Sixth-order accurate pseudo-spectral method for solving one-way wave equation

Alexander Pleshkevich, Dmitriy Vishnevskiy, Vadim Lisitsa

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this paper, we present a pseudo-spectral method to solve the one-way wave equation. The approach is a generalization of the phase-shift plus interpolation technique which is used in geophysical applications. We construct a solution at each depth layer as a linear combination of the solutions corresponding to the models with uniform reference velocities. We suggest using three-term relations to interpolate the solution with the sixth order of accuracy to the deviation from the vertical direction. Standard phase-shift plus interpolation technique uses two-terms relation interpolating the solution with the fourth order. As a result, the numerical error of the suggested approach is one half of that of the PSPI methods for a fixed set of reference velocities for a wide range of spatial discretizations and directions of wave propagation. Consequently, to compute a solution with prescribed accuracy, the presented approach allows using 20% fewer reference velocities than the PSPI. Additionally provided experiments illustrate the efficiency of the suggested approach for simulation of down-going wave propagation in complex geological media, making the algorithm a promising one for the seismic imaging procedures.

Original languageEnglish
Pages (from-to)34-51
Number of pages18
JournalApplied Mathematics and Computation
Volume359
DOIs
Publication statusPublished - 15 Oct 2019

Keywords

  • Numerical dispersion
  • One-way wave equation
  • Pseudo-spectral methods
  • MIGRATION
  • DISCONTINUOUS-GALERKIN
  • APPROXIMATION
  • BOUNDARY-CONDITIONS
  • INTERPOLATION
  • SCHEME
  • ELEMENT
  • NUMERICAL-SIMULATION
  • FINITE-DIFFERENCE
  • PROPAGATION

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