Research On Numerical Simulation And Full Waveform Inversion For Complex Attenuation Medium

Since the actual earth is a non-perfectly elastic medium,seismic waves are attenuated and dispersed by the medium during propagation,affecting the kinematic and dynamic characteristics of seismic waves,and thus reducing the reliability of seismic imaging and underground parameter inversion.In full waveform inversion and imaging,considering the attenuation effect of strata is conducive to constructing accurate velocity and quality factor(Q)models,obtaining high-resolution imaging results.Although the visco-acoustic wave equation based on decoupled fractional Laplace operators(DFLs)can accurately describe the attenuation properties of underground media,the boundary reflection,amplitude compensation stability,and crosstalk of multi-parameter inversion are still the important issues affecting the development of the method.This paper focuses on the research of complex attenuation media numerical simulation and full waveform inversion based on the DFLs viscoacoustic wave equation.To improve the suppression effect of boundary reflections in the numerical simulation of second-order DFLs viscoacoustic wave equation,this study proposes a hybrid absorbing boundary condition based on transmission boundary that adopts a smooth transition approach to gradually transition from the two-way wave equation to the one-way wave equation,which can suppress the boundary reflections caused by the abruptness of the simulation equation in the one-way wave absorbing boundary condition.Moreover,an adaptive weighted function is used to couple the two-way and the transmission wavefields,enhancing the absorption effect of boundary reflections.Three-dimensional numerical tests show that compared with commonly used absorbing boundary conditions,the proposed method achieves better absorbing effects with fewer layers.The traditional DFLs explicit compensation equation can clearly characterize the amplitude compensation operator and easy to select compensation parameters.Although,it can theoretically effectively compensate for amplitude attenuation effect,this equation contains fractional Laplacian operator that varies with space.It can not effectively deal with heterogeneous attenuation media.This paper uses Taylor expansion approximating the variableorder operator to the Laplace operator that does not change with space,and the equation based on the constant-order compensation operator is proposed to improve the amplitude compensation accuracy in the heterogeneous attenuation medium.Both the three-dimensional theoretical model and two-dimensional field data test prove the effectiveness of the proposed equation in compensated imaging.Full waveform inversion can theoretically reconstruct the high-precision velocity and Q model,and accurate characterization of the seismic wave propagation is the premise of reliable inversion results.Traditional DFLs viscoacoustic wave equations can not properly incorporate and compensating for the attenuation effects,resulting in insufficient gradient illumination in the high attenuation area,which affects the reconstruction accuracy of the velocity model.The proposed fixed-order explicit stable attenuation compensation equation can accurately compensate for the amplitude without altering the phase information during the simulation,effectively improving the gradient illumination in the high attenuation region and improving the velocity inversion result.In multi-parameter inversion,the crosstalk between velocity and Q seriously reduces the reliability of the inversion results.Theoretically,the inverse of Hessian matrix can alleviate the crosstalk between parameters,but directly calculating the inverse of the Hessian matrix has huge computational costs.In this study,the truncated Newton method is used to iteratively solve the Newton equation to obtain the decoupled descent direction at a lower computational cost,effectively alleviating the coupling between parameters.Moreover,a pseudo-Hessian preconditioner is introduced to further improve the convergence.Numerical examples demonstrate that the proposed method can effectively suppress the coupling between velocity and Q and improve the accuracy of the two-parameter inversion.