1887
Volume 51, Issue 4
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

Elastic wave modelling in the Laplace domain is the foundation of Laplace-domain elastic wave full waveform inversion. In order to use Laplace-domain numerical modelling schemes efficiently, appropriate grid intervals must be chosen correctly. The determination of grid intervals is based on numerical dispersion analysis of Laplace-domain elastic wave equation. A new method of numerical dispersion analysis is developed for Laplace-domain 2-D elastic wave equation. The novelty of the method lies in two aspects: (1) Based on the concept of the pseudo-wavelength for both - and -waves, I introduce a general quantity which is a combination of the Laplace constant, velocity and grid interval. Therefore, the dispersion relations no longer directly depend on the concrete Laplace constant, velocity and grid interval. Just like the frequency-domain dispersion analysis, a general conclusion with regard to the general quantity can be made; (2) The ratio of numerical eigenvalue to analytical eigenvalue can be interpreted as the normalised attenuation propagation velocity. The number of grid points per -wave pseudo-wavelength is determined by the accuracy of normalised - and -wave attenuation propagation velocities. Based on a commonly used finite-element scheme, the numbers of grid points per -wave pseudo-wavelength are determined for different Poisson ratios and for different ratios of directional grid intervals. These results are important in applying the finite-element scheme to Laplace-domain elastic wave modelling and full waveform inversion. Comparisons with the analytical solution validate the criterion on the numbers of grid points per -wave pseudo-wavelength.

© 2020 Australian Society of Exploration Geophysicists
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2020-07-03
2026-01-22

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/content/journals/10.1080/08123985.2020.1725385
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A new method for numerical dispersion analysis of Laplace-domain 2-D elastic wave equation
Exploration Geophysics 51, 456 (2020); https://doi.org/10.1080/08123985.2020.1725385
/content/journals/10.1080/08123985.2020.1725385
/content/journals/10.1080/08123985.2020.1725385
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  • Article Type: Research Article
Keyword(s): dispersion; finite element; modelling; Numerical

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