An extraction method of dispersion curve from vertical seismic profiling data

The dispersion curve describes the relationship between velocities and frequencies. The group velocity is a kind of dispersion, which presents the velocities of the energy with different frequencies. Although many studies have shown methods for estimating group velocity from a surface wave, the estimation of group velocity from body-wave data is still hard. In this paper, we propose a method to calculate the group velocity from vertical seismic profiling (VSP) data that is a kind of body-wave data. The generalised S-transform (GST) is used to map the seismic signal to the time-frequency (TF) domain and then the group delay (GD) can be extracted from the TF domain. The GD shows the travelling time of different frequency components. The group velocity can be calculated by the GD and the distance between receivers. Unfortunately, the GD is hard to measure accurately because of the noise. Inaccurate GD introduces errors in estimating the velocity. To reduce the errors, we make use of the multiple traces and the iterative least-squares fitting to extract the relationship line between GD and depths. The slope of the line is the reciprocal of the group velocity. Two numerical examples prove the effectiveness of the method. We also derive the formula of group velocity in diffusive-viscous media. In the field data example, the dispersion intensity at different depths and the geological layers can be well matched. These examples illustrate the proposed method is an alternative method for dispersion estimation from VSP.