Application of Joint Inversion of Different Electrode Arrays in Ancient Mausoleum Detection
-
摘要: 电阻率层析成像是一种广泛应用在水文、考古和地质等浅地表勘探领域的地球物理方法。为了增强电阻率层析成像的分辨率、应对复杂的地质问题，本文提出基于雅可比矩阵的不同电极阵列直流电阻率数据的加权联合反演算法，并以温纳和偶极-偶极电极阵列数据为例，在理论模型和古墓探测的野外实例中测试该算法的有效性。结果表明，加权联合反演结果的横向和纵向分辨率都优于单一电极阵列的反演结果，并在实例中缓解“U形”电极阵列的固有缺陷、减少反演模糊性、更好地约束墓室宽度的反演结果。Abstract: Electrical resistivity tomography is a popular geophysical method and has been applied in shallow exploration, involving hydrology, archaeology, and geology, in recent years. To enhance the resolution of electrical resistivity tomography and deal with complex geological settings, we propose the weighted combined inversion of different electrode arrays based on the Jacobian matrix, and then, taking Wenner and dipole-dipole datasets as examples, test its effectiveness on synthetic models and a field case of detecting ancient mausoleum. The results show that the resolution of the weighted combined inversion results is superior to that of a single electrode array in transverse and longitudinal directions, and in the field case, it is demonstrated that the weighted combined inversion algorithm can alleviate the inherent defects of U-shaped electrode array, reduce the ambiguity of inversion, and better constrain the width of the mausoleum.
-
-
![]()
图 2 嵌套模型及其反演结果
从上至下分别为理论模型、温纳单独反演、偶极-偶极单独反演、直接联合反演、加权联合反演结果；从左至右依次为立体图、纵切图、深度4 m处横切图。
Figure 2. Diagrams of the nested model and its inversion results
![]()
图 3 差异模型及其反演结果
从上至下分别为理论模型、温纳单独反演、偶极-偶极单独反演、直接联合反演、加权联合反演结果；从左至右依次为立体图、纵切图、深度4 m处横切图。
Figure 3. Diagrams of the discrepancy model and its inversion results
![]()
图 4 小馒头墩越国贵族墓相关信息
红色坐标系用于后文的反演。
Figure 4. Information related to noble tomb of Yue Kingdom in Xiaomantou Hill
![]()
图 5 越国贵族墓的反演结果
从上至下分别为温纳单独反演、偶极-偶极单独反演、直接联合反演、加权联合反演结果；从左至右依次为反演结果立体图、沿Y方向纵切图、沿X方向纵切图、深度3 m处横切图。
Figure 5. Inversion results of the noble tomb of Yue Kingdom
表 1 不同反演方法恢复嵌套模型的分析参数
Table 1 The analysis parameters of different inversion methods recovering nested model
类型 迭代次数 残差/％ 均方根误差 数据拟合 惩罚函数 温纳 13 36.56 2.137-2 5.961-2 2.945-2 偶极-偶极 18 21.03 2.560-2 3.197-1 3.129-1 直接联合反演 18 20.79 1.742-2 2.277-1 1.825-1 加权联合反演 17 29.98 2.709-2 1.772-1 1.155-1 
下载: 导出CSV
表 2 不同反演方法恢复差异模型的分析参数
Table 2 The analysis parameters of different inversion methods recovering the discrepancy model
类型 迭代次数 残差/％ 均方根误差 数据拟合 惩罚函数 温纳 9 22.53 1.441-2 1.476-2 1.415-2 偶极-偶极 6 32.26 9.270-3 8.206-2 4.396-2 直接联合反演 7 14.99 1.019-2 1.422-1 8.540-2 加权联合反演 9 19.29 1.257-2 1.167-1 5.748-2
下载: 导出CSV
-
[1] COSTALL A, HARRIS B, PIGOIS J P. Electrical resistivity imaging and the saline water interface in high-quality coastal aquifers[J]. Surveys in Geophysics, 2018, 39(4): 753−816. doi: 10.1007/s10712-018-9468-0
[2] PIDLISECKY A, MORAN T, HANSEN B, et al. Electrical resistivity imaging of seawater intrusion into the monterey bay aquifer system[J]. Groundwater, 2016, 54(2): 255−261. doi: 10.1111/gwat.12351
[3] ABBAS A M, GHAZALA H H, MESBAH H S, et al. Implementation of ground penetrating radar and electrical resistivity tomography for inspecting the greco-roman necropolis at kilo 6 of the golden mummies valley, Bahariya Oasis, Egypt[J]. Nriag Journal of Astronomy & Geophysics, 2016, 5(1): 147−159.
[4] KOLAWOLE F, ATEKWANA E A, LAÓ-DÁVILA D A, et al. High resolution electrical resistivity and aeromagnetic imaging reveal the causative fault of the 2009 Mw 6.0 Karonga, Malawi Earthquake[J]. Geophysical Journal International, 2018, 213(2): 1412−1425. doi: 10.1093/gji/ggy066
[5] DAHLIN T, ZHOU B. A numerical comparison of 2D resistivity imaging with 10 electrode arrays[J]. Geophysical Prospecting, 2004, 52(5): 379−398. doi: 10.1111/j.1365-2478.2004.00423.x
[6] NEYAMADPOUR A, wan ABDULLAH W A T, TAIB S, et al. Comparison of Wenner and dipole-dipole arrays in the study of an underground three-dimensional cavity[J]. Journal of Geophysics and Engineering, 2010, 7(1): 30−40. doi: 10.1088/1742-2132/7/1/003
[7] STUMMER P, MAURER H, GREEN A G. Experimental design: Electrical resistivity data sets that provide optimum subsurface information[J]. Geophysics, 2004, 69(1): 120−139. doi: 10.1190/1.1649381
[8] de la VEGA M, OSELLA A, LASCANO E. Joint inversion of Wenner and dipole-dipole data to study a gasoline-contaminated soil[J]. Journal of Applied Geophysics, 2003, 54: 97−109. doi: 10.1016/j.jappgeo.2003.08.020
[9] ATHANASIOU E N, TSOURLOS P I, PAPAZACHOS C B, et al. Combined weighted inversion of electrical resistivity data arising from different array types[J]. Journal of Applied Geophysics, 2007, 62(2): 124−140. doi: 10.1016/j.jappgeo.2006.09.003
[10] LOKE M H, WILKINSON P B, CHAMBERS J E. Fast computation of optimized electrode arrays for 2D resistivity surveys[J]. Computers and Geosciences, 2010, 36(11): 1414−1426. doi: 10.1016/j.cageo.2010.03.016
[11] ISHOLA K S, NAWAWI M N M, ABDULLAH K. Combining multiple electrode arrays for two-dimensional electrical resistivity imaging using the unsupervised classification technique[J]. Pure and Applied Geophysics, 2015, 172(6): 1615−1642. doi: 10.1007/s00024-014-1007-4
[12] 谭茂金, 石耀霖, 王晓杰. 多物理场测井数据联合反演研究进展[J]. 地球物理学进展, 2008,23(5): 1520−1525. [13] 江沸菠, 戴前伟, 董莉. 基于主成分-正则化极限学习机的超高密度电法非线性反演[J]. 地球物理学报, 2015,58(9): 3356−3369. DOI: 10.6038/cjg20150928. JIANG F B, DAI Q W, DONG L. Ultra-high density resistivity nonlinear inversion based on principal component-regularized ELM[J]. Chinese Journal of Geophysics, 2015, 58(9): 3356−3369. DOI: 10.6038/cjg20150928. (in Chinese).
[14] PIDLISECKY A, HABER E, KNIGHT R. Resinvm3D: A 3D resistivity inversion package[J]. Geophysics, 2007, 72(2): 1−10.
[15] 韩波, 窦以鑫, 丁亮. 电阻率成像的混合正则化反演算法[J]. 地球物理学报, 2012,55(3): 970−980. DOI: 10.6038/j.issn.0001-5733.2012.03.027. HAN B, DOU Y X, DING L. Electrical resistivity tomography by using a hybrid regularization[J]. Chinese Journal of Geophysics, 2012, 55(3): 970−980. DOI: 10.6038/j.issn.0001-5733.2012.03.027. (in Chinese).
[16] ARMIJO L. Minimization of functions having Lipschitz continuous first partial derivatives[J]. Pacific Journal of Mathematics, 1966, 16(1): 1−3. doi: 10.2140/pjm.1966.16.1
[17] LOKE M H, CHAMBERS J E, RUCKER D F, et al. Recent developments in the direct-current geoelectrical imaging method[J]. Journal of Applied Geophysics, 2013, 95: 135−156. doi: 10.1016/j.jappgeo.2013.02.017
[18] LOKE M H, BARKER R D. Practical techniques for 3D resistivity surveys and data inversion1[J]. Geophysical Prospecting, 2010, 44(3): 499−523.
[19] 高级, 张海江, 秦臻. 基于共轭梯度的全通道3D井地井电阻率成像研究[J]. 地球物理学进展, 2017, (1): 141-147. GAO J, ZHANG H J, QIN Z. 3D full channel well-surface-well resistivity tomography based on conjugate gradient[J]. Progress in Geophysics, 2017, 32(1): 135-0141, DOI:10.6038/pg20170118. (in Chinese).
[20] 余天祥, 石战结, 刘杰, 等. 多方位拟3D电法技术在古墓葬探测中的应用[J]. CT理论与应用研究, 2018,27(6): 727−738. DOI: 10.15953/j.1004-4140.2018.27.06.06. YU T X, SHI Z J, LIU J, et al. Application of multi-azimuth pseudo-3D electrical resistivity tomography in the investigation of ancient mausoleums[J]. CT Theory and Applications, 2018, 27(6): 727−738. DOI: 10.15953/j.1004-4140.2018.27.06.06. (in Chinese).
[21] DAS P, MOHANTY P R. Resistivity imaging technique to delineate shallow subsurface cavities associated with old coal working: A numerical study[J]. Environmental Earth Sciences, 2016, 75(8): 661. doi: 10.1007/s12665-016-5404-0
计量
- 文章访问数: 427
- HTML全文浏览量: 169
- PDF下载量: 55
