The Experts below are selected from a list of 13074 Experts worldwide ranked by ideXlab platform
Mrinal K. Sen - One of the best experts on this subject based on the ideXlab platform.
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time space domain dispersion relation based finite difference method with arbitrary even order accuracy for the 2d Acoustic Wave Equation
Journal of Computational Physics, 2013Co-Authors: Yang Liu, Mrinal K. SenAbstract:High-order finite-difference (FD) methods have been widely used for numerical solution of Acoustic Wave Equations. It has been reported that the modeling accuracy is of 2nd-order when the conventional (2M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the Acoustic Wave Equation. Under the same discretization, the present version of time-space domain dispersion-relation-based FD method can improve the accuracy from 2nd-order to (2M)th-order along eight directions for the 2D Acoustic Wave Equation. To increase the accuracy further, we propose a new FD stencil for 2D Acoustic Wave Equation modeling. This new time-space domain dispersion-relation-based FD stencil can reach the same arbitrary even-order accuracy along all directions, and is more accurate and more stable than the conventional one for the same M. Dispersion analysis and modeling examples demonstrate its advantages.
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Time-space Domain Finite-difference Method with Arbitrary Even-order Accuracy for the 2D Acoustic Wave Equation
73rd EAGE Conference and Exhibition incorporating SPE EUROPEC 2011, 2011Co-Authors: Yang Liu, Mrinal K. SenAbstract:High-order finite-difference (FD) methods have been widely used in numerically solving seismic Wave Equations. It has been reported that the modeling accuracy is 2nd-order when the conventional (2M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the Acoustic Wave Equation. Under the same discretization, the present version of time-space domain dispersion-relation-based FD method for the 2D Acoustic Wave Equation can improve the accuracy from second-order to (2M)th-order accuracy along eight directions. To increase the accuracy further, we propose a new FD stencil for the 2D Acoustic Wave Equation modeling. This new time-space domain dispersion-relation-based FD stencil can reach the same arbitrary even-order along all directions, and is more accurate and more stable than the conventional one for the same M. Dispersion analysis and modeling examples demonstrate its advantages.
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a new time space domain high order finite difference method for the Acoustic Wave Equation
Journal of Computational Physics, 2009Co-Authors: Yang Liu, Mrinal K. SenAbstract:A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D Acoustic Wave modeling using a plane Wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the Acoustic Wave Equation. However, under the same discretization, the new 1D method can reach (2M)th-order accuracy and is always stable. The 2D method can reach (2M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of Acoustic Wave Equation for homogeneous and inhomogeneous Acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D Acoustic Wave Equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference Equations arising in other fields of science and engineering.
Yang Liu - One of the best experts on this subject based on the ideXlab platform.
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time space domain dispersion relation based finite difference method with arbitrary even order accuracy for the 2d Acoustic Wave Equation
Journal of Computational Physics, 2013Co-Authors: Yang Liu, Mrinal K. SenAbstract:High-order finite-difference (FD) methods have been widely used for numerical solution of Acoustic Wave Equations. It has been reported that the modeling accuracy is of 2nd-order when the conventional (2M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the Acoustic Wave Equation. Under the same discretization, the present version of time-space domain dispersion-relation-based FD method can improve the accuracy from 2nd-order to (2M)th-order along eight directions for the 2D Acoustic Wave Equation. To increase the accuracy further, we propose a new FD stencil for 2D Acoustic Wave Equation modeling. This new time-space domain dispersion-relation-based FD stencil can reach the same arbitrary even-order accuracy along all directions, and is more accurate and more stable than the conventional one for the same M. Dispersion analysis and modeling examples demonstrate its advantages.
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Time-space Domain Finite-difference Method with Arbitrary Even-order Accuracy for the 2D Acoustic Wave Equation
73rd EAGE Conference and Exhibition incorporating SPE EUROPEC 2011, 2011Co-Authors: Yang Liu, Mrinal K. SenAbstract:High-order finite-difference (FD) methods have been widely used in numerically solving seismic Wave Equations. It has been reported that the modeling accuracy is 2nd-order when the conventional (2M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the Acoustic Wave Equation. Under the same discretization, the present version of time-space domain dispersion-relation-based FD method for the 2D Acoustic Wave Equation can improve the accuracy from second-order to (2M)th-order accuracy along eight directions. To increase the accuracy further, we propose a new FD stencil for the 2D Acoustic Wave Equation modeling. This new time-space domain dispersion-relation-based FD stencil can reach the same arbitrary even-order along all directions, and is more accurate and more stable than the conventional one for the same M. Dispersion analysis and modeling examples demonstrate its advantages.
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a new time space domain high order finite difference method for the Acoustic Wave Equation
Journal of Computational Physics, 2009Co-Authors: Yang Liu, Mrinal K. SenAbstract:A new unified methodology was proposed in Finkelstein and Kastner (2007) [39] to derive spatial finite-difference (FD) coefficients in the joint time-space domain to reduce numerical dispersion. The key idea of this method is that the dispersion relation is completely satisfied at several designated frequencies. We develop this new time-space domain FD method further for 1D, 2D and 3D Acoustic Wave modeling using a plane Wave theory and the Taylor series expansion. New spatial FD coefficients are frequency independent though they lead to a frequency dependent numerical solution. We prove that the modeling accuracy is 2nd-order when the conventional (2M)th-order space domain FD and the 2nd-order time domain FD stencils are directly used to solve the Acoustic Wave Equation. However, under the same discretization, the new 1D method can reach (2M)th-order accuracy and is always stable. The 2D method can reach (2M)th-order accuracy along eight directions and has better stability. Similarly, the 3D method can reach (2M)th-order accuracy along 48 directions and also has better stability than the conventional FD method. The advantages of the new method are also demonstrated by the results of dispersion analysis and numerical modeling of Acoustic Wave Equation for homogeneous and inhomogeneous Acoustic models. In addition, we study the influence of the FD stencil length on numerical modeling for 1D inhomogeneous media, and derive an optimal FD stencil length required to balance the accuracy and efficiency of modeling. A new time-space domain high-order staggered-grid FD method for the 1D Acoustic Wave Equation with variable densities is also developed, which has similar advantages demonstrated by dispersion analysis, stability analysis and modeling experiments. The methodology presented in this paper can be easily extended to solve similar partial difference Equations arising in other fields of science and engineering.
Wenyuan Liao - One of the best experts on this subject based on the ideXlab platform.
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a compact high order alternating direction implicit method for three dimensional Acoustic Wave Equation with variable coefficient
Journal of Computational and Applied Mathematics, 2019Co-Authors: Wenyuan Liao, Yaoting LinAbstract:Abstract 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 heterogeneous 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 Pade approximation based finite difference scheme for solving the Acoustic Wave Equation in three-dimensional heterogeneous media. The new method is obtained by combining the Pade 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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an efficient and high accuracy finite difference scheme for the Acoustic Wave Equation in 3d heterogeneous media
arXiv: Numerical Analysis, 2019Co-Authors: Wenyuan LiaoAbstract: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 $O(\tau^2) + O(h^4)$, where $\tau$ 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 Pade approximation based method.
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a compact high order alternating direction implicit method for three dimensional Acoustic Wave Equation with variable coefficient
arXiv: Numerical Analysis, 2019Co-Authors: Wenyuan Liao, Yaoting LinAbstract: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 a heterogeneous 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 the multi-dimensional Acoustic Wave Equation with variable velocity. In this paper, we proposed a Pade approximation based finite difference scheme for solving the Acoustic Wave Equation in three-dimensional heterogeneous media. The new method is obtained by combining the Pade 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 the 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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A Fourth-Order Compact Numerical Scheme for Three-Dimensional Acoustic Wave Equation with Variable Velocity
Springer Proceedings in Mathematics & Statistics, 2018Co-Authors: Wenyuan Liao, Ou WeiAbstract:In this paper we proposed an accurate and efficient numerical algorithm for solving the Acoustic Wave Equation in three-dimensional heterogeneous media. Numerical solution of the Wave Equation has been used in various science and engineering applications, such as the seismic full Waveform inversion (FWI) problem. FWI is a computationally intensive procedure, in which the Acoustic Wave Equation is numerically solved (forward modelling) repeatedly during the iterative process. Therefore, efficiency and accuracy of the numerical method for solving the Acoustic Wave Equation is critical in the success of seismic full Waveform inversion. The new method is obtained by combining the Pade approximation and a novel algebraic manipulation with the Alternative Directional Implicit (ADI) method. Numerical experiments have shown that the new method is accurate, efficient and stable.
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A Fourth-Order Compact Numerical Scheme for Three-Dimensional Acoustic Wave Equation with Variable Velocity
Recent Advances in Mathematical and Statistical Methods, 2018Co-Authors: Wenyuan Liao, Ou WeiAbstract:In this paper we proposed an accurate and efficient numerical algorithm for solving the Acoustic Wave Equation in three-dimensional heterogeneous media. Numerical solution of the Wave Equation has been used in various science and engineering applications, such as the seismic full Waveform inversion (FWI) problem. FWI is a computationally intensive procedure, in which the Acoustic Wave Equation is numerically solved (forward modelling) repeatedly during the iterative process. Therefore, efficiency and accuracy of the numerical method for solving the Acoustic Wave Equation is critical in the success of seismic full Waveform inversion. The new method is obtained by combining the Padé approximation and a novel algebraic manipulation with the Alternative Directional Implicit (ADI) method. Numerical experiments have shown that the new method is accurate, efficient and stable.
Changchun Yang - One of the best experts on this subject based on the ideXlab platform.
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A simplified staggered-grid finite-difference scheme and its linear solution for the first-order Acoustic Wave-Equation modeling
Journal of Computational Physics, 2018Co-Authors: Wenquan Liang, Yanfei Wang, Changchun YangAbstract:Abstract First-order staggered-grid finite-difference methods are widely used to synthesize seismograms theoretically. They are also the basis of least-squares reverse time migration and full Waveform inversion. It is important to accelerate the Wave-Equation simulation while still preserving high accuracy. Usually the same staggered-grid finite difference operator is used for all of the first-order spatial derivatives in the first-order Acoustic Wave-Equation. In this paper, we propose a simplified staggered-grid finite-difference scheme which uses different finite-difference operators for different first-order spatial derivatives in the first-order Acoustic Wave-Equation. Because the new dispersion relation is linear, the staggered-grid finite-difference coefficients are determined in the time-space domain with the previously proposed linear method. We demonstrate by dispersion analysis and numerical simulation the efficiency of the proposed method.
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determining finite difference weights for the Acoustic Wave Equation by a new dispersion relationship preserving method
Geophysical Prospecting, 2015Co-Authors: Wenquan Liang, Yanfei Wang, Changchun YangAbstract:Numerical simulation of the Acoustic Wave Equation is widely used to theoretically synthesize seismograms and constitutes the basis of reverse-time migration. With finite-difference methods, the discretization of temporal and spatial derivatives in Wave Equations introduces numerical grid dispersion. To reduce the grid dispersion effect, we propose to satisfy the dispersion relation for a number of uniformly distributed Wavenumber points within a Wavenumber range with the upper limit determined by the maximum source frequency, the grid spacing and the Wave velocity. This new dispersion-relationship-preserving method relatively uniformly reduces the numerical dispersion over a large-frequency range. Dispersion analysis and seismic numerical simulations demonstrate the effectiveness of the proposed method.
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Determining finite difference weights for the Acoustic Wave Equation by a new dispersion‐relationship‐preserving method
Geophysical Prospecting, 2014Co-Authors: Wenquan Liang, Yanfei Wang, Changchun YangAbstract:Numerical simulation of the Acoustic Wave Equation is widely used to theoretically synthesize seismograms and constitutes the basis of reverse-time migration. With finite-difference methods, the discretization of temporal and spatial derivatives in Wave Equations introduces numerical grid dispersion. To reduce the grid dispersion effect, we propose to satisfy the dispersion relation for a number of uniformly distributed Wavenumber points within a Wavenumber range with the upper limit determined by the maximum source frequency, the grid spacing and the Wave velocity. This new dispersion-relationship-preserving method relatively uniformly reduces the numerical dispersion over a large-frequency range. Dispersion analysis and seismic numerical simulations demonstrate the effectiveness of the proposed method.
Wenquan Liang - One of the best experts on this subject based on the ideXlab platform.
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a new staggered grid finite difference scheme optimised in the space domain for the first order Acoustic Wave Equation
Exploration Geophysics, 2018Co-Authors: Wenquan Liang, Yanfei Wang, Jingjie CaoAbstract:Staggered grid finite difference (FD) methods are widely used to synthesise seismograms theoretically, and are also the basis of reverse time migration and full Waveform inversion. Grid dispersion is one of the key problems for FD methods. It is desirable to have a FD scheme which can accelerate Wave Equation simulation while still preserving high accuracy. In this paper, we propose a totally new staggered grid FD scheme which uses different staggered grid FD operators for different first order spatial derivatives in the first order Acoustic Wave Equation. We determine the FD coefficient in the space domain with the least-squares method. The dispersion analysis and numerical simulation demonstrated the effectiveness of the proposed method.
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A simplified staggered-grid finite-difference scheme and its linear solution for the first-order Acoustic Wave-Equation modeling
Journal of Computational Physics, 2018Co-Authors: Wenquan Liang, Yanfei Wang, Changchun YangAbstract:Abstract First-order staggered-grid finite-difference methods are widely used to synthesize seismograms theoretically. They are also the basis of least-squares reverse time migration and full Waveform inversion. It is important to accelerate the Wave-Equation simulation while still preserving high accuracy. Usually the same staggered-grid finite difference operator is used for all of the first-order spatial derivatives in the first-order Acoustic Wave-Equation. In this paper, we propose a simplified staggered-grid finite-difference scheme which uses different finite-difference operators for different first-order spatial derivatives in the first-order Acoustic Wave-Equation. Because the new dispersion relation is linear, the staggered-grid finite-difference coefficients are determined in the time-space domain with the previously proposed linear method. We demonstrate by dispersion analysis and numerical simulation the efficiency of the proposed method.
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determining finite difference weights for the Acoustic Wave Equation by a new dispersion relationship preserving method
Geophysical Prospecting, 2015Co-Authors: Wenquan Liang, Yanfei Wang, Changchun YangAbstract:Numerical simulation of the Acoustic Wave Equation is widely used to theoretically synthesize seismograms and constitutes the basis of reverse-time migration. With finite-difference methods, the discretization of temporal and spatial derivatives in Wave Equations introduces numerical grid dispersion. To reduce the grid dispersion effect, we propose to satisfy the dispersion relation for a number of uniformly distributed Wavenumber points within a Wavenumber range with the upper limit determined by the maximum source frequency, the grid spacing and the Wave velocity. This new dispersion-relationship-preserving method relatively uniformly reduces the numerical dispersion over a large-frequency range. Dispersion analysis and seismic numerical simulations demonstrate the effectiveness of the proposed method.
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Determining finite difference weights for the Acoustic Wave Equation by a new dispersion‐relationship‐preserving method
Geophysical Prospecting, 2014Co-Authors: Wenquan Liang, Yanfei Wang, Changchun YangAbstract:Numerical simulation of the Acoustic Wave Equation is widely used to theoretically synthesize seismograms and constitutes the basis of reverse-time migration. With finite-difference methods, the discretization of temporal and spatial derivatives in Wave Equations introduces numerical grid dispersion. To reduce the grid dispersion effect, we propose to satisfy the dispersion relation for a number of uniformly distributed Wavenumber points within a Wavenumber range with the upper limit determined by the maximum source frequency, the grid spacing and the Wave velocity. This new dispersion-relationship-preserving method relatively uniformly reduces the numerical dispersion over a large-frequency range. Dispersion analysis and seismic numerical simulations demonstrate the effectiveness of the proposed method.
