Application of 2D inversion of magnetotelluric data bearing terrain information based on an unstructured mesh
-
摘要: 本文对基于自适应非结构三角形网格的带地形MT数据二维Occam反演进行应用研究。自适应非结构三角形网格能够准确地模拟起伏地形和复杂地质构造,正演网格由有限元解的后验误差估计指导自动细化,保证了模型响应的准确性,反演网格在反演目标区域采用精细网格剖分,在模型边界区域采用粗网格剖分,在满足反演精度的前提下减少了不必要的反演参数。基于快速Occam正则化反演方法,采用伴随方程法推导灵敏度矩阵并结合加权平方法计算模型粗糙度。通过对陆地起伏地形模型和起伏海底模型反演试算,验证了算法的精确性和适用性,能够对陆地及海底起伏地形下的多尺度结构进行成像。然后,将该方法应用于克拉玛依后山区域的实测数据反演处理中,反演得到的电阻率结构与地质资料以及采用非线性共轭梯度反演所得结果相吻合。Abstract: This paper focuses on the application of the 2D inversion of magnetotelluric data that bear terrain information based on an unstructured adaptive triangular mesh. An adaptive unstructured triangular grid can be used to accurately simulate undulating terrain and complex geological structures. The adaptive unstructured triangular grids for magnetotelluric forward modeling are automatically refined using the a posteriori error estimation with the finite element solution, which ensures the accuracy of the model response. As for adaptive unstructured triangular grids for magnetotelluric inversion, fine mesh generation is adopted for the inversion target areas, while coarse grid generation is utilized for the boundary areas of the model, thus reducing unnecessary inversion parameters on the premise of satisfying the inversion accuracy. According to the inversion of an undulating-terrain model of land and an undulating-seabed model, the accuracy and applicability of the algorithm are verified and the algorithm can be used to image the multi-scale structures under the undulating terrain of land and seabed. Then, the method was applied to the inversion of the measured data of the Houshan area in Karamay. As a result, the resistivity structure obtained through the inversion was consistent with the geological data and the results obtained through the nonlinear conjugate gradient inversion.
-
Key words:
- unstructured mesh /
- MT /
- 2D inversion /
- terrain /
- Karamay
-
-
[1] Huang X Y, Deng J Z, Chen X, et al. Magnetotelluric extremum boundary inversion based on different stabilizers and its application in a high radioactive waste repository site selection[J]. Applied Geophysics, 2019, 16(3) : 367-377.
[2] 李磊. 湘南骑田岭锡铅锌多金属矿区岩矿石电性研究[J]. 物探与化探, 2007(S1) : 77-80,93.
[3] Li L. Researchs on rock electrical properties in the Qittianling,lead and zinc polymetallic ore deposit,southern HuNan[J]. Geophysical and Geochemical Exploration, 2007(S1) : 77-80,93.
[4] 熊彬, 罗天涯, 蔡红柱, 等. 起伏地形大地电磁二维反演[J]. 物探与化探, 2016, 40(3):587-593.
[5] Xiong B, Luo T Y, Cai H Z, et al. Two-dimensional magnetotelluric inversion of undulating terrain[J]. Geophysical and Geochemical Exploration, 2016, 40(3): 587-593.
[6] Alan G J. Distortion decomposition of the magnetotelluric impedance tensors from a one-dimensional anisotropic Earth[J]. Geophysical Journal International, 2012, 189(1): 268-284.
[7] Juanjo L, Pilar Q, Jaume P. Effects of galvanic distortion on magnetotelluric data over a three-dimensional regional structure[J]. Geophysical Journal International, 1998(2) : 295-301.
[8] Franke A, Borner R, Spitzer K, et al. Adaptive unstructured grid finite element simulation of two-dimensional magnetotelluric fields for arbitrary surface and seafloor topography[J]. Geophysical Journal International, 2007, 171(1) : 71-86.
[9] Shewchuk J R. Delaunay refinement algorithms for triangular mesh generation[J]. Computational Geometry Theory & Applications, 2002, 47(1-3) : 741-778.
[10] Cao X Y, Yin C C, Zhang B, et al. 3D magnetotelluric inversions with unstructured finite-element and limited-memory quasi-Newton methods[J]. Chinese Geophysical Society, 2018, 15(3) : 556-565.
[11] 惠哲剑, 殷长春, 刘云鹤, 等. 基于非结构有限元的时间域海洋电磁三维反演[J]. 地球物理学报, 2020, 63(8) : 3167-3179.
[12] Hui Z J, Yin C C, Liu Y H, et al. 3D inversion of time-domain marine CSEM based on unstructured finite element method[J]. Chinese Journal of Geophysics, 2020, 63(8) : 3167-3179.
[13] Kerry K, Chester W. Adaptive finite-element modeling using unstructured grids: The 2D magnetotelluric example[J]. Society of Exploration Geophysicists, 2006, 71(6) : G291-G299.
[14] Li Y G, Key K. 2D marine controlled-source electromagnetic modeling: Part 1 — An adaptive finite-element algorithm[J]. Geophysics, 2007, 72(2) : WA51.
[15] Li Y G, Josef P, et al. Adaptive finite element modelling of two-dimensional magnetotelluric fields in general anisotropic media[J]. Geophysical Journal International, 2008, 175(3) : 942-954.
[16] 刘颖, 李予国, 韩波. 可控源电磁场三维自适应矢量有限元正演模拟[J]. 地球物理学报, 2017, 60(12) : 4874-4886.
[17] Liu Y, Li Y G, Han B. Adaptive edge finite element modeling of the 3D CSEM field on unstructured grids[J]. Chinese Journal of Geophysics, 2017, 60(12) : 4874-4886.
[18] Ovall J S. Asymptotically exact functional error estimators based on superconvergent gradient recovery[J]. Numerische Mathematik, 2006, 102(3) : 543-558.
[19] Key K, Ovall J. A parallel goal-oriented adaptive finite element method for 2.5D electromagnetic modelling[J]. Geophysical Journal International, 2011. 186(1) : 137-154.
[20] 韩骑, 胡祥云, 程正璞, 等. 自适应非结构有限元MT二维起伏地形正反演研究[J]. 地球物理学报, 2015, 58(12) : 4675-4684.
[21] Han Q, Hu X Y, Chen Z P, et al. A study of two dimensional MT inversion with steep topography using the adaptive unstructured finite element method[J]. Chinese Journal of Geophysics, 2015, 58(12) : 4675-4684.
[22] Key K. MARE2DEM: A 2D inversion code for controlled-source electromagnetic and magnetotelluric data[J]. Geophysical Journal International, 2016, 207(1) : 571-588.
[23] 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.
[24] 何梅兴, 胡祥云, 叶益信, 等. 2.5维可控源音频大地电磁法Occam反演理论及应用[J]. 地球物理学进展, 2011, 26(6) : 2163-2170.
[25] He M X, Hu X Y, Ye Y X, et al. 2.5D controlled source audio-frequency magnetotellurics occam inversion[J]. Progress in Geophysics, 2011, 26(6) : 2163-2170.
[26] 熊彬, 罗延钟, 强建科. 瞬变电磁2.5维反演中灵敏度矩阵计算方法(Ⅰ)[J]. 地球物理学进展, 2004, 19(3) : 616-620.
[27] Xiong B, Luo Y Z, Qiang J K. Methods for calculating sensitivities for 2.5D transient electromagnetic inversion[J]. Progress in Geophysics, 2004, 19(3) : 616-620.
[28] Farquharson C G, Oldenburg D W. Approximate sensitivities for the electromagnetic inverse problem[J]. Geophysical Journal International, 1996, 126(1) : 235-252.
[29] Mcgillivray P R, Oldenburg D W, Ellis R G, et al. Calculation of sensitivities for the frequency-domain electromagnetic problem[J]. Geophysical Journal International, 1994, 116(1) : 1-4.
[30] Parker R L. Geophysical inverse theory[M]. Princeton: Princeton University Press, 1994.
[31] Zhdanov M S. Inverse theory and applications in geophysics[M]. New York: Elsevier, 2002.
-
计量
- 文章访问数: 718
- PDF下载数: 131
- 施引文献: 0
下载: