Group Velocity Measurement of Surface Waves by the Wavelet Transform.

Abstract

A new time-series analysis called is applied to measure the group velocity of surface waves as compared with that obtained by the conventional Fourier transform. We use vertical-component Rayleigh waves for both synthetic seismograms and GDSN long-period data of oceanic paths. The results of this study are summarized as follows: for synthetic seismograms, moving-window analysis using the Fourier transform can measure the group velocity of the fundamental mode correctly, while the group velocity of the first-higher mode is systematically larger than the correct value. In contrast, the wavelet transform measures the group velocity of both modes precisely although the resolution in frequency may not be sufficiently high. For GDSN data propagating along the Pacific Ocean, both methods provide stable results for the group velocity of the fundamental mode in the period range of 20 to 100 s. Using the Fourier transform, we obtain the group velocities of the first-higher mode between 20 and 40 s although these values seem unreliable. In contrast, the wavelet transform can measure both modes precisely in the period range of 20 to 100 s for non-shallow events and even for shallow events with relatively small noise in the data. Another advantage of the wavelet analysis is that we can specify resolving power in group velocity measurement rigorously.