Seismic data analysis using local time-frequency decomposition

Example of Time-frequency Characterization

A simple 1-D example is shown in Figure 2. The input signal includes two crossing chirp signals and displays nonstationary characteristics (Figure 2a). We applied the LTF decomposition to obtain a time-frequency distribution. Figure 3a shows that the proposed method recovers the linear frequency trend with high resolution in both time and frequency. In comparison, the S transform has high resolution near low frequencies but loses resolution at high frequencies (Figure 2b). Figure 3b displays the LTF decomposition using a different smoothing parameter (14 points) to demonstrate adjustable time-frequency characteristics of the LTF decomposition.

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Figure 2. Synthetic signal with two crossing chirps (a) and time-frequency spectra from S transform (b).

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Figure 3. Time-frequency spectra from LTF decomposition with different sizes of the smoothing radius. Smoothing radius of 7 points (a) and smoothing radius of 14 points (b).

Seismic data analysis using local time-frequency decomposition