Research On High-Precision Seismic Wavefield Numerical Simulation And Reflection Transmission Coefficient At The Liquid-Solid Interface

With the change of oil and gas exploration areas,the shift from land to ocean,and the improvement of exploration accuracy requirements,it is necessary to construct a new seismic exploration theory to more accurately describe the propagation of seismic wave in the liquid-solid interface formed by sea water and seabed.Under such a context,a forward modeling method for seismic wave field simulation of liquid-solid interface is proposed,which can suppress the numerical dispersion under the condition with a larger spatial step.At the same time,the analytical expression of the reflection and transmission coefficient of P-wave incident from the liquid medium is derived by combining the ray parameter with the steady-state plane wave solution.In this thesis,the partitioned approach is used first.Considering the viscosity,anisotropy,and viscoelasticity of the medium,combining with liquid-solid interface conditions,five mathematical models are established to describe the propagation of seismic waves at liquid-solid interface.Model 1 and model 2 use the first-order inviscid acoustic equation and the first-order viscous acoustic equation in the liquid medium respectively,and the first-order elastic wave equation is used in the solid medium.Model 3,model 4 and model 5 use the second-order acoustic wave equation in liquid medium,and use the second-order isotropic elastic wave equation,the second-order anisotropic elastic wave equation and the second-order viscoelastic wave equation in solid medium respectively.According to the characteristics of different models,the corresponding finite difference methods are designed.Considering the viscous effect of liquid medium,combining the staggered grid(SG)and optimal nearly analytic discrete method(ONADM),a new hybrid method called SG-ONADM is proposed.This method can suppress the numerical dispersion effectively under the condition of large spatial step size(20m),and it is simple and efficient.Considering the characteristics of partitioned approach,two hybrid methods called SG2-ONADM and ONADM-LWC are proposed.SG2-ONADM is combining SG-ONADM and SG method,ONADM-LWC is combining ONADM and Lax-Wendroff modified scheme(LWC).Next,Fourier method,Monte-Carlo method and matrix eigenvalue theory are used to analyze the stability and dispersion of different models after discretization.The results show that the more obvious viscous influence of liquid,the anisotropy and viscoelasticity characteristics of solid are,the stricter the stability condition of the equation is.Although the suppression effect of numerical dispersion decreases with the enhancement of viscous effect,anisotropic and viscoelastic characteristics,the numerical dispersion can be suppressed effectively when the sampling rate is less thanThis thesis derives the construction scheme of the convolutional perfect matching layer(CPML)for second-order seismic wave equation and the processing method of the horizontal free surface of the liquid medium,and designs a uniform model for verification.Numerical experiment results show that the SG method,SG-ONADM method,ONADM method,and LWC method can be effectively combined with CPML to achieve the absorption of false reflection waves at the artificial boundary,and it is suitable for different media.The horizontal free surface treatment method proposed in this thesis can effectively deal wtih the free surface.Combining the ray parameter with the plane wave solutions of different waves at the interface,the analytical expressions of the reflection and transmission coefficient of plane P-wave incident from the liquid medium is derived.The results of theoretical analysis and numerical experiments show that the analytical expressions of reflection and transmission coefficient vary with the incident angle in a segmented manner with the critical angle as the dividing point,and the magnitude and type of the critical angle are related to the velocities of P wave and S wave.There are two critical angles of P wave and S wave in the reflection and transmission coefficient of the hard seabed model,showing a "three-stage" feature.While there is only a critical angle of P wave in the reflection and transmission coefficient of the soft seabed model,showing a"two-stage" feature.For the case that the solid medium is viscoelastic medium,part of the energy will be absorbed by the medium during reflection and transmission.The more obvious the viscoelastic characteristic of the medium is,the more energy will be attenuated in seismic wave propagation.The reflection and transmission coefficient not only changes with the incident angle,but also changes with the change of the medium parameters,so the properties of the medium can be determined according to the reflection and transmission curve.Finally,for the liquid-solid interface model with horizontal interface and inclined interface,five mathematical models describing the propagation of seismic waves at the liquid-solid interface with the corresponding finite difference method are used for numerical simulation.The results show that SG2-ONADM and ONADM-LWC method can effectively simulate the propagation of seismic wave in liquid-solid interface,and ONADM-LWC method can effectively suppress numerical dispersion with a large spatial step step.At the same time,based on the simulation results,the propagation law of seismic waves in the liquid-solid interface is studied.