| Finite-difference(FD)methods are commonly used in seismic wave equations modeling and reverse time migration(RTM).Numerical simulation of the forward source and backward receiver wavefields extrapolation is involved in the RTM,so the imaging accuracy and efficiency largely depend on the numerical simulation methods.In this dissertation,I focus on develop high-order spatial and temporal accuracy implicit FD schemes for modeling the constant density acoustic,variable density acoustic,and elastic wave equations.Besides,some key parts of the prestack acoustic and elastic RTM technology are studied.Compared with the explicit FD methods,the implicit ones can obtain higher spatial simulation accuracy.However,the currently developed implicit FD methods are designed in the space domain and can only approximate the spatial derivatives,without considering the propagation characteristics of the whole seismic wave equation in the time and space domain.In this dissertation,the propagation characteristics in time and space of constant density acoustic,variable density acoustic and elastic wave equations are fully considered.For these three types of seismic wave equations,the corresponding high-order temporal and spatial accuracy implicit FD schemes are proposed in the time-space domain,and the FD coefficients are obtained by approximating the time-space dispersion relation of these seismic wave equations.Numerical analysis shows that the newly proposed time-space domain implicit FD schemes can significantly improve the simulation accuracy of seismic wave equations.Furthermore,the developed new high-order accuracy implicit FD schemes are adopted to solve the forward and backward wavefields extrapolation of prestack acoustic and elastic RTM imaging process,and satisfactory imaging results are obtained.In order to save the computational resources,two efficient wavefields extrapolation strategies based on explicit FD methods are developed,i.e.,the improved equivalent staggered-grid(SG)FD method and the adaptive variable length of temporal and spatial operators-based FD strategy.Finally,the RTM imaging conditions,the joint RTM imaging technique of the primary and first-order surface related multiples,the P and S wavefields separation methods of elastic wavefields are also studied.Based on these aspects aforementioned,the following achievements are obtained:Firstly,aiming at solving the second-order constant density acoustic wave equation accurately,a time-space domain implicit regular-grid FD scheme is proposed,and the time-space dispersion relation of the newly proposed implicit FD scheme is derived.The new implicit FD scheme can suppress temporal dispersion by adding some extra grid points on the traditional cross FD scheme.Based on time-space dispersion relation and variable substitution idea,the corresponding FD coefficients are computed by using Taylor series expansion(TE)and linear optimization methods,respectively.Dispersion and stability analysis,and numerical examples show that the simulation accuracy and stability of the newly proposed temporal high-order and spatial implicit FD schemes are superior to the traditional implicit ones.Besides,compared with adopting the TE-based FD coefficients,utilizing the optimized FD coefficient can obtain higher accuracy simulation results in a larger wave number range.Secondly,a time-space domain SG implicit FD scheme is proposed for modeling the first-order variable density acoustic wave equation.At present,the SG implicit FD methods only approximate the spatial derivative,so the simulation accuracy of the whole wave equation is second order.The newly proposed temporal high-order and spatial implicit SG FD scheme directly approximates the whole wave equation and improves the simulation accuracy effectively.Numerical examples show that the time-space FD coefficients obtained based on the TE method can effectively reduce the temporal and spatial dispersion errors and obtain even order temporal and spatial accuracy for the variable density acoustic wave equation modeling.Besides,a linear optimization strategy by combining the TE and least squares(LS)method is developed based on the newly proposed SG implicit FD scheme.This strategy mitigates the drawbacks of nonlinear optimization,namely,its time-consuming nature and challenging convergence.Numerical examples show that the newly proposed SG implicit FD scheme maintains the spatial high accuracy advantage of the traditional implicit FD method,and significantly improves the temporal accuracy of the first-order variable density acoustic wave equation modeling.Furthermore,compared with the conventional implicit FD method,the new SG implicit FD scheme can adopt a larger time step while maintain the propagation stability,so the simulation efficiency is also improved.Thirdly,for improving the spatial and temporal accuracy of the elastic wave equation modeling,a high-order accuracy SG implicit FD scheme is developed in the time-space domain.Based on the TE and linear optimization strategies,the time-space domain FD coefficients based on the dispersion relation of P and S waves are derived,respectively.The dispersion analysis shows that the FD coefficients based on the P wave dispersion relation can only obtain high-accuracy simulation results of P wavefield,and the simulated S wavefield occurs serious numerical dispersion.The FD coefficients based on S wave dispersion relation can only obtain the simulation results of S wavefield with high accuracy,and the simulated P wavefield occurs serious numerical dispersion.By using the decouple elastic wave equation,the FD coefficients of P and S waves derived from the P and S wave dispersion relations are used to simulate P and S waves,respectively,so that the high accuracy elastic wavefields simulation results are obtained simultaneously.Compared with the traditional implicit FD method simulation results,the new time-space domain SG implicit FD scheme can effectively suppress the temporal dispersion and save the calculation time while enhancing the stability of elastic wavefields numerical simulation.Fourthly,the prestack acoustic RTM is studied.The improved equivalent SG and the adaptive variable length of spatial and temporal operators strategy are developed in enhancing the prestack acoustic RTM imaging efficiency and quality.Numerical examples show that these two wavefields extrapolation strategies can effectively reduce the calculation time and memory in prestack acoustic RTM process.Fifthly,multiples can provide more underground reflection information,and benefit from the complexity of its propagation path.In this dissertation,the RTM imaging method of combining primary and surface-related first-order multiples without prediction and separation is studied,so that the advantages of multiples can be utilized properly.Compared with the imaging results of primary wave,it can be concluded that the combined RTM imaging method can broaden the imaging range and improve the illumination.Sixthly,the newly proposed SG implicit FD scheme is utilized for the forward and backward wavefields extrapolation in acoustic and elastic RTM,aiming to obtain high quality imaging profiles. |
