Parsimonious finite-volume frequency-domain method for 2D P-SV-wave modeling

International audienceA new numerical technique for solving the 2D elastodynamic equations based on a finite volume approach is proposed. The associated discretization is through triangles. Only fluxes of required quantities are shared between cells, relaxing meshing conditions compared to finite element methods. The free surface is described along the edges of the triangles which may have different slopes. By applying a parsimonious strategy, stress components are eliminated from the discrete equations and only velocities are left as unknowns in triangles, minimizing the core memory requirement of the simulation. Efficient PML absorbing conditions have been designed for damping waves around the grid. Since the technique is devoted to full waveform inversion, we implemented the method in the frequency domain using a direct solver, an efficient strategy for multiple-source simulations. Standard dispersion analysis in infinite homogeneous media shows that numerical dispersion is similar to those of O(¢x2) staggeredgrid finite-difference formulations when considering structured triangular meshes. The method is validated against analytical solutions of several canonical problems and with numerical solutions computed with a well-established finite-difference time-domain method in heterogeneous media. In presence of a free surface, the finite-volume method requires ten triangles per wavelength for a flat topography and fifteen triangles per wavelength for more complex shapes, well below criteria required by the staircase approximation of finite-difference methods. Comparison between the frequency-domain finite-volume and the O(¢x2) rotated finite-difference methods also shows that the former is faster and less-memory demanding for a given accuracy level. We developed an efficient method for 2-D P-SV-wave modeling on structured triangular meshes as a tool for frequency-domain full-waveform inversion. Further work is required to assess the method on unstructured meshes

First-arrival Travel-Time Tomography using Second Generation Wavelets

International audienceWavelet decomposition of the slowness model has been proposed as a multiscale strategy for seismic first-arrival time tomography. We propose the introduction of so-called second generation wavelets which could be used for any mesh structure and does not need a number of samples as the power of two in each direction. Moreover, one can handle easily boundary effects. A linearized procedure for inverting delayed travel-times considering either slowness coefficients or wavelet coefficients. The ray tracing is solved at each iteration through an eikonal solver while the linear system to be solved at each iteration goes through an iterative solver as LSQR algorithm. We develop wavelet decomposition over constant patches (Haar wavelet) or over linear patches (Battle-Lemarie wavelet) of coefficients at different scales. This decomposition is introduced in the linear system to be solved and wavelet coefficients are considered as unknowns to be inverted. Synthetic examples show that the inversion behaves in a better way as wavelet decomposition seems to act as a preconditioner of the linear system. Local discretisation is possible but requires additional implementation as artefacs once built inside the model description never disappear because of the linearized approach. A binary mask operator is designed for each scale grid and could be applied locally leading to quite different spatial resolution depending on the analysis we could perform of the expected resolution at a given position of the medium. We show that indeed it is possible to design this binary operator and we apply it to synthetic examples as a crosswell experiment inside the Marmousi model. An application to a surface-surface experiment has been performed and the waveled decomposition shows that indeed we may recover detailed features nearby the free surface while preventing imprints of ray coverage at greater depths giving us smooth features at that depths. In spite of the increase demand of computer resources, the wavelet decomposition seems to be a rather promising alternative for controlling the resolution variation of seismic first-arrival tomography

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

International audienceFull 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

Modelling Seismic Wave Propagation for Geophysical Imaging

International audienceThe Earth is an heterogeneous complex media from the mineral composition scale (10−6m) to the global scale ( 106m). The reconstruction of its structure is a quite challenging problem because sampling methodologies are mainly indirect as potential methods (Günther et al., 2006; Rücker et al., 2006), diffusive methods (Cognon, 1971; Druskin & Knizhnerman, 1988; Goldman & Stover, 1983; Hohmann, 1988; Kuo & Cho, 1980; Oristaglio & Hohmann, 1984) or propagation methods (Alterman & Karal, 1968; Bolt & Smith, 1976; Dablain, 1986; Kelly et al., 1976; Levander, 1988; Marfurt, 1984; Virieux, 1986). Seismic waves belong to the last category. We shall concentrate in this chapter on the forward problem which will be at the heart of any inverse problem for imaging the Earth. The forward problem is dedicated to the estimation of seismic wavefields when one knows the medium properties while the inverse problem is devoted to the estimation of medium properties from recorded seismic wavefields

Plateau: a volcanic passive margin fragment

ABSTRACT The 21-25-hi-thick crust of the southern Kerguelen Plateau consists of three units: (1) a 52.3-km-thick sedimentary cover; (2) a 3-6-km-thick basaltic lager with velocities ranging from 3.5 to 6.2 km/s; and (3) a 15-17-hn-thick lower crust with velocities from 6.6 to 6.9 lun/s, including a 3-6-hi-thick transition zone located at the base of the crust. The low-velocity transition zone has an average velocity of 6.7 hn/s and exhibits several internal wide-angle refiections. The velocity-depth structure of the crust differs significantly from that of other hotspot-related oceanic plateaus and suggests that the southern Kerguelen Plateau may be a fragment of a volcanic passive margin composed of a thinned continental crust overlain by basalt ffovr-s

Imagerie sismique par inversion des formes d'onde en domaine fréquentiel

L'exploration sismique fondée sur la propagation des ondes élastiques dans la Terre est l'une des principales méthodes géophysiques pour imager plusieurs propriétés physiques du sous-sol telles que les vitesses de propagation des ondes élastiques, la densité, l'atténuation et l'anisotropie. Trois enjeux fondamentaux de l'imagerie sismique sont l'amélioration de la résolution spatiale des modèles, la construction de modèles en 3D et la prise en compte de plusieurs classes de paramètres. Pour atteindre ces trois objectifs, nous bénéficions notamment de l'évolution des dispositifs d'acquisition multicomposantes de plus en plus denses et longs et de l'utilisation de sources large bande. Les applications sont aussi variées que l'imagerie de la subsurface pour des applications géotechniques, la prospection pétrolière et l'imagerie crustale et lithosphérique pour des applications académiques. L'approche développée est fondée sur la résolution d'un problème inverse appliqué au champ d'onde complet en domaine fréquentiel. Elle est plus spécifiquement dédiée à des dispositifs dits grand-angle ou multi offsets. Ces dispositifs sont classiquement mis en oeuvre avec des stations sismiques sous-marines et terrestres multi-composantes et enregistrent des ondes s'étant propagées avec des angles d'incidence extrêmement variés. Dans ce contexte, une analyse de résolution montre que l'inversion de quelques fréquences suffit à focaliser l'image du milieu. Par ailleurs, ces fréquences peuvent être inversées séquentiellement plutôt que simultanément, définissant ainsi une imagerie multirésolution qui est favorable à la gestion de la non linéarité du problème inverse. Un ingrédient essentiel des algorithmes d'imagerie est la modélisation de la propagation des ondes. Nous utilisons une méthode par différences finies (DF) fréquence-espace qui permet le traitement rapide d'un grand nombre de sources et l'implémentation aisée d'effets d'atténuation. Ces concepts méthodologiques sont illustrés sur un cas synthétique et sur un jeu de données réelles

An overview of full-waveform inversion in exploration geophysics

International audienceFull-waveform inversion (FWI) is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of thewave-physics complexity. Different hierarchical multiscale strategies are designed to mitigate the nonlinearity and ill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as (1) building accurate starting models with automatic procedures and/or recording low frequencies, (2) defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and (3) improving computational efficiency by data-compression techniques to make 3D elastic FWI feasible

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

International audienceAbstract. 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