Pre-stack Seismic Inversion Based On Nonstationary Convolution Model

In practice,when the seismic waves propagate in the underground medium,their statistical laws,amplitudes,frequencies and phases vary with time.We call them nonstationary features.Usually,most of the inversion methods we used are based on steady state processing,assuming that the seismic wavelet is invariable,and losing the important reflection coefficient information without considering the time-varying characteristics of the signal.Margrave and others combine the nonstationary effect with the convolution model and use the Gabor transform to propose a nonstationary convolution model and its deconvolution method.This makes it possible to consider nonstationary properties.The hyperbolic smoothing algorithm is a simple algorithm for smoothing the seismic data in the time-frequency domain and estimating the amplitude.It uses the exponential decay form of the decay function,based on the hyperbolic stripe division,and is solved by statistical sampling points.The traditional hyperbolic smoothing algorithm has the problem of undersampling in shallow low-frequency regions where seismic energy is concentrated,making the estimation result less accurate.In this paper,the improved hyperbolic smoothing algorithms are used.One is exponential hyperbolic smoothing method.The other is variable step sampling hyperbolic smoothing algorithm.The improved algorithms are used to estimate the seismic records smoothly and obtain more ideal processing results.The improved hyperbolic algorithms can not only obtain a more accurate attenuation function,but also improve the processing efficiency.In this paper,we combine the nonstationary convolution model and prestack inversion,considering the wavelet attenuation and compensating the attenuation.The attenuation function obtained by the hyperbolic smoothing algorithm is used to compensate the seismic data,and then the compensated seismic data is used for inversion.AVO three-parameter inversion method based on Bayesian theory uses Zoeppritz equation and various approximate formulas to construct the convolution model.Regularization inversion process is obtained by adding prior information of model parameters.Cauchy probability distribution can produce a sparse solution,protect weak reflection information,and have high resolution,so it is very suitable as a prior probability distribution.Performing attenuation compensation can improve the effect of inversion and improve the accuracy and stability of the inversion.After inverting the P-wave velocity,S-wave velocity,and density of the formation,we can calculate the physical parameters to analyze the reservoir.In this paper,based on the nonstationary convolution model,the frequency domain inversion solution is studied and the obtained attenuation function is directly added into the inversion.Using the Fatti approximation as a forward physical model,the ternary Cauchy distribution as a priori information,the Gaussian distribution as a likelihood function,combining the smooth impedance model constraints to construct an inversion objective function.Finally,we use the iterative weighted least squares algorithm to solve the inversion.The frequency domain inversion method which considering the attenuation effect can get more abundant reflection information,highlight the weak and small reflection information,broaden the seismic frequency band and improve the resolution.