Optimized staggered-grid finite-difference operators using window functions

蹒跚格子有限差别(SGFD ) 方法广泛地在地震前面的建模被使用了。向前当模特儿的结果的精确直接影响随后的地震倒置和迁居的结果。数字分散是在这个方法的问题之一。由用窗口操作符代替有限差别的操作符的窗口函数方法罐头还原剂分散，由截断 pseudospectral 方法的空间卷绕旋转系列获得了。尽管窗户操作员在 low-wavenumber 领域有高精确，他们的精确在 high-wavenumber 领域很快减少。我们开发一个最少的广场优化方法提高窗口函数方法获得的操作符的精确。我们把 SGFD 问题转变成一个最少的广场问题并且反复地发现最好的答案。当起始的值和优化的域被错误阀值放，窗口操作符被选择。conjugate 坡度方法也被采用增加答案的稳定性。近似错误分析和数字模拟结果建议建议方法增加窗户功能操作员和减少的精确数字分散。

The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration. Numerical dispersion is one of the problems in this method. The window function method can reduce dispersion by replacing the finite-difference operators with window operators, obtained by truncating the spatial convolution series of the pseudospectral method. Although the window operators have high precision in the low-wavenumber domain, their precision decreases rapidly in the high-wavenumber domain. We develop a least squares optimization method to enhance the precision of operators obtained by the window function method. We transform the SGFD problem into a least squares problem and find the best solution iteratively. The window operator is chosen as the initial value and the optimized domain is set by the error threshold. The conjugate gradient method is also adopted to increase the stability of the solution. Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.