KMS of Xinjiang Astronomical Observatory, CAS
| 类地行星重磁及梯度张量数据物性反演方法研究与应用 | |
| Alternative Title | Inversion Methods of Physical Property and Applications in Terrestrial Planets from Gravity & Magnetic and Their Gradient Tensor Data |
刘升
| |
| Subtype | 博士 |
| Thesis Advisor | 刘祥 |
| 2022-05-25 | |
| Degree Grantor | 中国科学院大学 |
| Place of Conferral | 北京 |
| Degree Name | 理学博士 |
| Degree Discipline | 天体物理 |
| Keyword | 重磁反演，模糊聚类方法，交叉梯度约束，结构相似性指数，相关分析约束 |
| Abstract | 随着航空航天技术的发展，利用地球物理技术能够探测类地行星深部的物理性质，包括重力、磁法、电磁、地震与地热等手段。重磁数据具有采集便捷、代价小和效率高的特点，已经广泛地应用于类地行星内部结构探测中。重磁数据的物性反演能够得到物性模型参数的空间分布，能为后续的地质解释提供有效的参考资料。但是，重磁数据物性反演存在严重的非唯一性。因此，本文以改善重磁数据物性反演的多解性为出发点，开展重磁数据物性反演方法的研究，为类地行星深部探测提供高效的和高精度的技术方法。本文主要的内容如下： （1）总结了二度体与三度体的重磁及其梯度张量数据的正演理论。继而，介绍了物性反演的基本理论，包含反演的目标函数、不同的正则化技术、深度加权约束与正则化因子选取的方法等，为后续的物性反演奠定了一定的基础。 （2）提出了一种基于离散的先验物性信息的模糊聚类（FCM）反演方法，使用信息熵约束来充分考虑物性模型参数的空间分布特征，得到更合理的聚类中心值。进而提出了FCM约束项加权参数的自动搜索算法，得以快速地选择合适的加权参数。其次，基于边缘识别方法进行优化处理，降低剖分单元个数和优化局部加权参数。并将上述优化处理结合到FCM反演中，提升了反演效率和反演精度。最后，基于弹性网正则化技术、模型加权与重加权的策略实现了参数域中的重磁及梯度张量数据的模糊聚类联合反演，改善了反演物性模型的深度分辨率，降低了非唯一性。 （3）采用三元组策略进行优化存储与计算涉及到物性模型梯度向量的计算，实现了快速交叉梯度联合反演。使用三元组方法时，模型梯度以及交叉梯度约束项的梯度等所需的存储压缩量变为模型剖分单元个数分之一。通过模型数据与实际数据进行改进方法的验证，表明该方法能够实现结构一致性约束，降低非唯一性，节省计算资源，并提升了计算效率。 （4）提出了一种基于结构一致性约束的联合方法。将结构相似性指数（SSIM）的分数形式转化为相减形式，解决了可能会出现解析奇点的问题，并最终形成了用于重磁数据联合反演的新型的结构一致性约束。将合成数据和实际数据应用于SSIM联合反演，并与交叉梯度联合反演方法进行对比，证明了提出方法的正确性和有效性。 （5）提出了一种具有高精度和高效率的相关分析联合反演算法，将模型空间（MS）中的相关分析联合反演的计算转化为数据空间（DS）中的等效计算，这减少了计算公式中矩阵的维度。采用改进的共轭梯度（ICG）方法进行反演计算，此方法便于结合包含稀疏因子的稳定函数，得以提高反演模型的分辨率。使用合成数据和实际数据对DS-ICG相关分析联合反演方法进行测试，证明了拓展的方法可以有效地减少计算量，并改善反演的非唯一性。 |
| Other Abstract | With the development of aerospace technology, geophysical technology can be used to detect the physical properties of terrestrial planets, including gravity, magnetism, electromagnetism, earthquakes and geothermal methods. Gravity and magnetic data have been widely used in the detection of the internal structure of terrestrial planets due to its convenient acquisition, low cost and high efficiency. The physical property inversion of gravity and magnetic data can obtain the spatial distribution of physical property model parameters, which can provide effective reference materials for subsequent geological interpretation. However, the physical property inversion using gravity and magnetic data has serious non-uniqueness. Therefore, starting from the improvement of the multiple solutions of the physical property inversion for gravity and magnetic data, the physical property inversion methods for gravity and magnetic data are carried out, which provides efficient and high-precision technical methods for the deep detection of terrestrial planets. The main works are summarized as follows: (1) The forward theories of gravity, magnetic and their gradient tensor data of two-dimensional and three-dimensional bodies are summarized. Then, the basic theory of physical property inversion is introduced, including the objective function of inversion, different regularization techniques, depth weighting constraints and methods of regularization factor selection, etc., which provides certain foundation for subsequent physical property inversion. (2) A fuzzy C-means clustering method (FCM) based on discrete prior physical property information is proposed, which uses information entropy constraints to fully consider the spatial distribution characteristics of physical property model parameters to obtain more reasonable cluster center values. Furthermore, an automatic search algorithm for the weighting parameters of FCM constraints is proposed, which can quickly select the appropriate weighting parameters. Secondly, the optimization process is carried out based on the edge detection methods to reduce the number of meshing units and optimize the local weighting parameters. The above optimization processing is combined into the FCM inversion, which improves the inversion efficiency and inversion accuracy. Finally, the elastic-net regularization technology, model weighting and re-weighting strategies are used to realize the joint inversion of the gravity, magnetic and their gradient tensor data in the parameter domain, which improves the depth resolution of the recovered physical property models and reduces the non-uniqueness. (3) The triple strategy is used to optimize storages and calculations together with the calculations of the gradient vectors of the physical models, which realizes the fast cross-gradient joint inversion. When using the triple method, the storage of model gradients and gradients of cross-gradient terms, etc., is compressed to a fraction of the number of model partitions. The modified method is verified by model data and real data, which shows that the method can realize structural-consistency constraints, reduce non-uniqueness, save computing resources, and improve computing efficiency. (4) A joint method based on structural consistency constraints is proposed. The fractional form of the Structural Similarity Index (SSIM) is converted into a subtractive form to addresses the possibility of analytical singularities, and finally a novel structural-consistency constraint is formed for joint inversion of gravity and magnetic data. The synthetic data and actual data are applied to the SSIM joint inversion, which proves the correctness and effectiveness of the proposed method. (5) A high-precision and high-efficiency correlation-analysis joint inversion algorithm is proposed, which converts the calculations of the correlation-analysis joint inversion of the gravity and magnetic data in the model space (MS) into equivalent calculations in the data space (DS), which reduce the dimensions of the matrices in the calculation formulas. The improved Conjugate Gradient (ICG) method is used for the calculation of the inversion, which facilitates the use of stable functions with sparse factors and can improve the resolution of the inversion. The DS-ICG correlation analysis joint inversion method is tested using synthetic data and actual data, and it is proved that the extended method can effectively reduce the calculation amount and improve the non-uniqueness of the inversion. |
| Pages | 169 |
| Language | 中文 |
| Document Type | 学位论文 |
| Identifier | http://ir.xao.ac.cn/handle/45760611-7/5161 |
| Collection | 研究生学位论文 |
| Affiliation | 中国科学院新疆天文台 |
| First Author Affilication | Xinjiang Astronomical Observatory, Chinese Academy of Sciences |
| Recommended Citation GB/T 7714 | 刘升. 类地行星重磁及梯度张量数据物性反演方法研究与应用[D]. 北京. 中国科学院大学,2022. |
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| 类地行星重磁及梯度张量数据物性反演方法研（21299KB） | 学位论文 | 暂不开放 | CC BY-NC-SA | Application Full Text | ||
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