Fast Approximation of Nonlinearities for improving inversion algorithms of PNL mixtures and Wiener systems

This paper proposes a very fast method for blindly approximating a nonlinear mapping which transforms a sum of random variables. The estimation is surprisingly good even when the basic assumption is not satisfied.We use the method for providing a good initialization for inverting post-nonlinear mixtures and Wiener systems. Experiments show that the algorithm speed is strongly improved and the asymptotic performance is preserved with a very low extra computational cost.

Source wavelet estimation for waveform inversion of crosshole georadar data

AbstractFor a wide range of environmental, hydrological, and engineering applications there is a fast growing need for high-resolution imaging. In this context, waveform tomographic imaging of crosshole georadar data is a powerful method able to provide images of pertinent electrical properties in near-surface environments with unprecedented spatial resolution. In contrast, conventional ray-based tomographic methods, which consider only a very limited part of the recorded signal (first-arrival traveltimes and maximum first-cycle amplitudes), suffer from inherent limitations in resolution and may prove to be inadequate in complex environments. For a typical crosshole georadar survey the potential improvement in resolution when using waveform-based approaches instead of ray-based approaches is in the range of one order-of- magnitude. Moreover, the spatial resolution of waveform-based inversions is comparable to that of common logging methods. While in exploration seismology waveform tomographic imaging has become well established over the past two decades, it is comparably still underdeveloped in the georadar domain despite corresponding needs. Recently, different groups have presented finite-difference time-domain waveform inversion schemes for crosshole georadar data, which are adaptations and extensions of Tarantola's seminal nonlinear generalized least-squares approach developed for the seismic case. First applications of these new crosshole georadar waveform inversion schemes on synthetic and field data have shown promising results. However, there is little known about the limits and performance of such schemes in complex environments. To this end, the general motivation of my thesis is the evaluation of the robustness and limitations of waveform inversion algorithms for crosshole georadar data in order to apply such schemes to a wide range of real world problems.One crucial issue to making applicable and effective any waveform scheme to real-world crosshole georadar problems is the accurate estimation of the source wavelet, which is unknown in reality. Waveform inversion schemes for crosshole georadar data require forward simulations of the wavefield in order to iteratively solve the inverse problem. Therefore, accurate knowledge of the source wavelet is critically important for successful application of such schemes. Relatively small differences in the estimated source wavelet shape can lead to large differences in the resulting tomograms. In the first part of my thesis, I explore the viability and robustness of a relatively simple iterative deconvolution technique that incorporates the estimation of the source wavelet into the waveform inversion procedure rather than adding additional model parameters into the inversion problem. Extensive tests indicate that this source wavelet estimation technique is simple yet effective, and is able to provide remarkably accurate and robust estimates of the source wavelet in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity as well as significant ambient noise in the recorded data. Furthermore, our tests also indicate that the approach is insensitive to the phase characteristics of the starting wavelet, which is not the case when directly incorporating the wavelet estimation into the inverse problem.Another critical issue with crosshole georadar waveform inversion schemes which clearly needs to be investigated is the consequence of the common assumption of frequency- independent electromagnetic constitutive parameters. This is crucial since in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behaviour. In particular, in the presence of water, there is a wide body of evidence showing that the dielectric permittivity can be significantly frequency dependent over the GPR frequency range, due to a variety of relaxation processes. The second part of my thesis is therefore dedicated to the evaluation of the reconstruction limits of a non-dispersive crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. I show that the inversion algorithm, combined with the iterative deconvolution-based source wavelet estimation procedure that is partially able to account for the frequency-dependent effects through an "effective" wavelet, performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

3D geoelectrical monitoring to follow hydric soil behaviour during rainfall

RESUME Durant les dernières années, les méthodes électriques ont souvent été utilisées pour l'investigation des structures de subsurface. L'imagerie électrique (Electrical Resistivity Tomography, ERT) est une technique de prospection non-invasive et spatialement intégrée. La méthode ERT a subi des améliorations significatives avec le développement de nouveaux algorithmes d'inversion et le perfectionnement des techniques d'acquisition. La technologie multicanale et les ordinateurs de dernière génération permettent la collecte et le traitement de données en quelques heures. Les domaines d'application sont nombreux et divers: géologie et hydrogéologie, génie civil et géotechnique, archéologie et études environnementales. En particulier, les méthodes électriques sont souvent employées dans l'étude hydrologique de la zone vadose. Le but de ce travail est le développement d'un système de monitorage 3D automatique, non- invasif, fiable, peu coûteux, basé sur une technique multicanale et approprié pour suivre les variations de résistivité électrique dans le sous-sol lors d'événements pluvieux. En raison des limitations techniques et afin d'éviter toute perturbation physique dans la subsurface, ce dispositif de mesure emploie une installation non-conventionnelle, où toutes les électrodes de courant sont placées au bord de la zone d'étude. Le dispositif le plus approprié pour suivre les variations verticales et latérales de la résistivité électrique à partir d'une installation permanente a été choisi à l'aide de modélisations numériques. Les résultats démontrent que le dispositif pôle-dipôle offre une meilleure résolution que le dispositif pôle-pôle et plus apte à détecter les variations latérales et verticales de la résistivité électrique, et cela malgré la configuration non-conventionnelle des électrodes. Pour tester l'efficacité du système proposé, des données de terrain ont été collectées sur un site d'étude expérimental. La technique de monitorage utilisée permet de suivre le processus d'infiltration 3D pendant des événements pluvieux. Une bonne corrélation est observée entre les résultats de modélisation numérique et les données de terrain, confirmant par ailleurs que le dispositif pôle-dipôle offre une meilleure résolution que le dispositif pôle-pôle. La nouvelle technique de monitorage 3D de résistivité électrique permet de caractériser les zones d'écoulement préférentiel et de caractériser le rôle de la lithologie et de la pédologie de manière quantitative dans les processus hydrologiques responsables d'écoulement de crue. ABSTRACT During the last years, electrical methods were often used for the investigation of subsurface structures. Electrical resistivity tomography (ERT) has been reported to be a useful non-invasive and spatially integrative prospecting technique. The ERT method provides significant improvements, with the developments of new inversion algorithms, and the increasing efficiency of data collection techniques. Multichannel technology and powerful computers allow collecting and processing resistivity data within few hours. Application domains are numerous and varied: geology and hydrogeology, civil engineering and geotechnics, archaeology and environmental studies. In particular, electrical methods are commonly used in hydrological studies of the vadose zone. The aim of this study was to develop a multichannel, automatic, non-invasive, reliable and inexpensive 3D monitoring system designed to follow electrical resistivity variations in soil during rainfall. Because of technical limitations and in order to not disturb the subsurface, the proposed measurement device uses a non-conventional electrode set-up, where all the current electrodes are located near the edges of the survey grid. Using numerical modelling, the most appropriate arrays were selected to detect vertical and lateral variations of the electrical resistivity in the framework of a permanent surveying installation system. The results show that a pole-dipole array has a better resolution than a pole-pole array and can successfully follow vertical and lateral resistivity variations despite the non-conventional electrode configuration used. Field data are then collected at a test site to assess the efficiency of the proposed monitoring technique. The system allows following the 3D infiltration processes during a rainfall event. A good correlation between the results of numerical modelling and field data results can be observed since the field pole-dipole data give a better resolution image than the pole-pole data. The new device and technique makes it possible to better characterize the zones of preferential flow and to quantify the role of lithology and pedology in flood- generating hydrological processes.

Predição da hidroquímica da água (qualidade de água) usando sondagens electromagnéticas transientes (TEM)

This work aims the applicability of the Transient electromagnetic method at an arid and semiarid environmental condition in the Santiago Island – Cape Verde. Some seashore areas of this island show an increasing salt contamination of the groundwater. The main objective of present work is to relate this water-quality condition with parameters taken from the transient sounding’s data. In this context, transient soundings have been acquired from 2005 through 2009, at several chosen valleys near the sea, in a mean rate of one field campaign each year. The first phase of this work was the understanding of the geophysical method details, problems and applicability, as the chosen and acquired equipment was the first one to be permanently available to the Portuguese geosciences community. This first phase was also accomplished with field tests. Interpretation of the transient sounding’s data curves were done by application of 1-D inversion methods already developed and published, as also with quasi 2-D and quasi 3-D inversion algorithms, where applicability was feasible. This was the second phase. The 2-D and 3-D approximation results are satisfactory and promising; although a higher spatial sounding’s density should certainly allow for better results. At phase three, these results have been compared against the available lithologic, hydrologic and hydrochemical data, in the context of Santiago’s island settings. The analyses of these merged data showed that two distinct origins for the observed inland groundwater salinity are possible; seashore shallow mixing with contemporary seawater and mixing with a deep and older salty layer from up flow groundwater. Relations between the electric resistivity and the salt water content distribution were found for the surveyed areas. To this environment condition, the electromagnetic transient method proved to be a reliable and powerful technique. The groundwater quality can be accessed beyond the few available watershed points, which have an uneven distribution.

Surface topography and mixed-pixel effects on the simulated L-band brightness temperatures.

The impact of topography and mixed pixels on L-band radiometric observations over land needs to be quantified to improve the accuracy of soil moisture retrievals. For this purpose, a series of simulations has been performed with an improved version of the soil moisture and ocean salinity (SMOS) end-to-end performance simulator (SEPS). The brightness temperature generator of SEPS has been modified to include a 100-m-resolution land cover map and a 30-m-resolution digital elevation map of Catalonia (northeast of Spain). This high-resolution generator allows the assessment of the errors in soil moisture retrieval algorithms due to limited spatial resolution and provides a basis for the development of pixel disaggregation techniques. Variation of the local incidence angle, shadowing, and atmospheric effects (up- and downwelling radiation) due to surface topography has been analyzed. Results are compared to brightness temperatures that are computed under the assumption of an ellipsoidal Earth.

Modélisation de la diffraction des ondes de cisaillement en élastographie dynamique ultrasonore

L'élastographie ultrasonore est une technique d'imagerie émergente destinée à cartographier les paramètres mécaniques des tissus biologiques, permettant ainsi d’obtenir des informations diagnostiques additionnelles pertinentes. La méthode peut ainsi être perçue comme une extension quantitative et objective de l'examen palpatoire. Diverses techniques élastographiques ont ainsi été proposées pour l'étude d'organes tels que le foie, le sein et la prostate et. L'ensemble des méthodes proposées ont en commun une succession de trois étapes bien définies: l'excitation mécanique (statique ou dynamique) de l'organe, la mesure des déplacements induits (réponse au stimulus), puis enfin, l'étape dite d'inversion, qui permet la quantification des paramètres mécaniques, via un modèle théorique préétabli. Parallèlement à la diversification des champs d'applications accessibles à l'élastographie, de nombreux efforts sont faits afin d'améliorer la précision ainsi que la robustesse des méthodes dites d'inversion. Cette thèse regroupe un ensemble de travaux théoriques et expérimentaux destinés à la validation de nouvelles méthodes d'inversion dédiées à l'étude de milieux mécaniquement inhomogènes. Ainsi, dans le contexte du diagnostic du cancer du sein, une tumeur peut être perçue comme une hétérogénéité mécanique confinée, ou inclusion, affectant la propagation d'ondes de cisaillement (stimulus dynamique). Le premier objectif de cette thèse consiste à formuler un modèle théorique capable de prédire l'interaction des ondes de cisaillement induites avec une tumeur, dont la géométrie est modélisée par une ellipse. Après validation du modèle proposé, un problème inverse est formulé permettant la quantification des paramètres viscoélastiques de l'inclusion elliptique. Dans la continuité de cet objectif, l'approche a été étendue au cas d'une hétérogénéité mécanique tridimensionnelle et sphérique avec, comme objectifs additionnels, l'applicabilité aux mesures ultrasonores par force de radiation, mais aussi à l'estimation du comportement rhéologique de l'inclusion (i.e., la variation des paramètres mécaniques avec la fréquence d'excitation). Enfin, dans le cadre de l'étude des propriétés mécaniques du sang lors de la coagulation, une approche spécifique découlant de précédents travaux réalisés au sein de notre laboratoire est proposée. Celle-ci consiste à estimer la viscoélasticité du caillot sanguin via le phénomène de résonance mécanique, ici induit par force de radiation ultrasonore. La méthode, dénommée ARFIRE (''Acoustic Radiation Force Induced Resonance Elastography'') est appliquée à l'étude de la coagulation de sang humain complet chez des sujets sains et sa reproductibilité est évaluée.

Modelagem sísmica e inversão na presença de anisotropia

A necessidade da adoção de modelos elásticos anisotrópicos, no contexto da sísmica de exploração, vem crescendo com o advento de novas técnicas de aquisição de dados como VSP, walkway VSP, tomografia poço a poço e levantamentos sísmicos com grande afastamento. Meios anisotrópicos, no contexto da sísmica de exploração, são modelos efetivos para explicar a propagação de ondas através de meios que apresentam padrões de heterogeneidade em escala muito menor que o comprimento de onda das ondas sísmicas. Particularmente, estes modelos são muito úteis para explicar o dado sísmico mais robusto que são as medidas de tempo de trânsito. Neste trabalho, são investigados aspectos da propagação de ondas, traçado de raios e inversão de tempos de trânsito em meios anisotrópicos. É estudada a propagação de ondas SH em meios anisotrópicos estratificados na situação mais geral onde estas ondas podem ocorrer, ou seja, em meios monoclínicos com um plano vertical de simetria especular. É mostrado que o campo de ondas SH refletido a partir de um semi-espaço estratificado, não apresenta qualquer informação sobre a possível presença de anisotropia em subsuperfície. São apresentados métodos simples e eficientes para o traçado de raios em 3D através de meios anisotrópicos estratificados, baseados no princípio de Fermat. Estes métodos constituem o primeiro passo para o desenvolvimento de algoritmos de inversão de tempos de trânsito para meios anisotrópicos em 3D, a partir de dados de VSP e walkaway VSP. Esta abordagem é promissora para determinação de modelos de velocidade, que são necessários para migração de dados sísmicos 3D na presença de anisotropia. É efetuada a análise da inversão tomográfica não linear, para meios estratificados transversalmente isotrópicos com um eixo de simetria vertical(TIV). As limitações dos dados de tempo de trânsito de eventos qP para determinação das constantes elásticas, são estabelecidas e caracterizados os efeitos da falta de cobertura angular completa na inversão tomográfica. Um algoritmo de inversão foi desenvolvido e avaliado em dados sintéticos. A aplicação do algoritmo a dados reais demonstra a consistência de meios TIV. Esta abordagem é útil para casos onde há informação a priori sobre a estratificação quase plana das formações e onde os próprios dados do levantamento poço a poço apresentam um alto grau de simetria especular em relação a um plano vertical. Também pode ser útil em interpretações preliminares, onde a estimativa de um meio estratificado, serve como modelo de fundo para se efetuar análises mais detalhadas, por exemplo, como um modelo de velocidades anisotrópico para migração, ou como um modelo de calibração para análises de AVO.

NURBS-Based Geometry Parameterization for Aerodynamic Shape Optimization

La motivación de esta tesis es el desarrollo de una herramienta de optimización automática para la mejora del rendimiento de formas aerodinámicas enfocado en la industria aeronáutica. Este trabajo cubre varios aspectos esenciales, desde el empleo de Non-Uniform Rational B-Splines (NURBS), al cálculo de gradientes utilizando la metodología del adjunto continuo, el uso de b-splines volumétricas como parámetros de diseño, el tratamiento de la malla en las intersecciones, y no menos importante, la adaptación de los algoritmos de la dinámica de fluidos computacional (CFD) en arquitecturas hardware de alto paralelismo, como las tarjetas gráficas, para acelerar el proceso de optimización. La metodología adjunta ha posibilitado que los métodos de optimización basados en gradientes sean una alternativa prometedora para la mejora de la eficiencia aerodinámica de los aviones. La formulación del adjunto permite calcular los gradientes de una función de coste, como la resistencia aerodinámica o la sustentación, independientemente del número de variables de diseño, a un coste computacional equivalente a una simulación CFD. Sin embargo, existen problemas prácticos que han imposibilitado su aplicación en la industria, que se pueden resumir en: integrabilidad, rendimiento computacional y robustez de la solución adjunta. Este trabajo aborda estas contrariedades y las analiza en casos prácticos. Como resumen, las contribuciones de esta tesis son: • El uso de NURBS como variables de diseño en un bucle de automático de optimización, aplicado a la mejora del rendimiento aerodinámico de alas en régimen transónico. • El desarrollo de algoritmos de inversión de punto, para calcular las coordenadas paramétricas de las coordenadas espaciales, para ligar los vértices de malla a las NURBS. • El uso y validación de la formulación adjunta para el calculo de los gradientes, a partir de las sensibilidades de la solución adjunta, comparado con diferencias finitas. • Se ofrece una estrategia para utilizar la geometría CAD, en forma de parches NURBS, para tratar las intersecciones, como el ala-fuselaje. • No existen muchas alternativas de librerías NURBS viables. En este trabajo se ha desarrollado una librería, DOMINO NURBS, y se ofrece a la comunidad como código libre y abierto. • También se ha implementado un código CFD en tarjeta gráfica, para realizar una valoración de cómo se puede adaptar un código sobre malla no estructurada a arquitecturas paralelas. • Finalmente, se propone una metodología, basada en la función de Green, como una forma eficiente de paralelizar simulaciones numéricas. Esta tesis ha sido apoyada por las actividades realizadas por el Área de Dinámica da Fluidos del Instituto Nacional de Técnica Aeroespacial (INTA), a través de numerosos proyectos de financiación nacional: DOMINO, SIMUMAT, y CORESFMULAERO. También ha estado en consonancia con las actividades realizadas por el departamento de Métodos y Herramientas de Airbus España y con el grupo Investigación y Tecnología Aeronáutica Europeo (GARTEUR), AG/52. ABSTRACT The motivation of this work is the development of an automatic optimization strategy for large scale shape optimization problems that arise in the aeronautics industry to improve the aerodynamic performance; covering several aspects from the use of Non-Uniform Rational B-Splines (NURBS), the calculation of the gradients with the continuous adjoint formulation, the development of volumetric b-splines parameterization, mesh adaptation and intersection handling, to the adaptation of Computational Fluid Dynamics (CFD) algorithms to take advantage of highly parallel architectures in order to speed up the optimization process. With the development of the adjoint formulation, gradient-based methods for aerodynamic optimization become a promising approach to improve the aerodynamic performance of aircraft designs. The adjoint methodology allows the evaluation the gradients to all design variables of a cost function, such as drag or lift, at the equivalent cost of more or less one CFD simulation. However, some practical problems have been delaying its full implementation to the industry, which can be summarized as: integrability, computer performance, and adjoint robustness. This work tackles some of these issues and analyse them in well-known test cases. As summary, the contributions comprises: • The employment of NURBS as design variables in an automatic optimization loop for the improvement of the aerodynamic performance of aircraft wings in transonic regimen. • The development of point inversion algorithms to calculate the NURBS parametric coordinates from the space coordinates, to link with the computational grid vertex. • The use and validation of the adjoint formulation to calculate the gradients from the surface sensitivities in an automatic optimization loop and evaluate its reliability, compared with finite differences. • This work proposes some algorithms that take advantage of the underlying CAD geometry description, in the form of NURBS patches, to handle intersections and mesh adaptations. • There are not many usable libraries for NURBS available. In this work an open source library DOMINO NURBS has been developed and is offered to the community as free, open source code. • The implementation of a transonic CFD solver from scratch in a graphic card, for an assessment of the implementability of conventional CFD solvers for unstructured grids to highly parallel architectures. • Finally, this research proposes the use of the Green's function as an efficient paralellization scheme of numerical solvers. The presented work has been supported by the activities carried out at the Fluid Dynamics branch of the National Institute for Aerospace Technology (INTA) through national founding research projects: DOMINO, SIMUMAT, and CORESIMULAERO; in line with the activities carried out by the Methods and Tools and Flight Physics department at Airbus and the Group for Aeronautical Research and Technology in Europe (GARTEUR) action group AG/52.

Estudo comparativo de técnicas numéricas de inversão para obtenção de distribuição de tamanho de gotas em emulsões.

O desenvolvimento de algoritmos computacionais para a obtenção de distribuições de tamanho de partícula em dispersões e que utilizam dados espectroscópicos em tempo real e in-line a partir de sensores permitirá uma variedade de aplicações, como o monitoramento de propriedades em fluidos de corte industriais, acompanhamento de processos de polimerização, tratamento de efluentes e sensoriamento atmosférico. O presente estudo tem como objetivo a implementação e comparação de técnicas para resolução de problemas de inversão, desenvolvendo algoritmos que forneçam distribuição de tamanho de partículas em dispersões a partir de dados de espectroscopia UV-Vis-Nir (Ultravioleta, Visível e Infravermelho próximo). Foram implementadas quatro técnicas, sendo uma delas um método alternativo sem a presença de etapas de inversão. Os métodos que utilizaram alguma técnica de inversão evidenciaram a dificuldade em se obter distribuições de tamanho de gotas (DTG) de boa qualidade, enquanto o método alternativo foi aquele que se mostrou mais eficiente e confiável. Este estudo é parte de um programa cooperativo entre a Universidade de São Paulo e a Universidade de Bremen chamado programa BRAGECRIM (Brazilian German Cooperative Research Initiative in Manufacturing) e é financiado pela FAPESP, CAPES, FINEP e CNPq (Brasil) e DFG (Alemanha).

Retinotopic mapping of the primary visual cortex - a challenge for MEG imaging of the human cortex

Magnetoencephalography (MEG) can be used to reconstruct neuronal activity with high spatial and temporal resolution. However, this reconstruction problem is ill-posed, and requires the use of prior constraints in order to produce a unique solution. At present there are a multitude of inversion algorithms, each employing different assumptions, but one major problem when comparing the accuracy of these different approaches is that often the true underlying electrical state of the brain is unknown. In this study, we explore one paradigm, retinotopic mapping in the primary visual cortex (V1), for which the ground truth is known to a reasonable degree of accuracy, enabling the comparison of MEG source reconstructions with the true electrical state of the brain. Specifically, we attempted to localize, using a beanforming method, the induced responses in the visual cortex generated by a high contrast, retinotopically varying stimulus. Although well described in primate studies, it has been an open question whether the induced gamma power in humans due to high contrast gratings derives from V1 rather than the prestriate cortex (V2). We show that the beanformer source estimate in the gamma and theta bands does vary in a manner consistent with the known retinotopy of V1. However, these peak locations, although retinotopically organized, did not accurately localize to the cortical surface. We considered possible causes for this discrepancy and suggest that improved MEG/magnetic resonance imaging co-registration and the use of more accurate source models that take into account the spatial extent and shape of the active cortex may, in future, improve the accuracy of the source reconstructions.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

The REFLEX project: Comparing different algorithms and implementations for the inversion of a terrestrial ecosystem model against eddy covariance data

We describe a model-data fusion (MDF) inter-comparison project (REFLEX), which compared various algorithms for estimating carbon (C) model parameters consistent with both measured carbon fluxes and states and a simple C model. Participants were provided with the model and with both synthetic net ecosystem exchange (NEE) of CO2 and leaf area index (LAI) data, generated from the model with added noise, and observed NEE and LAI data from two eddy covariance sites. Participants endeavoured to estimate model parameters and states consistent with the model for all cases over the two years for which data were provided, and generate predictions for one additional year without observations. Nine participants contributed results using Metropolis algorithms, Kalman filters and a genetic algorithm. For the synthetic data case, parameter estimates compared well with the true values. The results of the analyses indicated that parameters linked directly to gross primary production (GPP) and ecosystem respiration, such as those related to foliage allocation and turnover, or temperature sensitivity of heterotrophic respiration, were best constrained and characterised. Poorly estimated parameters were those related to the allocation to and turnover of fine root/wood pools. Estimates of confidence intervals varied among algorithms, but several algorithms successfully located the true values of annual fluxes from synthetic experiments within relatively narrow 90% confidence intervals, achieving >80% success rate and mean NEE confidence intervals <110 gC m−2 year−1 for the synthetic case. Annual C flux estimates generated by participants generally agreed with gap-filling approaches using half-hourly data. The estimation of ecosystem respiration and GPP through MDF agreed well with outputs from partitioning studies using half-hourly data. Confidence limits on annual NEE increased by an average of 88% in the prediction year compared to the previous year, when data were available. Confidence intervals on annual NEE increased by 30% when observed data were used instead of synthetic data, reflecting and quantifying the addition of model error. Finally, our analyses indicated that incorporating additional constraints, using data on C pools (wood, soil and fine roots) would help to reduce uncertainties for model parameters poorly served by eddy covariance data.

Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.