王金铎,
王千军
中国石化胜利油田分公司勘探开发研究院, 山东东营 257000
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 收稿日期:2020-05-22
修回日期:2021-01-18
上线日期:2021-03-10
Gravity inversion based on sparse representation of density model
YU HuiZhen,WANG JinDuo,
WANG QianJun
Research Institute of Exploration and Development, Shengli Oilfield, SINOPEC, Shandong Dongying 257000, China
MSC: P631
--> Received Date: 22 May 2020
Revised Date: 18 January 2021
Available Online: 10 March 2021
摘要
摘要: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.
关键词: 稀疏表征/
重力反演/
模型特征矩阵/
稀疏求解算法
Abstract:Gravity inversion is an essential tool for imaging subsurface density distribution, and the selection of a proper density model constraining method is key for improving gravity inversion resolution and reliability. Conventional constraining methods match inversion target via adjusting smoothing or sparse constrain weight starting from density model in the mesh space. However, it is difficult to guarantee the reasonability and validity of model constrains when there exists a set of multi-style geologic bodies, an inaccurate anomaly separation or an unreasonable mesh-generation solution. To this end, a novel gravity inversion method has been proposed which is based on sparse representation of density model. Firstly, the representation of the density model to be recovered is assumed to be the linear combination of model feature matrix and sparse decomposition coefficient, then objective function of gravity inversion is re-derived and sparse solving process of decomposition coefficient also is provided. Comparing with traditional gravity inversion methods, the feature model for constructing model feature matrix contains prior geometrical information of multi-style geologic bodies, and the sparsity of decomposition coefficient ensures that the inversion target comes from combination of the most typical geological modes. Finally, the test of synthetic models and the application of field data demonstrate the validity of our proposed gravity inversion method which is based on sparse representation of density model.
Key words:Sparse representation/
Gravity inversion/
Model feature matrix/
Sparse algorithm
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