On a wavelet-based method for the numerical simulation of wave propagation

Tae Kyung Hong, Brian L.N. Kennett

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

A wavelet-based method for the numerical simulation of acoustic and elastic wave propagation is developed. Using a displacement-velocity formulation and treating spatial derivatives with linear operators, the wave equations are rewritten as a system of equations whose evolution in time is controlled by first-order derivatives. The linear operators for spatial derivatives are implemented in wavelet bases using an operator projection technique with nonstandard forms of wavelet transform. Using a semigroup approach, the discretized solution in time can be represented in an explicit recursive form, based on Taylor expansion of exponential functions of operator matrices. The boundary conditions are implemented by augmenting the system of equations with equivalent force terms at the boundaries. The wavelet-based method is applied to the acoustic wave equation with rigid boundary conditions at both ends in 1-D domain and to the elastic wave equation with a traction-free boundary conditions at a free surface in 2-D spatial media. The method can be applied directly to media with plane surfaces, and surface topography can be included with the aid of distortion of the grid describing the properties of the medium. The numerical results are compared with analytic solutions based on the Cagniard technique and show high accuracy. The wavelet-based approach is also demonstrated for complex media including highly varying topography or stochastic heterogeneity with rapid variations in physical parameters. These examples indicate the value of the approach as an accurate and stable tool for the simulation of wave propagation in general complex media.

Original languageEnglish
Pages (from-to)577-622
Number of pages46
JournalJournal of Computational Physics
Volume183
Issue number2
DOIs
Publication statusPublished - 2002 Dec 10

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Wave equations
Wave propagation
wave propagation
Elastic waves
Boundary conditions
Derivatives
Mathematical operators
Computer simulation
wave equations
linear operators
Acoustic waves
boundary conditions
elastic waves
simulation
Exponential functions
Surface topography
topography
Wavelet transforms
Topography
operators

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Cite this

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On a wavelet-based method for the numerical simulation of wave propagation. / Hong, Tae Kyung; Kennett, Brian L.N.

In: Journal of Computational Physics, Vol. 183, No. 2, 10.12.2002, p. 577-622.

Research output: Contribution to journalArticle

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