Time-Frequency Analysis Technology And Its Application

In this paper, the author introduces the basic idea and the mainly mathematics tool on the non-stationary signal and time-frequency analysis method. The author also analysis the relationship of each linear time-frequency analysis method and compare their advantage and disadvantage. Using the linear time-frequency theorem such as the short-time Fourier transform, wavelet transform and S-transform (include generalized S-transform) computes time-frequency parameter, time-frequency analysis of the seismic data, Seismic instantaneous frequency attributes extraction and instantaneous quality factor Q.The definition, derivation and characteristic of S-transform are mainly expatiated, S-transform combines the short-time Fourier transform and the continuous wavelet transform of time-frequency analysis methods advantage overcoming their disadvantage: S-transform has a direct relation with Fourier transform, the characteristics such as lossless invertibility; S-transform is a kind of linear time-frequency representation as short-time Fourier transform and wavelet transform, so it has not cross-term; S-transform has multi-resolution overcoming the problem s of fixed resolving of short-time Fourier transform; S-transform contains phase factor which wavelet transform has not. In order to understand the characters of S-transform, S-transform, short-time Fourier transform and continuous wavelet transform are compared and analyzed. The window function of generalized S-transform was analyzed in detail, improved and simplified. It has higher practicability and adaptability in actual application.Based on above theories, time-frequency analysis method is applied to some processing and interpretation of seismic prospecting. The main application contains processing the seismic with frequency division, obtaining Seismic instantaneous frequency attributes and instantaneous quality factor Q of seismic signals.On processing the seismic with time-frequency analysis technology, the method can get partial characteristics of time and frequency, the instantaneous seismic attributes section and the instantaneous quality factor Q. More the benefit is at the interpretation of seismic prospecting. Through processing the real seismic record, it proved that the effects of the time-frequency analysis method is implemented, which show the validity.