Elastic wave modelling method based on the displacement–velocity fields: an improving nearly analytic discrete approximation

Yang, Dinghui; Liu, Enru; Song, Guojie; Wang, Nian

doi:10.1007/s10950-008-9122-2

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…To get the high-order derivatives of the displacement, following Konddoh [9] and Yang et al [25], we can obtain the approximation formulae by using the local interpolation method, which have similar expressions as in [21]. For convenience, we present the ap-…”

Section: A Evaluation Of High-order Derivativesmentioning

confidence: 99%

“…However, numerical dispersion may still exist when too few samples per wavelength are used [15,22]. The nearly analytic discrete method (NADM) [25] proposed recently and its improved version (INADM) [21] are much superior with regard to suppressing the numerical dispersion. These methods, based on the truncated Taylor expansion and the local interpolation compensation for the truncated Taylor series, use the wave displacement-, the velocity-and their gradient-fields to reconstruct the wave displacement fields.…”

Section: Introductionmentioning

confidence: 99%

“…These methods, based on the truncated Taylor expansion and the local interpolation compensation for the truncated Taylor series, use the wave displacement-, the velocity-and their gradient-fields to reconstruct the wave displacement fields. Thus they can effectively suppress the numerical dispersion, as compared to the compact FD methods [21,24,25].…”

Section: Introductionmentioning

confidence: 99%

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A Weighted Runge-Kutta Method with Weak Numerical Dispersion for Solving Wave Equations

Chen¹

2010

CICP

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In this paper, we propose a weighted Runge-Kutta (WRK) method to solve the 2D acoustic and elastic wave equations. This method successfully suppresses the numerical dispersion resulted from discretizing the wave equations. In this method, the partial differential wave equation is first transformed into a system of ordinary differential equations (ODEs), then a third-order Runge-Kutta method is proposed to solve the ODEs. Like the conventional third-order RK scheme, this new method includes three stages. By introducing a weight to estimate the displacement and its gradients in every stage, we obtain a weighted RK (WRK) method. In this paper, we investigate the theoretical properties of the WRK method, including the stability criteria, numerical error, and the numerical dispersion in solving the 1D and 2D scalar wave equations. We also compare it against other methods such as the high-order compact or so-called Lax-Wendroff correction (LWC) and the staggered-grid schemes. To validate the efficiency and accuracy of the method, we simulate wave fields in the 2D homogeneous transversely isotropic and heterogeneous isotropic media. We conclude that the WRK method can effectively suppress numerical dispersions and source noises caused in using coarse grids and can further improve the original RK method in terms of the numerical dispersion and stability condition.

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Section: A Evaluation Of High-order Derivativesmentioning

confidence: 99%