CWT-Based Method for Extracting Seismic Velocity Dispersion

Time–frequency (T–F) analysis has powerful applications in various fields such as geoscience and engineering. Seismograms are distorted by dispersion and attenuation in such a way that they alter their amplitude and phase spectra. Velocity dispersion is usually neglected in the conventional seismic data processing. However, it has a severe effect on seismic data processing if dispersion is intense in high-attenuation media. Most of the studies on dispersion are theoretical models and laboratory measurements, whereas velocity dispersion analysis directly from field data is rare. In this letter, a method is proposed to estimate the dispersion of vertical seismic profile (VSP) data based on continuous wavelet transform (CWT) in time–frequency domain. The Morlet wavelet, three-parameter wavelet (TPW), and Cauchy wavelet are chosen and compared as mother wavelets in CWT to determine the variations of velocity with frequency. Then, the detailed process of extracting velocity dispersion of propagating waves in a dissipative medium is proposed by using their T–F spectra. Finally, the synthetic and field VSP data are used to demonstrate the validity of the proposed method. The results indicate that the velocity dispersion in synthetic data estimated by TPW and Cauchy wavelet generally match well with the theoretical values while it is not the case for the Morlet wavelet. The velocity dispersion of field data is weak and the estimated velocity basically matches well with the logging data.