粘弹性介质三维地震波场数值模拟研究——基于交错网格高阶有限差分法

Research on Forward Modeling of 3D Seismic Wave Field in Viscoelastic Media based on Finite Difference Method

为研究地震波在三维粘弹性介质中的传播规律,根据完全弹性各向同性介质位移与应力的运动与平衡微分方程,推导出三维完全弹性各向同性介质的一阶速度——应力弹性波方程;同时结合完全弹性介质与开尔芬粘弹性介质之间弹性参数存在的对应关系,利用交错网格理论导出开尔芬粘弹性介质模型在时间上2阶、空间上8阶的差分格式,进一步利用二维完全匹配层吸收边界条件延伸模拟了三维开尔芬粘弹性介质的地震波场,结果表明二维的边界处理思想适用于三维条件下边界反射的吸收。在此基础上,给定不同的品质因子进行数值模拟,通过频谱分析发现,随着品质因子的减小,地震波能量、振幅都会受到衰减,频带范围变窄,主频降低。

To study the law of seismic wave propagation in 3D viscoelastic media,based on the motion and the equilibrium differential equation of the displacement and stress of the fully elastic isotropic medium,the first order velocity and stress elastic wave equation of the three-dimensional fully elastic isotropic medium is derived.Secondly,according to the elastic parameters corresponding relation between the fully elastic medium and the Kelvin viscoelastic medium,Kelvin Viscoelastic medium model in time 2-order,8-order difference scheme in space is derived by using the interlaced grid theory.And the seismic wave field of three-dimensional Kelvin viscoelastic medium is simulated with the idea of two dimensional absorbing boundary fully matched layer,the result shows that the method is feasible.With the decrease of quality factor,the energy and amplitude of seismic wave will be attenuated,the frequency rangewill narrow,and the main frequency will decrease.