Summary
Instantaneous frequency (IF) extracted by the Hilbert transform (HT) and continuous wavelet transform (CWT) is sensitive to noise and also suffers from meaningless values. We propose a robust method to extract instantaneous frequency from seismic data based on timefrequency analysis, which is called the synchrosqueezing three parameter wavelet transform (SSTPWT) using the three parameter wavelet (TPW). Compared with conventional instantaneous frequency extraction methods, the proposed method is proved to yield higher precision and better anti-noise performance. Experimental results on synthetic signals and real seismic data demonstrate the effectiveness of our method.
Introduction
Instantaneous attributes extracted from seismic data, especially the instantaneous frequency (IF), are generally used in seismic stratigraphic interpretation. For instance, seismic attributes always highlight some characteristics of seismic data and are very useful to assist interpreters to find structural anomalies and other geological phenomenon (Barnes, 1993; Chopra and Marfurt, 2005). Although IF has been introduced in seismic exploration for decades, improving the estimation precision and extending its applications are still active areas of research (Yang and Gao, 2010, Wang and Gao, 2013).
The most common method to estimate instantaneous frequency is based on Hilbert transform presented by Taner et al. (1979). The analytic signal counterpart corresponding to the real-valued signal is found via the HT (Gabor, 1946). However this method is sensitive to noise, thus it brings difficulty for seismic attributes analysis, especially in a noisy environment. Gao et al. (1999) proved that the signal reconstruction after the continuous wavelet transform represents the corresponding analytic signal of the input real-valued signal in L2 (R) . Based this, a wavelet-based method of computing IF is introduced and gets some positive results.
In this paper, we present the synchrosqueezing three parameter wavelet transform to calculate the instantaneous frequency of the real signal. In the procedure, we combine the synchrosqueezing wavelet transform (Daubechies et al., 2011) and the three parameter wavelet (Gao et al., 2006) which substantially outperforms the popular morlet wavelet.
