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物探与化探  2022, Vol. 46 Issue (4): 946-954    DOI: 10.11720/wtyht.2022.2552
  方法研究·信息处理·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
重力位场小波多尺度分解性质的分析与应用
孟庆奎1,2(), 张文志2, 高维2, 舒晴1,2, 李瑞2, 徐光晶2, 张凯淞2
1.自然资源部 航空地球物理与遥感地质重点实验室,北京 100083
2.中国自然资源航空物探遥感中心,北京 100083
Property analysis and application of multi-scale wavelet decomposition of gravity potential field
MENG Qing-Kui1,2(), ZHANG Wen-Zhi2, GAO Wei2, SHU Qing1,2, LI Rui2, XU Guang-Jing2, ZHANG Kai-Song2
1. Key Laboratory of Airborne Geophysics and Remote Sensing Geology, Ministry of Natural Resources, Beijing 100083, China
2. China Aero Geophysical Survey and Remote Sensing Center for Natural Resources, Beijing 100083, China
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摘要 

小波多尺度分解是重力位场分离的常用方法之一,其最大的优点是突破了传统的二分重力异常的理念,实现了重力异常的多重分解,但对其性质及其存在的局限性还未进行系统研究。为了更好地指导实践,本文从基于剖面和格网的重力位场小波多尺度分解的定义出发,阐述了低阶小波细节不变准则等3个重要性质,通过设计简单和复杂两类典型理论模型,分析了小波多尺度定义及性质,并在应用实例中与插值切割法进行了对比。结果表明,小波多尺度分解可以实现重力位场多层分离并推估源体埋深,同时针对本文指出的异常尺度混叠和比例系数难以确定等局限,给出了改进思路。以上基础研究工作,可为重力位场资料的处理和解释提供一定参考。

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孟庆奎
张文志
高维
舒晴
李瑞
徐光晶
张凯淞
关键词 重力位场小波多尺度分解低阶小波细节不变理论分析实例应用    
Abstract

Multi-scale wavelet decomposition is one of the common methods for gravity potential field separation. The biggest advantage is that it breaks through the traditional concept of dichotomy gravity anomalies and achieves the multiple decomposition of gravity anomalies. However, no systematic study has been carried out on the limitations and properties of the multi-scale wavelet decomposition. To systematically investigate the multi-scale wavelet decomposition and provide guidance for its practical application, this study, starting from the definition of multi-scale wavelet decomposition of gravity potential field based on profiles and grids, expounded three important properties such as the criterion that low-order wavelet keeps details invariant. Then, it analyzed the definition and properties of multi-scale wavelet by designing simple and complex theoretical models. Afterward, this study compared the multi-scale wavelet decomposition with the interpolation cutting method using field data. The results show that multi-scale wavelet decomposition can achieve multi-layer separation of gravity potential field and estimate the burial depths of source bodies. In addition, the multi-scale wavelet decomposition can provide some ideas for solving the limitations pointed out in this study, such as abnormal scale aliasing and difficulty with the determination of scale coefficients. The above basic research can provide a certain degree of references for the processing and interpretation of gravitational potential field data.

Key wordsgravitational potential field    multi-scale wavelet decomposition    criterion that low-order wavelet keeps details invariant    theoretical analysis    field data application
收稿日期: 2020-12-07      修回日期: 2021-12-14      出版日期: 2022-08-20
ZTFLH:  P631  
基金资助:自然资源部航空地球物理与遥感地质重点实验室课题(2020YFL16);中国地质调查局地质调查项目(DD20191001);中国地质调查局地质调查项目(DD20191004)
作者简介: 孟庆奎(1987-),男,硕士,工程师,主要从事应用地球物理方法研究和数据处理解释工作。Email: qingkui_meng@163.com
引用本文:   
孟庆奎, 张文志, 高维, 舒晴, 李瑞, 徐光晶, 张凯淞. 重力位场小波多尺度分解性质的分析与应用[J]. 物探与化探, 2022, 46(4): 946-954.
MENG Qing-Kui, ZHANG Wen-Zhi, GAO Wei, SHU Qing, LI Rui, XU Guang-Jing, ZHANG Kai-Song. Property analysis and application of multi-scale wavelet decomposition of gravity potential field. Geophysical and Geochemical Exploration, 2022, 46(4): 946-954.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2022.2552      或      https://www.wutanyuhuatan.com/CN/Y2022/V46/I4/946
编号 左边界
/km
右边界
/km
前边界
/km
后边界
/km
上边界
/km
下边界
/km
剩余密度
/(g·cm-3)
备注
1 30 35 5 10 2.5 7.5 0.30 浅部
2 25 30 15 20 2.5 7.5 0.30 浅部
3 10 15 20 25 2.5 7.5 0.35 浅部
4 10 30 10 30 20 30 0.30 深部
Table 1  简单理论模型参数
编号 左边界
/km
右边界
/km
前边界
/km
后边界
/km
上边界
/km
下边界
/km
剩余密度
/(g·cm-3)
备注
1 10.2 11.9 68.8 69.5 0.2 1.2 0.15 第1层
2 64.4 65.3 70.8 71.8 0.2 1.2 0.15 第1层
3 16.1 56.0 8.7 9.5 0.2 1.2 0.15 第1层
4 34.1 36.1 69.8 72.5 3.0 5.0 0.40 第2层
5 38.1 40.4 45.8 48.3 3.0 5.0 0.40 第2层
6 67.9 71.2 32.7 61.7 6.5 9.5 0.45 第3层
7 11.9 15.9 27.4 63.7 14.0 18.0 0.60 第4层
Table 2  复杂理论模型参数
Fig.1  简单模型小波5重分解结果
a—理论重力异常;b~f—小波分解1~5阶逼近;g~k—小波分解1~5阶细节
Fig.2  简单模型理论异常与小波分解异常对比
a—理论重力异常;b—理论区域异常;c—理论局部异常;d—小波恢复异常;e—小波区域异常;f—小波局部异常
Fig.3  复杂模型理论异常与小波分解异常对比
a—理论重力异常;b~e—第1~4层模型重力异常;f~i—小波分解1~4阶细节
Fig.4  南沙群岛中北部重力局部异常(左)和区域异常(右)
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