Modified Symplectic Nearly Analytical Discrete Scheme Wavefield Simulation And Reverse Time Migration

In recent years,migration research has mainly focused on computational efficiency and imaging accuracy.Forward simulation is the core of reverse time migration,it is a powerful tool for imaging complex geological structures and controls the efficiency and accuracy of imaging.The finite difference method is a commonly used method in forward modeling,but its dispersion is strong,if the dispersion is reduced to improve the imaging accuracy,it will cause a larger amount of calculation.Therefore,for more efficient forward calculation and reverse time migration,in this paper,a sixth-order modified symplectic approximation analytic discrete scheme is constructed on the basis of finite difference,and it is applied to acoustic and elastic wave forward simulation and acoustic reverse time migration.Model calculation examples verify that the scheme is used in simulation with high efficiency and high precision.This article mainly studies the following aspects of seismic wavefield forward modeling and reverse time migration technology:First of all,the paper discusses the theoretical basis of symplectic algorithm in detail.Based on the theory of symplectic algorithm,the traditional and extended expressions of seismic waves in the Hamiltonian system under different conditions are derived in detail from the acoustic wave and elastic wave conditions,combined with any even-order difference operators and nearly analytical discrete operators.The sixth-order nearly analytic discrete operator is combined with the modified symplectic scheme to construct a new scheme: sixth-order modified symplectic nearly analytic discrete scheme.For comparison and analysis,this paper also provides the second-level sixth-order NSPRK scheme and the sixth-order CFD scheme.Secondly,the thesis makes a theoretical analysis of the six-order modified symplectic approximation analytical discrete scheme.Taking the acoustic wave equation as an example,the maximum Coulomb number that the sixth-order modified symplectic nearly analytic discrete scheme needs to meet is derived;the numerical dispersion analysis of the scheme is carried out,and the numerical dispersion curve is compared with the sixth-order NSPRK scheme and the sixth-order CFD scheme.In comparison,it is found that the numerical error of the sixth-order modified symplectic nearly analytical discrete format is the smallest,followed by the sixth-order NSPRK scheme,and the sixth-order CFD scheme has the largest dispersion error.By using the three schemes to simulate the homogeneous medium of acoustic wave,The calculation efficiency of the scheme is analyzed,and found that the calculation efficiency of the sixth-order modified symplectic nearly analysis discrete scheme is the highest.Then,the boundary conditions are introduced,and the CPML boundary condition are deduced in detail.The homogeneous acoustic wave model simulation verifies the effective combination of CPML boundary conditions with the sixth-order modified symplectic approximation analytic discrete scheme;the sixth-order modified symplectic approximation analytic discrete scheme constructed in this paper separately simulate the double-layer acoustic model,homogeneous acoustic model,homogeneous elastic wave model,and Marmousi model to verify high efficiency and stability of the sixth-order modified symplectic nearly analytical discrete scheme in the forward simulation.Finally,based on source-normalized cross-correlation imaging conditions and Laplacian filter,the three schemes are respectively applied to imaging the two-layer model and the fault model by isotropic acoustic wave reverse time migration,and the calculation examples verified the efficiency of the sixth-order modified symplectic nearly analytical discrete scheme in reverse time migration.