Traction image method for irregular free surface boundaries in finite difference seismic wave simulation
Traction image method for irregular free surface boundaries in finite difference seismic wave simulation
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DOI：
10.1111/j.1365-246x.2006.03113.x
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发表时间：
2006-10-01
影响因子：
2.8
通讯作者：
Chen, Xiaofei
中科院分区：
文献类型：
--
作者：
Zhang, Wei;Chen, Xiaofei
在这项研究中，我们提出了一种新的数值方法，命名为牵引图像方法，精确和有效地实现无牵引边界条件的有限差分模拟中存在的表面形貌。在该算法中，计算域离散的边界协调网格，其中不规则的表面转化为一个“平”的表面在计算空间。从而避免了对任意不规则曲面进行阶梯逼近时的人为误差。这种边界协调网格相当于一个曲线坐标系，其中一阶偏微分速度-应力方程由一种优化的高阶非交错差分格式（DRP/opt MacCormack格式）进行数值修正。为了满足自由面边界条件，通过反对称地设置自由面上方网格点的法向牵引力，将平面的应力镜像法推广到任意不规则曲面的牵引力镜像法。这种牵引力图像方法可以有效地实现。为了验证这种新方法，我们进行了数值试验，几个复杂的模型，通过比较我们的结果与其他独立的精确方法计算。虽然一些测试的例子有非常倾斜的地形，所有的测试结果表明，我们的结果和那些从参考解决方案，证实了我们的方法的有效性，模拟地震波在非均匀介质中的任意形状的地形。数值试验也证明了该方法的有效性。我们发现每个最短波长大约10个网格点足以保持模拟的全局精度。虽然目前的研究是针对二维P-SV问题，但它可以很容易地扩展到三维问题。
In this study, we propose a new numerical method, named as Traction Image method, to accurately and efficiently implement the traction-free boundary conditions in finite difference simulation in the presence of surface topography. In this algorithm, the computational domain is discretized by boundary-conforming grids, in which the irregular surface is transformed into a 'flat' surface in computational space. Thus, the artefact of staircase approximation to arbitrarily irregular surface can be avoided. Such boundary-conforming gridding is equivalent to a curvilinear coordinate system, in which the first-order partial differential velocity-stress equations are numerically updated by an optimized high-order non-staggered finite difference scheme, that is, DRP/opt MacCormack scheme. To satisfy the free surface boundary conditions, we extend the Stress Image method for planar surface to Traction Image method for arbitrarily irregular surface by antisymmetrically setting the values of normal traction on the grid points above the free surface. This Traction Image method can be efficiently implemented. To validate this new method, we perform numerical tests to several complex models by comparing our results with those computed by other independent accurate methods. Although some of the testing examples have extremely sloped topography, all tested results show an excellent agreement between our results and those from the reference solutions, confirming the validity of our method for modelling seismic waves in the heterogeneous media with arbitrary shape topography. Numerical tests also demonstrate the efficiency of this method. We find about 10 grid points per shortest wavelength is enough to maintain the global accuracy of the simulation. Although the current study is for 2-D P-SV problem, it can be easily extended to 3-D problem.