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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

SUMMARY 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 () and horizontal () 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. [ABSTRACT FROM AUTHOR]

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]

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.

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]

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]

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]

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]

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]

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]

The north Ligurian margin is a complex geological area in many ways. It has witnessed several phases of highly contrasting deformation styles, at both crustal scale and that of shallower cover tectonics, simultaneously or in quick succession, and with significant spatial variability. This complex interplay is mirrored in the resulting intricate structures that make it hard to identify active faults responsible for both, the significant seismicity observed, and the tectonic inversion undergone by the margin, identified at longer time scales on morphostructural grounds. We present here the first preliminary results of the leg 1 of SEFASILS cruise, conducted in 2018 offshore Monaco, in an effort to answer these questions by means of modern deep seismic acquisitions, using multichannel reflection and wide-angle sea-bottom records. Some first interpretations are provided and point towards an active basement deformation that focuses at the limits between main crustal domains. [ABSTRACT FROM AUTHOR]