| The finite difference method is a commonly used seismic wave numerical simulation method,which solves the seismic wave field in time and space by discretizing the wave equation.This method has the advantages of high calculation accuracy,good reliability and wide application range,so it has been widely used in the field of seismic exploration.However,in practical applications,underground structures often have complex geometry and medium heterogeneity,and there are free surfaces on the surface,which will affect the propagation of seismic waves,so they need to be considered and dealt with in the finitedifference time domain simulation.In order to make the simulation results of finite difference of seismic waves in time domain more consistent with the actual situation.In this paper,we adopt the viscoelastic fluctuation equation of the Kelvin medium for the study.Considering the free surface boundary,the free surface boundary of the adaptive parameter correction method proposed by previous authors is derived to meet the free surface boundary of the viscoelastic fluctuation equation selected in this paper,and the simulation effect is compared with the viscoelastic fluctuation equation with the free surface boundary by adding the memory variable.It is proved that the derived free surface boundary is also applicable to the viscoelastic fluctuation equation of the Kelvin medium.The free surface boundary of the viscoelastic fluctuation equation for the kelvin medium is realized,which makes the simulation results of the finite difference of the time domain seismic waves more consistent with the actual situation.At the same time,the finite difference coefficients of the Taylor expansion of the viscoelastic fluctuation equation of the Kelvin medium are replaced by the finite difference coefficients of the least squares method in order to reduce the complexity of the calculation. |
