Kinematically consistent slope tomography using eikonal solvers and the adjoint-state method : Theory and applications to velocity model building and event location

La construction du modèle de vitesse est crucial en imagerie sismique puisqu'elle contrôle la précision avec laquelle des méthodes d'imagerie haute résolution telles que la migration ou l'inversion des formes d'ondes complètes (FWI) peuvent imager le sous-sol. La stéréotomographie, une méthode de tomographie des pentes qui tire efficacement profit de la densité des données sismiques modernes, a été proposée comme une alternative aux approches classiques de tomographie en réflexion fondées sur le pointé d'horizons continus dans le volume sismique. La stéréotomographie est en revanche fondée sur le pointé semi-automatique d’événements localement cohérents, paramétrés par le temps double et les pentes aux sources et récepteurs et liés à des diffractants dans le sous-sol. Plus récemment, une variante de la stéréotomographie a été proposée en remplaçant le tracé de rai par un solveur eikonal dans le problème direct et l'inversion de la matrice des dérivés de Fréchet par la méthode de l'état adjoint dans le problème inverse. Cette nouvelle approche est massivement parallèle et de ce fait adaptée à des applications de grande dimension. Néanmoins, et de manière comparable à l'approche initiale, la position des diffractants et les paramètres du milieu sont conjointement mis à jour.Durant cette thèse, j'ai proposé une nouvelle formulation de la stéréotomographie qui gère plus efficacement le couplage vitesse-profondeur, inhérent aux approches en réflexion. Via une migration cinématique, je résous le problème de localisation et le projette dans le sous-problème principal de l'estimation des vitesses. Cette projection de variable garantit la consistance cinématique entre les deux classes de variables, consistance qui n'est pas garantie quand les deux classes de variables sont mis à jour conjointement. Par ailleurs, la projection de variable induit une paramétrisation compacte du problème inverse où une classe d'observables, en l’occurrence une pente, est utilisée pour mettre à jour une classe de paramètres, les vitesses. Je développe cette approche avec un solveur eikonal et la méthode de l'état adjoint pour des milieux TTI. Son évaluation sur deux cas d'étude synthétiques et réel confirme sa meilleur résilience au modèle initial et une vitesse de convergence plus rapide que l'approche conjointe.La stéréotomographie est principalement utilisée pour des dispositifs de sismique réflexion (flûte sismique) pour lesquels les sources et les récepteurs sont finement échantillonnés. Pour exploiter des dispositifs modernes à forts déports, j'ai introduit dans l'inversion les premières arrivées issues indifféremment de dispositifs de sismique réflexion multitrace ou de sismique grand-angle (OBN, OBC, terrestre). Dans un premier temps, j'ai illustré l'apport des pentes dans la tomographie des temps des premières arrivées (FATT) pour réduire l’ambiguïté temps-profondeur avec un cas synthétique et un cas réel sur la zone de subduction de Nankai. J'ai aussi évalué la tomographie des pentes en première arrivée pour construire un modèle initial pour la FWI avec un modèle complexe représentatif du Golfe du Mexique où la présence de sel génère de forts contrastes. J'ai pu illustrer la capacité de ma méthode à reconstruire les corps de sel tout en notant les difficultés héritées de l'éclairage incomplet de la zone située sous le sel. Cela m'a incité à combiner des données de sismique réflexion et des données grand-angle pour effectuer l'inversion conjointe des pentes et des temps de trajet des premières arrivées et des arrivées réfléchies pour bénéficier d'un éclairage angulaire optimal du milieu illustrée par des applications sur la zone de Nankai.Finalement, j'ai étendu l'utilisation de ma méthode par projection de variable pour localiser l'hypocentre des séismes en utilisant l'estimation des vitesses et des temps origine comme proxys. Cette approche originale a été validée avec deux exemples synthétiques.Velocity model building is a key step of seismic imaging since inferring high-resolution subsurface model by migration or full waveform inversion (FWI) is highly dependent on the kinematic accuracy of the retrieved velocity model. Stereotomography, a slope tomographic method that exploits well the density of the data, was proposed as an alternative to conventional reflection traveltime tomography. The latter is based on interpretive tracking of laterally-continuous reflections in the data volume whereas stereotomography relies on automated picking of locally coherent events. The densely picked attributes, namely the traveltimes and their spatial derivatives with respect to the source and receiver positions, are tied to scatterers in depth. More recently, a slope tomography variant was proposed under a framework based on eikonal solvers as an alternative to ray tracing and the adjoint-state method instead of Fréchet-derivative matrix inversion. This revamped stereotomography provides a scalable and flexible framework for large-scale applications. On the other hand, similarly to previous works, the scatterer positions and the subsurface parameters are updated jointly. In this thesis, I propose a new formulation of slope tomography that handles more effectively the ill-famed velocity-position coupling inherently present in reflection tomography. Through a kinematic migration, the scatterer position sub-problem is solved and projected into the main sub-problem for wavespeed estimation. Enforcing the kinematic consistency between the two kinds of variable, that is not guaranteed in the joint inversion, mitigates the ill-posedness generated by the velocity-position coupling. This variable projection leads to a reduced-parametrization inversion where the residuals of a single data class being a slope are minimized to update the subsurface parameters.I introduce this parsimonious strategy in the framework of eikonal solvers and the adjoint-state method for tilted transversely isotropic (TTI) media. I benchmark the method against the Marmousi model and present a field data case study previously tackled with the joint inversion strategy. Both case studies confirm that the parsimonious approach leads to a better-posed problem, with an improved robustness to the initial guess and convergence speed.Slope tomography is mainly used for streamer data due to the requirement of finely-sampled sources and receivers. To exploit cutting-edge long-offset datasets, I involve in the inversion first arrivals extracted from streamer or ocean bottom seismometer data. Before showing the complementarity between reflections and first arrivals, I examine the added value of introducing slopes in first-arrival traveltime tomography (FATT). Using a FWI workflow for quality control, I show with the Overthrust benchmark and a real data case study from the Nankai trough (Japan) how the joint inversion of slopes and traveltimes mitigates the ill-posedness of FATT. I also examine with the BP Salt model the limits of FATT to build an initial model for FWI in complex media. The results show how tomography suffers even with proper undershooting of the imaging targets due to the poor illumination of the subsalt area. On a crustal-scale benchmark, I first show the limits of reflection slope tomography induced by the limited streamer length before highlighting the added-value of the joint inversion of first-arrival and reflection picks.Finally, I introduce the same variable projection technique to tackle the velocity-hypocenter problem, which finds application in earthquake seismology and microseismic imaging. I propose a formulation where the hypocenter is located through the inversion of subsurface parameters and an origin time correction, both of them being used as a proxy and validate the proof of concept on two synthetic examples

Tomographie des pentes à cohérence cinématique fondée sur des solveurs eikonals et la méthode de l’état adjoint : Théorie et applications à la construction de modèles de vitesses et localisation d'événements

Velocity model building is a key step of seismic imaging since inferring high-resolution subsurface model by migration or full waveform inversion (FWI) is highly dependent on the kinematic accuracy of the retrieved velocity model. Stereotomography, a slope tomographic method that exploits well the density of the data, was proposed as an alternative to conventional reflection traveltime tomography. The latter is based on interpretive tracking of laterally-continuous reflections in the data volume whereas stereotomography relies on automated picking of locally coherent events. The densely picked attributes, namely the traveltimes and their spatial derivatives with respect to the source and receiver positions, are tied to scatterers in depth. More recently, a slope tomography variant was proposed under a framework based on eikonal solvers as an alternative to ray tracing and the adjoint-state method instead of Fréchet-derivative matrix inversion. This revamped stereotomography provides a scalable and flexible framework for large-scale applications. On the other hand, similarly to previous works, the scatterer positions and the subsurface parameters are updated jointly. In this thesis, I propose a new formulation of slope tomography that handles more effectively the ill-famed velocity-position coupling inherently present in reflection tomography. Through a kinematic migration, the scatterer position sub-problem is solved and projected into the main sub-problem for wavespeed estimation. Enforcing the kinematic consistency between the two kinds of variable, that is not guaranteed in the joint inversion, mitigates the ill-posedness generated by the velocity-position coupling. This variable projection leads to a reduced-parametrization inversion where the residuals of a single data class being a slope are minimized to update the subsurface parameters.I introduce this parsimonious strategy in the framework of eikonal solvers and the adjoint-state method for tilted transversely isotropic (TTI) media. I benchmark the method against the Marmousi model and present a field data case study previously tackled with the joint inversion strategy. Both case studies confirm that the parsimonious approach leads to a better-posed problem, with an improved robustness to the initial guess and convergence speed.Slope tomography is mainly used for streamer data due to the requirement of finely-sampled sources and receivers. To exploit cutting-edge long-offset datasets, I involve in the inversion first arrivals extracted from streamer or ocean bottom seismometer data. Before showing the complementarity between reflections and first arrivals, I examine the added value of introducing slopes in first-arrival traveltime tomography (FATT). Using a FWI workflow for quality control, I show with the Overthrust benchmark and a real data case study from the Nankai trough (Japan) how the joint inversion of slopes and traveltimes mitigates the ill-posedness of FATT. I also examine with the BP Salt model the limits of FATT to build an initial model for FWI in complex media. The results show how tomography suffers even with proper undershooting of the imaging targets due to the poor illumination of the subsalt area. On a crustal-scale benchmark, I first show the limits of reflection slope tomography induced by the limited streamer length before highlighting the added-value of the joint inversion of first-arrival and reflection picks.Finally, I introduce the same variable projection technique to tackle the velocity-hypocenter problem, which finds application in earthquake seismology and microseismic imaging. I propose a formulation where the hypocenter is located through the inversion of subsurface parameters and an origin time correction, both of them being used as a proxy and validate the proof of concept on two synthetic examples.La construction du modèle de vitesse est crucial en imagerie sismique puisqu'elle contrôle la précision avec laquelle des méthodes d'imagerie haute résolution telles que la migration ou l'inversion des formes d'ondes complètes (FWI) peuvent imager le sous-sol. La stéréotomographie, une méthode de tomographie des pentes qui tire efficacement profit de la densité des données sismiques modernes, a été proposée comme une alternative aux approches classiques de tomographie en réflexion fondées sur le pointé d'horizons continus dans le volume sismique. La stéréotomographie est en revanche fondée sur le pointé semi-automatique d’événements localement cohérents, paramétrés par le temps double et les pentes aux sources et récepteurs et liés à des diffractants dans le sous-sol. Plus récemment, une variante de la stéréotomographie a été proposée en remplaçant le tracé de rai par un solveur eikonal dans le problème direct et l'inversion de la matrice des dérivés de Fréchet par la méthode de l'état adjoint dans le problème inverse. Cette nouvelle approche est massivement parallèle et de ce fait adaptée à des applications de grande dimension. Néanmoins, et de manière comparable à l'approche initiale, la position des diffractants et les paramètres du milieu sont conjointement mis à jour.Durant cette thèse, j'ai proposé une nouvelle formulation de la stéréotomographie qui gère plus efficacement le couplage vitesse-profondeur, inhérent aux approches en réflexion. Via une migration cinématique, je résous le problème de localisation et le projette dans le sous-problème principal de l'estimation des vitesses. Cette projection de variable garantit la consistance cinématique entre les deux classes de variables, consistance qui n'est pas garantie quand les deux classes de variables sont mis à jour conjointement. Par ailleurs, la projection de variable induit une paramétrisation compacte du problème inverse où une classe d'observables, en l’occurrence une pente, est utilisée pour mettre à jour une classe de paramètres, les vitesses. Je développe cette approche avec un solveur eikonal et la méthode de l'état adjoint pour des milieux TTI. Son évaluation sur deux cas d'étude synthétiques et réel confirme sa meilleur résilience au modèle initial et une vitesse de convergence plus rapide que l'approche conjointe.La stéréotomographie est principalement utilisée pour des dispositifs de sismique réflexion (flûte sismique) pour lesquels les sources et les récepteurs sont finement échantillonnés. Pour exploiter des dispositifs modernes à forts déports, j'ai introduit dans l'inversion les premières arrivées issues indifféremment de dispositifs de sismique réflexion multitrace ou de sismique grand-angle (OBN, OBC, terrestre). Dans un premier temps, j'ai illustré l'apport des pentes dans la tomographie des temps des premières arrivées (FATT) pour réduire l’ambiguïté temps-profondeur avec un cas synthétique et un cas réel sur la zone de subduction de Nankai. J'ai aussi évalué la tomographie des pentes en première arrivée pour construire un modèle initial pour la FWI avec un modèle complexe représentatif du Golfe du Mexique où la présence de sel génère de forts contrastes. J'ai pu illustrer la capacité de ma méthode à reconstruire les corps de sel tout en notant les difficultés héritées de l'éclairage incomplet de la zone située sous le sel. Cela m'a incité à combiner des données de sismique réflexion et des données grand-angle pour effectuer l'inversion conjointe des pentes et des temps de trajet des premières arrivées et des arrivées réfléchies pour bénéficier d'un éclairage angulaire optimal du milieu illustrée par des applications sur la zone de Nankai.Finalement, j'ai étendu l'utilisation de ma méthode par projection de variable pour localiser l'hypocentre des séismes en utilisant l'estimation des vitesses et des temps origine comme proxys. Cette approche originale a été validée avec deux exemples synthétiques

Revisiting the hypocenter-velocity problem through a slope tomography inspiration

International audienceWe revisit the hypocenter-velocity problem which is of interest in different fields as for example microseismics and seismology. We show how, through a formulation based on kinematic migration focusing using two picked kinematic attributes in the two-dimensions case, the travel time and the slope (horizontal component of the slowness vector), we are able to invert jointly for the location, the origin time correction and the subsurface parameters mainly velocity. We present in this study a proof of concept validated by a toy test in two-dimensions. The method presented in this study is extendable to three-dimensions by incorporating the back-azimuth as a supplementary attribute

From slope tomography to FWI: Is the conventional workflow viable in complex settings?

International audienceUltra-long offset seabed acquisitions implemented with sparse array of ocean bottom nodes (OBN) are emerging as the goto strategy for velocity model building. These stationaryrecording geometries provide the flexibility to record a plethora of wave arrivals and in particular diving waves that undershoot the deepest targeted structures. These seabottom acquisitions are also amenable to the recording of frequencies as low as 1.5Hz. Full-Waveform Inversion (FWI) can be fed with this wide variety of low-frequency wave types to build broadband velocity models. Ultra-long offset surveys provide also a suitable framework to revive well proven tomography methods such as first-arrival slope+traveltime tomography to build kinematically-accurate initial velocity model for FWI. Here, we revisit the challenging 2004 BP salt benchmark by assessing a workflow combining first-arrival slope tomography and FWI against an ultra-long OBN survey involving a maximum offset of 97 km. Starting from a crude starting velocity gradient model, we manage to capture accurately the geometry of the salt and the subsalt structure down to 7km depth using 1.5-Hz starting frequency. Below 7km, the deficit of wide-angle coverage near the ends of the targeted structure combined with the inaccuracy of the tomography model in these areas prevents accurate reconstruction of subsalt structures by FWI when frequencies smaller than 1.5Hz are not used. The remedies to reconstruct subsalt structures in area suffering from deficit of wide-angle illumination should come from sophisticated sparsifying regularization in FWI and/or by the combination of first-arrival and short-spread + post-critical reflection slope tomography. The velocity model built by firstarrival slope tomography should be also beneficial for any variant of FWI involving more convex distances than the leastsquares norm of the differences

Anisotropic First-arrival Slope and Traveltime Tomography (FASTT)

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A fully scalable 3D non-periodic homogenization method to upscale elastic media

Main objectives In this study, we design an efficient and fully scalable parallel algorithm to implement the 3D nonperiodic homogenization method for elastic media upscaling, so as to make it easily applicable to seismic full waveform modelling and inversion on large-scale 3D problems. New aspects covered Instead of mathematical proofs and derivations of the homogenization theory, this study is developed from the application point of view. A fully scalable parallel conjugate-gradient iterative scheme is introduced into the 3D non-periodic homogenization process for solving its elastostatic equation systems and applying the low-pass filtering (here we use a cascade of elliptic PDE-defined Bessel filters to approximate the conventional convolution-based Gaussian low-pass filtering without the sacrifice of effectiveness)

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

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An accurate Eulerian travel-time computation: implication for slope tomography

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Strain to ground motion conversion of distributed acoustic sensing data for earthquake magnitude and stress drop determination

International audienceAbstract. The use of distributed acoustic sensing (DAS) presents unique advantages for earthquake monitoring compared with standard seismic networks: spatially dense measurements adapted for harsh environments and designed for remote operation. However, the ability to determine earthquake source parameters using DAS is yet to be fully established. In particular, resolving the magnitude and stress drop is a fundamental objective for seismic monitoring and earthquake early warning. To apply existing methods for source parameter estimation to DAS signals, they must first be converted from strain to ground motions. This conversion can be achieved using the waves' apparent phase velocity, which varies for different seismic phases ranging from fast body waves to slow surface and scattered waves. To facilitate this conversion and improve its reliability, an algorithm for slowness determination is presented, based on the local slant-stack transform. This approach yields a unique slowness value at each time instance of a DAS time series. The ability to convert strain-rate signals to ground accelerations is validated using simulated data and applied to several earthquakes recorded by dark fibers of three ocean-bottom telecommunication cables in the Mediterranean Sea. The conversion emphasizes fast body waves compared to slow scattered waves and ambient noise and is robust even in the presence of correlated noise and varying wave propagation directions. Good agreement is found between source parameters determined using converted DAS waveforms and on-land seismometers for both P and S wave records. The demonstrated ability to resolve source parameters using P waves on horizontal ocean-bottom fibers is key for the implementation of DAS-based earthquake early warning, which will significantly improve hazard mitigation capabilities for offshore earthquakes, including those capable of generating tsunami

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

International audienceIn 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