An improved nearly analytical discrete method: an efficient tool to simulate the seismic response of 2-D porous structures

Yang, Dinghui; Song, Guojie; Chen, Shan; Hou, Boyang

doi:10.1088/1742-2132/4/1/006

Cited by 30 publications

(13 citation statements)

References 41 publications

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“…3b) shows the desired circularly symmetric wave front. For method (1), the numerical dispersion and source-generated noises caused by the discretizing the wave equations with too-coarse grids in the finite difference implementation can be suppressed by using some damage-control techniques such as a flux-corrected transport technique (Yang et al 2002) or a nearly analytical discrete method (Yang et al 2007). But in this paper, we simply chose method (2) for all future implementations.…”

Section: Seismic Sourcementioning

confidence: 99%

Elastic wave modelling by an integrated finite difference method

Hall¹,

Wang²

2009

Geophysical Journal International

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Section: Seismic Sourcementioning

confidence: 99%

Elastic wave modelling by an integrated finite difference method

Hall¹,

Wang²

2009

Geophysical Journal International

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“…This approach uses a truncated Taylor expansion with respect to time to analytically approximate the wave displacement and its gradients at grid points, while the high-order space derivatives involved in these truncated Taylor formulae are determined through using some interpolation relations based on the functions of the truncated Taylor expansion with respect to spatial increments. Based on the same idea, several versions have been developed, including the nearly analytic discrete method (NADM), the optimal nearly analytic discrete method (ONADM) (Yang et al, 2006), Runge-Kutta method using high-order interpolation approximation (Yang et al, 2007a) for solving 2D acoustic and elastic wave equations, and the improved nearly analytical discrete method (INADM) for 2D porous elastic wave equations (Yang et al, 2007b). Numerical results of these schemes illustrate that the NADM-based approaches can effectively suppress numerical dispersions caused by the discretization of the wave equations when too-coarse grids are used.…”

Section: Introductionmentioning

confidence: 99%

High accuracy wave simulation – Revised derivation, numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic wave equation

Tong

Yang

Bao³

2011

International Journal of Solids and Structures

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a b s t r a c tThe nearly analytic integration discrete (NAID) method for solving the two-dimensional acoustic wave equation has been fully mathematically revised, analyzed and tested. The NAID method is an alternative numerical modeling method for generating synthetic seismograms. The acoustic wave equation is first transformed into a system of first-order ordinary differential equations (ODEs) with respect to time variable t, and then directly integrated at a small time interval of [t n , t n+1 ] to obtain semi-discrete ordinary differential equations. The integral kernel is expanded into a truncated Taylor series, to which the integration operator is explicitly applied. The high-order temporal derivatives involved in the integral kernel are replaced by high-order spatial derivatives, which then are approximately calculated as a weighted linear combination of the displacement, the particle-velocity, and their spatial gradients. In this article, we investigate the theoretical properties of the revised NAID method, including the discrete error and the stability criteria. Numerical results for constant and layered velocity models show that, comparing to the Lax-Wendroff correction (LWC) scheme and the staggered-grid finite difference method, the NAID method can effectively suppress the numerical dispersion and source-noises caused by the discretization of the acoustic wave equation with too-coarse spatial grids or when models have strong velocity contrasts between adjacent layers. The proposed NAID method has been applied in computing the acoustic wavefields for two heterogeneous models -the corner edge model and the Marmousi model. Promising numerical results illustrate that the NAID method provides an encouraging tool for large-scale and complex wave simulation and inversion problems based on the acoustic equation.

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“…Hence it enables effectively to suppress the numerical dispersion. However, the NADM has only second‐order time accuracy (Yang et al 2007). To increase the accuracy of the NADM and save the space storage for computer code, the so‐called the optimal NADM (ONADM) for solving acoustic‐ and elastic‐wave equations for the single‐phase medium case was also suggested by Yang et al (2004, 2006), however the ONADM cannot be applied to the two‐phase porous wave equations including the so‐called velocity ∂U/∂t of the wave displacement U because the ONADM does not compute the velocity‐fields.…”

Section: Introductionmentioning

confidence: 99%

An explicit split-step algorithm of the implicit Adams method for solving 2-D acoustic and elastic wave equations

Yang

Wang

Deng

2010

Geophysical Journal International

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S U M M A R YWe first transform the seismic wave equations in 2-D inhomogeneous anisotropic media into a system of first-order partial differential equations with respect to time t. And then we develop a new explicit split-step algorithm (SSA) to solve the transformed equations through using the implicit Adams method and high-order interpolation approximation. Our algorithm enables wave propagation to be simulated in two dimensions through generally isotropic and anisotropic models. The high-order space derivatives in this SSA are determined by using the wave displacement, particle-velocity and its gradients simultaneously, while the time advancing of modelling seismic propagation uses the slit-operator algorithm based on the thirdorder implicit Adams method. On the basis of such a structure, the so-called SSA can suppress effectively the numerical dispersion and source-generated noises caused by discretizing the wave equations when too-coarse grids are used, and is third-order accuracy in time and fourth-order accuracy in space. We explore the theoretical properties of the SSA including the stability criteria of the SSA for solving 1-D and 2-D scalar wave equations, numerical dispersion, theoretical error and numerical error and computational efficiency when using the SSA to model the acoustic wave fields. Meanwhile, we also present the synthetic seismograms generated by the SSA in the three-layer isotropic medium and the 2-D elastic two-layer isotropic and anisotropic wavefield snapshots computed by the fourth-order Lax-Wendroff correction (LWC) scheme and the SSA, respectively. Numerical calculations of the relative errors show that the numerical error of the SSA is less than those of the conventional finite difference (FD) method and the fourth-order LWC scheme. Promising numerical results further illustrate that the SSA has less numerical dispersions and can suppress effectively the source-generated noises, further resulting in both increasing the computational efficiency and saving the space storage.

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An improved nearly analytical discrete method: an efficient tool to simulate the seismic response of 2-D porous structures

Cited by 30 publications

References 41 publications

Elastic wave modelling by an integrated finite difference method

Elastic wave modelling by an integrated finite difference method

High accuracy wave simulation – Revised derivation, numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic wave equation

An explicit split-step algorithm of the implicit Adams method for solving 2-D acoustic and elastic wave equations

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