TY - JOUR

T1 - Sixth-order accurate pseudo-spectral method for solving one-way wave equation

AU - Pleshkevich, Alexander

AU - Vishnevskiy, Dmitriy

AU - Lisitsa, Vadim

N1 - Publisher Copyright: © 2019 Elsevier Inc.

PY - 2019/10/15

Y1 - 2019/10/15

N2 - 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.

AB - 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.

KW - Numerical dispersion

KW - One-way wave equation

KW - Pseudo-spectral methods

KW - MIGRATION

KW - DISCONTINUOUS-GALERKIN

KW - APPROXIMATION

KW - BOUNDARY-CONDITIONS

KW - INTERPOLATION

KW - SCHEME

KW - ELEMENT

KW - NUMERICAL-SIMULATION

KW - FINITE-DIFFERENCE

KW - PROPAGATION

UR - http://www.scopus.com/inward/record.url?scp=85065253849&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2019.04.029

DO - 10.1016/j.amc.2019.04.029

M3 - Article

AN - SCOPUS:85065253849

VL - 359

SP - 34

EP - 51

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -