Prestack Inversion Method Based On Analytic Solution Of Wave Equation

Aiming at the limitations and deficiencies exist in the conventional prestack inversion,thus obtain higher resolution and accuracy of elastic parameter,improve the ability of reservoir lithology and physical properties characterization as well as to ensure the detection accuracy of reservoir fluid distribution,this paper based on the wave equation the analytical solutions to solve the nonholonomy physical forward modeling and attenuation problem of conventional prestack inversion.Based on this theory,frequency-dependent seismic information is fully used for fluid identification,and direct depth domain inversion is carried out to avoid thin-layer information loss and time-depth conversion error accumulation.Firstly,a generalized prestack inversion method based on the analytic solution of the viscous acoustic equation is proposed to handle the situation where the shear-wave information in the prestack gather is submerged.Based on the recursive formula,the analytical solution of the zero-angle reflection response of the one-dimensional viscous acoustic wave equation is derived.Then,the Frechet derivative matrix is derived for the gradient inversion algorithm by using the chain rule;and the block constraint is introduced to obtain stable impedance results with clear boundary.On this basis,the elastic impedance inversion is used for reference,and the corresponding generalized acoustic impedance is obtained by inversion of partial stack sections.According to the nonlinear relationship between the generalized acoustic impedance and incident angle,velocity and density,stable density and velocity with higher accuracy are extracted.Both model and actual data test show that the method is stable and effective.Further,the compound matrix analytic solution method is extended to viscoelastic medium.After using this method to analyze the effects of the full wave field response and attenuation dispersion effect on seismic records,the sensitivity of the quality factor(Q)curve to the seismic record is analyzed from the forward and inverse aspects.The conclusion shows that the sensitivity of the elastic parameters in the order Vp,Vs,Rho;the sensitivity of the parameter Q value of seismic data is far less than the elastic parameters;and seismic records only sensitive to low-frequency trend of Q value curve.The inversion results of the model and the actual data show that the elastic parameters of the new method are more accurate and higher resolution than the AVO method.Then,the compound matrix method is used to analyze the frequency dependent AVO forward modeling.The analysis shows that the effect of interlayer on the reflection coefficient with frequency is much greater than that of interface,and the effect of interlayer attenuation dispersion must be considered.On this basis,the more perfect and effective nonlinear dispersion estimation method by using the analytical solution of the wave equation of one-dimensional viscoelastic medium as the forward modeling method and using inversion spectral decomposition to obtain the high-resolution time-frequency spectrum.Analysis and tests show that the proposed method is superior to the traditional linear dispersion estimation method in both accuracy and resolution.The new method can be used as a high precision reservoir fluid identification technology.Finally,the unstable state convolution depth domain inversion method is implemented based on the point spread function(PSF)and the analytical of the wave equation.In order to improve the whole inversion process,linear depth domain inversion based on PSF first is proposed.On this basis,the depth domain inversion algorithm based on analytical solution is implemented.Further,the validity of the above algorithms are verified by model data and actual data.This method can effectively avoid the problem of extracting the wavelet in the depth domain,ensure the uniform velocity representation in velocity inversion and time-depth conversion,avoid the resampling and stretching interpolation of inversion parameters and seismic records.In addition,the PSF depth domain inversion will make the numerical accuracy of inversion results higher and effectively avoid the phenomenon of horizon slip.