Efficient and accurate numerical simulation of acoustic wave propagation in a 2D heterogeneous media

Liao, Wenyuan; Yong, Peng; Dastour, Hatef; Huang, Jianping

doi:10.1016/j.amc.2017.10.052

Cited by 20 publications

(11 citation statements)

References 32 publications

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“…where the high-order derivatives are derived using the method in [21]. Now we state and prove the main result on the convergence of the compact ADI FD scheme defined in Eq.…”

Section: Derivation Of the Compact High-order Adi Methodsmentioning

confidence: 82%

“…Now we extend the novel algebraic manipulation introduced in [21] to the three-dimensional acoustic wave equation with variable velocity. We first demonstrate the difficulty in applying the Padé approximation to the finite difference operator for solving the acoustic wave equation with non-constant velocity.…”

Section: Derivation Of the Compact High-order Adi Methodsmentioning

confidence: 99%

“…x + h 4 y + h 4 z ), provided the solution u(x, y, z, t) and c(x, y, z) satisfy certain smoothness conditions. As shown in [21], the difficulty to develop high-order compact scheme for wave equation with non-constant velocity is that, one can not multiply the operator , which are difficult to implement. To overcome this problem, we develop an algebraic strategy which will be described in the next section.…”

Section: Acoustic Wave Equation and Existing Algorithmsmentioning

confidence: 99%

“…In [21] a new fourth-order compact ADI FD scheme was proposed to solve the two-dimensional acoustic wave equation with spatially variable velocity. Here we extended this method and the Padé approximation based high-order compact FD scheme in [8] to the 3D acoustic wave equation with non-constant velocity.…”

Section: Introductionmentioning

confidence: 99%

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A compact high order Alternating Direction Implicit method for three-dimensional acoustic wave equation with variable coefficient

Liao

Lin

2019

Journal of Computational and Applied Mathematics

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Efficient and accurate numerical simulation of seismic wave propagation is important in various Geophysical applications such as seismic full waveform inversion (FWI) problem. However, due to the large size of the physical domain and requirement on low numerical dispersion, many existing numerical methods are inefficient for numerical modelling of seismic wave propagation in an heterogenous media. Despite the great efforts that have been devoted during the past decades, it still remains a challenging task in the development of efficient and accurate finite difference method for multi-dimensional acoustic wave equation with variable velocity. In this paper we proposed a Padé approximation based finite difference scheme for solving the acoustic wave equation in threedimensional heterogeneous media. The new method is obtained by combining the Padé approximation and a novel algebraic manipulation. The efficiency of the new algorithm is further improved through the Alternative Directional Implicit (ADI) method. The stability of the new algorithm has been theoretically proved by energy method. The new method is conditionally stable with a better Courant -Friedrichs -Lewy condition (CFL) condition, which has been verified numerically. Extensive numerical examples have been solved, which demonstrated that the new method is accurate, efficient and stable.

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“…where the high-order derivatives are derived using the method in [21]. Now we state and prove the main result on the convergence of the compact ADI FD scheme defined in Eq.…”

Section: Derivation Of the Compact High-order Adi Methodsmentioning

confidence: 82%

Section: Derivation Of the Compact High-order Adi Methodsmentioning

confidence: 99%

Section: Acoustic Wave Equation and Existing Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A compact high order Alternating Direction Implicit method for three-dimensional acoustic wave equation with variable coefficient

Liao

Lin

2019

Journal of Computational and Applied Mathematics

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“…Some schemes attempt to address this drawback. For example, using a novel algebraic manipulation of finite difference operators, a high-order compact FDM was proposed in [16] for 2D acoustic wave equations with variable velocity. Then a similar compact scheme based on Padé approximation was developed in [14] to solve 3D problem.…”

Section: Introductionmentioning

confidence: 99%

An efficient and high accuracy finite-difference scheme for the acoustic wave equation in 3D heterogeneous media

Liao

2020

Journal of Computational Science

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Efficient and accurate numerical simulation of 3D acoustic wave propagation in heterogeneous media plays an important role in the success of seismic full waveform inversion (FWI) problem. In this work we employed the combined scheme and developed a new explicit compact high-order finite difference scheme to solve the 3D acoustic wave equation with spatially variable acoustic velocity. The boundary conditions for the second derivatives of spatial variables have been derived by using the equation itself and the boundary condition for u. Theoretical analysis shows that the new scheme has an accuracy order of O(τ 2 ) + O(h 4 ), where τ is the time step and h is the grid size. Combined with Richardson extrapolation or Runge-Kutta method, the new method can be improved to 4th-order in time. Three numerical experiments are conducted to validate the efficiency and accuracy of the new scheme. The stability of the new scheme has been proved by an energy method, which shows that the new scheme is conditionally stable with a Courant -Friedrichs -Lewy (CFL) number which is slightly lower than that of the Padé approximation based method.

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A Fourth-Order Compact Numerical Scheme for Three-Dimensional Acoustic Wave Equation with Variable Velocity

Liao

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Efficient and accurate numerical simulation of acoustic wave propagation in a 2D heterogeneous media

Cited by 20 publications

References 32 publications

A compact high order Alternating Direction Implicit method for three-dimensional acoustic wave equation with variable coefficient

A compact high order Alternating Direction Implicit method for three-dimensional acoustic wave equation with variable coefficient

An efficient and high accuracy finite-difference scheme for the acoustic wave equation in 3D heterogeneous media

A Fourth-Order Compact Numerical Scheme for Three-Dimensional Acoustic Wave Equation with Variable Velocity

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