Research On Finite-Difference Modeling And Inversion Methods Based On Acoustic And Elastic Wave Equations

Owing to making full use of dynamic and kinematic information,full waveform inversion(FWI)can provide accurate subsurface model parameters.Meanwhile,it suffers from serious problems of local minima,strong dependence on the initial model and huge computational amount.Besides,numerical modeling is involved in forward propagation of source wavefields and backward propagation of data residuals.Therefore,the accuracy and the efficiency of FWI are dependent on numerical solutions to some extent.Our work is focused on solving wave euqations accurately and efficiently,accelerating convergence rate and improving inversion accuracy.This dissertation includes four parts: numerical modeling,absorbing boundary condition(ABC),FWI and least-squares(LS)reverse time migration(RTM).The main achievements are as follows:Firstly,an optimal time-space domain staggered-grid(SG)finite-difference(FD)method is proposed.Three steps are included: establish objective function based on the time-space domain dispersion relations,transform the nonlinear and multi-extreme value optimization into a convex one by variable substitution;and then employ LS to compute FD coefficients.The proposed method is validated in numerical modeling of the variable density acoustic and the elastic wave equations.Numerical examples suggest that the optimal time-space domain SGFD method has smaller dispersion and stricter stability condition than the conventional,the time-space domain and the LS-based methods.Secondly,the hybrid ABC is extended into frequency-domain modeling,and a hybrid ABC method based on the first-order elastic wave equations is presented.Numerical examples reveal that the frequency-domain hybrid ABC and the hybrid ABC based on the first-order elastic wave equations are effective in absorbing artificial boundary reflections.Furthermore,hybrid ABC spends smaller computational time and has better absorption effect.Thirdly,a multi-scale FWI method based on the second generation wavelet transform is introduced.The transformation of source,data and model parameters between adjacent scales is conducted by the second wavelet transform and its inverse transform.Inversion results of acoustic,visco-acoustic and elastic synthetic examples demonstrate that the multi-scale method possesses better inversion accuracy and faster convergence rate than the single-scale method.Also,compared to the filtering-based multi-scale method,the FWI method based on the second generation wavelet provides more reasonable inversion results.Fourthly,acoustic,visco-acoustic and elastic FWI based on the adaptive operator length scheme are implemented.Numerical modeling is involved in forward propagation of source wavefields,backward propagation of data residuals,and reconstructions of source wavefields.Assigning different operator lengths for different model parameters(velocity and quality factor)can reduce computational time.Synthetic examples show that the the adaptive operator length scheme can improve the computational efficiency of FWI greatly.Fifthly,a wavefield-separation-based elastic FWI method is formulated.The dissertation derives the gradients expressed by different wave modes,analyzes the crosstalk between various parameters,and evaluates the sensitivity of separated P-wave,separated S-wave and P and S-wave misfit functions.Then,a practical hierachical inversion workflow is developed.Numerical examples reveal that our elastic FWI method based on wavefield separation can enhance the accuracy of P-and S-wave velocities.Finally,a new elastic LSRTM method is developed.Born approximation is used to formulate the de-migration operator in elastic media,and Lagrange multiplier method is utilized to derive adjoint equations and gradients with respect to reflectivity.On this basis,a proper inversion step is designed to update the reflectivity.Synthetic examples demonstrate that the proposed method can effectively perform the migration of elastic seismic data.The elastic LSRTM obtains better images than the conventional RTM.Also,P-and S-wave separation and polarity reversal correction are not involved.