Generalized S-Transform,TT-Transform And Their Applications Research In Seismic Data Processing

Over a long period, Signal processing is based on stable signal system. The non-stationary signal, such as seismic waves, used these methods to process with great limitations.We have developed a series of time-frequency analysis methods based on the traditional Fourier transform. Such as the short time Fourier transform (STFT), continuous wavelet transform (CWT), their algorithms are simple and without interference of crossover terms. But they are suffered the limit of interferences Heisenberg's uncertainty principle, the time-frequency resolution can not achieve the best. Therefore, there are some limitations when we used the methods above mentioned to process seismic data.In this paper, we analyzed the generalized S transform in detail, and introduced the TT transformation which based on the S transform. These two kinds of methods have their unique advantages in the analysis of signal of time local properties. S transform is a non-stationary signal processing method between short time Fourier transform (STFT) and continuous wavelet transform (CWT), which has many unique advantages compared with the STFT and CWT:S transform inverse transform and Fourier transform is directly linked to ensure that it is the non-destructive transform;linear transform ensure there is no cross-terms; time-frequency resolution and the signal frequency-related; basic wavelet do not have to meet the permit conditions; scale makes the generalized S transform have good aggregation ability for frequency. But because the form basic wavelet function of S transform is fixed, S transform suffered some limits in practical application. In order to overcome these limits, many scholars put forward various forms of generalized S transform through reforming and promoting the S transform. TT transform is a non-destructive transform, and has good ability in gathering frequency, it gathers the high frequency signal in diagonal position of TT spectrum. Namely, the range of high frequency signal is narrower than low frequency signal's near the diagonal of TT spectrum, the amplitude is also more higher. These properties of TT transform are the theoretical basis of its application in seismic data processing.We can apply the generalized S transform in time-frequency filtering between its unique advantages. Using the generalized S transform, time domain signal can be transformed into time-frequency domain. According the distribution of signal and noise in time-frequency spectrum, designing appropriate time-frequency filter, the energy of the noise would be suppressed, and then transforming the signal in time-frequency domain to time domain by using inverse transform of time-frequency analysis methods. Thus, the noise can be separated from the effective signal, which can improve the signal-to-noise ratio.In this paper, we also introduce the application of generalized S transform in stratigraphic absorption-compensation. Through the processing of Stratigraphic absorption-compensation for actual two-dimensional post-stack seismic data, results show that this method can do well on absorption-compensation, improve the resolution of seismic reflection, without the Q value of the Strata.Secondly, we apply S transform in Rayleigh surface wave frequency dispersion analysis, avoiding the limit of phase difference. The processing of experimental data and actual data show that this method is a new idea in Rayleigh wave frequency dispersion analysis.In addition, the generalized S transform also has a very good effect in thin inter-bed analysis.Finally, we try to use TT transform to suppress seismic surface wave. Because the surface wave has lower frequency than other effective wave and TT transform has good frequency conversion ability, it gathers the high frequency signal in diagonal position of TT spectrum. Namely, the range of high frequency signal is narrower than low frequency signal's near the diagonal of TT spectrum. So we can suppress the surface wave through extracting the diagonal elements of TT spectrum. The result of numerical simulation and real seismic data processing reflects the nature of the TT transform and its effect in suppressing surface wave.