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2. Three-dimensional finite-difference & finite-element frequency-domain wave simulation with multi-level optimized additive Schwarz domain-decomposition preconditioner: A tool for FWI of sparse node datasets

Author

Tournier, Pierre-Henri, Jolivet, Pierre, Dolean, Victorita, Aghamiry, Hossein, Operto, Stéphane, Riffo, Sebastian, Algorithms and parallel tools for integrated numerical simulations (ALPINES), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Algorithmes Parallèles et Optimisation (IRIT-APO), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Department of Mathematics and Statistics [Univ Strathclyde], University of Strathclyde [Glasgow], Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])

Subjects
Geophysics, Mathematics - Analysis of PDEs, Geochemistry and Petrology, GA, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], QC, Analysis of PDEs (math.AP)
Abstract

Efficient frequency-domain full-waveform inversion (FWI) of long-offset node data can be designed with a few discrete frequencies, which lead to modest data volumes to be managed during the inversion process. Moreover, attenuation effects can be straightforwardly implemented in the forward problem without the computational overhead. However, 3D frequency-domain seismic modeling is challenging because it requires solving a large and sparse linear indefinite system for each frequency with multiple right-hand sides (RHSs). This linear system can be solved by direct or iterative methods. The former allows efficient processing of multiple RHSs but may suffer from limited scalability for very large problems. Iterative methods equipped with a domain-decomposition preconditioner provide a suitable alternative to process large computational domains for sparse-node acquisition. We have investigated the domain-decomposition preconditioner based on the optimized restricted additive Schwarz (ORAS) method, in which a Robin or perfectly matched layer condition is implemented at the boundaries between the subdomains. The preconditioned system is solved by a Krylov subspace method, whereas a block low-rank lower-upper decomposition of the local matrices is performed at a preprocessing stage. Multiple sources are processed in groups with a pseudoblock method. The accuracy, the computational cost, and the scalability of the ORAS solver are assessed against several realistic benchmarks. In terms of discretization, we compare a compact wavelength-adaptive 27-point finite-difference stencil on a regular Cartesian grid with a P3 finite-element method on h-adaptive tetrahedral mesh. Although both schemes have comparable accuracy, the former is more computationally efficient, the latter being beneficial to comply with known boundaries such as bathymetry. The scalability of the method, the block processing of multiple RHSs, and the straightforward implementation of attenuation, which further improves the convergence of the iterative solver, make the method a versatile forward engine for large-scale 3D FWI applications from sparse node data sets.

Published
2021

3. Several ways to achieve robustness when solving wave propagation problems

Author

Bootland, Niall, Dolean, Victorita, Jolivet, Pierre, Nataf, Frédéric, Operto, Stéphane, and Tournier, Pierre-Henri

Subjects
QA
Abstract

Wave propagation problems are notoriously difficult to solve. Time-harmonic problems are especially challenging in mid and high frequency regimes. The main reason is the oscillatory nature of solutions, meaning that the number of degrees of freedom after discretisation increases drastically with the wave number, giving rise to large complex-valued problems to solve. Additional difficulties occur when the problem is defined in a highly heterogeneous medium, as is often the case in realistic physical applications. For time-discretised problems of Maxwell type, the main challenge remains the significant kernel in curl-conforming spaces, an issue that impacts on the design of robust preconditioners. This has already been addressed theoretically for a homogeneous medium but not yet in the presence of heterogeneities. In this review we provide a big-picture view of the main difficulties encountered when solving wave propagation problems, from the first step of their discretisation through to their parallel solution using two-level methods, by showing their limitations on a few realistic examples. We also propose a new preconditioner inspired by the idea of subspace decomposition, but based on spectral coarse spaces, for curl-conforming discretisations of Maxwell's equations in heterogeneous media.

Published
2021

7. Seismic Exploration of the Deep Structure and Seismogenic Faults in the Ligurian Sea by Joint Multi Channel and Ocean Bottom Seismic Acquisitions: Preliminary Results of the SEFASILS Cruise

Author

Dessa, Jean-Xavier, Beslier, Marie-Odile, Schenini, Laure, Chamot-Rooke, Nicolas, Corradi, Nicolà, Delescluse, Matthias, Déverchère, Jacques, Larroque, Christophe, Sambolian, Serge, Canva, Albane, Operto, Stéphane, Ribodetti, Alessandra, Agurto-Detzel, Hans, Bulois, Cédric, Chalumeau, Caroline, Combe, Laure, Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Laboratoire de géologie de l'ENS (LGENS), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Département des Géosciences - ENS Paris, École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Dipartimento Scienze della Terra, Universita degli studi di Genova, Domaines Océaniques (LDO), Institut national des sciences de l'Univers (INSU - CNRS)-Université de Brest (UBO)-Observatoire des Sciences de l'Univers-Institut d'écologie et environnement-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), and Università degli studi di Genova = University of Genoa (UniGe)

Subjects
Western Mediterranean, [SDU.STU.TE]Sciences of the Universe [physics]/Earth Sciences/Tectonics, crustal geophysical exploration, lcsh:QE1-996.5, imaging, [SDU.STU]Sciences of the Universe [physics]/Earth Sciences, salt tectonics, Ligurian basin, wide-angle seismic recording, multichannel seismic, lcsh:Geology, [SDU]Sciences of the Universe [physics], [SDU.STU.ST]Sciences of the Universe [physics]/Earth Sciences/Stratigraphy, tectonic inversion, multichannel seismic imaging, salt, tectonics, [SDU.STU.OC]Sciences of the Universe [physics]/Earth Sciences/Oceanography
Abstract

International audience; The north Ligurian margin is a complex geological area in many ways. It has witnessedseveral phases of highly contrasting deformation styles, at both crustal scale and that of shallower covertectonics, simultaneously or in quick succession, and with significant spatial variability. This complexinterplay is mirrored in the resulting intricate structures that make it hard to identify active faultsresponsible for both, the significant seismicity observed, and the tectonic inversion undergone bythe margin, identified at longer time scales on morphostructural grounds. We present here the firstpreliminary results of the leg 1 of SEFASILS cruise, conducted in 2018 offshore Monaco, in an effort toanswer these questions by means of modern deep seismic acquisitions, using multichannel reflectionand wide-angle sea-bottom records. Some first interpretations are provided and point towards anactive basement deformation that focuses at the limits between main crustal domains.

Published
2020

8. High resolution seismic imaging in shallow salt environment: preliminary results from the SEFASILS campaign, NS11A-04

Author

Dessa, Jean-Xavier, Sambolian, Serge, Bachir Miguil, Mohamed, Schenini, Laure, Operto, Stéphane, Ribodetti, Alessandra, Beslier, Marie-Odile, Larroque, Christophe, Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Beslier, Marie-Odile, Institut national des sciences de l'Univers (INSU - CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])-Centre National de la Recherche Scientifique (CNRS)-Observatoire de la Côte d'Azur, and Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)

Subjects
[SDU] Sciences of the Universe [physics], [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [SDU]Sciences of the Universe [physics], [SDU.STU] Sciences of the Universe [physics]/Earth Sciences, [SDU.STU]Sciences of the Universe [physics]/Earth Sciences, [SDU.STU.GP] Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph]
Abstract

International audience; In the last decade, seismic imaging below salt/basaltic bodies proved beyond doubt to be the most challenging task using conventional strategies in terms of surveying, processing and inversion. Recent innovations across the whole workflow pushed further the resolution limit in such complex environments for resource exploration purposes. On the other hand, for instance, the western Mediterranean basin, a fairly studied seismogenic zone, still raises some questions due to the lack of clear-cut imaging results. The latter is caused by the presence of the ill-famed Messinian salt at shallow depth in this region which generates a wavefield dominated by backscattering and diffractions due to the abrupt high velocity contrast and structural complexity.We take a fresh look at a new batch of towed-streamer data acquired in the Ligurian basin during the SEFASILS campaign. During this study, we examine preliminary results using a conventional velocity model building strategy based on velocity analysis techniques and another based on a state of the art tomographic method.We review the theory behind slope tomography, a reflection/diffraction tomography method based upon inversion of locally-coherent events. A locally-coherent seismic event, described by its two-way traveltimes and the slopes, in a common-shot or common-receiver gather can be interpreted as a reflection/diffraction from a small reflector segment or diffractor in depth. A key advantage of slope tomography methods in such settings is the automatic densely picked data cube of locally-coherent events opposed to a very challenging tracking of continuous events. We also explain the advantages of our parsimonious formulation in tackling the velocity-position trade-off.We illustrate the resolution power of slope tomography compared to more conventional techniques. We point out the main challenges and insurmountable obstacles encountered while assessing the quality of the reconstructed models and depth migrated images.

Published
2019

11. Building Initial Model for FWI From Ultra Long-Offset OBN Data by First-Arrival Traveltime + Slope Tomography

Author

Sambolian, Serge, Górszczyk, A., Operto, Stéphane, Ribodetti, Alessandra, Tavakoli F., B., Virieux, Jean, Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Institut des Sciences de la Terre (ISTerre), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut national des sciences de l'Univers (INSU - CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])-Centre National de la Recherche Scientifique (CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut national des sciences de l'Univers (INSU - CNRS)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université Joseph Fourier - Grenoble 1 (UJF), and Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])

Subjects
Regional geology, Offset (computer science), 010504 meteorology & atmospheric sciences, [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], Engineering geology, Gemology, 010502 geochemistry & geophysics, 01 natural sciences, Glaciology, 14. Life underwater, Economic geology, Igneous petrology, Geology, Seismology, ComputingMilieux_MISCELLANEOUS, 0105 earth and related environmental sciences, Environmental geology
Abstract

Summary Ultra-long offset stationary-receiver acquisitions implemented with multi-component Ocean Bottom Nodes (OBN) are emerging as a suitable technology for deep offshore subsalt imaging by full waveform inversion (FWI). Ultra-long offsets allow to undershoot the deepest targeted structures with diving waves. In this framework, first-arrival traveltime + slope tomography (FASTT) provides a simple and efficient tool to build kinematically-accurate initial velocity model for full waveform inversion (FWI). In particular, the incorporation of slopes in the first-arrival tomography in addition to traveltimes removes artifacts in poorly illuminated areas and better reconstruct structural dips. Either the FASTT or the FWI velocity models can be used as reliable background models for prestack depth migration of co-incident towed-streamer data. However, the high resolution of the FWI velocity model facilitates the integrated interpretation of the reflectivity mapped by migration and the intermediate-scale velocity variations reconstructed by waveform inversion. We illustrate the workflow combining first-arrival tomography + FWI of ultra-long offset OBN data and migration of co-incident towed-streamer data with a challenging deep crustal case study in the eastern Nankai subduction zone.

Published
2019

12. GO_3D_OBS: the multi-parameter benchmark geomodel for seismic imaging method assessment and next-generation 3D survey design (version 1.0).

Author

Górszczyk, Andrzej and Operto, Stéphane

Subjects
*IMAGING systems in seismology, *SEISMIC surveys, *SUBDUCTION zones, *OCEAN bottom, *INVERSE problems
Abstract

Detailed reconstruction of deep crustal targets by seismic methods remains a long-standing challenge. One key to address this challenge is the joint development of new seismic acquisition systems and leading-edge processing techniques. In marine environments, controlled-source seismic surveys at a regional scale are typically carried out with sparse arrays of ocean bottom seismometers (OBSs), which provide incomplete and down-sampled subsurface illumination. To assess and minimize the acquisition footprint in high-resolution imaging process such as full waveform inversion, realistic crustal-scale benchmark models are clearly required. The deficiency of such models prompts us to build one and release it freely to the geophysical community. Here, we introduce GO_3D_OBS – a 3D high-resolution geomodel representing a subduction zone, inspired by the geology of the Nankai Trough. The 175km×100km×30km model integrates complex geological structures with a viscoelastic isotropic parameterization. It is defined in the form of a uniform Cartesian grid containing ∼ 33.6e9 degrees of freedom for a grid interval of 25 m. The size of the model raises significant high-performance computing challenges to tackle large-scale forward propagation simulations and related inverse problems. We describe the workflow designed to implement all the model ingredients including 2D structural segments, their projection into the third dimension, stochastic components, and physical parameterization. Various wavefield simulations that we present clearly reflect in the seismograms the structural complexity of the model and the footprint of different physical approximations. This benchmark model is intended to help to optimize the design of next-generation 3D academic surveys – in particular, but not only, long-offset OBS experiments – to mitigate the acquisition footprint during high-resolution imaging of the deep crust. [ABSTRACT FROM AUTHOR]

Published
2021
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13. Complex-Valued Imaging with Total Variation Regularization: An Application to Full-Waveform Inversion in Visco-acoustic Media.

Author

Aghamiry, Hossein S., Gholami, Ali, and Operto, Stéphane

Subjects
QUALITY factor, CONSTRAINED optimization, WAVE equation, INVERSE problems, PHASE velocity, VELOCITY, PHOTOACOUSTIC effect
Abstract

Full-waveform inversion (FWI) is a nonlinear PDE constrained optimization problem which seeks to estimate the constitutive parameters of a medium by fitting waveforms. Among these parameters, attenuation needs to be taken into account in viscous media to exploit the full potential of FWI. Attenuation is easily implemented in the frequency domain by using complex-valued velocities in the time-harmonic wave equation. These complex velocities are frequency-dependent to guarantee causality and account for dispersion. Since estimating a complex frequency-dependent velocity at each grid point in space is not realistic, the optimization is generally performed in the real domain by processing the phase velocity (or slowness) at a reference frequency and attenuation (or quality factor) as separate real parameters. This real parametrization requires an a priori empirical relation (such as the nonlinear Kolsky--Futterman (KF) or standard linear solid (SLS) attenuation models) between the complex velocity and the two real quantities, which is prone to generate modeling errors if it does not represent accurately the attenuation behavior of the medium. Moreover, it leads to a multivariate inverse problem, which is ill-posed due to the cross-talk between the two classes of real parameters. To alleviate these issues, we solve directly the optimization problem in the complex domain by processing narrow bands of frequencies in sequence under the assumption of bandwise frequency dependence of the complex velocities. Moreover, we use a relaxation method to extend the FWI search space by processing the wave equation as a weak constraint with the alternating direction method of multipliers (ADMM) to mitigate the risk of spurious local minima. To mitigate the ill-posedness of the inversion, three total variation (TV) regularization schemes based upon ADMM and proximity algorithms are presented. In the first, regularization is applied directly on the complex velocities. In the other two, separate TV regularizations are tailored to different attributes of the complex velocities (real and imaginary parts, magnitude and phase). The real phase velocity and attenuation factor are then reconstructed a posteriori at each spatial position from the estimated complex velocity using arbitrary empirical relation. The numerical results first show that the regularization of the amplitude and phase provides the most reliable results. Moreover, they show that the band-by-band design of the inversion limits the sensitivity of the recovered phase velocity and attenuation factor to the attenuation model used for their a posteriori extraction. [ABSTRACT FROM AUTHOR]

Published
2021
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14. GO_3D_OBS - The Nankai Trough-inspired benchmark geomodel for seismic imaging methods assessment and next generation 3D surveys design (version 1.0).

Author

Górszczyk, Andrzej and Operto, Stéphane

Subjects
*IMAGING systems in seismology, *SEISMIC surveys, *SUBDUCTION zones, *OCEAN bottom, *DEGREES of freedom
Abstract

Detailed reconstruction of deep crustal targets by seismic methods remains a long-standing challenge. One key to address this challenge is the joint development of new seismic acquisition systems and leading-edge processing techniques. In marine environments, controlled-source seismic surveys at regional scale are typically carried out with sparse arrays of ocean bottom seismometers (OBSs), which provide incomplete and down-sampled subsurface illumination. To assess and minimize the acquisition footprint in high-resolution imaging process such as full waveform inversion, realistic crustal-scale benchmark models are clearly required. The deficiency of such models prompts us to build one and release it freely to the geophysical community. Here we introduce GO_3D_OBS - a 3D high-resolution geomodel representing a subduction zone, inspired by the geology of the Nankai Trough. The 175 km x 100 km x 30 km model integrates complex geological structures with a visco-elastic isotropic parametrization. It is defined in form of a uniform Cartesian grid containing 33.6e9 degrees of freedom for a grid interval of 25 m. The size of the model raises significant high-performance computing challenges to tackle large-scale forward propagation simulations and related inverse problems. We describe the workflow designed to implement all the model ingredients including 2D structural segments, their projection into the third dimension, stochastic components and physical parametrisation. Various wavefield simulations we present clearly reflect in the seismograms the structural complexity of the model and the footprint of different physical approximations. This benchmark model shall help to optimize the design of next generation 3D academic surveys - in particular but not only long-offset OBS experiments - to mitigate the acquisition footprint during high-resolution imaging of the deep crust. [ABSTRACT FROM AUTHOR]

Published
2020
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15. Toward a robust workflow for deep crustal imaging by FWI of OBS data: The eastern Nankai Trough revisited

Author

Górszczyk, Andrzej, Operto, Stéphane, Malinowski, Michał, Institute of Geophysics Polish Academy of Sciences, Géoazur (GEOAZUR 7329), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud]), Institute of Geophysics [Warsaw], Polska Akademia Nauk = Polish Academy of Sciences (PAN), Université Côte d'Azur (UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])-Centre National de la Recherche Scientifique (CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD [France-Sud])

Subjects
[SDU.STU]Sciences of the Universe [physics]/Earth Sciences
Abstract

International audience; Crustal‐scale imaging by the full‐waveform inversion (FWI) of long‐offset seismic data is inherently difficult because the large number of wavelengths propagating through the crust makes the inversion prone to cycle skipping. Therefore, efficient crustal‐scale FWI requires an accurate starting model and a stable workflow minimizing the nonlinearity of the inversion. Here we attempt to reprocess a challenging 2‐D ocean‐bottom seismometer (OBS) data set from the eastern Nankai Trough. The starting model is built by first‐arrival traveltime tomography (FAT), which is FWI assisted for tracking cycle skipping. We iteratively refine the picked traveltimes and then reiterate the FAT until the traveltime residuals remain below the cycle‐skipping limit. Subsequently, we apply Laplace‐Fourier FWI, in which progressive relaxation of time damping is nested within frequency continuation to hierarchically inject more data into the inversion. These two multiscale levels are complemented by a layer‐stripping approach implemented through offset continuation. The reliability of the FWI velocity model is assessed by means of source wavelet estimation, synthetic seismogram modeling, ray tracing modeling, dynamic warping, and checkerboard tests. Although the viscoacoustic approximation is used for wave modeling, the synthetic seismograms reproduce most of the complexity of the data with a high traveltime accuracy. The revised FWI scheme produces a high‐resolution velocity model of the entire crust that can be jointly interpreted with migrated images derived from multichannel seismic data. This study opens a new perspective on the design of OBS crustal‐scale experiments amenable to FWI; however, a further assessment of the optimal OBS spacing is required for reliable FWI.

Published
2017

16. Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures

Author

Métivier, Ludovic, Bretaudeau, François, Brossier, Romain, Operto, Stéphane, Virieux, Jean, Institut des Sciences de la Terre (ISTerre), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Computing aspects, Full Waveform, 49M15, Numerical study, [SDU.STU]Sciences of the Universe [physics]/Earth Sciences, Theory, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Imaging
Abstract

Submitted version.; International audience; Full waveform inversion is a powerful tool for quantitative seismic imaging from wide‐azimuth seismic data. The method is based on the minimization of the misfit between observed and simulated data. This amounts to the solution of a large‐scale nonlinear minimization problem. The inverse Hessian operator plays a crucial role in this reconstruction process. Accounting accurately for the effect of this operator within the minimization scheme should correct for illumination deficits, restore the amplitude of the subsurface parameters, and help to remove artefacts generated by energetic multiple reflections. Conventional minimization methods (nonlinear conjugate gradient, quasi‐Newton methods) only roughly approximate the effect of this operator. In this study, we are interested in the truncated Newton minimization method. These methods are based on the computation of the model update through a matrix‐free conjugate gradient solution of the Newton linear system. We present a feasible implementation of this method for the full waveform inversion problem, based on a second‐order adjoint state formulation for the computation of Hessian‐vector products. We compare this method with conventional methods within the context of 2D acoustic frequency full waveform inversion for the reconstruction of P‐wave velocity models. Two test cases are investigated. The first is the synthetic BP 2004 model, representative of the Gulf of Mexico geology with high velocity contrasts associated with the presence of salt structures. The second is a 2D real data‐set from the Valhall oil field in North sea. Although, from a computational cost point of view, the truncated Newton method appears to be more expensive than conventional optimization algorithms, the results emphasize its increased robustness. A better reconstruction of the P‐wave velocity model is provided when energetic multiple reflections make it difficult to interpret the seismic data. A better trade‐off between regularization and resolution is obtained when noise contamination of the data requires one to regularize the solution of the inverse problem.

Published
2014

17. Crustal-scale depth imaging via joint full-waveform inversion of ocean-bottom seismometer data and pre-stack depth migration of multichannel seismic data: a case study from the eastern Nankai Trough.

Author

Górszczyk, Andrzej, Operto, Stéphane, Schenini, Laure, and Yamada, Yasuhiro

Subjects
*SEISMIC migration, *SEISMOMETERS, *VERTICAL seismic profiling, *CASE studies, *GEODYNAMICS
Abstract

Imaging via pre-stack depth migration (PSDM) of reflection towed-streamer multichannel seismic (MCS) data at the scale of the whole crust is inherently difficult. This is because the depth penetration of the seismic wavefield is controlled, firstly, by the acquisition design, such as streamer length and air-gun source configuration, and secondly by the complexity of the crustal structure. Indeed, the limited length of the streamer makes the estimation of velocities from deep targets challenging due to the velocity–depth ambiguity. This problem is even more pronounced when processing 2-D seismic data due to the lack of multi-azimuthal coverage. Therefore, in order to broaden our knowledge about the deep crust using seismic methods, we present the development of specific imaging workflows that integrate different seismic data. Here we propose the combination of velocity model building using (i) first-arrival tomography (FAT) and full-waveform inversion (FWI) of wide-angle, long-offset data collected by stationary ocean-bottom seismometers (OBSs) and (ii) PSDM of short-spread towed-streamer MCS data for reflectivity imaging, with the former velocity model as a background model. We present an application of such a workflow to seismic data collected by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) and the Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER) in the eastern Nankai Trough (Tokai area) during the 2000–2001 Seize France Japan (SFJ) experiment. We show that the FWI model, although derived from OBS data, provides an acceptable background velocity field for the PSDM of the MCS data. From the initial PSDM, we refine the FWI background velocity model by minimizing the residual move-outs (RMOs) picked in the pre-stack-migrated volume through slope tomography (ST), from which we generate a better-focused migrated image. Such integration of different seismic datasets and leading-edge imaging techniques led to greatly improved imaging at different scales. That is, large to intermediate crustal units identified in the high-resolution FWI velocity model extensively complement the short-wavelength reflectivity inferred from the MCS data to better constrain the structural factors controlling the geodynamics of the Nankai Trough. [ABSTRACT FROM AUTHOR]

Published
2019
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18. SMART: dissipative absorbing layer technique for general elastodynamics equations. Application as S-waves filter in acoustic TI media

Author

Métivier, Ludovic, Brossier, Romain, Labbé, Stéphane, Operto, Stéphane, Virieux, Jean, Institut des Sciences de la Terre (ISTerre), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; Seismic imaging methods such as FullWaveform Inversion (FWI Virieux and Operto [38], M´etivier et al. [30, 28]) or Reverse Time Migration (RTM Baysal et al. [6]) require accurate modeling engines for the propagation of seismic waves in infinite or semi-infinite media. To this end, the use of efficient absorbing boundary conditions is mandatory. Moreover, one should be sure that the modeling engine will provide always an answer at each iteration of the inversion and of the migration. The stability is, therefore, a very important property of absorbing conditions.

Published
2014

19. Full Waveform Inversion and the truncated Newton: quantitative imaging of complex subsurface structures

Author

Métivier, Ludovic, Bretaudeau, François, Brossier, Romain, Operto, Stéphane, Virieux, Jean, Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut des Sciences de la Terre (ISTerre), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Géoazur (GEOAZUR 6526), Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, and Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Optimization, Seismic Imaging, Newton method, [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], Full Waveform Inversion, 49M15, [SDE.MCG]Environmental Sciences/Global Changes, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

Submitted version.; Full Waveform Inversion (FWI) is a powerful tool for quantitative seismic imaging from wide-azimuth seismic data. The method is based on the minimization of the misfit between observed and simulated data. This amounts to the resolution of a large-scale nonlinear minimization problem. The inverse Hessian operator plays a crucial role in this reconstruction process. Accounting accurately for the effect of this operator within the minimization scheme should correct for illumination deficits, restore the amplitude of the subsurface parameters, and help to remove artifacts generated by energetic multiple reflections. Conventional preconditioned gradient-based minimization methods only roughly approximate the effect of this operator. We are interested in this study to another class of minimization methods, named as truncated Newton methods. These methods are based on the computation of the model update through a matrix-free conjugate gradient resolution of the Newton linear system. The aim of this study is to present a feasible implementation of this method for the FWI problem, based on a second-order adjoint state formulation for the computation of Hessian-vector products. We compare this method with the nonlinear conjugate gradient and the l-BFGS method within the context of 2D acoustic frequency FWI for the reconstruction of P-wave velocity models. Two test cases are investigated. The first is the synthetic BP 2004 model, representative of the Gulf Of Mexico geology with high velocity contrasts associated with the presence of salt structures. The second is a 2D real data-set from the Valhall oil field in North sea. These tests emphasize the interesting properties of the truncated Newton method regarding conventional optimization methods within the context of FWI.

Published
2013

20. Seismic elastic modeling for seismic imaging

Author

Virieux, Jean, Brossier, Romain, Chaillat, Stéphanie, Duchkov, A. D., Etienne, Vincent, Lombard, Bruno, Operto, Stéphane, Institut des Sciences de la Terre (ISTerre), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS), ​Trofimuk Institute of Petroleum Geology and Geophysics of the Siberian Branch of the RAS (IPGG SB RAS), Siberian Branch of the Russian Academy of Sciences (SB RAS), Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Ondes et Imagerie (O&I), Laboratoire de Mécanique et d'Acoustique [Marseille] (LMA ), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Lombard, Bruno, Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Trofimuk Institute of Petroleum Geology and Geophysics, SB RAS, Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM), and Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)

Subjects
[SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph], [SPI.ACOU] Engineering Sciences [physics]/Acoustics [physics.class-ph], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2013

21. Application of a preconditoned truncated Newton method to full waveform inversion

Author

Brossier, Romain, Métivier, Ludovic, Operto, Stéphane, Virieux, Jean, Institut des Sciences de la Terre (ISTerre), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), SEISCOPE II, Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), and Métivier, Ludovic

Subjects
numerical optimization, [SDE.MCG] Environmental Sciences/Global Changes, [PHYS.PHYS.PHYS-GEO-PH] Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], Newton method, seismic imaging, [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], Full Waveform Inversion, [SDE.MCG]Environmental Sciences/Global Changes, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [SDU.STU.GP] Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; Full Waveform Inversion (FWI) is a powerful seismic imaging method, based on the iterative minimization of the distance between simulated and recorded wavefields. The inverse Hessian operator related to this misfit function plays an important role in the reconstruction scheme. As conventional methods use direct approximations of this operator, we investigate an alternative optimization scheme: the truncated Newton method. This two-nested-loops algorithm is based on the resolution of the Newton linear system through a matrix-free iterative solver at each outer iteration. On the 2D BP 2004 model widely used as a benchmark for FWI, the contrasts in wave velocities between salt structures and the upper water layer generate high amplitude multiple reflections. These multiple reflections strengthen the need for quite accurate approximation of the inverse Hessian operator and the truncated Newton method is shown to outperform than more conventional algorithms (l-BFGS, nonlinear conjugate gradient).

Published
2013

22. Complex structures imaging using Full Waveform Inversion: the benefits of the preconditioned truncated Newton method

Author

Métivier, Ludovic, Brossier, Romain, Operto, Stéphane, Virieux, Jean, Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Ondes et Structures, Institut des Sciences de la Terre (ISTerre), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), and Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [SDE.MCG]Environmental Sciences/Global Changes, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2012

23. Optimization schemes for Full Waveform Inversion: the preconditioned truncated Newton method

Author

Métivier, Ludovic, Brossier, Romain, Virieux, Jean, Operto, Stéphane, Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), Ondes et Structures, Institut des Sciences de la Terre (ISTerre), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [SDE.MCG]Environmental Sciences/Global Changes, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; Full Waveform Inversion (FWI) methods use generally gradient based method, such as the nonlinear conjugate gradient method or more recently the l-BFGS quasi-Newton method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framework for the implementation of these methods inside a truncated Newton procedure. We demonstrate that the exact Newton method can outperform the standard gradient-based methods in a near-surface application case for recovering high-velocity concrete structures. In this particular configuration, large amplitude multi-scattered waves are generated, which are better taken into account using the exact-Newton method.

Published
2012

24. Applying Gauss-Newton and Exact Newton method to Full Waveform Inversion

Author

Métivier, Ludovic, Brossier, Romain, Operto, Stéphane, Virieux, Jean, Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF), Ondes et Structures, Institut des Sciences de la Terre (ISTerre), Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [SDE.MCG]Environmental Sciences/Global Changes, MathematicsofComputing_NUMERICALANALYSIS, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; Full Waveform Inversion (FWI) applications classically rely on efficient first-order optimization schemes, as the steepest descent or the nonlinear conjugate gradient optimization. However, second-order information provided by the Hessian matrix is proven to give a useful help in the scaling of the FWI problem and in the speed-up of the optimization. In this study, we propose an efficient matrix-free Hessian-vector formalism, that should allow to tackle Gauss-Newton (GN) and Exact-Newton (EN) optimization for large and realistic FWI targets. Our method relies on general second order adjoint formulas, based on a Lagrangian formalism. These formulas yield the possibility of computing Hessian-vector products at the cost of 2 forward simulations per shot. In this context, the computational cost (per shot) of one GN or one EN nonlinear iteration amounts to the resolution of 2 forward simulations for the computation of the gradient plus 2 forward simulations per inner linear conjugate gradient iteration. A numerical test is provided, emphasizing the possible improvement of the resolution when accounting for the exact Hessian in the inversion algorithm.

Published
2012

25. Second-order adjoint state methods for Full Waveform Inversion

Author

Métivier, Ludovic, Brossier, Romain, Operto, Stéphane, Virieux, Jean, Institut des Sciences de la Terre (ISTerre), Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-PRES Université de Grenoble-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), SEISCOPE, Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), and Métivier, Ludovic

Subjects
[SDE.MCG] Environmental Sciences/Global Changes, [PHYS.PHYS.PHYS-GEO-PH] Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], inverse problems, seismic imaging, [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], Full Waveform Inversion, [SDE.MCG]Environmental Sciences/Global Changes, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [SDU.STU.GP] Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], nonlinear optimization
Abstract

International audience; Full Waveform Inversion (FWI) is becoming an efficient tool to derive high resolution quantitative models of the subsurface parameters. The method relies on the minimization, through an iterative procedure, of the residual between recorded data and synthetic data computed by solving the two-way wave equation in a subsurface model. The growth of available computational resources and recent developments of the method makes now possible applications to 2D and 3D data in the acoustic approximation (see for example Prieux et al., 2011; Plessix et al., 2010) and even in the elastic approximation (Brossier et al 2009). Most of the FWI applications rely on fast optimization schemes as preconditioned steepest descent or preconditioned conjugate-gradient methods (PCG). Second-order information provided by the Hessian is often neglected in FWI, due to the high computational cost to build this matrix and solve the normal equation system. However, a significant improvement of the results can be obtained using this information: Pratt et al. (1998) have shown the improved resolution of Gauss-Newton method compared to the steepest descent one in a canonical application. Hu et al. (2011) have shown results improvement provided by a non-diagonal truncated Hessian in PCG. Brossier et al. (2009) have shown the estimated Hessian's impact of a quasi-Newton l-BFGS (Nocedal, 1980), on image resolution and convergence speed compared to PCG. Epanomeritakis et al. (2008); Fichtner and Trampert (2011) have also discussed the interest of Hessian for inversion and uncertainty estimation, and also the prohibitive cost of Hessian computation and storage. In this study, we develop the mathematical framework to propose an efficient matrix-free Hessian-vector product algorithm for FWI, and give an illustration of the interest of accounting for the exact Hessian in the inversion process. The final aim is to tackle Gauss-Newton and Full-Newton method for large scale applications. Our development relies on a general second-order adjoint-state formula, valid either in the time or in the frequency domain.

Published
2012

26. On the footprint of anisotropy on isotropic full waveform inversion: the Valhall case study

Author

Prieux, Vincent, Brossier, Romain, Gholami, Yaser, Operto, Stéphane, Virieux, Jean, Barkved, O.I., Kommedal, J.H., Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Risques (Risques), Laboratoire de Géophysique Interne et Tectonophysique (LGIT), Observatoire des Sciences de l'Univers de Grenoble (OSUG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Central des Ponts et Chaussées (LCPC)-Centre National de la Recherche Scientifique (CNRS)-Observatoire des Sciences de l'Univers de Grenoble (OSUG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Central des Ponts et Chaussées (LCPC)-Centre National de la Recherche Scientifique (CNRS), SEISCOPE consortium, Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut de Recherche pour le Développement (IRD)-Centre National de la Recherche Scientifique (CNRS), Risques, Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Laboratoire Central des Ponts et Chaussées (LCPC)-Institut des Sciences de la Terre (ISTerre), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut national des sciences de l'Univers (INSU - CNRS)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Observatoire des Sciences de l'Univers de Grenoble (OSUG), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut national des sciences de l'Univers (INSU - CNRS)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR), BP Norge, BP NORGE, Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Central des Ponts et Chaussées (LCPC)-Observatoire des Sciences de l'Univers de Grenoble (OSUG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Central des Ponts et Chaussées (LCPC)-Observatoire des Sciences de l'Univers de Grenoble (OSUG), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Computational seismology, Controlled source seismology, Seismic tomography, Wave propagation, [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph], [SDU.STU]Sciences of the Universe [physics]/Earth Sciences, Inverse theory, Seismic anisotropy
Abstract

International audience; The validity of isotropic approximation to perform acoustic full waveform inversion (FWI) of real wide-aperture anisotropic data can be questioned due to the intrinsic kinematic inconsistency between short- and large-aperture components of the data. This inconsistency is mainly related to the differences between the vertical and horizontal velocities in vertical-transverse isotropic (VTI) media. The footprint of VTI anisotropy on 2-D acoustic isotropic FWI is illustrated on a hydrophone data set of an ocean-bottom cable that was collected over the Valhall field in the North Sea. Multiscale FWI is implemented in the frequency domain by hierarchical inversions of increasing frequencies and decreasing aperture angles. The FWI models are appraised by local comparison with well information, seismic modelling, reverse-time migration (RTM) and source-wavelet estimation. A smooth initial VTI model parameterized by the vertical velocity V0 and the Thomsen parameters δ and ε were previously developed by anisotropic reflection traveltime tomography. The normal moveout (inline image) and horizontal (inline image) velocity models were inferred from the anisotropic models to perform isotropic FWI. The VNMO models allows for an accurate match of short-spread reflection traveltimes, whereas the Vh model, after updating by first-arrival traveltime tomography (FATT), allows for an accurate match of first-arrival traveltimes. Ray tracing in the velocity models shows that the first 1.5 km of the medium are sampled by both diving waves and reflections, whereas the deeper structure at the reservoir level is mainly controlled by short-spread reflections. Starting from the initial anisotropic model and keeping fixed δ and ε models, anisotropic FWI allows us to build a vertical velocity model that matches reasonably well the well-log velocities. Isotropic FWI is performed using either the NMO model or the FATT model as initial model. In both cases, horizontal velocities are mainly reconstructed in the first 1.5 km of the medium. This suggests that the wide-aperture components of the data have a dominant control on the velocity estimation at these depths. These high velocities in the upper structure lead to low values of velocity in the underlying gas layers (either equal or lower than vertical velocities of the well log), and/or a vertical stretching of the structure at the reservoir level below the gas. This bias in the gas velocities and the mispositioning in depth of the deep reflectors, also shown in the RTM images, are required to match the deep reflections in the isotropic approximation and highlight the footprint of anisotropy in the isotropic FWI of long-offset data. Despite the significant differences between the anisotropic and isotropic FWI models, each of these models produce a nearly-equivalent match of the data, which highlights the ill-posedness of acoustic anisotropic FWI. Hence, we conclude with the importance of considering anisotropy in FWI of wide-aperture data to avoid bias in the velocity reconstructions and mispositioning in depth of reflectors. Designing a suitable parameterization of the VTI acoustic FWI is a central issue to manage the ill-posedness of the FWI.

Published
2011

27. Parallel algebraic hybrid linear solver for frequency domain acoustic wave modeling

Author

Ben-Hadj-Ali, Hafedh, Giraud, Luc, Haidar, Azzam, Operto, Stéphane, Virieux, Jean, TOTAL-Scientific and Technical Center Jean Féger (CSTJF), TOTAL FINA ELF, High-End Parallel Algorithms for Challenging Numerical Simulations (HiePACS), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Innovative Computing Laboratory [Knoxville] (ICL), The University of Tennessee [Knoxville], Risques, Laboratoire de Géophysique Interne et Tectonophysique (LGIT), Observatoire des Sciences de l'Univers de Grenoble (OSUG), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Laboratoire Central des Ponts et Chaussées (LCPC)-Institut des Sciences de la Terre (ISTerre), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut national des sciences de l'Univers (INSU - CNRS)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Observatoire des Sciences de l'Univers de Grenoble (OSUG), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut national des sciences de l'Univers (INSU - CNRS)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR), SIAM, Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Inria Bordeaux - Sud-Ouest, Risques (Risques), Laboratoire Central des Ponts et Chaussées (LCPC)-Observatoire des Sciences de l'Univers de Grenoble (OSUG), Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Central des Ponts et Chaussées (LCPC)-Observatoire des Sciences de l'Univers de Grenoble (OSUG), Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Centre scientifique et Technique Jean Feger (CSTJF), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Central des Ponts et Chaussées (LCPC)-Centre National de la Recherche Scientifique (CNRS)-Observatoire des Sciences de l'Univers de Grenoble (OSUG), and Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut national des sciences de l'Univers (INSU - CNRS)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Central des Ponts et Chaussées (LCPC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2009

28. 3D frequency-domain finite-difference modeling of accoustic wave propagation using a masively parallel direct solver: a feasable study

Author

Operto, Stéphane, Virieux, Jean, Amestoy, Patrick, Giraud, Luc, L'Excellent, Jean-Yves, Géoazur (GEOAZUR 6526), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure d'Electrotechnique, d'Electronique, d'Informatique, d'Hydraulique et de Télécommunications (ENSEEIHT), Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université de Toulouse (UT), Université de Toulouse (UT), Algorithms and Scheduling for Distributed Heterogeneous Platforms (GRAAL), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Laboratoire de l'Informatique du Parallélisme (LIP), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche pour le Développement (IRD)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées, Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-École normale supérieure - Lyon (ENS Lyon)

Subjects
[INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], ComputingMilieux_MISCELLANEOUS
Abstract

International audience; no abstract

Published
2006

29. Full waveform inversion of diving & reflected waves for velocity model building with impedance inversion based on scale separation.

Author

Wei Zhou, Brossier, Romain, Operto, Stéphane, and Virieux, Jean

Subjects
WAVE analysis, INVERSION (Geophysics), VELOCITY, ELECTRIC impedance, SEISMIC waves
Abstract

Full waveform inversion (FWI) aims to reconstruct high-resolution subsurface models from the full wavefield, which includes diving waves, post-critical reflections and short-spread reflections. Most successful applications of FWI are driven by the information carried by diving waves and post-critical reflections to build the long-to-intermediate wavelengths of the velocity structure. Alternative approaches, referred to as reflection waveform inversion (RWI), have been recently revisited to retrieve these long-to-intermediate wavelengths from shortspread reflections by using some prior knowledge of the reflectivity and a scale separation between the velocity macromodel and the reflectivity. This study presents a unified formalism of FWI, named as Joint FWI, whose aim is to efficiently combine the diving and reflected waves for velocity model building. The two key ingredients of Joint FWI are, on the data side, the explicit separation between the short-spread reflections and the wide-angle arrivals and, on the model side, the scale separation between the velocity macromodel and the shortscale impedance model. The velocity model and the impedance model are updated in an alternate way by Joint FWI and waveform inversion of the reflection data (least-squares migration), respectively. Starting from a crude velocity model, Joint FWI is applied to the streamer seismic data computed in the synthetic Valhall model. While the conventional FWI is stuck into a local minimum due to cycle skipping, Joint FWI succeeds in building a reliable velocity macromodel. Compared with RWI, the use of diving waves in Joint FWI improves the reconstruction of shallow velocities, which translates into an improved imaging at deeper depths. The smooth velocity model built by Joint FWI can be subsequently used as a reliable initial model for conventional FWI to increase the high-wavenumber content of the velocity model. [ABSTRACT FROM AUTHOR]

Published
2015
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30. Fast full waveform inversion with source encoding and second-order optimization methods.

Author

Castellanos, Clara, Métivier, Ludovic, Operto, Stéphane, Brossier, Romain, and Virieux, Jean

Subjects
WAVE analysis, HIGH performance computing, GEOLOGY, ALGORITHMS
Abstract

Full waveform inversion (FWI) of 3-D data sets has recently been possible thanks to the development of high performance computing. However, FWI remains a computationally intensive task when high frequencies are injected in the inversion or more complex wave physics (viscoelastic) is accounted for. The highest computational cost results from the numerical solution of the wave equation for each seismic source. To reduce the computational burden, one well-known technique is to employ a random linear combination of the sources, rather that using each source independently. This technique, known as source encoding, has shown to successfully reduce the computational cost when applied to real data. Up to now, the inversion is normally carried out using gradient descent algorithms. With the idea of achieving a fast and robust frequency-domain FWI, we assess the performance of the random source encoding method when it is interfaced with second-order optimization methods (quasi-Newton l-BFGS, truncated Newton). Because of the additional seismic modelings required to compute the Newton descent direction, it is not clear beforehand if truncated Newton methods can indeed further reduce the computational cost compared to gradient algorithms. We design precise stopping criteria of iterations to fairly assess the computational cost and the speed-up provided by the source encoding method for each optimization method. We perform experiment on synthetic and real data sets. In both cases, we confirm that combining source encoding with second-order optimization methods reduces the computational cost compared to the case where source encoding is interfaced with gradient descent algorithms. For the synthetic data set, inspired from the geology of Gulf of Mexico, we show that the quasi-Newton l-BFGS algorithm requires the lowest computational cost. For the real data set application on the Valhall data, we show that the truncated Newton methods provide the most robust direction of descent. [ABSTRACT FROM AUTHOR]

Published
2015
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33. Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field. Part 1: imaging compressional wave speed, density and attenuation.

Author

Prieux, Vincent, Brossier, Romain, Operto, Stéphane, and Virieux, Jean

Subjects
WAVE analysis, OCEAN bottom, DATA analysis, ATTENUATION of seismic waves, SEISMIC wave velocity, IMAGE compression, INVERSIONS (Geology)
Abstract

Multiparameter full waveform inversion (FWI) is a challenging quantitative seismic imaging method for lithological characterization and reservoir monitoring. The difficulties in multiparameter FWI arise from the variable influence of the different parameter classes on the phase and amplitude of the data, and the trade-off between these. In this framework, choosing a suitable parametrization of the subsurface and designing the suitable FWI workflow are two key methodological issues in non-linear waveform inversion. We assess frequency-domain visco-acoustic FWI to reconstruct the compressive velocity (VP), the density (ρ) or the impedance (IP) and the quality factor (QP), from the hydrophone component, using a synthetic data set that is representative of the Valhall oil field in the North Sea. We first assess which of the (VP, ρ) and (VP, IP) parametrizations provides the most reliable FWI results when dealing with wide-aperture data. Contrary to widely accepted ideas, we show that the (VP, ρ) parametrization allows a better reconstruction of both the VP, ρ and IP parameters, first because it favours the broad-band reconstruction of the dominant VP parameter, and secondly because the trade-off effects between velocity and density at short-to-intermediate scattering angles can be removed by multiplication, to build an impedance model. This allows for the matching of the reflection amplitudes, while the broad-band velocity model accurately describes the kinematic attributes of both the diving waves and reflections. Then, we assess different inversion strategies to recover the quality factor QP, in addition to parameters VP and ρ. A difficulty related to attenuation estimation arises because, on the one hand the values of QP are on average one order of magnitude smaller than those of VP and ρ, and on the other hands model perturbations relative to the starting models can be much higher for QP than for VP and ρ during FWI. In this framework, we show that an empirical tuning of the FWI regularization, which is adapted to each parameter class, is a key issue to correctly account for the attenuation in the inversion. We promote a hierarchical approach where the dominant parameter VP is reconstructed first from the full data set (i.e. without any data preconditioning) to build a velocity model as kinematically accurate as possible before performing the joint update of the three parameter classes during a second step. This hierarchical imaging of compressive wave speed, density and attenuation is applied to a real wide-aperture ocean-bottom-cable data set from the Valhall oil field. Several geological features, such as accumulation of gas below barriers of claystone and soft quaternary sediment are interpreted in the FWI models of density and attenuation. The models of VP, ρ and QP that have been developed by visco-acoustic FWI of the hydrophone data can be used as initial models to perform visco-elastic FWI of the geophone data for the joint update of the compressive and shear wave speeds. [ABSTRACT FROM AUTHOR]

Published
2013
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34. Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field. Part 2: imaging compressive-wave and shear-wave velocities.

Author

Prieux, Vincent, Brossier, Romain, Operto, Stéphane, and Virieux, Jean

Subjects
WAVE analysis, MULTIPHASE flow, SHEAR waves, IMAGING systems in seismology, FEASIBILITY studies, HYDROPHONE
Abstract

Multiparameter elastic full waveform inversion (FWI) is a promising technology that allows inferences to be made on rock and fluid properties, which thus narrows the gap between seismic imaging and reservoir characterization. Here, we assess the feasibility of 2-D vertical transverse isotropic visco-elastic FWI of wide-aperture multicomponent ocean-bottom-cable data from the Valhall oil field. A key issue is to design a suitable hierarchical data-driven and model-driven FWI workflow, the aim of which is to reduce the nonlinearity of the FWI. This nonlinearity partly arises because the shear (S) wavespeed can have a limited influence on seismic data in marine environments. In a preliminary stage, visco-acoustic FWI of the hydrophone component is performed to build a compressional (P)-wave velocity model, a density model and a quality-factor model, which provide the necessary background models for the subsequent elastic inversion. During the elastic FWI, the P and S wavespeeds are jointly updated in two steps. First, the hydrophone data are inverted to mainly update the long-to-intermediate wavelengths of the S wavespeeds from the amplitude-versus-offset variations of the P–P reflections. This S-wave velocity model is used as an improved starting model for the subsequent inversion of the better-resolving data recorded by the geophones. During these two steps, the P-wave velocity model is marginally updated, which supports the relevance of the visco-acoustic FWI results. Through seismic modelling, we show that the resulting visco-elastic model allows several P-to-S converted phases recorded on the horizontal-geophone component to be matched. Several elastic quantities, such as the Poisson ratio, and the ratio and product between the P and S wavespeeds, are inferred from the P-wave and S-wave velocity models. These attributes provide hints for the interpretation of an accumulation of gas below lithological barriers. [ABSTRACT FROM AUTHOR]

Published
2013
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35. A parametric analysis of two-dimensional elastic full waveform inversion of teleseismic data for lithospheric imaging.

Author

Pageot, Damien, Operto, Stéphane, Vallée, Martin, Brossier, Romain, and Virieux, Jean

Subjects
*WAVE analysis, *LITHOSPHERE, *SEISMOLOGY, *HIGH resolution imaging, *SHEAR waves, *QUASI-Newton methods, *SEISMIC tomography, *SCATTERING (Physics), *THEORY of wave motion
Abstract

The development of dense networks of broad-band seismographs makes teleseismic data amenable to full-waveform inversion (FWI) methods for high-resolution lithospheric imaging. Compared to scattered-field migration, FWI seeks to involve the full seismic wavefield in the inversion. We present a parametric analysis of 2-D frequency-domain FWI in the framework of lithospheric imaging from teleseismic data to identify the main factors that impact on the quality of the reconstructed compressional (P)-wave and shear (S)-wave speed models. Compared to controlled-source seismology, the main adaptation of FWI to teleseismic configuration consists of the implementation with a scattered-filed formulation of plane-wave sources that impinge on the base of the lithospheric target located below the receiver network at an arbitrary incidence angle. Seismic modelling is performed with a hp-adaptive discontinuous Galerkin method on unstructured triangular mesh. A quasi-Newton inversion algorithm provides an approximate accounting for the Hessian operator, which contributes to reduce the footprint of the coarse acquisition geometry in the imaging. A versatile algorithm to compute the gradient of the misfit function with the adjoint-state method allows for abstraction between the forward-problem operators and the meshes that are during seismic modelling and inversion, respectively. An approximate correction for obliquity is derived for future application to real teleseismic data under the two-dimension approximation. Comparisons between the characteristic scales involved in exploration geophysics and in teleseismic seismology suggest that the resolution gain provided by full waveform technologies should be of the same order of magnitude for both applications. We first show the importance of the surface-reflected wavefield to dramatically improve the resolving power of FWI by combining tomography-like and migration-like imaging through the incorporation of the forward-scattered and the backscattered wavefields in the inversion. The resolution of FWI is assessed through checkerboard tests and confirms a resolution of the order of the wavelength for both the P and S speeds, when the full wavefield is incorporated in the inversion. Secondly, we show that computationally efficient strategies, which consist of decimating the number of frequency components involved in the inversion, do not apply to teleseismic acquisitions, because the scattering-angle bandwidth sampled by plane-wave sources can be narrow and coarsely sampled, compared to that provided by dense profiles of point sources in exploration seismology. The waveform inversion is less sensitive to the band of incidence angles spanned by the plane-wave sources and to the sampling of this band. However, the deficit of vertically propagating plane waves hampers the vertical resolution of planar layers. Aliasing artefacts created by coarse arrays of receivers are illustrated. We show how taking into account the Hessian in the inversion and the suitable management of frequencies in the inversion help to mitigate these artefacts. Acceptable reconstructions are shown for both the P- and S-wave speeds for a receiver spacing of up to 20 km in the 0.1–0.4 Hz frequency range. Building a reliable initial model for FWI is a highly non-linear problem in exploration seismology. We show how the low-frequency content of the teleseismic sources allow us to build accurate P- and S-wave speed models starting from simple vertical-gradient velocity models. All of these results are derived using a 2-D realistic synthetic experiment that was performed with noise-free data. Most of conclusions of this parametric study should apply in three dimensions. The impact of noise and the footprint of other experimental parameters ... [ABSTRACT FROM AUTHOR]

Published
2013
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36. Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 2: Synthetic and real data case studies from Valhall.

Author

Gholami, Yaser, Brossier, Romain, Operto, Stéphane, Prieux, Vincent, Ribodetti, Alessandra, and Virieux, Jean

Subjects
WAVES (Physics), WAVELENGTHS, AZIMUTH, ACOUSTIC emission, PARAMETER estimation
Abstract

It is necessary to account for anisotropy in full waveform inversion (FWI) of wide-azimuth and wide-aperture seismic data in most geologic environments, for correct depth positioning of reflectors, and for reliable estimations of wave speeds as a function of the direction of propagation. In this framework, choosing a suitable anisotropic subsurface parameterization is a central issue in monoparameter and multiparameter FWI. This is because this parameterization defines the influence of each physical parameter class on the data as a function of the scattering angle, and hence the resolution of the parameter reconstruction, and on the potential trade-off between different parameter classes. We apply monoparameter and multiparameter frequency-domain acoustic vertical transverse isotropic FWI to synthetic and real wide-aperture data, representative of the Valhall oil field. We first show that reliable monoparameter FWI can be performed to build a high-resolution velocity model (for the vertical, the horizontal, or normal move-out velocity), provided that the background models of two Thomsen parameters describe the long wavelengths of the subsurface sufficiently accurately. Alternatively, we show the feasibility of the joint reconstruction of two wave speeds (e.g., the vertical and horizontal wave speeds) with limited trade-off effects, while Thomsen parameter ,5 is kept fixed during the inversion. The influence of the wave speeds on the data for a limited range of scattering angles when combined each other can, however, significantly hamper the resolution with which the two wave speeds are imaged. These conclusions inferred from the application to the mat data are fully consistent with those inferred from the theoretical parameterization analysis of acoustic vertical transverse isotropic FWI performed in the companion report. [ABSTRACT FROM AUTHOR]

Published
2013
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37. Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 1: Sensitivity and trade-off analysis.

Author

Gholami, Yaser, Brossier, Romain, Operto, Stéphane, Ribodetti, Alessandra, and Virieux, Jean

Subjects
ANISOTROPY, AZIMUTH, SEISMIC wave studies, ACOUSTIC emission, MATHEMATICAL models
Abstract

In most geologic environments, accounting for anisotropy is necessary to perform acoustic full waveform inversion (FWI) of wide-azimuth and wide-aperture seismic data because of the potential dependence of wave speeds on the direction of the wave propagation. In the framework of multiparameter FWI, the subsurface parameterization controls the influence of the different parameter classes on the modeled seismic data as a function of the scattering angle and hence the resolution with which the parameters can be reconstructed and the potential trade-off between different parameters. We have evaluated a numerical procedure based on computation of the scattering patterns of the different parameters to assess the sensitivity of the seismic data to different parameterizations of vertical transverse isotropic media in the acoustic approximation. Among the different categories we have tested, a monoparametric FWI was found for imaging one wave speed with a broad wavenumber content, keeping the Thomsen parameters fixed, which have a small influence on the data relative to the wave speed. This raises the question of the initial information required in the background models of the Thomsen parameters to perform reliable monoparameter FWI. Alternatively, simultaneously inverting the horizontal and vertical wave speeds introduces limited trade-off effects because these wave speeds have significant influence on the data for distinct Panges of scattering angles, while the influence of the Thomsen parameter δ remains weak. With such parameterization, the short-to-intermediate wavelengths of the vertical velocity are updated from the short-to-intermediate scattering angles, while the long-to-intermediate wavelengths of the horizontal velocity are updated from the wide-to-intermediate scattering angles. We concluded that the choice of the subsurface parameterization can be driven by the acquisition geometry, which controls the scattering-angle coverage and hence the resolving power of FWI, and by the accuracy of the available initial FWI models. [ABSTRACT FROM AUTHOR]

Published
2013
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38. Shallow-structure characterization by 2D elastic full-waveform inversion.

Author

Romdhane, Anouar, Grandjean, Gilles, Brossier, Romain, Rejiba, Fayçal, Operto, Stéphane, and Virieux, Jean

Subjects
CATHODE ray oscillographs, INVERSION (Geophysics), ALGORITHMS, EARTHFLOWS, GALERKIN methods
Abstract

Assessing the effectiveness of elastic full-waveform-inversion (FWI) algorithms when applied to shallow 2D structures in the presence of a complex topography is critically important. By using FWI, we overcome inherent limitations of conventional seismic methods used for near-surface prospecting (acoustic tomography and multichannel spectral analysis of surface waves). The elastic forward problem, formulated in the frequency domain, is based on a mixed finite-element P0PI discontinuous Galerkin method to ensure accurate modeling of complex topography effects at a reasonable computing cost. The inversion problem uses an FWI algorithm to minimize the misfit between observed and calculated data. Based on results from a numerical experiment performed on a realistic landslide model inspired from the morphostructure of the Super-Sauze earthflow, we analyzed the effect of using a hierarchical preconditioning strategy, based on a simultaneous multifrequency inversion of damped data, to mitigate the strong nonlinearities coming from the surface waves. This strategy is a key point in alleviating the strong near-surface effects and avoiding convergence toward a local minimum. Using a limited-memory quasi-Newton method improved the convergence level. These findings are analogous to recent applications on large-scale domains, although limited source-receiver offset ranges, low-frequency content of the source, and domination of surface waves on the signal led to some difficulties. Regarding the impact of data decimation on the inversion results, we have learned that an inversion restricted to the vertical data component can be successful without significant loss in terms of parameter imagery resolution. In our investigations of the effect of increased source spacing, we found that a sampling of 4 m (less than three times the theoretical maximum of one half-wavelength) led to severe aliasing. [ABSTRACT FROM AUTHOR]

Published
2011
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39. Imaging and inversion -- Introduction.

Author

Buske, Stefan, Lecomte, Isabelle, Nemeth, Tamas, Operto, Stéphane, and Sallares, Valenti

Subjects
WAVE equation, GEOPHYSICS
Abstract

The article discusses various reports in this issue, including one about the prestack depth migration approach and another on a new wave equation for P-waves.

Published
2009
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40. Quantitative imaging of the Permo-Mesozoic complex and its basement by frequency domain waveform tomography of wide-aperture seismic data from the Polish Basin.

Author

Malinowski, Michal and Operto, Stéphane

Subjects
*CATHODE ray oscillographs, *SEISMOGRAMS, *TOMOGRAPHY, PENNSYLVANIAN stratigraphic geology
Abstract

In this study we present the workflow and results of 2D frequency domain waveform tomography applied to the global-offset seismic data acquired in central Poland along a 50-km long profile during the GRUNDY 2003 experiment. The waveform tomography method allows full exploitation of the wide-aperture content of these data and produces in a semi-automatic way both the detailed P-wave velocity model and the structural image (i.e., perturbations in respect to the starting model). Thirteen frequencies ranging from 4 to 16 Hz were inverted sequentially, gradually introducing higher wavenumbers and more details into the velocity models. Although the data were characterised by relatively large shot spacings (1.5 km), we obtained clear images both of the Mesozoic and Permian sedimentary cover. Velocity patterns indicated facies changes within the Jurassic and Zechstein strata. A high velocity layer (ca. 5500 m/s) was found near the base of Triassic (Scythian), which made the imaging of a deeper layer difficult. Nevertheless, we were able to delineate the base of the Permian (i.e., base of the Rotliegend), which was not possible to derive from conventional common-depth-point processing, as well as some deeper events, attributed to the Carboniferous. The sub-Permian events formed a syn-form which favoured our previous interpretation of a depression filled with Upper Carboniferous molasse. The validity of the waveform tomography-derived model was confirmed by well-log data. Forward ray-tracing modelling and synthetic seismograms calculations provided another justification for the key structures present in the waveform tomography model. [ABSTRACT FROM AUTHOR]

Published
2008
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41. Potential and limits of double-difference tomographic methods.

Author

Got, Jean-Luc, Monteiller, Vadim, Virieux, Jean, and Operto, Stéphane

Subjects
HARMONIC analysis (Mathematics), SEISMIC tomography, SEISMOLOGICAL research, SEISMIC traveltime inversion, OPTICAL resolution
Abstract

Double-difference tomographic methods use directly accurate time delays computed between similar signals. Such methods are designed to image very heterogeneous media, such as volcanoes or fault zones. In seismological applications, similar signals are recorded at a given station from earthquakes sharing similar and close-by sources. In seismic exploration experiments, similar signals are often recorded at neighbouring receivers. After a brief presentation of the tomographic algorithm used, a seismological application is summarized. The potential and limits of double-difference tomographic methods are explored using various numerical experiments. They show that two effects are competing in double-difference tomography: (i) the degradation of the stability of the inversion due to the geometrical proximity of the rays used in the differentiation and (ii) the decrease in modelling error, which allows improving the stability of the inversion and using smaller quantities of a priori information when data are sufficiently accurate. The best resolution is obtained for an optimal value of the inter-source or inter-receiver distance. For optimal values of these distances and a priori information, tomography using traveltime differences provides significantly better resolved results than using traveltimes. [ABSTRACT FROM AUTHOR]

Published
2008
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42. First-arrival traveltime tomography using second generation wavelets.

Author

Delost, Matthieu, Virieux, Jean, and Operto, Stéphane

Subjects
WAVELETS (Mathematics), SEISMIC tomography, OPTICAL resolution, SMOOTHING (Numerical analysis), SEISMIC traveltime inversion
Abstract

Wavelet decomposition of the slowness model allows a multiscale description of the seismic first-arrival time tomography. We propose the introduction of the so-called second generation wavelets that could be used for any mesh structure and do not require a number of samples, such as the power of two in each direction for fast wavelet transform. A linearized procedure for inverting delayed travel-times considering either slowness coefficients or wavelet coefficients has been set up with an efficient ray tracing at each iteration of the inversion procedure. Wavelet decomposition over constant patches (Haar wavelet) or over linear patches (Battle-Lemarie wavelet) of coefficients at different scales are inverted as unknowns of the tomographic linearized system. Reconstruction of these coefficients depends dynamically on the local resolution when considering dense ray coverage. On simple synthetic examples, it has been found necessary to perform a local resolution analysis for specifying wavelet coefficients to be inverted. This resolution analysis could be performed for an initial smooth reconstructed medium and by designing a bit mask operator it allows fine scales to be inverted in specific areas of the model where the resolution is high while not being inverted in other areas where the resolution is poor: the wavelet decomposition will ease the multiscale reconstruction. A few synthetic examples, such as crosshole tomography or surface-surface tomography illustrate the multiscale feature of wavelet tomography. The second generation wavelet approach seems to be a flexible and rather promising tool for controlling the resolution variation of seismic first-arrival tomography. [ABSTRACT FROM AUTHOR]

Published
2008
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43. Mixed-grid and staggered-grid finite-difference methods for frequency-domain acoustic wave modelling.

Author

Hustedt, Bernhard, Operto, Stéphane, and Virieux, Jean

Subjects
*SOUND waves, *SEISMIC waves, *FINITE differences, *WAVE equation, *MATHEMATICAL models
Abstract

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. [ABSTRACT FROM AUTHOR]

Published
2004
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44. A multi-level direct-iterative solver for seismic wave propagation modelling: space and wavelet approaches.

Author

Hustedt, Bernhard, Operto, Stéphane, and Viri, Jean

Subjects
*FINITE differences, *SEISMIC waves, *GEOPHYSICS
Abstract

We present a new numerical modelling approach for frequency-domain finite-difference (FDFD) wave simulations. The new approach is developed as an extension to standard FDFD modelling schemes, when wave propagation simulations are performed in large-scale 2-D or 3-D models with complex heterogeneous rheology. Partial differential equations are presented in matrix-type form. Wavefield solutions are computed on different coarse- and fine-discretized numerical grids by a combination of a direct solver with an iterative solver. Two different connection strategies are designed. Both compute a coarse-grid wavefield solution using a direct matrix solver. The obtained solution is projected on a fine-discretized grid, which is used as an initial solution for an iterative solver to compute the desired fine-grid solution. The wavefield projection that combines coarse and fine grids, is either based on a space interpolation scheme, called the direct iterative space solver (DISS) or on a multi-scale wavelet expansion, called the direct iterative wavelet solver (DIWS). The DISS scheme mimics a nested iteration scheme of a full multi-grid method, since numerical grids are prolonged by a simple bilinear interpolation scheme. The simple grid combination leads to wavefield solutions that are affected by spatial phase-shift artefacts (aliasing), which may be suppressed by a large number of iteration steps or a standard V- and W-cycles sequence between grids. The actual DIWS matrix construction implementation is computationally more expensive, though the wavelet iteration scheme guarantees fast and stable iterative convergence. Coarse-grid wavefield solutions are combined with fine-grid solutions through the multi-resolution scaling property of a standard orthogonal wavelet expansion. Since the wavelet transformation accounts for grid interactions, phase-shift artefacts are greatly reduced and significantly fewer iteration steps are required for convergence. We demonstrate the performance and accuracy of the DISS and DIWS strategies for two complex 2-D heterogeneous wave simulation examples. [ABSTRACT FROM AUTHOR]

Published
2003
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46. Small-scale crustal variability within an intraplate structure: the Crozet Bank (southern Indian Ocean).

Author

Recq, Maurice, Goslin, Jean, Charvis, Philippe, and Operto, Stéphane

Subjects
VOLCANOES, SEISMIC refraction method
Abstract

The Crozet Bank, the easternmost region of the Crozet Plateau (austral Indian Ocean), is capped by two groups of islands which form the Crozet Archipelago (Terres Australes and Antarctiques Françaises). A N-S-trending 2 km deep basin, the Indivat Basin, extends between the two groups of islands and bisects the Crozet Bank into two separate domains. The interpretation of the KeOBS8 seismic refraction profile shot during the KeOBS/MD66 cruise (January-February 1991) over the eastern Crozet Plateau was carried out by ray tracing and the computation of synthetic seismograms. This interpretation leads to a rather complex seismic structure and outlines a pronounced eastward crustal thinning from 16.5 to 10 km at the expense of layer 2. The thinning of the crust is abrupt east of the Indivat Basin. Unlike below the Hawaiian Islands and the Marquesas Islands, no underplated mantle material underlies the crust of the Crozet Bank. Moreover, this deep seismic sounding has further revealed that a high-velocity feature outcropping the seabed 30 km east of Ile aux Cochons could be a major structural feature, deeply rooted within the lower crust. The occurrence of this feature (a submarine volcano?) is associated with a mantle dyke causing a steep shallowing of the lower crustal interfaces. Gravity modelling was performed along line KeOBS8, with a density structure deduced from the seismic section, to model free-air anomalies derived from altimetry data. This modelling confirms that the Indivat Basin, underlined by a gravity low running roughly N-S between the two groups of islands, is a major structural boundary. As the model generates medium-wavelength anomalies of adequate amplitude, it also confirms that the volcano, located west of the Indivat Basin, is a deeply rooted feature. The Crozet Bank clearly appears as a plume-affected structure, which may have originated from a deep thermal anomaly within the lithosphere. More recent volcanic episodes, related to a... [ABSTRACT FROM AUTHOR]

Published
1998
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