基于波场分离的双相各向同性介质正演模拟

Seismic Forward Simulation in Two-phase Isotropic Media based on the Method of Wave Field Separation

基于双相各向同性介质一阶速度-应力方程,利用旋度和散度理论的波场分离方法进行纵横波场解耦,借助高阶交错网格有限差分技术,推导出了其任意偶数阶精度交错网格有限差分格式,最后运用空间八阶时间二阶差分精度及PML边界条件,完成了双相各向同性介质中地震波场正演模拟。结果表明,该方法可准确获得双相各向同性介质固、流相中的高精度纯纵波波场和纯横波波场,有效描述双相各向同性介质中的波场传播规律。同时得出:双相各向同性介质中快、慢纵波相互耦合,无法单独分离;也指出了分界面处波的传播和转换关系,是油气勘探的重要理论依据。

Based on the first-order hyperbolic stress-velocity elastic wave equation in two-phrase isotropic media, the compress wave and shear wave equations were developed by using the method of wave field separation which based on the theory of divergence and curl. With the using of staggered-grid high-order finite-difference technolo- gy, the any even-order finite-difference scheme of elastic wave equation was derived. Choosing second-order accu- racy difference scheme in time and eight-order accuracy difference scheme in space and combining with PML ab- sorbing boundary, the numerical simulation was completed. The results of numerical modeling show that the com- press shear waves and pure wave can be obtained and the seismic wave propagation can be described accurately by using the method of wave field separation; and it also can be seen that the slow compress wave and fast compress wave cannot be separated which because they are coupled in two-phase medium; at the same time, the relation- ship of propagation and conversion can be described clearly in the interface of model. It is the important theoreti- cal foundation for oil-gas exploration.