A 3D Helmholtz iterative solver with a semi-analytical preconditioner for acoustic wavefield modeling in seismic exploration problems

Authors

  • D.A. Neklyudov
  • I.Yu. Silvestrov
  • V.A. Tcheverda

Keywords:

Helmholtz equation
iterative methods
preconditioners
acoustic waves
seismic exploration

Abstract

An approach to the iterative solution of the 3D acoustic wave equation in a frequency domain is proposed, substantiated, and verified numerically. Our method is based on Krylov-type linear solvers, similarly to several other iterative solver approaches. The distinctive feature of our method is the use of a right preconditioner obtained as the solution of the complex dumped Helmholtz equation in a 1D medium, where velocities vary only with depth. The actual Helmholtz operator is represented as a perturbation of the preconditioner. As a result, a matrix-by-vector multiplication of the preconditioned system can be efficiently evaluated via 2D FFT in x and y directions followed by the solution of a number of ordinary differential equations in z directions. While solving ODE’s. it is possible to treat the 1D velocity function as a piecewise constant one and to search for the exact solution as a superposition of upgoing and downgoing waves. This approach allows one not to use explicit finite-difference approximations of derivatives at all. The method has excellent dispersion properties in both lateral and vertical directions.

New computational technologies

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Published

2014-09-08

Issue

Vol. 15 (2014): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

D.A. Neklyudov

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Senior Researcher

I.Yu. Silvestrov

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Senior Researcher

V.A. Tcheverda

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Head of Department

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