Finite Element-finite Difference Method in 2-D Seismic Modeling

Liu, T.; Hu, Tianyue; Yang, Jianwei

doi:10.3997/2214-4609.20148076

Cited by 8 publications

(8 citation statements)

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“…Some values of these coefficients are presented in Table 1, and the formula to find all coefficients can be found in Liu [8].…”

Section: Finite Difference Operatorsmentioning

confidence: 99%

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Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

Abdulkadir¹

2015

JAMP

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Finite difference techniques are widely used for the numerical simulation of time-dependent partial differential equations. In order to get better accuracy at low computational cost, researchers have attempted to develop higher order methods by improving other lower order methods. However, these types of methods usually suffer from a high degree of numerical dispersion. In this paper, we review three higher order finite difference methods, higher order compact (HOC), compact Padé based (CPD) and non-compact Padé based (NCPD) schemes for the acoustic wave equation. We present the stability analysis of the three schemes and derive dispersion characteristics for these schemes. The effects of Courant Friedrichs Lewy (CFL) number, propagation angle and number of cells per wavelength on dispersion are studied.

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“…Some values of these coefficients are presented in Table 1, and the formula to find all coefficients can be found in Liu [8].…”

Section: Finite Difference Operatorsmentioning

confidence: 99%

“…However, the scheme suffers from a moderate numerical dispersion [5]. Therefore, we modify the scheme by substituting one of the spacial grids (in x-direction) in Equation (30) by non-compact one in Equation (8) to obtain a hybrid scheme.…”

Section: Hybrid Schemementioning

confidence: 99%

Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

Abdulkadir¹

2015

JAMP

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“…The aim of this procedure is to inherit the qualities of both methods over the entire spatial domain. We developed and applied it to 2-D acoustic simulation for a complex subsurface model by introducing a non-linear interpolation function for FEM and a perfectly matched layer (PML) absorbing condition to make the algorithm more accurate and stable (Liu et al, 2008). The second seismic forward modeling method is the arbitrary difference precise integration method (ADPI), which employs a FDM scheme in the spatial domain with an integration scheme in the temporal domain.…”

Section: Introductionmentioning

confidence: 99%

Modeling seismic wave propagation within complex structures

et al. 2009

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Seismic modeling is a useful tool for studying the propagation of seismic waves within complex structures. However, traditional methods of seismic simulation cannot meet the needs for studying seismic wavefi elds in the complex geological structures found in seismic exploration of the mountainous area in Northwestern China. More powerful techniques of seismic modeling are demanded for this purpose. In this paper, two methods of fi nite element-fi nite difference method (FE-FDM) and arbitrary difference precise integration (ADPI) for seismic forward modeling have been developed and implemented to understand the behavior of seismic waves in complex geological subsurface structures and reservoirs. Two case studies show that the FE-FDM and ADPI techniques are well suited to modeling seismic wave propagation in complex geology.

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“…Matrix-free stencil operators based on explicit finite difference schemes are widely used in industry and academic research, although they merely represent one of many approaches to solving PDEs [Baba16], [Liu09], [Rai91]. In this paper we therefore limit our discussion of numerical methods and instead focus on the ease with which these operators can be created symbolically.…”

Section: Introductionmentioning

confidence: 99%

Optimised finite difference computation from symbolic equations

Lange¹,

Kukreja²,

Luporini³

et al. 2017

Proceedings of the 16th Python in Science Conference

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Abstract-Domain-specific high-productivity environments are playing an increasingly important role in scientific computing due to the levels of abstraction and automation they provide. In this paper we introduce Devito, an opensource domain-specific framework for solving partial differential equations from symbolic problem definitions by the finite difference method. We highlight the generation and automated execution of highly optimized stencil code from only a few lines of high-level symbolic Python for a set of scientific equations, before exploring the use of Devito operators in seismic inversion problems.

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Finite Element-finite Difference Method in 2-D Seismic Modeling

Cited by 8 publications

References 0 publications

Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

Modeling seismic wave propagation within complex structures

Optimised finite difference computation from symbolic equations

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