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<p>The time-fractional viscoacoustic wave model, based on Kjartansson's constant-<i>Q</i> theory, has garnered significant attention in geophysics due to its frequency-independent attenuation behavior. This model effectively captures wave attenuation and velocity dispersion in subsurface media, which is crucial for improving the accuracy of seismic exploration. However, two key factors hinder its practical application: (1) solving the fractional-order wave equation requires storing the entire time history of the wavefield, leading to excessive memory and computational costs; (2) traditional finite-difference schemes approximate irregular free-surface topography using stair-step boundaries on Cartesian grids, often resulting in stair-step scattering and reduced accuracy. To address these limitations, this study develops an efficient short-memory algorithm for simulating viscoacoustic wave propagation over complex surface topography. The algorithm significantly reduces memory usage for fractional-derivative evaluations while maintaining high accuracy. Furthermore, by embedding a stable immersed boundary method within a Cartesian framework, the proposed approach accurately represents irregular surfaces, enhancing both the fidelity and efficiency of wavefield simulations.</p>

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An efficient algorithm for viscoacoustic wavefield simulation in complex topography

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Xu Guo,
  • Dongbo Wang,
  • Feng Wang

摘要

The time-fractional viscoacoustic wave model, based on Kjartansson's constant-Q theory, has garnered significant attention in geophysics due to its frequency-independent attenuation behavior. This model effectively captures wave attenuation and velocity dispersion in subsurface media, which is crucial for improving the accuracy of seismic exploration. However, two key factors hinder its practical application: (1) solving the fractional-order wave equation requires storing the entire time history of the wavefield, leading to excessive memory and computational costs; (2) traditional finite-difference schemes approximate irregular free-surface topography using stair-step boundaries on Cartesian grids, often resulting in stair-step scattering and reduced accuracy. To address these limitations, this study develops an efficient short-memory algorithm for simulating viscoacoustic wave propagation over complex surface topography. The algorithm significantly reduces memory usage for fractional-derivative evaluations while maintaining high accuracy. Furthermore, by embedding a stable immersed boundary method within a Cartesian framework, the proposed approach accurately represents irregular surfaces, enhancing both the fidelity and efficiency of wavefield simulations.