Attenuation estimation using high resolution time-frequency transforms

Wave attenuation is often measured using spectral techniques such as the spectral ratio method and the frequency shift method, comparing the spectral content of pairs of waveforms along the ray path. The recent introduction of novel highly-localized time-frequency transforms leads to high-resolution but discontinuous spectra. It prevents the use of these time-frequency transforms with conventional attenuation measurement methods. We show how three highly-localized time-frequency transforms, namely basis pursuit, the synchrosqueezing wavelet transform, and complete ensemble empirical mode decomposition, can still be used to estimate attenuation using the peak frequency method. Assuming a Ricker source wavelet, the decrease in peak frequency of a wave spectrum as it propagates in a given medium is used to estimate attenuation. When applied to a synthetic benchmarking signal corrupted by Gaussian white noise, the three transforms show different degrees of performance and robustness for different signal-to-noise ratios. The developed methodology is suitable for geophysical investigations, but may also find application in other fields such as biomedicine, acoustics and engineering.