Hilbert-Huang Transform
Speaker: Hong-Jia Chen
Abstract
Even though the tidal effect on triggering earthquakes has been investigated for a long time since 1930s, it is still debatable whether the Earth tide is one of the triggering mechanisms. The tidal triggering effect is that if tide could induce earthquakes, higher seismicity appears at some specific time more frequently. Studying seismicity by time domain analysis or frequency domain analysis might find out some clues of tidal triggering effect. Someone used Fourier analysis to investigate the tidal triggering effect, but did not found significant results. The reason might be that Fourier analysis can not deal with complex data sets or nonlinear and non-stationary data. We then apply a novel method called Hilbert-Huang Transform (HHT) proposed by Huang et al. [1998] on this analysis. HHT consists of two steps: Hilbert Transform and Empirical Mode Decomposition (EMD). In this report, we focus on the development of the method. The contents of the report include comparison between Fourier transform and Hilbert transform through a known periodic nonlinear functions and illustration of EMD process. Finally, we introduce some application of HHT and summarize the differences among FFT, Wavelet Transform, and HHT.
Reference
Huang, N.-E., Z. Shen, S.-R. Long, M.-C. Wu, E.-H. Shih, Q. Zheng, N.-C. Yen, C.-C. Tung, and H.-H. Liu, The empirical mode decomposition method and the Hilbert spectrum for non-stationary time series analysis, Proc. R. Soc. Lond. A, 454, 903-995, 1998.
Huang, N. E., M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen, K. L. Fan, A confidence limit for the empirical mode decomposition and Hilbert spectral analysis, Proc. R. Soc. Lond. A, 459, 2317-2345, 2003.
Kizhner, S., T.P. Flatley, N.-E. Huang, K. Blank, E. Conwell, and E. Smith, On the Hilbert-Huang Transform data processing system development, Proc. IEEE Aerospace Conf., 1961-1979, 2004.