利用小波变换提取面波群速度

选取了几种常见的小波母函数，分别提取了同一理论下的面波数据的群速度，并与理论群速度进行对比，结果表明Morlet小波提取面波群速度的效果最好.此外，将Morlet小波与常用的多重滤波提取群速度的结果进行了比较，结果表明: ① 多重滤波法非常依赖高斯滤波系数α的取值，α的取值应随面波周期的增大而减小；② 在α取值得当的前提下，在20—35 s周期范围内多重滤波法提取面波群速度的相对误差比Morlet小波小，在周期大于35 s时，两者相对误差相近; ③ 合适的α值的选取需在不同周期段耗费大量时间进行大量试验，这说明多重滤波法不具备自适应性；而采用小波变换分析短周期信号时，时间窗变窄，频率窗变长，当分析长周期信号时，时间窗变长，频率窗变窄，具有对信号的自适应性，这是小波变换相比多重滤波法的最大优点. 

Measurement of surface wave group velocity using wavelet transform

Wavelet transform is proposed to measure surface wave group velocity in this paper. Several common mother wavelets are respectively used to calculate Rayleigh wave group velocities of the same synthetic seismograms, the results are compared with the theoretical group velocities. The comparison results indicate that Morlet wavelet is the most effective one in calculating group velocities. Furthermore, we compare Morlet wavelet transform with the most common used multiple filter technique in calculating group velocity, from which the following conclusions are drawn: ① multiple filter analysis method extremely depends on the value of Gaussain filter parameter α, and smaller value of α should be chosen during long period of surface wave; ② when the value of α is chosen adaptively, multiple filter analysis method is more accurate than Morlet wavelet transform in calculating group velocities when the period of surface wave is between 20 seconds and 35 seconds, while multiple filter analysis method has the similar accuracy with Morlet wavelet transform when the period of surface wave is over 35 seconds; ③ multiple filter analysis method will cost much more time to choose adaptive value of Gaussain filter parameter α for different periods without self-adaptivity to signals; however, wavelet transform can narrow the time window and lengthen the frequency window when analyzing short period signals and lengthen the time window and narrow the frequency window when analyzing long period signals with self-adaptivity to signals, which shows the outstanding advantage of wavelet transform over the multiple filter analysis method.