Accuracy of the staggered-grid finite-difference method of the acoustic wave equation for marine seismic reflection modeling

Jin, Qingjun; Wu, Shiguo; Ruo-fei, Cui

doi:10.1007/s00343-013-2074-6

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…Finite difference (FD) modeling methods have been actively applied to seismic wave propagation problems on the last fifty years. In this area, advanced methods use staggered grids (SG) in combination to fourth-and higher-order FD formulas to resolve the wave equation in first order formulation, and then solving for all dependent variables [2], [17], [19], [26], [35], [38] [41], [42]. In particular, the velocity-pressure formulation of the acoustic wave equation allows stating free surface and rigid wall boundary conditions as simple Dirichlet conditions, and is also well suited for the implementation of absorbing boundaries.…”

Section: Introductionmentioning

confidence: 99%

Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence

et al. 2020

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Section: Introductionmentioning

confidence: 99%

Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence

et al. 2020

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“…Finite difference (FD) modeling methods have been actively applied to seismic wave propagation problems on the last fifty years. In this area, advanced methods use staggered grids (SG) in combination to fourth-and higherorder FD formulas to resolve the wave equation in first order formulation, and then solving for all dependent variables [2], [17], [19], [26], [35], [38] [41], [42]. In particular, the velocity-pressure formulation of the acoustic wave equation allows stating free surface and rigid wall boundary conditions as simple Dirichlet conditions, and is also well suited for the implementation of absorbing boundaries.…”

Section: Introductionmentioning

confidence: 99%

Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence

Otero,

Rojas,

Moya

et al. 2020

Preprint

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This work studies the parallelization and empirical convergence of two finite difference acoustic wave propagation methods on 2-D rectangular grids, that use the same alternating direction implicit (ADI) time integration. This ADI integration is based on a second-order implicit Crank-Nicolson temporal discretization that is factored out by a Peaceman-Rachford decomposition of the time and space equation terms. In space, these methods highly diverge and apply different fourth-order accurate differentiation techniques. The first method uses compact finite differences (CFD) on nodal meshes that requires solving tridiagonal linear systems along each grid line, while the second one employs staggered-grid mimetic finite differences (MFD). For each method, we implement three parallel versions: (i) a multithreaded code in Octave, (ii) a C++ code that exploits OpenMP loop parallelization, and (iii) a CUDA kernel for a NVIDIA GTX 960 Maxwell card. In these implementations, the main source of parallelism is the simultaneous ADI updating of each wave field matrix, either column-wise or row-wise, according to the differentiation direction. In our numerical applications, the highest performances are displayed by the CFD and MFD CUDA codes that achieve speedups of 7.21x and 15.81x, respectively, relative to their C++ sequential counterparts with optimal compilation flags. Our test cases also allow to assess the numerical convergence and accuracy of both methods. In a problem with exact harmonic solution, both methods exhibit convergence rates close to 4 and the MDF accuracy is practically higher. Alternatively, both convergences decay to second order on smooth problems with severe gradients at boundaries, and the MDF rates degrade in highly-resolved grids leading to larger inaccuracies. This transition of empirical convergences agrees with the nominal truncation errors in space and time.

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“…On these grids, each wave field is computed at a separate nodal grid displaced by half of the grid spacing (in one or more directions) from the remaining individual grids. The advantage of such geometrical distribution of discrete values is that each scalar field is located at the center of those it depends upon, and numerical differentiation gains accuracy by halving the grid step . Grid staggering has been also successfully applied for FD simulations of wave propagation in the case of more general elastic or viscoelastic media .…”

Section: Introductionmentioning

confidence: 99%

A performance analysis of a mimetic finite difference scheme for acoustic wave propagation on GPU platforms

Otero

Francés

Rodriguez

et al. 2016

Concurrency and Computation

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, J. A performance analysis of a mimetic finite differencescheme for acoustic wave propagation on GPU platforms. "Concurrency and computation. Practice and experience", 1 Febrer 2017, vol. 29, núm. 4, p. 1-18 SUMMARYRealistic applications of numerical modeling of acoustic wave dynamics usually demand high performance computing because of the large size of study domains and demanding accuracy requirements on simulation results. Forward modeling of seismic motion on a given subsurface geological structure is by itself a good example of such applications, and when used as a component of seismic inversion tools or as a guide for the design of seismic surveys, its computational cost increases enormously. In the case of finite difference methods (or any other volumen-discretization scheme), memory and computing demands rise with grid refinement which may be neccesary to reduce errors on numerical wave patterns and better capture target physical devices. In this work, we present several implementations of a mimetic finite difference method for the simulation of acoustic wave propagation on highly dense staggered grids. These implementations evolve as different optimization strategies are employed starting from appropriate setting of compilation flags, code vectorization by using SSE and AVX instructions, CPU parallelization by exploiting the OpenMP framework, to the final code parallelization on GPU platforms. We present and discuss the increasing processing speed-up of this mimetic scheme achieved by the gradual implementation and testing of all these performance optimizations. In terms of simulation times, the performance of our GPU parallel implementations is consistently better than the best CPU version.Received . . . KEY WORDS: Acoustic waves; mimetic finite differences; SIMD extensions; GPU; CUDA programming * Correspondence to: C/ Jordi Girona 1.3, Edf. 08034, This is the peer reviewed version of the following article: Otero, B., Frances, J., Rodriguez-Cruz, R., Rojas, O., Solano, F., Guevara-Jordan, J. A performance analysis of a mimetic finite difference scheme for acoustic wave propagation on GPU platforms. "Concurrency and computation.

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Accuracy of the staggered-grid finite-difference method of the acoustic wave equation for marine seismic reflection modeling

Cited by 7 publications

References 18 publications

Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence

Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence

Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence

A performance analysis of a mimetic finite difference scheme for acoustic wave propagation on GPU platforms

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