基于密度模型稀疏表征的重力反演方法

于会臻, 王金铎, 王千军. 2021. 基于密度模型稀疏表征的重力反演方法. 地球物理学报, 64(3): 1061-1073, doi: 10.6038/cjg2021O0113
引用本文: 于会臻, 王金铎, 王千军. 2021. 基于密度模型稀疏表征的重力反演方法. 地球物理学报, 64(3): 1061-1073, doi: 10.6038/cjg2021O0113
YU HuiZhen, WANG JinDuo, WANG QianJun. 2021. Gravity inversion based on sparse representation of density model. Chinese Journal of Geophysics (in Chinese), 64(3): 1061-1073, doi: 10.6038/cjg2021O0113
Citation: YU HuiZhen, WANG JinDuo, WANG QianJun. 2021. Gravity inversion based on sparse representation of density model. Chinese Journal of Geophysics (in Chinese), 64(3): 1061-1073, doi: 10.6038/cjg2021O0113

基于密度模型稀疏表征的重力反演方法

  • 基金项目:

    国家科技重大专项"准噶尔盆地碎屑岩层系油气富集规律与勘探评价"(2016ZX05002-002)资助

详细信息
    作者简介:

    于会臻, 男, 1981年生, 博士研究生, 副研究员, 主要从事综合地球物理勘探技术研究.E-mail: yhzabc@163.com

  • 中图分类号: P631

Gravity inversion based on sparse representation of density model

  • 重力反演是恢复地下密度空间分布的有效工具,而选择合理的密度模型约束方法是提升重力反演分辨率和可靠性的关键.常规约束方法大多是从剖分网格空间中的密度模型出发,通过调整光滑或稀疏约束权重来匹配反演目标,但当地质体类型多样、异常分离不准确及网格剖分方案不合理时,模型约束的合理性与灵活性难以得到有效保证.为此,本文提出了一种基于密度模型稀疏表征的重力反演方法.首先假设待反演的密度模型表征为模型特征矩阵和稀疏分解系数的线性组合,之后重新推导了重力反演目标函数,并给出了分解系数的稀疏求解过程.相比现有重力反演方法,用于构建模型特征矩阵的特征模型可包含不同类型地质体的先验几何信息,分解系数的稀疏性保证了待反演目标来自于最典型的地质模式组合.最后,通过模型试验及实际资料验证了基于密度模型稀疏表征的重力反演方法的有效性.

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  • 图 1 

    一维密度模型分解示意图

    Figure 1. 

    Diagram of 1D density model decomposition

    图 2 

    构建模型特征矩阵的特征模型

    Figure 2. 

    Feature models for building model feature matrix

    图 3 

    特征模型Ⅰ对应的模型特征矩阵构建过程

    Figure 3. 

    Building process of model feature matrix corresponding to feature model Ⅰ

    图 4 

    反演结果对比

    Figure 4. 

    Comparison of inversion results

    图 5 

    反演结果对比

    Figure 5. 

    Comparison of inversion results

    图 6 

    构建模型特征矩阵的二维特征模型

    Figure 6. 

    2D feature model for building model feature matrix

    图 7 

    反演结果对比

    Figure 7. 

    Comparison of inversion results

    图 8 

    三维密度模型及重力异常

    Figure 8. 

    3D density model and gravity anomaly

    图 9 

    构建模型特征矩阵的三维特征模型

    Figure 9. 

    3D feature model for building model feature matrix

    图 10 

    反演结果对比

    Figure 10. 

    Comparison of inversion results

    图 11 

    实际资料反演结果

    Figure 11. 

    Inversion results of actual data

    表 1 

    二维密度模型参数

    Table 1. 

    Parameters of 2D density model

    Z最小
    (m)
    Z最大
    (m)
    X最小
    (m)
    X最大
    (m)
    剩余密度
    (g·cm-3)
    模型一 块体Ⅰ 400 700 700 1500 0.5
    块体Ⅱ 100 250 3100 4700 0.3
    模型二 块体Ⅲ 250 650 700 1700 0.5
    块体Ⅳ 650 1050 3700 4900 -0.3
    块体Ⅴ 1150 1400 -100 5900 0.2
    模型三 倾斜体Ⅵ 150 800 900 3700 0.5
    下载: 导出CSV

    表 2 

    “Y”字型地质体密度模型参数

    Table 2. 

    Parameters of Y-type geological body density model

    Z最小
    (m)
    Z最大
    (m)
    X最小
    (m)
    X最大
    (m)
    Y最小
    (m)
    Y最大
    (m)
    剩余密度
    (g·cm-3)
    倾斜体Ⅰ 200 800 700 2100 1100 2100 0.5
    倾斜体Ⅱ 200 1800 1100 2900 700 2900 0.5
    下载: 导出CSV
  •  

    Bertete-Aguirre H, Cherkaev E, Oristaglio M. 2002. Non-smooth gravity problem with total variation penalization functional. Geophysical Journal International, 149(2): 499-507. doi: 10.1046/j.1365-246X.2002.01664.x

     

    Boyd S, Parikh N, Chu E, et al. 2010. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends® in Machine Learning, 3(1): 1-122. doi: 10.1561/2200000016

     

    Chen S S, Donoho D L, Saunders M A. 2001. Atomic decomposition by basis pursuit. SIAM Review, 43(1): 129-159. doi: 10.1137/S003614450037906X

     

    Farquharson C G, Oldenburg D W. 1998. Non-linear inversion using general measures of data misfit and model structure. Geophysical Journal International, 134(1): 213-227. doi: 10.1046/j.1365-246x.1998.00555.x

     

    Farquharson C G. 2008. Constructing piecewise-constant models in multidimensional minimum-structure inversions. Geophysics, 73(1): K1-K9. doi: 10.1190/1.2816650

     

    Figueiredo M A T, Bioucas-Dias J M, Nowak R D. 2007. Majorization-minimization algorithms for wavelet-based image restoration. IEEE Transactions on Image Processing, 16(12): 2980-2991. doi: 10.1109/TIP.2007.909318

     

    Gao X H, Huang D N. 2017. Research on 3D focusing inversion of gravity gradient tensor data based on a conjugate gradient algorithm. Chinese Journal of Geophysics (in Chinese), 60(4): 1571-1583, doi:10.6038/cjg20170429.

     

    Guan Z N, Hou J S, Huang L P, et al. 1998. Inversion of gravity and magnetic anomalies using pseudo-BP neural network method and its application. Chinese Journal of Geophysics (Acta Geophysica Sinica) (in Chinese), 41(2): 242-251.

     

    Last B J, Kubik K. 1983. Compact gravity inversion. Geophysics, 48(6): 713-721. doi: 10.1190/1.1441501

     

    Lelièvre P G, Oldenburg D W. 2009. A comprehensive study of including structural orientation information in geophysical inversions. Geophysical Journal International, 178(2): 623-637. doi: 10.1111/j.1365-246X.2009.04188.x

     

    Li Y G, Oldenburg D W. 1996. 3-D inversion of magnetic data. Geophysics, 61(2): 394-408. doi: 10.1190/1.1443968

     

    Li Y G, Oldenburg D W. 1998. 3-D inversion of gravity data. Geophysics, 63(1): 109-119. doi: 10.1190/1.1444302

     

    Li Z L, Yao C L, Zheng Y M. 2019. 3D inversion of gravity data using Lp-norm sparse optimization. Chinese Journal of Geophysics (in Chinese), 62(10): 3699-3709, doi:10.6038/cjg2019M0430.

     

    Liu Z, Yu H Z, Chen T. 2011. 3D inversion method of density based on double constraint. Journal of China University of Petroleum (Edition of Natural Science) (in Chinese), 35(6): 43-50.

     

    Meng X H, Liu G F, Chen Z X, et al. 2012. 3-D gravity and magnetic inversion for physical properties based on residual anomaly correlation. Chinese Journal of Geophysics (in Chinese), 55(1): 304-309, doi:10.6038/j.issn.0001-5733.2012.01.030.

     

    Nguyen H D. 2017. An introduction to Majorization-Minimization algorithms for machine learning and statistical estimation. WIREs Data Mining and Knowledge Discovery, 7(3): e1198.

     

    Oldenburg D W, Li Y G, Ellis R G. 1997. Inversion of geophysical data over a copper gold porphyry deposit: A case history for Mt. Milligan. Geophysics, 62(5): 1419-1431. doi: 10.1190/1.1444246

     

    Paterson N R, Reeves C V. 1985. Applications of gravity and magnetic surveys: The state-of-the-art in 1985. Geophysics, 50(12): 2558-2594. doi: 10.1190/1.1441884

     

    Peng G M, Liu Z, Yu H Z, et al. 2018. 3D gravity inversion based on Cauchy distribution constraint and fast proximal objective function optimization. Chinese Journal of Geophysics (in Chinese), 61(12): 4934-4941, doi:10.6038/cjg2018L0776.

     

    Phillips N, Oldenburg D, Chen J P, et al. 2001. Cost effectiveness of geophysical inversions in mineral exploration: Applications at San Nicolas. The Leading Edge, 20(12): 1351-1360. doi: 10.1190/1.1487264

     

    Portniaguine O, Zhdanov M S. 1999. Focusing geophysical inversion images. Geophysics, 64(3): 874-887. doi: 10.1190/1.1444596

     

    Qin P B, Huang D N. 2016. Integrated gravity and gravity gradient data focusing inversion. Chinese Journal of Geophysics (in Chinese), 59(6): 2203-2224, doi:10.6038/cjg20160624.

     

    Sahoo S K, Makur A. 2015. Signal recovery from random measurements via extended orthogonal matching pursuit. IEEE Transactions on Signal Processing, 63(10): 2572-2581. doi: 10.1109/TSP.2015.2413384

     

    Selesnick I W, Bayram İ. 2014. Sparse signal estimation by maximally sparse convex optimization. IEEE Transactions on Signal Processing, 62(5): 1078-1092. doi: 10.1109/TSP.2014.2298839

     

    Sun J J, Li Y G. 2014. Adaptive Lp inversion for simultaneous recovery of both blocky and smooth features in a geophysical model. Geophysical Journal International, 197(2): 882-899. doi: 10.1093/gji/ggu067

     

    Utsugi M. 2019. 3-D inversion of magnetic data based on the L1-L2 norm regularization. Earth, Planets and Space, 71(1): 73. doi: 10.1186/s40623-019-1052-4

     

    Vatankhah S, Renaut R A, Ardestani V E. 2017. 3-D Projected L1 inversion of gravity data using truncated unbiased predictive risk estimator for regularization parameter estimation. Geophysical Journal International, 210(3): 1872-1887. doi: 10.1093/gji/ggx274

     

    Yao C L, Hao T Y, Guan Z N, et al. 2003. High-speed computation and efficient storage in 3-D gravity and magnetic inversion based on genetic algorithms. Chinese Journal of Geophysics (in Chinese), 46(2): 252-258, doi:10.3321/j.issn:0001-5733.2003.02.020.

     

    Zhdanov M S. 2002. Geophysical Inverse Theory and Regularization Problems. Methods in Geochemistry and Geophysics. Amsterdam: Elsevier Science, 36: 3-609.

     

    Zhdanov M S, Ellis R, Mukherjee S. 2004. Three-dimensional regularized focusing inversion of gravity gradient tensor component data. Geophysics, 69(4): 925-937. doi: 10.1190/1.1778236

     

    Zhu Z Q, Cao S J, Lu G Y. 2014. 3D gravity inversion with bound constraint based on hyper-parameter regularization. The Chinese Journal of Nonferrous Metals (in Chinese), 24(10): 2601-2608.

     

    高秀鹤, 黄大年. 2017. 基于共轭梯度算法的重力梯度数据三维聚焦反演研究. 地球物理学报, 60(4): 1571-1583, doi:10.6038/cjg20170429.

     

    管志宁, 侯俊胜, 黄临平等. 1998. 重磁异常反演的拟BP神经网络方法及其应用. 地球物理学报, 41(2): 242-251. doi: 10.3321/j.issn:0001-5733.1998.02.013

     

    李泽林, 姚长利, 郑元满. 2019. 基于Lp范数稀疏优化算法的重力三维反演. 地球物理学报, 62(10): 3699-3709, doi:10.6038/cjg2019M0430.

     

    刘展, 于会臻, 陈挺. 2011. 双重约束下的密度三维反演. 中国石油大学学报(自然科学版), 35(6): 43-50. https://www.cnki.com.cn/Article/CJFDTOTAL-SYDX201106009.htm

     

    孟小红, 刘国峰, 陈召曦等. 2012. 基于剩余异常相关成像的重磁物性反演方法. 地球物理学报, 55(1): 304-309, doi:10.6038/j.issn.0001-5733.2012.01.030.

     

    彭国民, 刘展, 于会臻等. 2018. 基于柯西分布约束和快速近端目标函数优化的三维重力反演方法. 地球物理学报, 61(12): 4934-4941, doi:10.6038/cjg2018L0776.

     

    秦朋波, 黄大年. 2016. 重力和重力梯度数据联合聚焦反演方法. 地球物理学报, 59(6): 2203-2224, doi:10.6038/cjg20160624.

     

    姚长利, 郝天珧, 管志宁等. 2003. 重磁遗传算法三维反演中高速计算及有效存储方法技术. 地球物理学报, 46(2): 252-258, doi:10.3321/j.issn:0001-5733.2003.02.020.

     

    朱自强, 曹书锦, 鲁光银. 2014. 基于混合正则化的重力场约束反演. 中国有色金属学报, 24(10): 2601-2608. https://www.cnki.com.cn/Article/CJFDTOTAL-ZYXZ201410024.htm

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出版历程
收稿日期:  2020-05-22
修回日期:  2021-01-18
上线日期:  2021-03-10

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