Fractional Laplacians viscoacoustic wavefield modeling with k -space-based time-stepping error compensating scheme

Ning Wang, Tieyuan Zhu, Hui Zhou, Hanming Chen, Xuebin Zhao, Yukun Tian

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The spatial derivatives in decoupled fractional Laplacian (DFL) viscoacoustic and viscoelastic wave equations are the mixed-domain Laplacian operators. Using the approximation of the mixed-domain operators, the spatial derivatives can be calculated by using the Fourier pseudospectral (PS) method with barely spatial numerical dispersions, whereas the time derivative is often computed with the finite-difference (FD) method in second-order accuracy (referred to as the FD-PS scheme). The time-stepping errors caused by the FD discretization inevitably introduce the accumulative temporal dispersion during the wavefield extrapolation, especially for a long-time simulation. To eliminate the time-stepping errors, here, we adopted the k-space concept in the numerical discretization of the DFL viscoacoustic wave equation. Different from existing k-space methods, our k-space method for DFL viscoacoustic wave equation contains two correction terms, which were designed to compensate for the time-stepping errors in the dispersion-dominated operator and loss-dominated operator, respectively. Using theoretical analyses and numerical experiments, we determine that our k-space approach is superior to the traditional FD-PS scheme mainly in three aspects. First, our approach can effectively compensate for the time-stepping errors. Second, the stability condition is more relaxed, which makes the selection of sampling intervals more flexible. Finally, the k-space approach allows us to conduct high-accuracy wavefield extrapolation with larger time steps. These features make our scheme suitable for seismic modeling and imaging problems.

Original languageEnglish (US)
Pages (from-to)T1-T13
Issue number1
StatePublished - Jan 1 2020

All Science Journal Classification (ASJC) codes

  • Geochemistry and Petrology
  • Geophysics


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