重力异常小波多分辨分析分解阶次的确定

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. 

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

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.