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Jean Virieux - One of the best experts on this subject based on the ideXlab platform.
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Accuracy of qP Wave Modeling in Anisotropic Acoustic Media by a Finite-difference Frequency-domain Method
70th EAGE Conference and Exhibition incorporating SPE EUROPEC 2008, 2014Co-Authors: Alessandra Ribodetti, Stéphane Operto, Jean VirieuxAbstract:We assess the kinematic and dynamic accuracies of a finite-difference frequency-domain method for qP wave modelling in transversally isotropic acoustic media with tilted symmetry axis. This method was developed as a tool for frequency-domain full-waveform inversion which requires accurate traveltime and amplitude modelling. The modelling method is based on the parsimonious Mixed-Grid method which requires 5 Grid points per wavelength in homogeneous media to mitigate numerical dispersion. We compare seismograms computed with the acoustic frequency-domain method with that provided by the complete solution of the transversally isotropic elastic wave equation. As expected we observed strong traveltime and amplitude mismatches in the case of strongly anisotropic materials such as zinc crystals. For weak anisotropy, we obtain a reasonable agreement although slight delay of the acoustic wide-angle reflections was observed in the case of a two-layer medium. The footprint of these inaccuracies in full-waveform inversion will need to be assessed before considering application to real data.
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A Frequency-domain Seismic Modeling Engine for 3D Visco-acoustic VTI Full Waveform Inversion of Fixed-spread Data
Proceedings 76th EAGE Conference and Exhibition 2014, 2014Co-Authors: Stéphane Operto, Lila Combe, Romain Brossier, Ludovic Métivier, Alessandra Ribodetti, Jean VirieuxAbstract:Frequency-domain full waveform inversion (FWI) of fixed-spread data can be limited to a few discrete frequencies thanks to the redundant control of frequency and scattering angle on the wavenumber coverage. In this framework, 3D finite-difference frequency-domain seismic modeling can be efficiently performed for multiple sources in the visco-acoustic approximation with sparse direct solver. We extend the so-called Mixed-Grid finite-difference stencil to account for vertical transverse isotropy in viscoacoustic frequency-domain seismic modeling without extra computational cost. The VTI acoustic wave equation is recast as a fourth-order wave equation, which can be decomposed into an elliptic wave equation and an anelliptic term. The discretization of this equation only requires a straightforward adaptation of the existing isotropic stencil. A discretization rule of 4 Grid points per minimum wavelength, which is suitable for FWI applications, is used for frequency-domain seismic modeling. We validate our finite-difference frequency-domain method against a finite-difference time-domain method using a smooth VTI acoustic model of the Valhall oil field. Comparison between the real and modeled data for the 7-Hz frequency suggests that our method can provide a suitable modeling engine to perform multi-parameter FWI of fixed-spread data in visco-acoustic VTI media.
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Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media
Geophysics, 2009Co-Authors: Stéphane Operto, Jean Virieux, Alessandra Ribodetti, John E. AndersonAbstract:A 2D finite-difference, frequency-domain method was developed for modeling viscoacoustic seismic waves in transversely isotropic media with a tilted symmetry axis. The medium is parameterized by the P-wave velocity on the symmetry axis, the density, the attenuation factor, Thomsen's anisotropic parameters delta and epsilon, and the tilt angle. The finite-difference discretization relies on a parsimonious Mixed-Grid approach that designs accurate yet spatially compact stencils. The system of linear equations resulting from discretizing the time-harmonic wave equation is solved with a parallel direct solver that computes monochromatic wavefields efficiently for many sources. Dispersion analysis shows that four Grid points per P-wavelength provide sufficiently accurate solutions in homogeneous media. The absorbing boundary conditions are perfectly matched layers (PMLs). The kinematic and dynamic accuracy of the method wasassessed with several synthetic examples which illustrate the propagation of S-waves excited at the source or at seismic discontinuities when epsilon
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Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media
GEOPHYSICS, 2009Co-Authors: Stéphane Operto, Jean Virieux, Alessandra Ribodetti, John E. AndersonAbstract:A 2D finite-difference, frequency-domain method was developed for modeling viscoacoustic seismic waves in transversely isotropic media with a tilted symmetry axis. The medium is parameterized by the P-wave velocity on the symmetry axis, the density, the attenuation factor, Thomsen’s anisotropic parameters δ and ϵ , and the tilt angle. The finite-difference discretization relies on a parsimonious Mixed-Grid approach that designs accurate yet spatially compact stencils. The system of linear equations resulting from discretizing the time-harmonic wave equation is solved with a parallel direct solver that computes monochromatic wavefields efficiently for many sources. Dispersion analysis shows that four Grid points per P-wavelength provide sufficiently accurate solutions in homogeneous media. The absorbing boundary conditions are perfectly matched layers (PMLs). The kinematic and dynamic accuracy of the method wasassessed with several synthetic examples which illustrate the propagation of S-waves excited at t...
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Mixed-Grid Finite-difference Frequency-domain Viscoacoustic Modeling In 2D TTI Anisotropic Media
SEG Technical Program Expanded Abstracts 2007, 2007Co-Authors: Stéphane Operto, Alessandra Ribodetti, Mehdi Grini, Jean VirieuxAbstract:We present a 2D finite-difference frequency-domain method for modeling viscoacoustic wave propagation in TTI media. The numerical method relies on a parsimonious staggered-Grid method implemented in the frequency domain. Differential operators are discretized along different rotated coordinate systems (the classic Cartesian one and a 45o rotated one) with second-order accurate staggered-Grid stencils. The resulting discrete operators are combined linearly to mitigate numerical anisotropy. An anti-lumped mass strategy is applied to mitigate numerical dispersion. A dispersion analysis for infinite homogeneous media suggests a discretization rule of 5 Grid points per wavelength. Numerical tests confirm the accuracy of the stencil.
Stéphane Operto - One of the best experts on this subject based on the ideXlab platform.
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Accuracy of qP Wave Modeling in Anisotropic Acoustic Media by a Finite-difference Frequency-domain Method
70th EAGE Conference and Exhibition incorporating SPE EUROPEC 2008, 2014Co-Authors: Alessandra Ribodetti, Stéphane Operto, Jean VirieuxAbstract:We assess the kinematic and dynamic accuracies of a finite-difference frequency-domain method for qP wave modelling in transversally isotropic acoustic media with tilted symmetry axis. This method was developed as a tool for frequency-domain full-waveform inversion which requires accurate traveltime and amplitude modelling. The modelling method is based on the parsimonious Mixed-Grid method which requires 5 Grid points per wavelength in homogeneous media to mitigate numerical dispersion. We compare seismograms computed with the acoustic frequency-domain method with that provided by the complete solution of the transversally isotropic elastic wave equation. As expected we observed strong traveltime and amplitude mismatches in the case of strongly anisotropic materials such as zinc crystals. For weak anisotropy, we obtain a reasonable agreement although slight delay of the acoustic wide-angle reflections was observed in the case of a two-layer medium. The footprint of these inaccuracies in full-waveform inversion will need to be assessed before considering application to real data.
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A Frequency-domain Seismic Modeling Engine for 3D Visco-acoustic VTI Full Waveform Inversion of Fixed-spread Data
Proceedings 76th EAGE Conference and Exhibition 2014, 2014Co-Authors: Stéphane Operto, Lila Combe, Romain Brossier, Ludovic Métivier, Alessandra Ribodetti, Jean VirieuxAbstract:Frequency-domain full waveform inversion (FWI) of fixed-spread data can be limited to a few discrete frequencies thanks to the redundant control of frequency and scattering angle on the wavenumber coverage. In this framework, 3D finite-difference frequency-domain seismic modeling can be efficiently performed for multiple sources in the visco-acoustic approximation with sparse direct solver. We extend the so-called Mixed-Grid finite-difference stencil to account for vertical transverse isotropy in viscoacoustic frequency-domain seismic modeling without extra computational cost. The VTI acoustic wave equation is recast as a fourth-order wave equation, which can be decomposed into an elliptic wave equation and an anelliptic term. The discretization of this equation only requires a straightforward adaptation of the existing isotropic stencil. A discretization rule of 4 Grid points per minimum wavelength, which is suitable for FWI applications, is used for frequency-domain seismic modeling. We validate our finite-difference frequency-domain method against a finite-difference time-domain method using a smooth VTI acoustic model of the Valhall oil field. Comparison between the real and modeled data for the 7-Hz frequency suggests that our method can provide a suitable modeling engine to perform multi-parameter FWI of fixed-spread data in visco-acoustic VTI media.
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Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media
Geophysics, 2009Co-Authors: Stéphane Operto, Jean Virieux, Alessandra Ribodetti, John E. AndersonAbstract:A 2D finite-difference, frequency-domain method was developed for modeling viscoacoustic seismic waves in transversely isotropic media with a tilted symmetry axis. The medium is parameterized by the P-wave velocity on the symmetry axis, the density, the attenuation factor, Thomsen's anisotropic parameters delta and epsilon, and the tilt angle. The finite-difference discretization relies on a parsimonious Mixed-Grid approach that designs accurate yet spatially compact stencils. The system of linear equations resulting from discretizing the time-harmonic wave equation is solved with a parallel direct solver that computes monochromatic wavefields efficiently for many sources. Dispersion analysis shows that four Grid points per P-wavelength provide sufficiently accurate solutions in homogeneous media. The absorbing boundary conditions are perfectly matched layers (PMLs). The kinematic and dynamic accuracy of the method wasassessed with several synthetic examples which illustrate the propagation of S-waves excited at the source or at seismic discontinuities when epsilon
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Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media
GEOPHYSICS, 2009Co-Authors: Stéphane Operto, Jean Virieux, Alessandra Ribodetti, John E. AndersonAbstract:A 2D finite-difference, frequency-domain method was developed for modeling viscoacoustic seismic waves in transversely isotropic media with a tilted symmetry axis. The medium is parameterized by the P-wave velocity on the symmetry axis, the density, the attenuation factor, Thomsen’s anisotropic parameters δ and ϵ , and the tilt angle. The finite-difference discretization relies on a parsimonious Mixed-Grid approach that designs accurate yet spatially compact stencils. The system of linear equations resulting from discretizing the time-harmonic wave equation is solved with a parallel direct solver that computes monochromatic wavefields efficiently for many sources. Dispersion analysis shows that four Grid points per P-wavelength provide sufficiently accurate solutions in homogeneous media. The absorbing boundary conditions are perfectly matched layers (PMLs). The kinematic and dynamic accuracy of the method wasassessed with several synthetic examples which illustrate the propagation of S-waves excited at t...
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Mixed-Grid Finite-difference Frequency-domain Viscoacoustic Modeling In 2D TTI Anisotropic Media
SEG Technical Program Expanded Abstracts 2007, 2007Co-Authors: Stéphane Operto, Alessandra Ribodetti, Mehdi Grini, Jean VirieuxAbstract:We present a 2D finite-difference frequency-domain method for modeling viscoacoustic wave propagation in TTI media. The numerical method relies on a parsimonious staggered-Grid method implemented in the frequency domain. Differential operators are discretized along different rotated coordinate systems (the classic Cartesian one and a 45o rotated one) with second-order accurate staggered-Grid stencils. The resulting discrete operators are combined linearly to mitigate numerical anisotropy. An anti-lumped mass strategy is applied to mitigate numerical dispersion. A dispersion analysis for infinite homogeneous media suggests a discretization rule of 5 Grid points per wavelength. Numerical tests confirm the accuracy of the stencil.
Hua Guo - One of the best experts on this subject based on the ideXlab platform.
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full dimensional wave packet studies of collisional vibrational relaxation of both p and o h2
Journal of Physical Chemistry A, 2003Co-Authors: Shi Ying Lin, Hua GuoAbstract:We report converged full-dimensional quantum dynamical calculations of the vibrational relaxation in the collision: H 2 (ν 1 = I, j 1 = 0,1) + H 2 (ν 2 = 0, j 2 = 0,1) → H 2 (ν' 1 = 0, j' 1 ) + H 2 (ν' 2 = 0, j' 2 ), employing a recent global potential energy surface fitted to a large number of high-level ab initio points. The scattering dynamics is characterized by a time-independent wave packet approach based on the Chebyshev polynomial expansion of Green's operator, which requires repetitive calculations of the action of the system Hamiltonian onto the propagating wave packet. The full-dimensional Hamiltonian within the coupled-states approximation is discretized in a Mixed Grid/basis representation with the adaptation of the parity and diatomic exchange symmetry, and its action is efficiently computed in the appropriate representation facilitated by a series of one-dimensional pseudospectral transformations. Scattering involving both p- and o-H 2 are studied. Rate constants up to a high temperature (3500 K) are obtained from S-matrix elements and compared with available experimental measurements as well as with previous theoretical results.
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Full-dimensional quantum wave packet study of collision-induced vibrational relaxation between para-H2
Chemical Physics, 2003Co-Authors: Shi Ying Lin, Hua GuoAbstract:Abstract An accurate quantum investigation of vibrational relaxation induced by collision: para -H 2 (v 1 =1, j 1 =0)+para -H 2 (v 2 =0, j 2 =0)→para -H 2 (v ′ 1 =0, j ′ 1 )+para -H 2 (v ′ 2 =0, j ′ 2 ) , is presented. The Hamiltonian within the coupled-states approximation is discretized in a Mixed Grid/basis representation and its action is computed in appropriate representations facilitated by a series of one-dimensional pseudo-spectral transformations. Furthermore, the parity and diatomic exchange symmetry are adapted to improve efficiency. S-matrix elements at numerous collision energies up to 2.2 eV are calculated from the Fourier transform of correlation functions obtained from the Chebyshev propagation. Partial wave contributions from J=0 to 90 are obtained explicitly. Finally, thermal rate constants are computed over a wide range of temperatures (0–3500 K) and compared with available experimental measurements. In addition, the effect of initial rotational excitation on the relaxation probability is investigated.
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Full-dimensional quantum wave packet study of rotationally inelastic transitions in H2+H2 collision
The Journal of Chemical Physics, 2002Co-Authors: Shi Ying Lin, Hua GuoAbstract:We report full-dimensional accurate quantum dynamical calculations of the rotationally inelastic collision: para-H2(ν1=0,j1=0)+para-H2(ν2=0,j2=0)→para-H2(ν1=0,j1′)+para-H2(ν2=0,j2′), using a wave packet approach based on the Chebyshev polynomial expansion of Green’s operator. The six-dimensional Hamiltonian within the coupled-states approximation is discretized in a Mixed Grid/basis representation and its action is computed in appropriate representations facilitated by a series of one-dimensional pseudo-spectral transformations. Both the parity and diatomic exchange symmetry are adapted. The S-matrix elements for the rotational transitions are obtained at all energies by the Fourier transform of Chebyshev correlation functions and used to compute transition probabilities, differential and integral cross sections, and state-resolved thermal rate constants. Results are compared for two recently proposed ab initio based potential energy surfaces and with previous quantum results.
Bernhard Hustedt - One of the best experts on this subject based on the ideXlab platform.
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Mixed Grid and staggered Grid finite difference methods for frequency domain acoustic wave modelling
Geophysical Journal International, 2004Co-Authors: Bernhard Hustedt, Stéphane Operto, Jean VirieuxAbstract:SUMMARY We compare different finite-difference schemes for two-dimensional (2-D) acoustic frequency-domain forward modelling. The schemes are based on staggered-Grid stencils of various accuracy and Grid rotation strategies to discretize the derivatives of the wave equation. A combination of two staggered-Grid stencils on the classical Cartesian coordinate system and the 45° rotated Grid is the basis of the so-called Mixed-Grid stencil. This method is compared with a parsimonious staggered-Grid method based on a fourth-order approximation of the first derivative operator. Averaging of the mass acceleration can be incorporated in the two stencils. Sponge-like perfectly matched layer absorbing boundary conditions are also examined for each stencil and shown to be effective. The deduced numerical stencils are examined for both the wavelength content and azimuthal variation. The accuracy of the fourth-order staggered-Grid stencil is slightly superior in terms of phase velocity dispersion to that of the Mixed-Grid stencil when averaging of the mass acceleration term is applied to the staggered-Grid stencil. For fourth-order derivative approximations, the classical staggered-Grid geometry leads to a stencil that incorporates 13 Grid nodes. The Mixed-Grid approach combines only nine Grid nodes. In both cases, wavefield solutions are computed using a direct matrix solver based on an optimized multifrontal method. For this 2-D geometry, the staggered-Grid strategy is significantly less efficient in terms of memory and CPU time requirements because of the enlarged bandwidth of the impedance matrix and increased number of coefficients in the discrete stencil. Therefore, the Mixed-Grid approach should be suggested as the routine scheme for 2-D acoustic wave propagation modelling in the frequency domain.
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Mixed‐Grid and staggered‐Grid finite‐difference methods for frequency‐domain acoustic wave modelling
Geophysical Journal International, 2004Co-Authors: Bernhard Hustedt, Stéphane Operto, Jean VirieuxAbstract:SUMMARY We compare different finite-difference schemes for two-dimensional (2-D) acoustic frequency-domain forward modelling. The schemes are based on staggered-Grid stencils of various accuracy and Grid rotation strategies to discretize the derivatives of the wave equation. A combination of two staggered-Grid stencils on the classical Cartesian coordinate system and the 45° rotated Grid is the basis of the so-called Mixed-Grid stencil. This method is compared with a parsimonious staggered-Grid method based on a fourth-order approximation of the first derivative operator. Averaging of the mass acceleration can be incorporated in the two stencils. Sponge-like perfectly matched layer absorbing boundary conditions are also examined for each stencil and shown to be effective. The deduced numerical stencils are examined for both the wavelength content and azimuthal variation. The accuracy of the fourth-order staggered-Grid stencil is slightly superior in terms of phase velocity dispersion to that of the Mixed-Grid stencil when averaging of the mass acceleration term is applied to the staggered-Grid stencil. For fourth-order derivative approximations, the classical staggered-Grid geometry leads to a stencil that incorporates 13 Grid nodes. The Mixed-Grid approach combines only nine Grid nodes. In both cases, wavefield solutions are computed using a direct matrix solver based on an optimized multifrontal method. For this 2-D geometry, the staggered-Grid strategy is significantly less efficient in terms of memory and CPU time requirements because of the enlarged bandwidth of the impedance matrix and increased number of coefficients in the discrete stencil. Therefore, the Mixed-Grid approach should be suggested as the routine scheme for 2-D acoustic wave propagation modelling in the frequency domain.
Shi Ying Lin - One of the best experts on this subject based on the ideXlab platform.
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full dimensional wave packet studies of collisional vibrational relaxation of both p and o h2
Journal of Physical Chemistry A, 2003Co-Authors: Shi Ying Lin, Hua GuoAbstract:We report converged full-dimensional quantum dynamical calculations of the vibrational relaxation in the collision: H 2 (ν 1 = I, j 1 = 0,1) + H 2 (ν 2 = 0, j 2 = 0,1) → H 2 (ν' 1 = 0, j' 1 ) + H 2 (ν' 2 = 0, j' 2 ), employing a recent global potential energy surface fitted to a large number of high-level ab initio points. The scattering dynamics is characterized by a time-independent wave packet approach based on the Chebyshev polynomial expansion of Green's operator, which requires repetitive calculations of the action of the system Hamiltonian onto the propagating wave packet. The full-dimensional Hamiltonian within the coupled-states approximation is discretized in a Mixed Grid/basis representation with the adaptation of the parity and diatomic exchange symmetry, and its action is efficiently computed in the appropriate representation facilitated by a series of one-dimensional pseudospectral transformations. Scattering involving both p- and o-H 2 are studied. Rate constants up to a high temperature (3500 K) are obtained from S-matrix elements and compared with available experimental measurements as well as with previous theoretical results.
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Full-dimensional quantum wave packet study of collision-induced vibrational relaxation between para-H2
Chemical Physics, 2003Co-Authors: Shi Ying Lin, Hua GuoAbstract:Abstract An accurate quantum investigation of vibrational relaxation induced by collision: para -H 2 (v 1 =1, j 1 =0)+para -H 2 (v 2 =0, j 2 =0)→para -H 2 (v ′ 1 =0, j ′ 1 )+para -H 2 (v ′ 2 =0, j ′ 2 ) , is presented. The Hamiltonian within the coupled-states approximation is discretized in a Mixed Grid/basis representation and its action is computed in appropriate representations facilitated by a series of one-dimensional pseudo-spectral transformations. Furthermore, the parity and diatomic exchange symmetry are adapted to improve efficiency. S-matrix elements at numerous collision energies up to 2.2 eV are calculated from the Fourier transform of correlation functions obtained from the Chebyshev propagation. Partial wave contributions from J=0 to 90 are obtained explicitly. Finally, thermal rate constants are computed over a wide range of temperatures (0–3500 K) and compared with available experimental measurements. In addition, the effect of initial rotational excitation on the relaxation probability is investigated.
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Full-dimensional quantum wave packet study of rotationally inelastic transitions in H2+H2 collision
The Journal of Chemical Physics, 2002Co-Authors: Shi Ying Lin, Hua GuoAbstract:We report full-dimensional accurate quantum dynamical calculations of the rotationally inelastic collision: para-H2(ν1=0,j1=0)+para-H2(ν2=0,j2=0)→para-H2(ν1=0,j1′)+para-H2(ν2=0,j2′), using a wave packet approach based on the Chebyshev polynomial expansion of Green’s operator. The six-dimensional Hamiltonian within the coupled-states approximation is discretized in a Mixed Grid/basis representation and its action is computed in appropriate representations facilitated by a series of one-dimensional pseudo-spectral transformations. Both the parity and diatomic exchange symmetry are adapted. The S-matrix elements for the rotational transitions are obtained at all energies by the Fourier transform of Chebyshev correlation functions and used to compute transition probabilities, differential and integral cross sections, and state-resolved thermal rate constants. Results are compared for two recently proposed ab initio based potential energy surfaces and with previous quantum results.