基于多倍角公式的一步波场外推法

为了提高地震波场正演模拟的准确性和稳定性，针对一步波场外推法地震波场正演，本文提出了基于多倍角公式的耦合方程组解法.借助欧拉公式，将一步波场外推法的复数波场延拓方程转化为两个实数波场耦合的方程组，结合多倍角公式和泰勒展开式精确逼近包含拟微分算子的简谐函数算子，利用谱方法求解拟微分算子，进而推导了一种基于多倍角公式的一步波场外推法的耦合方程组.相比于常规一步波场外推法中复数方程的矩阵解法，本文方法能够显著减少傅里叶变换次数，降低计算成本.此外，本文推导了稳定性条件，为正确选取地震波场模拟参数提供了理论依据.基于二维匀速模型和复杂构造模型的数值测试表明，本文方法能够在大时间步长情况下保持外推波场稳定，计算效率较高.

One-step extrapolation method based on the multiple-angle formula

We propose a coupled-equations solution for the one-step extrapolation method to solve the acoustic wave equation. We use the Euler formula to transform the one-step extrapolation equation for a complex wavefield into coupled equations of two real wavefields. Then this multiple-angle formula is applied to more accurate and stable approximations of the harmonic function operators of pseudodifferential operators. The polynomial Taylor expansions are adopted in the coupled equations and then the Fourier method is used to solve this operator and we derive a kind of coupled equations of the one-step extrapolation method. The method workflow requires fewer iterations of the Fourier transform than the existing one-step wave extrapolation matrix method. Besides, we also derive the stability conditions, which could provide a quantitative basis for choosing the multiple-angle parameters and the orders of polynomials to ensure the proposed algorithm stable. Numerical experiments for a two-dimensional constant-velocity model and complex structural model show that our method can keep stable of the extrapolation of the wavefield with a large time step and is more effective than the one-step wave extrapolation matrix method.