Viscoelastic Seismic Attenuation Compensation And Inversion Method Based On Sparse Regularization

Viscoelasticity is general for subsurface media.In seismic exploration,anelastic attenuation is the primary reason of decreasing the seismic resolution.Media viscoelasticity is not considered in traditional seismic inversion,therefore the inversion resolution and accuracy are decreased.Meanwhile,the subsurface attenuation information contained in seismic signal is wasted.Starting from the viscoelastic wave theories,this thesis deduces the forward equations of attenuation compensation and seismic inversion.The corresponding sparse regularized objective functions are established by transforming seismic data and elastic parameters to sparse domains,then these objective functions are solved via convex algorithms in order to obtain the compensated signal,elastic parameters and attenuation model?Q-value?.So,a set of viscoelastic attenuation compensation and seismic inversion method is developed based on sparse regularization.Incomplete amplitude compensation operator?IACO?is adopted to suppress the amplification of high frequency noise in traditional inverse Q filtering?IQF?.However,to a certain extent,IACO can also suppress the signal compensation in effective frequency band.In this thesis,according to the exploding reflector imaging principle,the forward equation of simulating attenuated signal through the stationary one is deduced by changing the sign of amplitude and phase operators in viscoelastic wave continuation formula.Then,IQF is expressed by a time domain inverse problem and the use of IACO is avoided.Given the sparsity of seismic data in wavelet and curvelet domains,this inverse problem is regularized by wavelet,curvelet and double transform sparse constraints.The bijection relationship between equivalent Q-value?Q_e?and centroid frequency is proved using Schwarz inequality.A Newton iterative Q_eestimation method is proposed,by which reasonable Q_e model can be provided for attenuation compensation.Poststack viscoelastic inversion method is proposed to jointly estimate acoustic impedance?AI?,Q_e and source wavelet?SW?,where nonstationary convolution model?NCM?that is obtained by time-varying wavelet integration formula is adopted as the forward model.This nonlinear inverse problem is separated into two sparse regularized and one Tikhonov regularized inverse subproblems according to the sparsity of AI in ITV domain,the sparsity of SW in wavelet domain and the Gabor domain NCM factorization.AI,Q_e and SW are inverted through one-time stepwise inversion in multi-borehole areas,whereas these three parameters are inverted through repeatedly alternative optimization in sparse-borehole areas.The Q_e value formulas of nonzero offset and incident angle are deduced based on the seismic ray path,by which time-varying wavelet of different offset and incident angle can be calculated by NCM.Then,viscoelastic AVO forward equation is obtained by convoluting the time-varying wavelet of different offset and incident angle with reflectivity determined by Aki-Richards equation.Under the framework of Bayes inversion,the noise is assumed to satisfy Cauchy distribution.Through assuming the decorrelated reflectivity of Vp,Vs and?satisfy Cauchy distribution,Cauchy constrained viscoelastic AVO inversion is realized.Alternatively,by dividing the reflectivity of same time into same group and assuming the l₂ norm of each group satisfies exponential distribution,group sparse regularized viscoelastic AVO inversion is realized.