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**Summary**

For modeling scalar-wave propagation using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes suppress only spatial but not temporal dispersion errors. We develop a novel optimized finitedifference scheme to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within a given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally two times faster than the high-order finite-difference scheme using the same new stencil or the optimized finitedifference schemes using the standard stencil. This new optimized finite-difference scheme is particularly useful for largescale 3D scalar-wave modeling, reverse-time migration, and full-waveform inversion.

Artificial Intelligence, dispersion error, FD scheme, finite-difference scheme, modeling, new stencil, objective function, optimized fd scheme, optimized scheme, phase velocity, propagation, relative error, Reservoir Characterization, scalar-wave propagation, staggered-grid finite-difference scheme optimized, standard stencil, stencil, time interval, time-space domain, Upstream Oil & Gas, waveform, wavenumber

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Yan, Hongyong (Institute of Geology and Geophysics, Chinese Academy of Sciences) | Yang, Lei (Institute of Geology and Geophysics, Chinese Academy of Sciences) | Dai, Hengchang (British Geological Survey) | Li, Xiang-Yang (British Geological Survey)

Staggered-grid finite-difference (SFD) schemes have been used widely in numerical modeling. The spatial SFD coefficients are usually derived by a Taylor-series expansion (TE) method or optimization methods. However, high accuracy is not guaranteed both at small and large wavenumbers by using these conventional methods. In this paper, we present a new optimal SFD scheme using TE with a minimax approximation for high accuracy modeling. The optimal spatial SFD coefficients are calculated by using TE with a minimax approximation based on a Remez algorithm. We use the optimal SFD coefficients to solve first-order spatial derivatives of the elastic wave equations and then perform numerical modeling. Dispersion analyses and numerical modeling show the advantage of the optimal method. The optimal SFD scheme has better accuracy than the TE-based SFD scheme for the same spatial difference operator length, and can also adopt a shorter operator length to achieve the same accuracy reducing the computational cost.

Presentation Date: Wednesday, October 19, 2016

Start Time: 2:20:00 PM

Location: Lobby D/C

Presentation Type: POSTER

accuracy, Artificial Intelligence, coefficient, dispersion, elastic wave modeling, equation, finite-difference scheme, minimax approximation, modeling, numerical dispersion, numerical modeling, optimal SFD scheme, optimal staggered-grid finite-difference scheme, Reservoir Characterization, seg seg international exposition, sfd coefficient, SFD scheme, spatial sfd coefficient, staggered-grid finite-difference scheme, tebased sfd scheme, Upstream Oil & Gas, wavenumber

SPE Disciplines:

Technology: Information Technology > Artificial Intelligence > Representation & Reasoning > Search (0.83)

The acoustic wave equation has been widely used for the modeling and reverse-time migration of seismic data. The finite-difference method has long been the favored approach to solve this equation. To ensure quality results, accurate approximations are required for the spatial and time derivatives. This can be achieved numerically by using either very fine computation grids or very long finite-difference operators. Otherwise, the numerical error, called numerical dispersion, will be present in the data and contaminate the signals. However, either approach increases the computation cost dramatically. In this paper, we propose a new approach to address this problem by constructing a new wave equation, which we call the anti-dispersion wave equation. It involves introducing a dispersion attenuation term to the standard wave equation. When it is solved using finite difference, numerical dispersion in the original wave equation is attenuated significantly, leading to a much more accurate finite difference scheme with little additional computation cost.

annual international meeting, anti-dispersion wave equation, equation, finite-difference scheme, geophysics, grid, migration, nd order finite-difference scheme, new wave equation, numerical dispersion, order finite-difference scheme, order scheme, Reservoir Characterization, Reverse Time Migration, reverse-time migration, shot gather, th order scheme, Upstream Oil & Gas, Wave Equation

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

**Summary**

In this study, rotated staggered-grid (RSG) scheme is optimized by introducing compact finite-difference operator and global optimization. RSG is widely used in seismic forward modeling field because it needs no elastic moduli interpolations, so it is better suited for anisotropic media forward modeling than standard staggered-grid (SSG). However, for the same size of grid cells, rotated staggered-grid needs longer step than standard staggered- grid and tend to produce spatial numerical dispersion. To solve this problem, we introduce the compact finite-difference operator. Although the compact finite-difference operator is more accurate and has less numerical dispersion than conventional finite-difference operator, there still is non-negligible numerical dispersion when the wavenumber is big. So to further broaden the wavenumber or frequency range without lengthening the operator length, global optimization is carried out. Both the dispersion analysis and modeling tests show that the optimized compact finite-difference rotated staggered-grid scheme (CRSG) has lower dispersion than conventional RSG scheme.

10-order compact operator, Artificial Intelligence, coefficient, compact finite difference scheme, conventional compact fd 1, equation, finite-difference operator, finite-difference scheme, forward modeling, global optimization, numerical dispersion, operator, optimization, sabased operator, seg denver 2014, staggered-grid scheme, Upstream Oil & Gas

SPE Disciplines:

No preview is available for this paper.

acoustic layer, acoustic-elastic media, finite-difference grid, finite-difference scheme, finite-difference synthetic, formulation, fourth-order velocity stress finite-difference scheme, gm cm3, grid dispersion, propagation, reflectivity algorithm, Reservoir Characterization, seismogram, solid synthetic, source pulse, synthetic, transition layer, Upstream Oil & Gas, virieux

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Thank you!