中文摘要：

本文提出了一种新的基于平均导数优化方法（average-derivative optimal method,简称ADM）的二维VTI介质qP波波动方程频率空间域二阶9点格式,这种新算法将二维VTI介质qP波波动方程中中心空间导数项的差分近似表示为正交方向上3个网格点的加权平均形式.通过最小二乘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3.57个网格点数,而VTI介质常规9点差分格式在相同的误差范围内则需要约12个网格点数,新方法的计算精度明显提高.复杂BP2007 2D VTI海洋标准模型数值模拟结果也验证了本文VTI介质9点ADM算法的有效性和准确性。

英文摘要：

Seismic anisotropy exists extensively in the earth,whereas the TI medium is the most common anisotropic one.The conventional finite difference modeling（FDFDM）of 2DVTI media frequency-space domain with 9-point scheme can cause serious numerical dispersion because of its poor computational accuracy.The average-derivative optimal method（ADM）not only is suitable for equal and unequal directional sampling intervals,but also retains high precision.We introduce this idea into the qP wave equation of 2D VTI media to improve the computational accuracy.We firstly deal with the P-SV wave phase velocity dispersion equation for VTI media and derive the frequency-space domain qP wave equation for 2DVTI media following Alkhalifah′s TI acoustic approximation theory.Then we propose a new kind of qP wave equation for 2D VTImedia with a second-order 9-point FDFDM scheme based on ADM.Specifically,we represent the finite-difference approximations of the second-order centered spatial-derivative terms as the weighted average of 3 grid points in orthogonal directions and the acceleration term as the weighted average of all 9grid points.Afterwards we use the least-square optimal method to resolve the optimized coefficients of the VTI media with the ADM 9-point scheme and perform numerical dispersion analysis towards this new scheme.The results show that the ADM 9-point scheme for VTI media can decrease the required number of grid points per wavelength from 12to3.57 bounded by aphase velocity error range of 1%.Therefore this scheme significantly increases the computational accuracy of VTI media FDFDM compared to the VTI media conventional 9-point scheme.So the VTI media ADM 9-point scheme allows using a larger grid interval in the modeling and obviously improves the computational efficiency.Finally we derive the 2D VTI media ADM 9-point frequency-space domain with the perfectly matched layer（PML）wave equation and perform seismic wave modeling in the frequency-space domain.We use a complex BP2007 2D VTI ocean standard model t