual method for non-Hermitian linear systems: Numerische Mathematik, 60, 315–339
| QMR: a quasi-minimal residual method for non-Hermitian linear systems:Crossref | GoogleScholarGoogle Scholar |
Fu, C., Di, Q., and An, Z., 2013, Application of the CSAMT method to groundwater exploration in a metropolitan environment: Geophysics, 78, B201–B209
| Application of the CSAMT method to groundwater exploration in a metropolitan environment:Crossref | GoogleScholarGoogle Scholar |
Garcia, X., Boerner, D., and Pedersen, L. B., 2003, Electric and magnetic galvanic distortion decomposition of tensor CSAMT data. Application to data from the Buchans Mine (Newfoundland, Canada): Geophysical Journal International, 154, 957–969
| Electric and magnetic galvanic distortion decomposition of tensor CSAMT data. Application to data from the Buchans Mine (Newfoundland, Canada):Crossref | GoogleScholarGoogle Scholar |
Hu, X., Peng, R., Wu, G., Wang, W., Huo, G., and Han, B., 2013, Mineral exploration using CSAMT data: application to Longmen region metallogenic belt, Guangdong Province, China: Geophysics, 78, B111–B119
| Mineral exploration using CSAMT data: application to Longmen region metallogenic belt, Guangdong Province, China:Crossref | GoogleScholarGoogle Scholar |
Hu, Y., Li, T., Fan, C., Wang, D., and Li, J., 2015, Three-dimensional tensor controlled-source electromagnetic modeling based on the vector finite-element method: Applied Geophysics, 12, 35–46
| Three-dimensional tensor controlled-source electromagnetic modeling based on the vector finite-element method:Crossref | GoogleScholarGoogle Scholar |
Key, K., 2012, Marine EM inversion using unstructured grids: a 2D parallel adaptive finite element algorithm: SEG Technical Program Expanded Abstracts, 1–5.
Li, Y., and Key, K., 2007, 2D marine controlled-source electromagnetic modeling: part I – an adaptive finite-element algorithm: Geophysics, 72, WA51–WA62
| 2D marine controlled-source electromagnetic modeling: part I – an adaptive finite-element algorithm:Crossref | GoogleScholarGoogle Scholar |
Li, X., and Pedersen, L. B., 1991, Controlled source tensor magnetotellurics: Geophysics, 56, 1456–1461
| Controlled source tensor magnetotellurics:Crossref | GoogleScholarGoogle Scholar |
Li, X., and Pedersen, L. B., 1992, Controlled-source tensor magnetotelluric responses of a layered earth with azimuthal anisotropy: Geophysical Journal International, 111, 91–103
| Controlled-source tensor magnetotelluric responses of a layered earth with azimuthal anisotropy:Crossref | GoogleScholarGoogle Scholar |
Li, X., Oskooi, B., and Pedersen, L. B., 2000, Inversion of controlled-source tensor magnetotelluric data for a layered earth with azimuthal anisotropy: Geophysics, 65, 452–464
| Inversion of controlled-source tensor magnetotelluric data for a layered earth with azimuthal anisotropy:Crossref | GoogleScholarGoogle Scholar |
Lin, C., Tan, H., Shu, Q., Tong, T., and Tan, J., 2012, Three-dimensional conjugate gradient inversion of CSAMT data: Chinese Journal of Geophysics, 55, 3829–3839
| Three-dimensional conjugate gradient inversion of CSAMT data:Crossref | GoogleScholarGoogle Scholar |
Liu, Y., and Yin, C., 2013a, Electromagnetic divergence correction for 3D anisotropic EM modeling: Journal of Applied Geophysics, 96, 19–27
| Electromagnetic divergence correction for 3D anisotropic EM modeling:Crossref | GoogleScholarGoogle Scholar |
Liu, Y., and Yin, C., 2013b, 3D inversion for frequency-domain HEM data: Chinese Journal of Geophysics, 56, 4278–4287
| 3D inversion for frequency-domain HEM data:Crossref | GoogleScholarGoogle Scholar |
Lu, X., Unsworth, M., and Booker, J., 1999, Rapid relaxation inversion of CSAMT data: Geophysical Journal International, 138, 381–392
| Rapid relaxation inversion of CSAMT data:Crossref | GoogleScholarGoogle Scholar |
Mackie, R. L., Madden, T. R., and Wannamaker, P. E., 1993, Three dimensional magnetotelluric modeling using difference equations – theory and comparisons to integral equation solutions: Geophysics, 58, 215–226
| Three dimensional magnetotelluric modeling using difference equations – theory and comparisons to integral equation solutions:Crossref | GoogleScholarGoogle Scholar |
McMillan, M. S., and Oldenburg, D. W., 2014, Cooperative constrained inversion of multiple electromagnetic data sets: Geophysics, 79, B173–B185
| Cooperative constrained inversion of multiple electromagnetic data sets:Crossref | GoogleScholarGoogle Scholar |
Newman, G. A., and Alumbaugh, D. L., 2000, Three-dimensional magnetotelluric inversion using non-linear conjugate gradients: Geophysical Journal International, 140, 410–424
| Three-dimensional magnetotelluric inversion using non-linear conjugate gradients:Crossref | GoogleScholarGoogle Scholar |
Nocedal, J., and Wright, S. J., 2006, Numerical optimization (2nd edition): Springer Verlag.
Routh, P. S., and Oldenburg, D. W., 1999, Inversion of controlled-source audio-frequency magnetotellurics data for a horizontally layered earth: Geophysics, 64, 1689–1697
| Inversion of controlled-source audio-frequency magnetotellurics data for a horizontally layered earth:Crossref | GoogleScholarGoogle Scholar |
Siripunvaraporn, W., Egbert, G. D., and Lenbury, Y., 2002, Numerical accuracy of magnetotelluric modeling: a comparison of finite difference approximations: Earth, Planets, and Space, 54, 721–725
| Numerical accuracy of magnetotelluric modeling: a comparison of finite difference approximations:Crossref | GoogleScholarGoogle Scholar |
Siripunvaraporn, W., Egbert, G. D., Lenbury, Y., and Uyeshima, M., 2005, Three-dimensional magnetotelluric inversion: data-space method: Physics of the Earth and Planetary Interiors, 150, 3–14
| Three-dimensional magnetotelluric inversion: data-space method:Crossref | GoogleScholarGoogle Scholar |
Smith, J. T., 1996, Conservative modeling of 3-D electromagnetic fields, part II: biconjugate gradient solution and an accelerator: Geophysics, 61, 1319–1324
| Conservative modeling of 3-D electromagnetic fields, part II: biconjugate gradient solution and an accelerator:Crossref | GoogleScholarGoogle Scholar |
Streich, R., 2009, 3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: direct solution and optimization for high accuracy: Geophysics, 74, F95–F105
| 3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: direct solution and optimization for high accuracy:Crossref | GoogleScholarGoogle Scholar |
Troiano, A., Giuseppe, M. G. D., Petrillo, Z., and Patella, D., 2009, Imaging 2D structures by the CSAMT method: application to the Pantano di S. Gregorio Magno faulted basin (Southern Italy): Journal of Geophysics and Engineering, 6, 120–130
| Imaging 2D structures by the CSAMT method: application to the Pantano di S. Gregorio Magno faulted basin (Southern Italy):Crossref | GoogleScholarGoogle Scholar |
Wannamaker, P. E., 1997, Tensor CSAMT survey over the Sulphur Springs thermal area, Valles Caldera, New Mexico, U.S.A., part I: implications for structure of the western caldera: Geophysics, 62, 451–465
| Tensor CSAMT survey over the Sulphur Springs thermal area, Valles Caldera, New Mexico, U.S.A., part I: implications for structure of the western caldera:Crossref | GoogleScholarGoogle Scholar |
Weiss, C. J., and Constable, S., 2006, Mapping thin resistors and hydrocarbons with marine EM methods, part II — modeling and analysis in 3D: Geophysics, 71, G321–G332
| Mapping thin resistors and hydrocarbons with marine EM methods, part II — modeling and analysis in 3D:Crossref | GoogleScholarGoogle Scholar |
Weng, A., Liu, Y., Jia, D., Liao, X., and Yin, C., 2012, Three-dimensional controlled source electromagnetic inversion using non-linear conjugate gradients: Chinese Journal of Geophysics, 55, 3506–3515
Younis, A., El-Qady, G., Alla, M. A., Zaher, M. A., Khalil, A., Ibiary, M. A., and Saraev, A., 2015, AMT and CSAMT methods for hydrocarbon exploration at Nile Delta, Egypt: Arabian Journal of Geosciences, 8, 1965–1975
| AMT and CSAMT methods for hydrocarbon exploration at Nile Delta, Egypt:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC2MXmslOmtrY%3D&md5=bb58aa31f6cf7c936e275f6c9c88c213CAS |
Zonge, K. L., and Hughes, L. J., 1991, Controlled source audio-frequency magnetotellurics, in M. S. Nabighian, ed., Electromagnetic methods in applied geophysics: Society of Exploration Geophysicists, 713–810.