A New Instantaneous Frequency Measure Based on The Stockwell Transform

We propose the use of a new transform, the Stockwell transform[1], as a means of creating time-frequency maps and applying them to distinguish blasts from earthquakes. This new transform, the Stockwell transform can be considered as a variant of the continuous wavelet transform, that preserves the absolute phase.The Stockwell transform employs a complex Morlet mother wavelet. The novelty of this transform lies in its resolution properties. High frequencies in the candidate signal are well-resolved in time but poorly resolved in frequency, while the converse is true for low frequency signal components. The goal of this research is to obtain the instantaneous frequency as a function of time for both the earthquakes and the blasts. Two methods will be compared. In the first method, we will compute the analytic signal, the envelope and the instantaneous phase as a function of time[2]. The instantaneous phase derivative will yield the instantaneous angular frequency. The second method will be based on time-frequency analysis using the Stockwell transform. The Stockwell transform will be computed in non-redundant fashion using a dyadic representation[3]. For each time-point, the frequency centroid will be computed -- a representation for the most likely frequency at that time. A detailed comparison will be presented for both approaches to the computation of the instantaneous frequency. An advantage of the Stockwell approach is that no differentiation is applied. The Hilbert transform method can be less sensitive to edge effects. The goal of this research is to see if the new Stockwell-based method could be used as a discriminant between earthquakes and blasts. References [1] Stockwell, R.G., Mansinha, L. and Lowe, R.P. "Localization of the complex spectrum: the S transform", IEEE Trans. Signal Processing, vol.44, no.4, pp.998-1001, (1996). [2]Taner, M.T., Koehler, F. "Complex seismic trace analysis", Geophysics, vol. 44, Issue 6, pp. 1041-1063 (1979). [3] Brown, R.A., Lauzon, M.L. and Frayne, R. "General Description of Linear Time-Frequency Transforms and Formulation of a Fast, Invertible Transform That Samples the Continuous S-Transform Spectrum Nonredundantly", IEEE Transactions on Signal Processing, 1:281-90 (2010).