Modeling of Wave Dispersion Using Continuous Wavelet Transforms II: Wavelet-based Frequency-velocity Analysis

In this paper, we show how to estimate the phase velocities of multi-mode signals as present in 2-D shallow seismic surveys along a seismic line with the help of a method that is based on the deformation of the wavelet spectra of the seismic traces. In analogy with frequency-wavenumber (f–k) analysis, we perform ‘‘frequency-velocity’’ analysis using the correlations between phases of the wavelet spectra. Our method has two tuning parameters — the parameter of an analyzing wavelet and the parameter of a threshold operation. Numerical and experimental examples are presented to illustrate how the method accurately extracts the phase velocity from single- and multi-mode signals.