基于正交贴体网格的黏弹介质地震波模拟

Numerical simulation of seismic waves in viscoelastic media based on orthogonal body⁃fitted grid

常规的有限差分地震波数值模拟采用笛卡尔坐标系的规则网格对计算区域进行网格剖分,在模拟起伏地表下的地震波场时,不仅不利于实现自由边界条件,而且由于阶梯状网格近似,在网格角点处容易产生虚假散射波,从而影响模拟精度。为此,将计算流体力学中的正交贴体网格生成技术引入起伏地表下黏弹介质的网格剖分中,采用优化的同位网格有限差分法计算曲线坐标系的一阶速度—应力方程,并通过选择性滤波法消除同位网格差分产生的格点振荡。正交贴体网格能够精确地描述起伏地表,网格的正交性也使得实施自由边界条件时无需做复杂的坐标转换和插值运算。数值算例表明:该方法得到的数值解与解析解完全吻合;与规则网格有限差分法模拟结果相比,在相同网格间距条件下,该方法能够有效消除阶梯状网格引起的虚假散射波,从而提高数值模拟精度。此外,起伏地表两层和三层黏弹介质模型模拟结果表明,该方法对复杂模型同样有较强的适用性。

Conventional finite difference numerical simulation of seismic waves employs regular grids in Cartesian coordinates to divide the calculated region.During simulating seismic wavefields under undulating surfaces,it is not only unfavorable to realize the free boundary conditions,but also prone to generate false scattered waves at the corners of the grid due to stepped grid approximation,thus affecting the simulation accuracy.To this end,the orthogonal body‑fitted grid generation technique in computational fluid dynamics is introduced into the grid generation of viscoelastic media under undulating surfaces.The first‑order velocity‑stress equation in curvilinear coordinates is calculated by the optimized homologous grid finite difference method,and the point oscillation generated by the homologous grid difference is eliminated by the selective filtering method.The orthogonal body‑fitted grid can accurately describe the undulating surface,and due to the orthogonality of the grid,free boundary conditions can be implemented without complicated coordinate transformation and interpolation operations.Numerical examples show that the numerical solutions obtained by this method are in good agreement with the analytical ones.By comparing the simulation results of the proposed method with those of the regular grid finite difference method,the proposed method can effectively eliminate the false scattered waves caused by the stepped grid in the condition of the same grid spacing,thus improving the numerical simulation accuracy.In addition,the simulation results of two‑layers and three‑layers viscoelastic medium models on undulating surfaces show that the proposed method is also applicable for complex models.