地球物理学进展 ›› 2019, Vol. 34 ›› Issue (6): 2247-2255.doi: 10.6038/pg2019CC0404

• 应用地球物理学Ⅰ(油气及金属矿产地球物理勘探) • 上一篇    下一篇

Morlet小波匹配追踪方法的时频原子参数分析

成谷1, 2, 3, 张宝金4   

  1. 1. 中山大学地球科学与工程学院, 珠海 519082;
    2. 广东省地质过程与矿产资源探查重点实验室, 广州 510275;
    3. 南方海洋科学与工程广东省实验室, 珠海 519082;
    4. 广州海洋地质调查局, 广州 510275
  • 收稿日期:2019-01-26 修回日期:2019-08-18 出版日期:2019-12-20 发布日期:2019-12-29
  • 作者简介:成谷,女,1975生,博士,副教授,主要从事信号分析、地震数据处理方法研究.(E-mail:chenggu@mail.sysu.edu.cn)
  • 基金资助:
    广东省自然科学基金(2016A030313311)项目资助.

Analysis on parameters of time-frequency atoms in matching pursuit based on Morlet wavelet

CHENG Gu1, 2, 3, ZHANG Bao-jin4   

  1. 1. School of Earth Sciences and Engineering, Sun Yat-Sen University, Zhuhai 519082, China;
    2. Guangdong Key Laboratory of Geological Process and Mineral Resources Exploration, Guangzhou 510275, China;
    3. Southern Marine Science and Engineering Guangdong Laboratory, Zhuhai 519082, China;
    4. Guangzhou Marine Geological Survey, Guangzhou 510275, China
  • Received:2019-01-26 Revised:2019-08-18 Online:2019-12-20 Published:2019-12-29

摘要: 匹配追踪方法是目前时频分辨率最高的时频分析方法.但传统的匹配追踪方法在寻找与信号匹配最佳的时频原子时,需在较大的参数搜索范围内对时频原子参数进行多重循环寻优迭代,计算效率较低.针对匹配追踪算法实现方式,本文主要工作及结论如下:(1)以Morlet小波为时频原子,以频率、相位、时延和尺度为时频原子参数,分析了信号在时频原子上的投影振幅对这四项时频原子参数的灵敏度,结果表明灵敏度顺序为:时延、频率、尺度和相位,据此结论可在算法实现时根据灵敏度顺序调整不同参数寻优迭代时的参数搜索范围,改善算法的计算效率;(2)针对频率、相位和时延参数已知尺度参数变化的时频原子,分析了利用Hilbert变换得到的瞬时参数表征时频原子参数初值的准确度,结果表明准确度顺序为:时延、频率和相位.据此结论可在算法实现时确定参数寻优的优先级顺序,改善算法的计算效率.与连续小波变换、广义S变换等时频分析方法的对比及在地震数据去噪中的应用效果表明匹配追踪方法效果较好.

关键词: 时频分析, 匹配追踪, Morlet小波

Abstract: Matching pursuit is the time-frequency analysis method with best time-frequency resolution. But the traditional matching pursuit method has lower computational efficiency compared with the other time-frequency analysis methods, because it need optimization iteration of time-frequency atoms parameters within the large neighborhood scope to find the best time-frequency atom matching the local features of signal. In this paper, the main work and conclusions are as follows:(1)Aiming at the matching pursuit method based on Morlet wavelet, taking frequency, phase, time delay and scale as parameters, the sensitivity of signal projection amplitude on time-frequency atoms are analyzed, the results indicate that the projection amplitude has highest sensitivity on the time delay parameter, in turn is the frequency and scale, and no sensitivity on the phase parameter, this conclusion can be used to adjust the neighborhood scope of parameters in time-frequency atoms when making the optimization iteration in matching pursuit algorithm;(2)The fitness between the instantaneous parameters obtained by Hilbert transformation and the parameters of time-frequency atoms is compared, aiming at time-frequency atoms with different scale parameters, the results indicate that the time delay parameter obtained by Hilbert transform and given by known time-frequency atom has best fitness, in turn is the frequency parameter and phase parameter, this conclusion can be used to determine the order of optimization iteration of time-frequency atoms parameters.Comparison with other time-frequency analysis methods and application in noise attenuation of seismic data denotes that Matching pursuit method is effective.

Key words: Time-frequency analysis, Matching pursuit, Morlet wavelet

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