Frequency-dependent AVO Analysis Using Generalized S Transforms

AVO(Amplitude versus offset) analysis is a seismic technique to understand lithological properties and detect the hydrocarbon through the variety of the seismic amplitude with the offset. The theoretical basis of conventional AVO technique is the Zoeppritz equation established on the assumption of elastic media. But frequency-dependent behavior of seismic waves through reservoirs has been found in more and more researches. This paper is aimed at improving the ability of AVO technique to detect gas reservoirs by taking frequency dependency into account and combining spectra decomposition and AVO techniques.Firstly, various approximations of Zoeppritz equations with different emphases are stated and analyzed in this paper. Several theories on the dynamic mechanism of seismic waves in double-phases medium are presented, such as Gassmann equation, Biot theory and BISQ model. The influence of parameters in Chapman model on P-wave velocity and the frequency-dependent reflection coefficient of three common AVO model has been discussed. To establish the theoretical foundation of frequency-dependent AVO, frequency is taken into account in Zoeppritz equations.Furthermore, In the respect of modern spectral decomposition technique, several basic mothods are introduced. Specially a wavelet with adjustable parameters is used in S-transform, the discrete formula for numerical calculation of General S-transform is given. For the purpose of confirming its flexibility in time-frequency analysis, the result of General S-transform on a synthetic trace is compared with those of short time Fourier transform(STFT), Morlet wavelet transform, S-transform and WVD. And then General S-transform is used for extracting single-frequency section from real seismic data for fluid prediction. Last but not least, AVO inversion formulas in the frequency domain are given, then applied on Class Ⅰ,Ⅲ AVO model and real seismic data based on the combination of General S transform spectral decomposition and frequency-dependent AVO, and then the frequency-dependent attributes and dispersion attribute are obtained. The result shows that a strong attenuation and velocity dispersion is caused by the hydrocarbons in the porous media, which provides an indicator to predict reservoirs.