基于改进FCM聚类算法的三维重力反演

刘乃征; 朱培民; 杜利明

doi:10.19509/j.cnki.dzkq.tb20210606

基于改进FCM聚类算法的三维重力反演

doi: 10.19509/j.cnki.dzkq.tb20210606

刘乃征^1a,,
朱培民^1a, ,,
杜利明^{2, 1b}

1a.
中国地质大学(武汉)地球物理与空间信息学院, 武汉 430074
1b.
中国地质大学(武汉)高等研究院, 武汉 430074
2.
中国冶金地质总局山东正元地质勘查院, 济南 250101

基金项目:

国家重点研发计划项目"城市地下空间开发地下全要素信息精准探测技术与装备" 2019YFC0605101

详细信息

作者简介:
刘乃征(1996—), 男, 现正攻读地球物理学专业硕士学位, 主要从事地球物理数据联合反演研究。E-mail: nzliu@cug.edu.cn

通讯作者:
朱培民(1963—), 男, 教授, 博士生导师, 主要从事地球物理反演和地震勘探的研究。E-mail: zhupm@cug.edu.cn

中图分类号: P631.1⁺4
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- 文章访问数: 322
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- 被引次数: 0
出版历程
- 收稿日期: 2022-03-08

Three-dimensional gravity inversion based on improved FCM clustering algorithm

Liu Naizheng^{1a
,},
Zhu Peimin^{1a
, ,},
Du Liming^{2, 1b}

1a.
Institute of Geophysics & Geomatics, China University of Geosciences(Wuhan), Wuhan 430074, China
1b.
Institute of Advanced Studies, China University of Geosciences(Wuhan), Wuhan 430074, China
2.
Geological Exploration Institute of Shandong Zhengyuan, China Metallurgical Geology Bureau, Jinan 250101, China

摘要

摘要:
在重力反演中, 传统的反演方法通常会生成平滑的反演结果, 即不同的地质单元之间没有明显的边界。为了提高反演结果的空间分辨率和反演精度, 采用模糊C均值聚类算法(fuzzy C-means, 简称FCM)解决上述问题。但当异常体体积远小于围岩体积以及目标函数FCM聚类项权重系数选择不当时, 该算法容易造成异常体反演结果均匀收缩, 导致反演精度降低, 甚至反演失败。反演失败的主要原因通常是因为异常体体积比围岩体积小很多。为此在反演的目标函数FCM聚类项中引入了缩放因子, 用以平衡模型参数对每个聚类的隶属度, 减小异常体体积远小于围岩体积的影响。通过建立缩放指数e_k与归一化的聚类中心与实际聚类中心间距离S_normal的简单正相关关系, 使得缩放因子ρ_k随反演过程不断更新, 从而显著降低了目标函数FCM聚类项权重系数的选择难度, 避免了异常体反演结果均匀收缩的问题, 增强了反演的稳定性。理论重力异常数据反演数值试验和实际数据反演表明, 相比于此前的FCM方法, 改进算法有更高的反演稳定性和反演精度。
- 三维重力反演 /
- FCM聚类 /
- 缩放因子
Abstract:
In gravity inversion, traditional inversion methods usually generate smooth inversion results, that is, there are no obvious boundaries between different geological units. Fuzzy C-Means (FCM) algorithm is introduced into the inversion to solve the problem mentioned above to improve the accuracy and spatial resolution of inversion results. However, when the volume of an anomalous body is much smaller than that of the surrounding rock, and the weight coefficient of the FCM clustering term in the objective function is not selected properly, the algorithm is prone to cause uniform shrinkage of the anomaly inversion results, resulting in lower inversion accuracy, or even failure of the inversion.The main reason for the inversion failure is usually because the total volume of the anomalous bodies is much smaller than the volume of the surrounding rock.For this reason, in this paper, the scaling factor is introduced into the FCM clustering term of the objective function to balance the membership degree of the model parameters to each cluster, so as to reduce the influence of small anomalous body volume compared with the surrounding rock volume. By establishing a simple positive correlation between the scaling exponent e_k and the distance s_normal from the normalized clustering center and the real clustering center, the scaling factor ρ_k is continuously updated during the inversion process, which significantly reduces the difficulty in selecting the weight coefficient of the FCM clustering term in the objective function, and avoids the problem of volume shrinkage of the inverted anomalous bodies, thus enhancing the stability of the inversion. The numerical experiments of inversion with theoretical gravity anomaly data and actual data inversion show that the improved algorithm has higher inversion stability and accuracy compared with the previous FCM method.
- three-dimensional gravity inversion /
- FCM clustering /
- scaling factor

HTML全文

图 1 FCM聚类例子

a.模型参数空间分布图；b.FCM聚类后，模型参数被分为C1、C2和C3三类

Figure 1. An example of FCM clustering

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图 2 双块体模型及其观测数据

Figure 2. Model with two blocks and its observation data

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图 3 无聚类约束反演结果(黑色方框表示异常块体理论模型边界)

Figure 3. Inversion results without the clustering constraint

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图 4 反演中目标函数Φ值随迭代次数的变化

Figure 4. Change of objective function Φ with number of iteration in inversion

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图 5 FCM聚类约束反演结果(黑色方框表示异常块体理论模型边界)

Figure 5. Inversion results with the FCM clustering constraint

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图 6 改进FCM聚类约束反演结果(黑色方框表示异常块体理论模型边界)

Figure 6. Inversion results with the improved FCM clustering constraint

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图 7 反演结果网格数统计直方图

a.无聚类约束反演；b.FCM聚类约束反演；c.改进FCM聚类约束反演

Figure 7. Histograms of grid number for inversion results

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图 8 “引导”聚类中心v_k与实际聚类中心v_{real, k}随迭代次数增加的变化

a.FCM聚类约束反演；b.改进FCM聚类约束反演

Figure 8. Change of guided cluster center v_k and real cluster center v_{real, k} with the increaseing of iteration number

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图 9 目标靶区局部高重力异常和已控制矿体水平投影(粗白线包围区域)

Figure 9. Local high gravity anomaly in the target area and horizontal projection of controlled ore bodies surrounded by a thick white line

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图 10 目标靶区A-B地质剖面图^[23]

ZK1，ZK2，ZK3.钻孔编号；Qs.第四系；Om.奥陶纪马家沟组；Fe.磁铁矿；γδ.闪长岩

Figure 10. A-B geological profile in the target area

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图 11 无聚类约束反演结果

a.三维透视图；b.A-B剖面图和地质剖面图；c.C-D剖面图；d.水平切片(z=350 m)和已控制矿体水平投影(白线包围区域)

Figure 11. Inversion results without the clustering constraint

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图 12 FCM聚类约束反演结果

a.三维透视图；b.A-B剖面图和地质剖面图；c.C-D剖面图；d.水平切片(z=350 m)和已控制矿体水平投影(白线包围区域)

Figure 12. Inversion results with the FCM clustering constraint

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图 13 改进FCM聚类约束反演结果

a.三维透视图；b.A-B剖面和地质剖面图；c.C-D剖面图；d.水平切片(z=350 m)和已控制矿体水平投影(白线包围区域)图

Figure 13. Inversion results with improved the FCM clustering constraint

下载: 全尺寸图片幻灯片

图 14 “引导”聚类中心v_k与实际聚类中心v_{real, k}随迭代次数增加的变化

a.FCM聚类约束反演；b.改进FCM聚类约束反演

Figure 14. Change of guided cluster center v_k and real cluster center v_{real, k} with the increaseing of iteration number

下载: 全尺寸图片幻灯片

表 1 缩放指数e_k不同取值对FCM聚类约束反演的影响(表中各物理量的含义见正文)

Table 1. Influence of different scaling exponent e_k on improved FCM clustering constrained inversion

缩放指数e_k	方差			高密度异常体				低密度异常体
缩放指数e_k	v_ar(s_{normal, 1})	v_ar(s_{normal, 2})	v_ar(s_{normal, 3})	a_high	b_high	c_high	A_high/%	a_low	b_low	c_low	A_low/%
0	0.008 0	0.009 7	4.14×10^-8	32	28	64	38.3	30	26	64	35.2
s_{normal, k}^2.5	0.005 0	0.005 4	4.43×10^-8	56	50	64	69.8	51	47	64	67.7
s_{normal, k}^2.3	0.003 8	0.004 0	4.08×10^-8	66	59	64	82.4	64	59	64	85.0
s_{normal, k}^2.0	0.002 4	0.002 5	4.01×10^-8	85	61	64	68.4	84	63	64	73.8

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参考文献(23)

[1]	Oldenburg D W. The inversion and interpretation of gravityanomalies[J]. Geophysics, 1974, 39(4): 526-536. doi: 10.1190/1.1440444
[2]	Li Y, Oldenburg D W. 3-D inversion of gravity data[J]. Geophysics, 1998, 63(1): 109-119. doi: 10.1190/1.1444302
[3]	于炳飞, 罗恒, 李端, 等. 金牛火山岩盆地重磁异常综合分析及找矿预测[J]. 地质科技通报, 2022, 41(3): 282-299. doi: 10.19509/j.cnki.dzkq.2021.0029 Yu B F, Luo H, Li D, et al. Comprehensive analysis of gravity and magnetic anomalies in Jinniu volcanic basin for prediction of ore deposits[J]. Bulletin of Geological Science and Technology, 2022, 41(3): 282-299(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2021.0029
[4]	马杰, 王万银, 纪晓琳. 利用重力场研究塞萨尔盆地及邻区构造特征[J]. 地质科技情报, 2019, 38(1): 285-294. https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201901033.htm Ma J, Wang W Y, Ji X L. Tectonic characteristics of Cesar Basin and its adjacent areas according to gravity field[J]. Geological Science and Technology Information, 2019, 38(1): 285-294(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201901033.htm
[5]	Portniaguine O, Zhdanov M S. Focusing geophysical inversion images[J]. Geophysics, 1999, 64(3): 874-887. doi: 10.1190/1.1444596
[6]	Zhdanov M S, Ellis R, Mukherjee S. Three-dimensional regularized focusing inversion of gravity gradient tensor component data[J]. Geophysics, 2004, 69(4): 925-937. doi: 10.1190/1.1778236
[7]	Zhdanov M S. New advances in regularized inversion of gravity and electromagnetic data[J]. Geophysical Prospecting, 2009, 57(4): 463-478. doi: 10.1111/j.1365-2478.2008.00763.x
[8]	Commer M. Three-dimensional gravity modelling and focusing inversion using rectangular meshes[J]. Geophysical Prospecting, 2011, 59(5): 966-979. http://publications.lbl.gov/islandora/object/ir:156804/datastream/PDF/view
[9]	Paasche H, Tronicke J, Holliger K, et al. Integration of diverse physical-property models: Subsurface zonation and petrophysical parameter estimation based on fuzzy C-means cluster analyses[J]. Geophysics, 2006, 71(3): 33-44. http://adsabs.harvard.edu/abs/2006Geop...71...33P
[10]	Lelièvre P G, Farquharson C G, Hurich C A. Joint inversion of seismic traveltimes and gravity data on unstructured grids with application to mineral exploration[J]. Geophysics, 2012, 77(1): K1-K15. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SEGEAB000029000001001758000001&idtype=cvips&gifs=Yes
[11]	Sun J, Li Y. Joint inversion of multiple geophysical data: A petrophysical approach using guided fuzzy C-means clustering[M]//Anon. SEG Technical Program Expanded Abstracts 2012. [S. l. ]: Society of Exploration Geophysicists, 2012: 1-5.
[12]	Sun J, Li Y. Joint inversion of multiple geophysical data using guided fuzzy C-means clustering[J]. Geophysics, 2016, 81(3): 37-57. doi: 10.1190/geo2015-0457.1
[13]	Colombo D, Rovetta D. Coupling strategies in multiparameter geophysical joint inversion[J]. Geophysical Journal International, 2018, 215(2): 1171-1184. doi: 10.1093/gji/ggy341
[14]	Liu S, Jin S. 3-D gravity anomaly inversion based on improved guided fuzzy C-means clustering algorithm[J]. Pure and Applied Geophysics, 2020, 177(2): 1005-1027. doi: 10.1007/s00024-019-02306-0
[15]	Farquharson C G, Oldenburg D W. Non-linear inversion using general measures of data misfit and model structure[J]. Geophysical Journal International, 1998, 134(1): 213-227. doi: 10.1046/j.1365-246x.1998.00555.x
[16]	Peng G, Liu Z. 3D inversion of gravity data using reformulated Lp-norm model regularization[J]. Journal of Applied Geophysics, 2021: 104378. http://www.sciencedirect.com/science/article/pii/S0926985121001257
[17]	Kim H J, Kim Y H. A unified transformation function for lower and upper bounding constraints on model parameters in electrical and electromagnetic inversion[J]. Journal of Geophysics and Engineering, 2011, 8(1): 21-26. doi: 10.1088/1742-2132/8/1/004
[18]	Dunn J C. A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters[J]. Journal of Cybernetics, 1973, 3(3): 32-57. doi: 10.1080/01969727308546046
[19]	Bezdek J C, Ehrlich R, Full W. FCM: The fuzzy C-means clustering algorithm[J]. Computers & Geosciences, 1984, 10(2/3): 191-203. http://www.u-aizu.ac.jp/course/bmclass/documents/FCM%20-%20The%20Fuzzy%20c-Means%20Clustering%20Algorithm.pdf
[20]	Pham D L. Spatial modelsfor fuzzy clustering[J]. Computer Vision and Image Understanding, 2001, 84(2): 285-297. doi: 10.1006/cviu.2001.0951
[21]	Davari A, Marhaban M H, Noor S B M, et al. Parameter estimation of K-distributed sea clutter based on fuzzy inference and Gustafson-Kessel clustering[J]. Fuzzy Sets and Systems, 2011, 163(1): 45-53. http://core.kmi.open.ac.uk/download/pdf/12226788.pdf
[22]	Li Y, Oldenburg D W. 3-D inversion of magnetic data[J]. Geophysics, 1996, 61(2): 394-408. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SEGEAB000012000001000400000001&idtype=cvips&gifs=Yes
[23]	杜利明. 基于重磁联合反演的金岭矿田深部找矿预测[D]. 武汉: 中国地质大学(武汉), 2020. Du L M. Deep prospecting and reserve prediction of Jinling Orefield based on gravity and magnetic joint inversion[D]. Wuhan: China University of Geosciences(Wuhan), 2020(in Chinese with English abstract).