重力异常小波多分辨分析分解阶次的确定

刁博; 王家林; 程顺有

重力异常小波多分辨分析分解阶次的确定

1.
同济大学海洋地质教育部重点实验室, 上海 200092
2.
西北大学大陆动力学教育部重点实验室, 陕西西安 710069

详细信息

作者简介:
刁博(1978-), 男, 博士研究生, 主要从事综合地球物理研究.E-mail: shendiao97@163.com

中图分类号: P631.1
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出版历程
- 收稿日期: 2006-12-31
- 刊出日期: 2007-07-25

The Confirmation of Decomposition Level in Wavelet Multi-Resolution Analysis for Gravity Anomalies

1.
Key Laboratory of Marine Geology of the Minsitry of Education, Tongji University, Shanghai 200092, China
2.
Key Laboratory of Continental Dynamics of the Minsitry of Education, North west University, Xi′an 710069, China

摘要

摘要: 分解阶次的确定是重力异常小波多分辨分析中的基本问题之一.以塔里木及天山地区布格重力异常数据为例, 通过讨论信号长度、小波母函数的支撑长度与分解阶次的关系, 以及对比分解结果与大地水准面异常的特征, 提出了分解阶次的确定方法.发现对于该重力异常数据, 使用bior3.5小波, 5阶小波分解细节可以避免小波母函数特征过多的干扰, 其结果与相应大地水准面异常特征比较吻合, 而6阶小波分解细节结果却与相应大地水准面异常特征存在较大差异.从信号处理和重力异常的地球物理意义两方面表明, 恰当的小波分解阶次为5阶, 更高阶次的分解结果并不合理.所使用的方法对重力异常小波分解阶次的确定是有效和易行的, 为小波分析在重力场数据处理中的应用, 进行了新的有益探索.
- 小波多分辨分析 /
- 小波分解阶次 /
- 大地水准面异常 /
- 塔里木盆地
Abstract: How to confirm the decomposition level is a basic issue in wavelet multi-resolution analysis for gravity anomalies. In this paper, the relations between the decomposition level and the length of signal, and the relations between the decomposition level and the support width of mother wavelets are discussed. Based on the comparison between the result of wavelet multi-resolution analysis for Bouger gravity anomalies in Tarim basin and Tianshan orogenic belt and the fearures of corresponding geoid anomaly, the authors proposed a method for confirming the decomposition level. Using bior3.5 wavelet, the 5th level detail can avoid the interference of wavelet generating functions and thereby its result accords with the features of corresponding geoid anomaly. However, there are many differences between the 6th and its corresponding geoid anomaly. Therefore, in terms of signal processing and geophysics theory, the proper decomposition level is 5, and any higher-level decomposition is unreasonable. All these researches have contributed a lot to confirming the decomposition level in processing gravity anomalies by providing effective and feasible methods.
- wavelet multi-resolution analysis /
- wavelet decomposition level /
- geoid anomaly /
- Tarim basin

HTML全文

图 1 塔里木盆地及天山东部布格重力异常小波多分辨分析5、6阶细节(单位: 10^-5m/s²) 和192~360、85~192阶大地水准面异常(单位: m)

a.5阶小波细节; b.6阶小波细节; c.192~360阶大地水准面异常; d.85~192阶大地水准面异常

Fig. 1. 5th and 6th level detail of wavelet multi-resolution analysis for Bouger gravity anomalies and geoid anomaly of 192-360 and 85-192 degree in eastern Tarim and Tianshan orogenic belt

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参考文献(19)

Bowin, C., 1986. Depth estimates fromratios of gravity, geoid, and gradient anomalies. Geophysics, 51 (1): 123-136. doi: 10.1190/1.1442025
Cheng, Z. X., 1998. Algorithms and applications of the Wavelet analysis. Xi′an Jiaotong University Press, Xi′an (in Chinese).
Grossman, A., Morlet, J., 1984. Decomposition of Hardy function into square integrable wavelets of constant shape. J. Math. Anal. , 15: 723-736.
Li, J., Zhou, Y. X., Xu, H. P., et al., 2001. The selection of wavelet generating functions in data-processing of gravity field. Geophysical & Geochemical Exploration, 25 (6): 410-417 (in Chinese with English abstract).
Liu, T. Y., Wu, Z. C., Zhan, Y. L., et al., 2007. Wavelet multi-scale decomposition of magnetic anomaly and its application in searching for deep-buried minerals in crisis mines: A case study from Daye iron mines. Earth Science—Journal of China University of Geosciences, 32 (1): 135-140.
Lou, H., Wang, C. Y., 2005. Wavelet analysis and interpre-tation of gravity data in Sichuan-Yunnan region, China. Acta Seismologica Sinica, 27 (5): 515-523 (in Chinese with English abstract).
Luděk, V., Catherine, A., Hier, M., et al., 2003. Multiresolution tectonic features over the Earth inferred from a wavelet transformed geoid. Visual Geosciences, 8: 26-44.
Mallat, S., 1989. A theory for multi-resolution signal decomposition: The wavelet representation. IEEE Trapson PAMI, 11 (7): 674-693. doi: 10.1109/34.192463
Mallat, S., 2002. A Wavelet tour of signal processing (Second edition). Translated by Yang, L. H., Dai, D. Q., Huang, W. L., et al. . China Machine Press, Beijing (in Chinese).
Michel, M., Yves, M., Georges, O., et al., 2004. Wavelet toolbox user's guide (Version 3). The Mathworks Inc., Massachusetts.
Yang, W. C., Shi, Z. Q., Hou, Z. Z., et al., 2001. Discrete wavelet transform for multiple decomposition of gravity anomalies. Chinese J. Geophys. , 44 (4): 534-541 (in Chinese with English abstract).
Yin, X. H., Li, Y. S., Liu, Z. P., 1998. Gravity field and crust-upper mantle structure over the Tarim basin. Seismology and Geology, 20 (4): 370-378 (in Chinese with English abstract).
程正兴, 1998. 小波分析算法与应用. 西安: 西安交通大学出版社.
李健, 周云轩, 许惠平, 等, 2001. 重力场数据处理中小波母函数的选择. 物探与化探, 25 (6): 410-417. https://www.cnki.com.cn/Article/CJFDTOTAL-WTYH200106002.htm
刘天佑, 吴招才, 詹应林, 等, 2007. 磁异常小波多尺度分解及危机矿山的深部找矿: 以大冶铁矿为例. 地球科学——中国地质大学学报, 32 (1): 135-140. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX200701020.htm
楼海, 王椿镛, 2005. 川滇地区重力异常的小波分解与解释. 地震学报, 27 (5): 515-523. https://www.cnki.com.cn/Article/CJFDTOTAL-DZXB200505005.htm
Mallat, S., 2002. 信号处理的小波导引(第2版). 杨力华, 戴道清, 黄文良, 等, 译. 北京: 机械工业出版社.
杨文采, 施志群, 侯遵泽, 等, 2001. 离散小波变换与重力异常多重分解. 地球物理学报, 44 (4): 534-541. https://www.cnki.com.cn/Article/CJFDTOTAL-DQWX200104011.htm
殷秀华, 黎益仕, 刘占坡, 1998. 塔里木盆地重力场与地壳上地幔结构. 地震地质, 20 (4): 370-378. https://www.cnki.com.cn/Article/CJFDTOTAL-DZDZ804.010.htm