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时间空间域有限差分正演模拟方法比较成熟,但是,该方法存在截断误差,并且该误差会随着计算量的增加不断累积。而频率空间域有限差分正演模拟方法是对空间网格后的所有网格点按照频率切片进行整体求解方程组,计算的误差被分配到了每一个网格点上。因为每个频率切片是单独计算的,不存在累积的舍入误差。推导了二维弹性波方程频率空间域的最优化旋转有限差分格式,通过模型的正演模拟试算,验证了频率空间域有限差分方法算法的有效性。
However, this method has truncation error, and the error will accumulate with the increase of computation. In the method of forward modeling of finite difference in frequency domain, the whole system of equations is solved according to the frequency slice for all the grid points after the space grid, and the calculated error is assigned to each grid point. Because each frequency slice is calculated separately, there is no cumulative rounding error. The optimal rotation finite difference scheme of two-dimensional elastic wave equation in frequency-space domain is deduced. The validity of the finite-difference method in frequency-space domain is verified by forward modeling test.