基于平均导数方法的声波方程频率域高阶正演

本文首先阐明了基于旋转坐标系的频率域正演算法只能适用于相同横纵向空间采样间隔的局限性，并发展了一种新的基于平均导数方法（average-derivative method，简称ADM）的25点有限差分格式来实现声波方程频率域高精度正演.这种基于平均导数方法的算法将声波频率域方程中空间导数项的差分近似表示为正交方向上5个网格点的加权平均形式，能适用于不同的横纵向空间采样间隔，因此能作为四阶声波频率域正演的一种统一格式，具有很好的适用性.通过优化方法求取空间导数项和加速度项的加权优化系数，从而使数值频散达到极小化，每个波长所需要的网格点数在1%的误差范围内仅为2.78个网格点数.本文通过引入完全匹配层（perfectly matched layer，简称PML）吸收边界条件，有效地消除了人工边界反射.数值模拟结果验证了本文25点ADM算法的有效性和准确性.

Frequency domain acoustic equation high-order modeling based on an average-derivative method

This paper firstly illustrates the limitation of frequency-domain finite-difference forward modeling algorithm based on the rotation coordinate which can only be applied to the same horizontal and vertical spatial sampling interval. Then we develop a new kind of 25-point scheme based on an average-derivative method. This scheme represents the approximations of the spatial derivatives as the weighted average of 5 grid points in the orthogonal directions and can be applied to different ratio of horizontal and vertical sampling interval. Therefore this scheme can be used as a general fourth-order scheme, so this method possesses excellent applicability. By determining the weighting coefficients of spatial derivative terms and the acceleration terms to minimize numerical dispersion, the number of grid points per wavelength bounded by the error range of 1% is only 2.78. We apply perfectly matched layer absorbing boundary condition to eliminate the artificial boundary reflection efficiently. The numerical examples prove the validity and precision of the ADM 25-point scheme.