Argun H. Kocaoglu and Leland T. Long

Abstract

Time-frequency analysis techniques, including the classical use of zero crossings to measure period, have been widely used in seismology for the estimation of surface wave group velocities. Group velocity estimation by the short-time Fourier transform and the multiple filter techniques are equivalent. Although these techniques are used most often, their resolution is limited. The resolution is controlled by the window length in the short time Fourier transform and the filter band width in the multiple filter technique. The moving-window autoregressive spectral estimation provides the highest resolution with the shortest possible window length by predicting the properties of the signal outside the analysis window; however, high resolution is obtained at the expense of uncertainty in the amplitude. Recently, the Wigner distribution has been introduced as a tool for mapping dispersed surface waves into the time-frequency domain. Resolution of the Wigner distribution is comparable to that of the moving-window autoregressive spectral estimation. When the spectral density at a given time contains two or more dominant frequencies, their interference causes the Wigner distribution to introduce spurious spectral peaks complicating the interpretation. The Choi-Williams distribution, in which these interference effects are minimized, can be used for such dispersed signals. However, the implementation is computationally complex and the distribution offers only a medium resolution.