Jiajun Han

Spectral estimation—What is new? What is next?

Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.

Spectral Decomposition by Synchrosqueezing Transform

The synchrosqueezing transform (SST) is a wavelet-based time-frequency reassignment method, which has a grounded mathematical foundation. It produces a well defined time-frequency representation allowing the identification of instantaneous frequencies to highlight individual components. The field data examples demonstrate the high time-frequency resolution feature of SST, therefore render this technique is promising for seismic processing and interpretation.