Viscoelastic Wave Simulation with High Temporal Accuracy Using Frequency-Dependent Complex Velocity
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Viscoelastic Wave Simulation with High Temporal Accuracy Using Frequency‑Dependent Complex Velocity Yabing Zhang1,2 · Yang Liu1,2,3 · Shigang Xu1,2 Received: 2 September 2019 / Accepted: 23 July 2020 © Springer Nature B.V. 2020
Abstract 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. Keywords Viscoelastic · Complex velocity · Normalized pseudo-Laplacian · Staggeredgrid finite-difference · Pseudo-spectral · Low-rank decomposition
* Yang Liu [email protected] Extended author information available on the last page of the article
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Surveys in Geophysics
1 Introduction The ubiquitous seismic attenuation caused by the viscoelastic property of the earth usually has a profound effect on the wave propagation (Aki and Richards 2002; Dutta and Schuster 2014; Bai and Tsvankin 2016; Yang and Zhu 2018a). This behaviour is commonly embodied in the amplitude dissipation and phase dispersion. Without considering these effects, poor illumination and incorrect position of reflectors may occur in reverse-time migration (RTM) imaging (Zhu et al. 2014; Sun and Zhu 2018; Chen et al. 2019b). Given this issue, Q-compensated RTM which incorporates the attenuation effect into wave propagation is beco
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