In recent decades, the study of seismic attenuation has received more and more concerns because it can stimulate the development of wave propagation simulation and improve the accuracy of structure imaging and reservoir prediction. In this paper, we review the attenuation theory and the development of high temporal accuracy wave simulation. The conventional mathematical models to describe the characteristics of viscoelastic are based on constant- Q model or standard linear solids theory. However, these approaches possess some noticeable shortcomings. Therefore, we introduce a frequency-dependent complex velocity to derive the novel viscoelastic wave equations with decoupled amplitude dissipation and phase dispersion. To obtain high temporal accuracy viscoelastic wave simulation, we adopt the normalized pseudo-Laplacian to compensate for the temporal dispersion errors caused by the second-order finite-difference discretization in the time domain. During the implementation, we incorporate the normalized pseudo-Laplacian into the optimized staggered-grid finite-difference coefficients. Therefore, it can greatly reduce the times of low-rank decomposition and Fourier transform and largely improve the computational efficiency. Based on this strategy, we can implement the high temporal accuracy viscoelastic wavefield extrapolation by comprehensively exploiting the staggered-grid finite-difference scheme, pseudo-spectral method and low-rank decomposition algorithm. Meanwhile, a linear velocity model is employed to evaluate the accuracy of low-rank approximation. Furthermore, we use several numerical examples to carry out the comparison between our scheme and other conventional methods. The numerical results reveal that our proposed scheme can effectively compensate for temporal dispersion errors and help generate high temporal accuracy viscoelastic wave solutions.

中文翻译：

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使用频率相关的复速度进行高时间精度的粘弹性波模拟

近几十年来，地震衰减研究受到越来越多的关注，因为它可以刺激波传播模拟的发展，提高构造成像和储层预测的准确性。在本文中，我们回顾了衰减理论和高时间精度波浪模拟的发展。描述粘弹性特性的传统数学模型是基于恒定 Q 模型或标准线性固体理论。然而，这些方法具有一些明显的缺点。因此，我们引入了一个与频率相关的复速度来推导出具有解耦幅度耗散和相位色散的新型粘弹性波动方程。为了获得高时间精度的粘弹性波模拟，我们采用归一化伪拉普拉斯算子来补偿时域中二阶有限差分离散化引起的时间色散误差。在实现过程中，我们将归一化伪拉普拉斯算子合并到优化的交错网格有限差分系数中。因此，它可以大大减少低秩分解和傅立叶变换的次数，大大提高计算效率。基于该策略，我们可以综合利用交错网格有限差分格式、伪谱方法和低秩分解算法来实现高时间精度的粘弹性波场外推。同时，采用线速度模型来评估低秩逼近的准确性。此外，我们使用几个数值例子来进行我们的方案与其他常规方法的比较。数值结果表明，我们提出的方案可以有效地补偿时间色散误差，并有助于生成高时间精度的粘弹性波解。