小波多尺度分解特征分析

介绍了小波多尺度分析的数学原理，以三峡13期流动重力资料为例进行了小波分解。讨论了网格距对三峡流动重力资料分解结果的影响，提出了一种计算平均点距的方法；讨论了小波阶数与重力变化波长的关系．根据网格距及小波理论计算了各阶小波及逼近对应的波长范围。讨论了重力变化区移动与数据延拓、网格加密、网形完整性以及小波计算起始点之间的关系。结果表明．如重力网形不完整，分解结果中重力变化区随小波阶增加的移动没有规律．如果网形完整．分解结果普遍存在随小波阶增加而有规律移动的负重力变化区。重力变化区移动与小波分解起始点密切相关。

ANALYSIS OF CHARACTERISTICS OF WAVELET MULTI-SCALE DECOMPOSITION

The mathematic principle of wavelet multi-scale analysis is introduced. The 13 terms of gravity data, which are observed in the Three Gorges region, are decomposed by wavelet method. The effect of average station distance on the decomposition results is discussed and a method for calculating the average station distance is put forward. The relation between the wavelet order and the gravity change wavelength is discussed and according to the gridding interval and wavelet theory the wavelength range corresponding to the different wavelet order and approximation is calculated. The relations between the shift of gravity change area and data continuation, the relations between the shift of the gravity change area and the gridding interval, the relation between the shift of the gravity change area and integrality of observation networks and the relation between the shift of the gravity change area and the start calculating point are discussed. The result shows that if the observation network is incomplete, the gravity change area irregularly shifts with the increase of wavelet and if the observation network is complete, there exist a negative gravity change area that regularly shifts with the increase of the wavelet order. The gravity change area shift closely correlates with the start calculating point of wavelet.