Comment on Group Velocity Measurement of Surfac Waves by Wavelet Transform

Abstract

ABSTRACT1 Department of Geophysics, Graduate School of Science, Kyoto University, Sakyo, Kyoto, Japan * Corresponding author address: Prof. Taishi Okamoto, Department of Geophysics, Graduate School of Science, Kyoto University, Sakyo, Kyoto, Japan; E-mail: dollar@kugi.kyoto-u.ac.jp doi: 10.3319/ TAO.2007.18.4.681(T) Yamada and Yomogida (1997) applied the discrete wavelet transform (DWT) to group velocity measurements for the first time. Although their study is one of the pioneering works in application of DWT to seismological analysis, their method gives an inaccurate value as a group velocity in some cases and requires modification. In this report, we point out the problem and propose a modified DWT method for overcoming the problem. In our method, DWT is carried out not for an analysed signal itself but for its complex envelope (Farnbach 1975). A computation algorithm for DWT coefficients for our method is given and shown to be almost the same as that by Yamada and Ohkitani (1991). The influence of the difference between the conventional method and our method on identification of group arrival times of a wave is also shown by a numerical experiment. If analysts want to identify group arrival times using DWT, our method must be adopted instead of the conventional method.