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Spacecraft navigation is a critical component of any space mission. Space navigation uses on-board sensors and other techniques to determine the spacecraft’s current position and velocity, with permissible accuracy. It also provides requisite information to navigate to a desired position, while following the desired trajectory. Developments in technology have resulted in new techniques of space navigation. However, inertial navigation systems have consistently been the bedrock for space navigation. Recently, the successful space mission GOCE used on-board gravity gradiometer for mapping Earth’s gravitational field. This has motivated the development of new techniques like cold atom accelerometers, to create ultra-sensitive gravity gradiometers, specifically suited for space applications, including autonomous orbital navigation. This research aims to highlight the existing developments in the field of gravity gradiometry and its potential space navigation applications. The study aims to use the Linear Covariance Theory to determine specific sensor requirements to enable autonomous space navigation for different flight regimes.

Ce mémoire présente le développement d'un dispositif expérimental permettant de mesurer deux composantes du gradient de pesanteur, Γzz et Γzx, ainsi que l'accélération de pesanteur. Ces grandeurs sont déterminées en mesurant l'accélération d'atomes froids de rubidium, en chute libre dans le vide, par interférométrie atomique. Pour la gradiométrie, la mesure différentielle est réalisée entre deux nuages atomiques spatialement distants. Pour la mesure de Γzz, l'utilisation de réseaux optiques mobiles permet d'obtenir deux nuages atomiques à partir d'une unique source atomique. Ce travail présente la mise en place du dispositif complet, avec notamment la réalisation de l'enceinte à vide, et des systèmes laser et micro-onde. Les lasers sont basés sur la technologie télécom doublée, permettant d'obtenir des modules compacts et robustes, afin d'envisager des applications embarquées. L'architecture laser originale permet de réaliser des expériences d'atomes froids combinant interférométrie atomique et réseaux optiques, en réduisant au minimum le nombre de composants. Le bruit du laser a été caractérisé, et il limite la sensibilité gravimétrique à 10-9 g en monocoup, la sensibilité différentielle à 10-10 g en monocoup, et la sensibilité gradiométrique à 38 E, en monocoup. / This thesis presents the development of the experimental setup allowing the measurement of two gravity gradient components, Γzz and Γzx, and the gravity acceleration. These quantities are resulted from the measuring of rubidium cold atoms acceleration, in free fall in vacuum, by atom interferometry. For gradiometry, the differential measurement is realized between two atomic clouds spatially separated. For the measurement of Γzz, the use of mobile optical lattices allows to get two atom clouds from a single atomic source. This work presents the setting up of the complete device, in particular with the built of the vaccum chamber, laser and micro-wave systems. Lasers are based on frequency-doubled telecom technology, which allows to obtain compact and robust systems, dedicated for onboard applications. The innovative laser architecture allows to combine atom interferometry and optical lattices, while minimizing the amount of components. The laser noise has been characterized, and limits the single shot gravimetric sensitivity to 10-9 g, the single shot differential sensitivity to 10-10 g, and the single shot gradiometric sensitivity to 38 E.

<p><strong>Airborne gravity gradiometry (AGG) is a relatively new technology to the mineral exploration industry which has been increasingly used over the past decade. AGG systems are capable of separating linear accelerations due to aircraft movement from the accelerations related that represent the gravity signal, resulting in a much higher resolution measurement than airborne gravity. The rapid and cost-effective deployment of an AGG survey gives it an advantage when compared to traditional ground gravity survey. With the momentum of existing AGG technology in the exploration industry and the multitude of next-generation AGG sensors currently in development the technique promises to be a valuable exploration tool for the foreseeable future. This thesis focuses on the capabilities of the AGG technology as an exploration tool, its niche within the exploration process, and how AGG compares to other gravity methods. An overview of the AGG method provides context for the aim of the study. A history of airborne gravimetry is presented, as well as a detailed technical description of AGG measurements and units. A summary of all existing airborne gravity and airborne gravity gradiometry technology is provided, along with the major research initiatives aimed at making more sensitive AGG sensors in the future. A discussion of the potential sources of error and uncertainty when working with AGG data highlights many of the technique’s obstacles that we will be closely examining within this study. The AGG case study which is examined includes an AGG dataset collected as part of a nickel exploration program to image prospective troctolite chambers in Northern Labrador, by Vale. The study focuses on the portion of the survey over the Voisey’s Bay main block that contains several economic nickel deposits, including the world-class Ovoid deposit. This area has been characterized both geologically and geophysically in the past, and contains multiple datasets, including ground gravity. Forward modeling is completed using Voisey’s Bay physical rock properties to calculate the response that could be expected over a nickel-bearing troctolite chamber. The methodology and considerations of AGG data acquisition are reviewed in the context of this survey and the dataset is then taken through a terrain correction involving the determination of the best possible background density choice. The limitations and potential pitfalls of the terrain correction are examined in relation to the digital elevation model being used. The problem of thick, variable overburden in portions of the survey is also examined. Several filtering techniques are completed on the data, including vertical integration and the removal of the regional signal. The AGG resolution is then quantitatively compared to the historical ground gravity data and an upward continued version of the ground gravity (representing the response of an airborne gravity survey) by using 2D power spectra and radially averaged power spectra plots. Although the ground gravity is found to contain better resolution in some areas due to its proximity to the ground, the more regular spatial sampling of the AGG survey provided resolution advantages in other areas. The much higher sensitivity of the AGG sensor resulted in a strong resolution advantage over the upward continued gravity. This comparison is extended to include the differences in interpretive products produced from each dataset, in the form of 3D gravity inversions. Inversions were completed on all three datasets and the results are compared. Although the resolution of an individual ground gravity measurement is greater than that of an AGG measurement, the uniformity of the AGG survey provides superior coverage and leads to a more detailed inversion model, particularly for features greater than ~200-400m, such as the prospective nickel bearing troctolite chambers. </strong></p> / Master of Science (MSc)

Dans la première partie de ce travail de thèse, on a étudié les causes d'anomalie de pesanteur, et plusieurs causes de bruit afin d'en tirer des conclusions sur la faisabilité de certaines applications industrielles qui impliqueraient notamment l'utilisation de gravimètres ou de gradiomètres embarqués. On envisage en particulier la possibilité de constituer un système de prévention des collisions pour la navigation sous-marine, d'utiliser un gravimètre pour détecter des cavités enfouies ou encore d'observer l'anomalie de pesanteur créée par le passage d'une vague de tsunami d'une part, et d'autre part on cherche autant que possible à quantifier en spectre de puissance les bruits classiques rencontrés en gravimétrie embarquée, ainsi que le bruit gravitationnel causé par les vagues. Dans la seconde partie, on décrit la réalisation d'un gravimètre à ondes de matière, qui aura la particularité d'utiliser des atomes piégés au voisinage d'une puce en carbure de silicium. Le développement des gravimètres à ondes de matière est en effet extrêmement prometteur en terme d'exactitude de mesure du champ de pesanteur, mais le principe de réalisation utilisé jusqu'à maintenant implique que la sensibilité limite de l'instrument est proportionnelle à sa taille. D'un autre côté depuis une dizaine d'années des puces constituées de fils conducteurs déposés sur un substrat en silicium ont été développées pour le piégeage et le refroidissement d'atomes. L'utilisation d'une puce à atomes devra permettre de démontrer la possibilité de mesurer le champ de pesanteur avec une sensibilité indépendante de la taille de l'instrument, ce qui mènera à la réalisation d'un gravimètre à atomes froids compact, donc potentiellement utilisable dans un véhicule. Le défi de ce démonstrateur est d'effectuer pour la première fois la séparation spatiale cohérente d'un nuage d'atomes sur une puce atomique, à des fins de métrologie / In the first part of this work causes of gravity anomalies are studied, along with causes of noise. The feasibilities of a few industrial applications involving mobile gravity or gravity gradient meters were hence evaluated. These applications include in particular the realization of a collision avoidance device for underwater navigation, detection of underground void spaces and tsunami wave detection. Classical noises encountered in on-board gravity measurements are studied, as well as the less conventional gravity noise caused by ocean waves. The second part of the work is devoted to the implementation of a matter waves interferometry gravimeter. The particularity of the device is to use atoms trapped in the vicinity of a silicon carbide atom chip. The goal of the project is to reach for the measurement accuracies of current matter waves gravimeters with free falling atoms, with a principle that does not imply a proportionality between the size of the device and its sensitivity limit. We hope to demonstrate a proof of concept that may lead to a new generation of atomic gravimeters that are compact and therefore better suited for mobile uses. Coherent splitting of a non-condensed atom cloud for metrology purposes is probably the main challenge of the project

Um dos sistemas utilizados na geofísica de exploração são os sistemas gravimétricos aerotransportados. Estes sistemas, no entanto,necessitam parametrizações para aferir a qualidade dos levantamentos executados. Com a introdução da aerogravimetria no Brasil, através do levantamento da Bacia do Parnaíba, foi necessário desenvolver uma área de testes para aferição destes equipamentos. Em 2004 foram implantadas 166 estações gravimétricas na região da pista de teste, localizada no município de Tietê, SP. Devido ao crescente interesse na utilização do tensor gradiente da gravidade no estudo de localização de jazidas minerais tornou-se necessário gerar modelos geofísicos mais detalhados com o objetivo de localizar alvos rasos em subsuperfície. Com a finalidade de melhorar o limite de resolução dos testes realizados utilizando diferentes sistemas gravimétricos aerotransportados foi realizado um adensamento da malha gravimétrica da pista teste de Tietê. Para tanto, foram implementadas novas estações gravimétricas, distribuídas em diferentes espaçamentos, estabelecendo a primeira pista brasileira para calibração de aerogravimetria escalar e sistemas de aerogradiometria gravimétrica 3D. / Airborne gravimetric systems are among geophysical systems applied to expl oration. These systems rely on parametrization to gauge the quality of surveys. With the introduction of airborne gravity surveys in Brazil, with the Parnaiba Basin survey, demand for an equipment calibration lane arose.In 2004, 166 gravity stations were set in the test lane area located in the municipality of Tietê, SP. The need for more detailed geophysical models capable of identifying shallow targets resulted from surging interest in applying gravity gradiometric tensor to locate mineral deposits. The Tietê test lane was densified in order to improve the resolution limitation in tests of a range of airborne gravity systems. To achieve that, new gravity stations were set with different spacing. This stablished the first Brazilian calibration lane for scalar gravimetry and 3D airborne gravity gradiometry systems.

Um dos sistemas utilizados na geofísica de exploração são os sistemas gravimétricos aerotransportados. Estes sistemas, no entanto,necessitam parametrizações para aferir a qualidade dos levantamentos executados. Com a introdução da aerogravimetria no Brasil, através do levantamento da Bacia do Parnaíba, foi necessário desenvolver uma área de testes para aferição destes equipamentos. Em 2004 foram implantadas 166 estações gravimétricas na região da pista de teste, localizada no município de Tietê, SP. Devido ao crescente interesse na utilização do tensor gradiente da gravidade no estudo de localização de jazidas minerais tornou-se necessário gerar modelos geofísicos mais detalhados com o objetivo de localizar alvos rasos em subsuperfície. Com a finalidade de melhorar o limite de resolução dos testes realizados utilizando diferentes sistemas gravimétricos aerotransportados foi realizado um adensamento da malha gravimétrica da pista teste de Tietê. Para tanto, foram implementadas novas estações gravimétricas, distribuídas em diferentes espaçamentos, estabelecendo a primeira pista brasileira para calibração de aerogravimetria escalar e sistemas de aerogradiometria gravimétrica 3D. / Airborne gravimetric systems are among geophysical systems applied to expl oration. These systems rely on parametrization to gauge the quality of surveys. With the introduction of airborne gravity surveys in Brazil, with the Parnaiba Basin survey, demand for an equipment calibration lane arose.In 2004, 166 gravity stations were set in the test lane area located in the municipality of Tietê, SP. The need for more detailed geophysical models capable of identifying shallow targets resulted from surging interest in applying gravity gradiometric tensor to locate mineral deposits. The Tietê test lane was densified in order to improve the resolution limitation in tests of a range of airborne gravity systems. To achieve that, new gravity stations were set with different spacing. This stablished the first Brazilian calibration lane for scalar gravimetry and 3D airborne gravity gradiometry systems.

Full tensor gravity (FTG) data are known for their high resolution but also for higher noise in its components due to the dynamic nature of the platform used for data acquisition. Although a review of the literature suggests steady increase in the success of gravity gradiometry, we still cannot take advantage of the full potential of the method, mostly because of the noise with the same amplitude and wavenumber characteristics as the signal that affects these data. Smoothing from common low pass filters removes small wavelength features and makes it difficult to detect structural features and other density variations of interest to exploration. In Kalman filtering the components of the FTG are continuously updated to calculate the best estimation of the state. The most important advantage of the Kalman filter is that it can be applied on gravity gradiometry components simultaneously. In addition, one can incorporate constraints. We use the Laplace’s equation that is the most meaningful constraint for potential field data to extract signal from noise and improve the detection and continuity of density variations. We apply the Kalman filter on the FTG data acquired by Bell Geospace over the Vinton salt dome in southwest Louisiana.

Aujourd’hui, la communauté scientifique dispose de jeux de données gravimétriques avec une précision et une résolution spatiale sans précédent qui améliorent nos connaissances du champ gravitationnel terrestre à différentes échelles et longueurs d’ondes, obtenues de mesures du sol à des satellites. Parallèlement à la gravimétrie, l’avancement des observations par satellite fournit à la communauté des modèles d’élévation numérique plus détaillés pour refléter la géométrie de la structure terrestre. Ensemble, ces nouveaux jeux de données offrent une excellente occasion de mieux comprendre les structures et la dynamique de la Terre à l’échelle locale, régionale et mondiale. L'utilisation et l'interprétation de ces données de haute qualité exigent le raffinement des approches standards dans le traitement et l'analyse des données liées à la gravité. Cette thèse consiste en une série d’études visant à améliorer la précision du traitement des données de gravité et gravité de gravité gradients pour les études géodynamiques. Pour ce faire, nous développons un outil, appelé GEEC (Gal Eötvös Earth Calculator), pour calculer précisément les effets gravimétriques dues à tout corps de masse, indépendamment de sa géométrie et de sa distance par rapport aux mesures. Les effets de gravité et des gravité gradients sont calculés analytiquement en utilisant la solution intégrale linéaire d'un polyèdre irrégulier. Les validations aux échelles locale, régionale et mondiale confirment la robustesse des performances du GEEC, où la résolution du modèle, qui dépend à la fois de la taille de la masse corporelle et de sa distance par rapport au point de mesure, contrôle fortement la précision des résultats. Nous présentons une application pour évaluer les paramètres optimaux dans le calcul des gradients de gravité et de gravité dus aux variations de topographie. La topographie joue un rôle majeur dans l'attraction gravitationnelle de la Terre; par conséquent, l'estimation des effets topographiques doit être soigneusement prise en compte dans le traitement des données gravimétriques, en particulier dans les zones de topographie accidentée ou à grande échelle. Pour les études de gravité de haute précision à l'échelle mondiale, le processus de correction de la topographie doit prendre en compte l'effet topographique de la Terre entière. Mais pour les applications locales à régionales basées sur des variations relatives à l'intérieur de la zone, nous montrons que la topographie tronquée à une distance spécifique peut être adéquate, même si ignorer la topographie de cette distance peut générer des erreurs. Pour soutenir ces arguments, nous montrons les relations entre les erreurs relatives à la gravité, la distance de troncature de la topographie et l'étendue de la zone d'étude. Enfin, nous abordons le problème: les mesures GOCE sont-elles pertinentes pour obtenir une image détaillée de la structure d'une plaque de subduction, y compris sa géométrie et ses variations latérales? Les résultats du calcul des avec des modèles de subduction synthétiques calculés à l’altitude moyenne du GOCE (255 km) démontrent que les bords de subduction et les variations latérales du pendage produisent des variations des gradients détectables avec le jeu de données GOCE. Dans l'application à la zone de subduction Izu-Bonin-Mariana (IBM), la topographie et les effets bathymétriques ont été supprimés avec succès. Cependant, dans l'application au cas réel de la zone de subduction Izu-Bonin-Mariana, les caractéristiques géométriques du second ordre du slab sont difficiles à détecter en raison de la présence des effets crustaux restants. Ceci est dû à l'imprécision du modèle crustal global existant qui est utilisée, qui conduit à une élimination impropre de l'effet crustal. / Nowadays, the scientific community has at its disposal gravity and gravity gradient datasets with unprecedented accuracy and spatial resolution that enhances our knowledge of Earth gravitational field at various scales and wavelengths, obtained from ground to satellite measurements. In parallel with gravimetry, the advancement of satellite observations provides the community with more detailed digital elevation models to reflect the Earth’s structure geometry. Together, these novel datasets provide a great opportunity to better understand the Earth’s structures and dynamics at local, regional, and global scales. The use and interpretation of these high-quality data require refinement of standard approaches in gravity-related data processing and analysis. This thesis consists of a series of studies aiming to improve the precision in the chain of gravity and gravity gradient data processing for geodynamic studies. To that aim, we develop a tool, named GEEC (Gal Eötvös Earth Calculator) to compute precisely the gravity and gravity gradients effects of due to any mass body regardless of its geometry and its distance from measurements. The gravity and gravity gradients effects are computed analytically using the line integral solution of an irregular polyhedron. The validations at local, regional, and global scales confirm the robustness of GEEC’s performance, where the resolution of the model, that depends on both size of the body mass and its distance from the measurement point, control strongly the accuracy of the results. We present an application for assessing the optimum parameters in computing gravity and gravity gradients due to topography variations. Topography has a major contribution in Earth gravitational attraction, therefore the estimation of topography effects must be carefully considered in the processing of gravity data, especially in areas of rugged topography or in large-scale studies. For high-accuracy gravity studies at a global scale, the topography correction process must consider the topography effect of the entire Earth. But for local to regional applications based on relative variations within the zone, we show that truncated topography at a specific distance can be adequate, although, ignoring the topography pas this distance could produce errors. To support these arguments, we show the relationships between gravity relative errors, topography truncation distance, and the extent of study zone. Lastly, we approach the issue: Are GOCE measurements relevant to obtain a detailed image of the structure of a subducting plate, including its geometry and lateral variation? The results of gravity gradient forward modelling using synthetic subduction models computed at GOCE’s mean altitude (255 km) demonstrate that both subduction edges and lateral variations of subduction angle produce gravity gradient variations that are detectable with GOCE dataset (∼100 km wavelength and 10 mE amplitude). However, in the application to the real case of Izu-Bonin-Mariana subduction zone, the second-order geometric features of the subducting plate are difficult to be detected due to the presence of the remaining crustal effects. This is caused by the inaccuracy of the existing global crustal model, that leads to inaccurate crustal effect removal.