ISSN 1004-4140
    CN 11-3017/P

    基于光流法的TTI介质纯qP波方程正演模拟及逆时偏移

    Forward Modeling and Reverse Time Migration of Pure qP-waves in TTI Media Based on the Optical Flow Method

    • 摘要: 地下介质的各向异性显著影响地震波传播,若在逆时偏移(RTM)中忽略该特性,将导致成像精度下降。针对传统TTI介质纯qP波RTM中,椭圆分解法依赖波场梯度渐进近似计算传播方向,进而引发振幅不均衡、强各向异性下数值不稳定的问题,本文将光流法引入到TTI介质纯qP波的波场传播方向估计中,推导了适配规则网格有限差分求解的传播方向矢量迭代格式。本文基于Li提出的精确qP波频散关系,采用椭圆分解法推导VTI介质纯qP波方程,经旋转波数法扩展得到TTI介质波动方程,利用光流法代替传统波场梯度渐进近似方法计算波场传播方向,实现了高精度、高稳定性的波场传播方向提取。强各向异性洼陷模型和Hess模型的数值实验表明,本文方法有效压制了渐进近似引起的振幅不均衡,成像精度与伪谱法相当,且计算效率显著提升,具有良好的应用前景。

       

      Abstract: The anisotropy of subsurface media significantly affects seismic wave propagation, and ignoring this characteristic in reverse time migration (RTM) degrades imaging accuracy. The reliance of the elliptic decomposition method on the asymptotic approximation of wavefield gradients for propagation direction calculations in conventional pure qP-wave RTM for tilted transversely isotropic (TTI) media leads to strong anisotropy, which induces amplitude imbalance and numerical instability. Therefore, this study introduced an optical flow method for the estimation of the wavefield propagation directions of pure qP-waves in TTI media and derived an iterative format for propagation direction vectors adapted to regular-grid finite-difference solutions. Based on the accurate qP-wave dispersion relation proposed by Li, this study derived a pure qP-wave equation for vertical transversely isotropic (VTI) media using the elliptic decomposition method and extended it to obtain the TTI media wave equation via the wavenumber rotation method. By replacing the conventional asymptotic approximation of wavefield gradients with the optical flow method, high-precision and high-stability extraction of the wavefield propagation directions was achieved. Numerical experiments on the strongly anisotropic depression and Hess models demonstrated that the proposed method effectively suppressed the amplitude imbalance caused by asymptotic approximation and achieved an imaging accuracy comparable to that of the pseudo-spectral method with significantly improved computational efficiency. Thus, this method has promising application prospects.

       

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