频率域八阶NAD有限差分模拟及全波形反演

全波形反演是一种利用波动方程与最优化算法定量获取地下介质物性参数的高分辨率成像方法。正演模拟是反演的基础，为进一步提高正演计算效率，提出用八阶频率域近似解析离散化（NAD）方法离散二维声波方程，详细推导了高阶NAD格式的构造过程，并采用一类不精确旋转分块三角预处理算子加速Krylov迭代方法求解离散后得到的大型稀疏线性代数方程组。波场模拟与数值频散分析结果体现了该方法在压制数值频散和提高计算效率方面的优势，即每个波长少于2个点即可准确恢复波场，突破了采样频率极限。运用所构造的正演算法进行反演，并对两种典型的分层介质模型和Marmousi模型进行频率域全波形反演，得到了高分辨率、高保真的计算结果，结合反演误差曲线验证了所提方法的有效性和适用性。

The eighth-order frequency-domain NAD method and full-waveform inversion

The full waveform inversion (FWI) is a high precise imaging method which uses wave equation and optimal algorithm to obtain physical parameters of underground media.The forward modeling is the basis of inversion.In order to further improve the efficiency of forward modelings,this paper proposes an eighth-order nearly-analytic discretization (NAD) method to discretize a 2D acoustic wave equation in the frequency domain.The construction of high-order NAD method is deduced in detail and a class of inexact rotated block triangular preconditioned Krylov subspace method is used to solve large-scale sparse linear algebraic equations obtained after the discretization.The wavefield simulation and numerical dispersion ana-lysis show the advantages of the proposed method in suppressing the numerical dispersion and improving the computational efficiency.Specifically the wavefield can be accurately recovered when the sampling points per wave length is less than two.This exceeds the limit of sampling rate.Finally,inversion researches are carried out with the constructed forward-modeling algorithm.The frequency domain full waveform inversion is performed in two typical layered models and the Marmousi mo-del,and the high resolution,high fidelity results are obtained.These test results and inversion error curves illustrate the effectiveness and applicability of the proposed method.