基于数据空间和稀疏约束的三维重力和重力梯度数据联合反演

张镕哲, 李桐林, 刘财, 李福元, 邓馨卉, 石会彦. 2021. 基于数据空间和稀疏约束的三维重力和重力梯度数据联合反演. 地球物理学报, 64(3): 1074-1089, doi: 10.6038/cjg2021O0104
引用本文: 张镕哲, 李桐林, 刘财, 李福元, 邓馨卉, 石会彦. 2021. 基于数据空间和稀疏约束的三维重力和重力梯度数据联合反演. 地球物理学报, 64(3): 1074-1089, doi: 10.6038/cjg2021O0104
ZHANG RongZhe, LI TongLin, LIU Cai, LI FuYuan, DENG XinHui, SHI HuiYan. 2021. Three-dimensional joint inversion of gravity and gravity gradient data based on data space and sparse constraints. Chinese Journal of Geophysics (in Chinese), 64(3): 1074-1089, doi: 10.6038/cjg2021O0104
Citation: ZHANG RongZhe, LI TongLin, LIU Cai, LI FuYuan, DENG XinHui, SHI HuiYan. 2021. Three-dimensional joint inversion of gravity and gravity gradient data based on data space and sparse constraints. Chinese Journal of Geophysics (in Chinese), 64(3): 1074-1089, doi: 10.6038/cjg2021O0104

基于数据空间和稀疏约束的三维重力和重力梯度数据联合反演

  • 基金项目:

    国家重点研发计划(2017YFC0601606), 中国地质调查局项目(DD 20201118), 中国博士后科学基金特别资助(站前)项目(2020TQ0114), 中国博士后科学基金资助项目(2020M681036)联合资助

详细信息
    作者简介:

    张镕哲, 男, 博士后, 主要从事地球物理正反演理论与应用研究.E-mail: zhangrz@jlu.edu.cn

    通讯作者: 刘财, 男, 教授, 主要从事地震波场正反演理论、综合地球物理等研究.E-mail: liucai@jlu.edu.cn
  • 中图分类号: P631

Three-dimensional joint inversion of gravity and gravity gradient data based on data space and sparse constraints

More Information
  • 随着重力和重力梯度测量技术的日趋成熟,基于重力和重力梯度数据的反演技术得到了广泛关注.针对反演多解性严重、计算效率低和内存消耗大等难点问题,本文开展了三维重力和重力梯度数据的联合反演研究,该方法结合重力和重力梯度两种数据,将L0范数正则化项加入到目标函数中,并在数据空间下采用改进的共轭梯度算法求解反演最优化问题.同时,本文摒弃了依赖先验信息的深度加权函数,引入了自适应模型积分灵敏度矩阵,用来克服因重力和重力梯度数据核函数随深度增加而衰减引起的趋肤效应问题.为了提高反演计算效率,本文又推导出基于规则网格化的重力和重力梯度快速正演计算方法.模拟试算表明,改进的共轭梯度法可以降低反演的迭代次数,提高反演的收敛速度;自适应模型积分灵敏度矩阵,可以有效解决趋肤效应,提高反演纵向分辨能力;数据空间和改进的共轭梯度算法结合,可以更好地降低反演求解方程的维度,避免存储灵敏度矩阵,有效地降低反演计算时间和内存消耗量.野外实例表明,该算法可以在普通计算机下快速地获得地下密度分布模型,表现出较强的稳定性和适用性.

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  • 图 1 

    三维模型网格剖分图

    Figure 1. 

    3D model meshing

    图 2 

    模型一的理论模型和正演响应等值线图

    Figure 2. 

    Theoretical model and forward response contour map of model 1

    图 3 

    不同观测数据反演结果对比图

    Figure 3. 

    Comparison of different observation data inversion results

    图 4 

    模型二的理论模型和正演响应等值线图

    Figure 4. 

    Theoretical model and forward response contour map of model 2

    图 5 

    传统和改进的共轭梯度法反演结果对比图

    Figure 5. 

    Comparison of traditional and improved conjugate gradient inversion results

    图 6 

    不同S矩阵的平滑和稀疏约束反演结果的对比图

    Figure 6. 

    Comparison of smooth and sparse constraint inversion results of different S matrices

    图 7 

    模型三的理论模型和正演响应等值线图

    Figure 7. 

    Theoretical model and forward response contour map of model 3

    图 8 

    模型空间和数据空间联合反演结果对比图

    Figure 8. 

    Comparison of model space and data space joint inversion results

    图 9 

    模型四的理论模型和正演响应等值线图

    Figure 9. 

    Theoretical model and forward response contour map of model 4

    图 10 

    数据空间共轭梯度法联合反演结果图

    Figure 10. 

    The data space conjugate gradient method joint inversion results

    图 11 

    实测重力和重力梯度数据等值线图

    Figure 11. 

    Contour plots of measured gravity and gravity gradient data

    图 12 

    重力和重力梯度数据联合反演获得的密度分布垂向切片图

    Figure 12. 

    Cross section of density distribution obtained by joint inversion of gravity and gravity gradient data

    图 13 

    重力和重力梯度数据联合反演获得的密度分布横向切片图

    Figure 13. 

    Depth section of density distribution obtained by joint inversion of gravity and gravity gradient data

    表 1 

    反演模型和理论模型的均方根误差

    Table 1. 

    The root mean square error of each inversion model and the theoretical model

    gz gzVxx gzVxy gzVzx gzVzy gzVzz gz和(Vxx, Vxy, Vzx, Vzy, Vzz)
    RMSE 0.1184 0.0862 0.0871 0.0867 0.0775 0.0787 0.0774
    下载: 导出CSV

    表 2 

    理论模型异常体属性情况

    Table 2. 

    Theoretical model anomaly attributes

    单元 剩余密度值 几何大小 顶部埋深
    A 1 g·cm-3 200 m×200 m×150 m 150 m
    B 1 g·cm-3 150 m×150 m×200 m 200 m
    C 1 g·cm-3 400 m×150 m×150 m 150 m
    D 1 g·cm-3 100 m×400 m×200 m 200 m
    下载: 导出CSV
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出版历程
收稿日期:  2020-08-26
修回日期:  2021-01-05
上线日期:  2021-03-10

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