Dispersion estimation from linear array data in the time-frequency plane

We consider the problem of estimating the dispersion of a wave field from data recorded by a linear array of geophones. The fact that the data we are looking at may contain several propagating waves make this even more challenging. In this paper, a new algorithm is proposed to solve this issue. Currently, there are two methods for estimating wave dispersion described in the literature. The first method estimates the group delay function from the time-frequency representation (TFR) of each sensor separately. It is efficient as long as the patterns of the different waves do not overlap in the time-frequency plane. The second method estimates the dispersion from the two-dimensional (2-D) Fourier transform of the profile (or more generally from a velocity-frequency representation). This assumes that the dispersion is constant along the entire sensor array. It is efficient as long as the patterns of the waves do not overlap in the frequency domain. Our method can be thought of as a hybrid of the above two methods as it is based on the construction of a TFR where the energy of waves that propagate at a selected velocity are amplified. The primary advantage of our algorithm is the use of the velocity variable to separate the patterns of the propagating waves in the time-frequency plane. When applied to both synthetic and real data, this new algorithm gives much improved results when compared with other standard methods.