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In this dissertation, we consider two different strategies for improving the projection-based reduced order model (ROM) accuracy: (I) adding closure terms to the standard ROM; (II) using Lagrangian data to improve the ROM basis. Following strategy (I), we propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS-ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS-ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS-ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS-ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient $nu = 10^{-3}$; (ii) a 2D flow past a circular cylinder at Reynolds numbers $Re=100$, $Re=500$, and $Re=1000$; (iii) the quasi-geostrophic equations at Reynolds number $Re=450$ and Rossby number $Ro=0.0036$; and (iv) a 2D flow over a backward facing step at Reynolds number $Re=1000$. The numerical results show that the data-driven VMS-ROM is significantly more accurate than standard ROMs. Furthermore, we propose a new hybrid ROM framework for the numerical simulation of fluid flows. This hybrid framework incorporates two closure modeling strategies: (i) A structural closure modeling component that involves the recently proposed data-driven variational multiscale ROM approach, and (ii) A functional closure modeling component that introduces an artificial viscosity term. We also utilize physical constraints for the structural ROM operators in order to add robustness to the hybrid ROM. We perform a numerical investigation of the hybrid ROM for the three-dimensional turbulent channel flow at a Reynolds number $Re = 13,750$. In addition, we focus on the mathematical foundations of ROM closures. First, we extend the verifiability concept from large eddy simulation to the ROM setting. Specifically, we call a ROM closure model verifiable if a small ROM closure model error (i.e., a small difference between the true ROM closure and the modeled ROM closure) implies a small ROM error. Second, we prove that a data-driven ROM closure (i.e., the data-driven variational multiscale ROM) is verifiable. For strategy (II), we propose new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct new Lagrangian ROMs. We show that the new Lagrangian ROMs are orders of magnitude more accurate than the standard Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis. / Doctor of Philosophy / Reduced order models (ROMs) are popular in physical and engineering applications: for example, ROMs are widely used in aircraft designing as it can greatly reduce computational cost for the aircraft's aeroelastic predictions while retaining good accuracy. However, for high Reynolds number turbulent flows, such as blood flows in arteries, oil transport in pipelines, and ocean currents, the standard ROMs may yield inaccurate results. In this dissertation, to improve ROM's accuracy for turbulent flows, we investigate three different types of ROMs. In this dissertation, both numerical and theoretical results show that the proposed new ROMs yield more accurate results than the standard ROM and thus can be more useful.

[pt] Nos últimos anos, a geofísicos tem se dedicado ao aprimoramento da qualidade dos dados sísmicos por meio da atenuação de ruído e interpolação de sismogramas usando métodos puramente baseados em CNN. Métodos baseados em CNN podem alcançar resultados estado-da-arte para remoção de ruídos. No entanto, eles não se aplicam a cenários sem dados de treinamento emparelhados (ou seja, dados sísmicos ruidosos e dados sísmicos sem ruído correspondentes). Neste trabalho, tratamos a atenuação de ruídos de dados sísmicos como um problema de atenuação de ruído cega, que consiste em remover ruídos desconhecidos sem dados pareados. Em outras palavras, a base usada pelo modelo de denoiser é aprendida a partir das próprias amostras ruidosas durante o treinamento. Motivado por este contexto, o principal objetivo deste trabalho é propor um método autosupervisionado para atenuação cega de dados sísmicos, que não requer análise prévia do sinal sísmico, nenhuma estimativa do ruído e nenhum dado de treinamento pareado. O método proposto assume dois conjuntos de dados: um contendo shot gathers com ruídos e o outro com shot gathers sem ruídos. A partir desses dados, treinamos dois modelos: (1) Seismic Noise Transfer (SNT), que aprende a produzir shot gathers com ruído sintético contendo o ruído dos shot gathers com ruído e o sinal dos shot gathers sem ruído; E (2) Sismic Neural Denoiser (SND), que aprende a mapear os shot gathers com ruído sintético de volta aos shot gathers sem ruído original. Após o treinamento, o SND sozinho é usado para remover o ruído das capturas ruidosas originais. Nosso modelo SNT adapta o algoritmo Neural Style Transfer (NST) ao domínio sísmico. Além disso, nosso modelo SND consiste em uma nova arquitetura CNN baseada em fusão de atributos em várias escalas para eliminação de ruído em shot gathers. Nosso método produziu resultados promissores em experimentos, alcançando um ganho de PSNR de 0,9 em comparação com outros modelos de última geração. / [en] In the last years, the geophysics community has been devoted to seismic data quality enhancement by noise attenuation and seismogram interpolation using CNN-based methods. Discriminative CNN-based methods can achieve state-of-the-art denoising results. However, they do not apply to scenarios without paired training data (i.e., noisy seismic data and corresponding ground-truth noise-free seismic data). In this work, we treat seismic data denoising as a blind denoising problem to remove unknown noise from noisy shot gathers without ground truth training data. The basis used by the denoiser model is learned from the noisy samples themselves during training. Motivated by this context, the main goal of this work is to propose a selfsupervised method for blind denoising of seismic data, which requires no prior seismic signal analysis, no estimate of the noise, and no paired training data. Our proposed self-supervised method assumes two given datasets: one containing noisy shot gathers and the other noise-free shot gathers. From this data, we train two models: (1) Seismic Noise Transfer (SNT), which learns to produce synthetic-noisy shot gathers containing the noise from noisy shot gathers and the signal from noise-free shot gathers; And (2) Seismic Neural Denoiser (SND), which learns to map the syntheticnoisy shot gather back to original noise-free shot gather. After training, SND alone is used to remove the noise from the original noisy shot gathers. Our SNT model adapts the Neural Style Transfer (NST) algorithm to the seismic domain. In addition, our SND model consists of a novel multi-scale feature-fusion-based CNN architecture for seismic shot gather denoising. Our method produced promising results in a holdout experiment, achieving a PSNR gain of 0.9 compared to other state-of-the-art models.

In tracing the history of the TIROS meteorological satellite system, this dissertation details the convergence of two communities: the DOD space scientists who established US capability to launch and operate these remote sensing systems and the US Weather Bureau meteorologists who would be the managers and users of satellite data. Between 1946 and 1964, these persons participated in successive coalitions. These coalitions were necessary in part because satellite systems were too big—geographically, fiscally, and technically—to be developed and operated within a single institution. Thus, TIROS technologies and people trace their roots to several research centers—institutions that the USWB and later NASA attempted to coordinate for US R&D. The gradual transfer of persons and hardware from the armed services to the non-military NASA sheds light on the US’s evolution as a Cold War global power, shaped from the “top-down” (by the executive and legislative branches) as well as the “bottom-up” (by military and non-military scientific communities). Through these successive coalitions, actor terms centered on “basic science” or the circulation of atmospheric data were used to help define bureaucratic places (the Upper Atmospheric Rocket Research Panel, International Geophysical Year, NASA, and the World Weather Watch) in which basic research would be supported by sustained and collaboration could take place with international partners.

In studies of the ocean it has become conventional to retain only the component of the Coriolis force associated with the radial component of the Earth’s rotation vector, the so-called “traditional approximation”. We investigate the role of the “non-traditional” component of the Coriolis force, corresponding to the non-radial component of the rotation vector, in transporting abyssal waters across the equator. We first derive a non-traditional generalisation of the multi-layer shallow water equations, which describe the flow of multiple superposed layers of inviscid, incompressible fluid with constant densities over prescribed topography in a rotating frame. We derive these equations both by averaging the three-dimensional governing equations over each layer, and via Hamilton’s principle. The latter derivation guarantees that conservation laws for mass, momentum, energy and potential vorticity are preserved. Within geophysically realistic parameters, including the complete Coriolis force modifies the domain of hyperbolicity of the multi-layer equations by no more than 5%. By contrast, long linear plane waves exhibit dramatic structural changes due to reconnection of the surface and internal wave modes in the long-wave limit. We use our non-traditional shallow water equations as an idealised model of an abyssal current flowing beneath a less dense upper ocean. We focus on the Antarctic Bottom Water, which crosses the equator in the western Atlantic ocean, where the bathymetry forms an almost-westward channel. Cross-equatorial flow is strongly constrained by potential vorticity conservation, which requires fluid to acquire a large relative vorticity in order to move between hemispheres. Including the complete Coriolis force accounts for the fact that fluid crossing the equator in an eastward/westward channel experiences a smaller change in angular momentum, and therefore acquires less relative vorticity. Our analytical and numerical solutions for shallow water flow over idealised channel topography show that the non-traditional component of the Coriolis force facilitates cross-equatorial flow through an almost-westward channel.

La caractérisation de la réalité matérielle du paysage impose d’une part de reconnaitre avec précision le cadre physique et d’autre part de saisir les interrelations entre les hommes et l’environnement, conditions indispensables à l’appréciation des origines du modelé du paysage. La compréhension des paysages passés se fonde en partie sur l’analyse de différentes sources documentaires qui permettent ensemble de caractériser bon nombre des évolutions paysagères intervenues notamment depuis l’époque moderne. Toutefois, les aménagements plus anciens ne sont ni localisés ni représentés sur des cartes. Leurs traces sont alors décelées dans le paysage actuel de manière efficace grâce notamment à la mise en oeuvre conjointe de diverses méthodes de détection : la photographie aérienne, enregistrant des variations topographiques ou colorimétriques à la surface du sol et le système LiDAR (Light Detection And Ranging), mesurant les variations microtopographiques à l’aide d’un laser. L’étude d’autres paramètres, imperceptibles à nos sens, permettent également d’appréhender les traces des paysages passés. Les méthodes géophysiques détectent la présence de vestiges ou de structures enfouies qu’aucun indice ne signale en surface grâce à la mesure des propriétés physiques du sol. Il est largement admis que les méthodes de prospection sont susceptibles de fournir des données archéologiques quant à l’occupation du sol et/ou l’exploitation du territoire. A ce titre, elles ont été appliquées depuis plusieurs années sur le site de l’agglomération antique d’Epomanduodurum (Mandeure-Mathay, Doubs) dans le nord Franche-Comté. Cette ville est considérée, par sa taille, son équipement urbain et sa parure monumentale comme la seconde de Séquanie derrière la capitale de cité Vesontio (Besançon, Doubs). Ce travail de recherche se propose donc de comparer, à différentes échelles spatiales, l’apport respectif de plusieurs méthodes de prospection à l’étude de dynamiques naturelles et anthropiques dans un espace géographique de 80 km², centré sur la ville antique, associant un tronçon de plaine alluviale du Doubs aux plateaux calcaires environnants. Durant cette étude, il a été possible, entre autre, de développer des outils aidant à la détection des structures archéologiques et géologiques. Les résultats ont aussi permis de redéfinir en partie la topographie de l’agglomération antique. / The characterization of the material reality of the landscape requires to accurately identify the physical geography and to capture the interrelationships between humans and their environment. These conditions are essential to the estimation of the origins of the landscape shaping. The analysis of documentary sources offers the opportunity to determine the organization of former landscapes and to characterize a large part of their evolutions since the Modern period. However, older land settlements are not localised or symbolised on maps. Their signs are efficiently detected in present landscape through the joint implementation of various detection methods: aerial photography, recording topographic or colorimetric variations on the soil surface, and the LiDAR (Light Detection And Ranging) system, measuring micro-topographic variations using a laser beam. Other methods can be used to identify the elements conserved in present landscape and reflect their past uses. The measure of physical properties of soils by the geophysical methods can detected the presence of archaeological remains or structures buried while nothing is perceptible to the soil surface. It is widely supported that survey methods can provide archaeological data of the land use and / or the exploitation of the territory. Thus, they have been applied since several at the site of the ancient city of Epomanduodurum (Mandeure-Mathay, Doubs) in the north of the Franche-Comte. This city is considered by its size, urban equipment and monuments as the second behind de civitas capital of Sequani, Vesontio (Besancon). This research intends to compare, at different spatial scales, the contribution of several prospecting methods for the study of natural and anthropogenic dynamics in an area of 80 km². The study area is centred on the ancient city and combines a section of the alluvial plain of the Doubs river and the surrounding calcareous plateaus. In this study, it was possible, among other things, to develop tools for the detection of archaeological

Ce travail numérique porte sur le comportement de la lutocline (interface entre l'eau et la vase fluide) en écoulement cisaillé et vise à une meilleure compréhension des mécanismes de remise en suspension de sédiments cohésifs. La crème de vase, ou vase partiellement solidifiée, est modélisée par un fluide homogène équivalent miscible dans l'eau, de rhéologie newtonienne ou viscoplastique. Une étude de l'hydrodynamique de cet écoulement stratifié en densité ainsi qu'en viscosité est ensuite proposée. Considérant une crème de vase initialement non-turbulente, l'étude se focalise sur le développement des instabilités au niveau de la lutocline et de la transition vers une couche de mélange turbulente. La particularité de cet écoulement réside dans la forte viscosité de vase et son seuil de mise en mouvement lorsqu'elle présente un caractère viscoplastique. Une étude de stabilité linéaire permet d'évaluer l'influence des différents paramètres de l'écoulement, notamment les stratifications en densité et en viscosité. La stratification en viscosité augmente sensiblement le taux de croissance de l'instabilité pour des nombres de Reynolds intermédiaires. L'évolution non-linéaire de l'écoulement est ensuite étudiée en utilisant des simulations numériques directes, la stratification en viscosité entrainant un épaississement de la couche de mélange finale. Enfin, des simulations numériques directes basées sur un modèle de fluide de Bingham régularisé permettent d'étudier l'influence de la contrainte seuil sur le développement de l'instabilité. / This numerical study focuses on the behavior of the lutocline in a shear flow and aims to better understand the mechanism of resuspension of cohesive sediment. Mud flow, or mud partially consolidated, is modeled by an equivalent homogenous fluid miscible in water, with newtonian or viscoplastic rheology. A study of the hydrodynamics of this shear flow, stratified both in density and viscosity, is presented. Considering an initially laminar mud flow, the focus of the study is on the development of instabilities on the lutocline and the transition to a turbulent mixing layer. The specificity of this flow lies on the large viscosity of the mud and its threshold to be put in motion, when it presents a viscoplastic feature. A linear stability study assesses the influence of the various parameters of the flow, especially of density and viscosity stratification. The viscosity stratification slightly increases the growth rate of the instability for intermediate Reynolds numbers. Then, the non linear evolution of the flow is studied by using direct numerical simulations, viscous stratification leading to a thicker mixing layer. At last, direct numerical simulations based on a Bingham regularized model, permits to study the influence of the critical strain on the development of the instability.

L'objectif principal de cette thèse est d'acquérir de nouvelles connaissances sur la structure tectonique et la lithosphérique de la région des Carpates et du bassin pannonien. Nous avons appliqué trois méthodes différentes: modélisation 1D,modélisation 2D géophysique intégrée et inversion 3D pour atteindre cet objectif. Ces méthodes sont similaires concernant les bases de données utilisées, mais diffèrent par le traitement et l'interprétation de données. Au début, nous avons appliqué la modélisation automatique 1D pour obtenir un premier aperçu de la région étudiée. Deuxièmement, nous avons appliqué la modélisation 2D intégré de la lithosphère qui combine l'interprétation du flux de chaleur,du géoïde, de la gravité et des données topographiques de la région des Carpates et du bassin pannonien et des régions avoisinantes. Cette approche est capable de contraindre des structures lithosphériques compliquées de la région étudiée mieux que l'interprétation de chaque donnée indépendamment. Nous présentons quatre modèles intégrés 2Dde la lithosphère dans la région des Carpates et du bassin pannonien et des régions avoisinantes. Enfin, sur la base de l'algorithme d'inversion 3D, nous présentons les modèles géophysiques de la lithosphère dans la région des Carpates et du bassin pannonien. L'algorithme calcule la structure de la densité lithosphèrique par l'inversion conjointe de la gravité, géoïde et données topographiques basé sur une approche bayésienne. Les modèles sont basés sur différents ensembles de données d'entrée et ils sont contraints par différentes données a priori. Sur la base de notre modélisation, nous ne pouvons pas confirmer l'amincissement extrême (moins de 70 km)de la lithosphère du bassin pannonien proposé par d'autres auteurs. D'autre part, les résultats montrent la tendance à l'augmentation de l'épaisseur lithosphérique de Carpates d'occidentales vers de Carpates de l'est ce que confirme les théories antérieures sur la propagation du processus de subduction. Nous avons obtenu des résultats controversés dans la région des Carpates du sud.Les résultats basés sur l'inversion 3D montrent une lithosphère extrêmement mince dans ce domaine mais les résultats basés sur la modélisation 2D intégrée ne supportent pas cet amincissement. Cependant, les deux méthodes indiquent qu'il est plausible que la plateforme Moésienne soit courbée et chevauchée sous les Carpates du sud. Dans le modèle 3D, le bord sud-est du bassin Pannonien montre une lithosphère inattendue et étonnamment mince. Puisque la zone est assez grande, nous pouvons exclure un effet de flexion, par conséquent, cette région pourrait être potentiellement intéressante pour une recherche plus approfondie. / The main aim of this thesis is to gain new knowledge about the lithospherical structure and tectonics of the Carpathian–Pannonian Basin region. We applied three different methods: 1Dautomatic modelling, 2D integrated geophysical modelling and 3D inversion to achieve this goal.These methods are similar concerning the used databases but differ by used processing andinterpretation. At first we apply 1D automatic modelling to get a very first overview of thestudied region. Secondly, we apply 2D integrated modelling of the lithosphere which combines the interpretation of surface heat flow, geoid, gravity, and topography data in the Carpathian–Pannonian Basin region and surrounding areas. This approach is able to constrain the complicated lithospheric structures of the studied region better than interpreting each data set onits own. We present four 2D integrated models of the lithosphere in the Carpathian–PannonianBasin region and surrounding areas. Finally, based on the 3D Inversion algorithm, we present the geophysical models of the lithosphere in the Carpathian–Pannonian region. The algorithm returns the density structure of the lithosphere from joint inversion of free air gravity, geoid andtopography data based on a Bayesian approach. The models are based on different input data sets and constrained by different a priori data. Based on our modelling we cannot confirm theextreme thinning (less than 70 km) of the Pannonian Basin lithosphere proposed by other authors.On the other hand, the results show the increasing trend of the lithospherical thickness of theCarpathian Arc from the Western Carpathians toward the Eastern Carpathians which confirms theprevious theories about the propagation of subduction process. We got some controversial resultsin the area of the Southern Carpathians. The results based on 3D inversion show extremely thinlithosphere in the area; on the other hand, the results based on 2D integrated modelling do notsupport such thinning. However both methods indicate that it is probable that the MoesianPlatform is bend and underthrusted underneath the Southern Carpathians. The south-eastern edge of the Pannonian Basin based on 3D inversion shows unexpected and surprisingly thinlithosphere. Since the area is quite large, we could exclude an effect of flexure, therefore this area might be potentially interesting for further investigation. / Hlavnou myšlienkou tejto práce bolo rozšírenie poznatkov o štruktúre a tektonike karpatsko–panónskej oblasti. Na výskum študovanej oblasti sme použili tri rôzne metódy, 1D automatickémodelovanie, 2D integrované geofyzikálne modelovanie a 3D inverziu. Tieto metódy sú podobnév zmysle použitých vstupných databáz, ale líšia sa spôsobom spracovania a interpretácie. Akoprvé sme aplikovali 1D automatické modelovanie, ktoré slúžilo ako prvý náhľad na študovanéúzemie. Ako druhé sme použili 2D integrované geofyzikálne modelovanie litosféry, ktorékombinuje interpretáciu povrchového toku, geoidu, tiažových anomálií a topografie v karpatsko–panónskej oblasti a okolitých tektonických jednotkách. Tento prístup k interpretácii je schopnývymedziť komplikované štrúktúry v litosfére lepšie, ako interpretácia každého jednéhogeofyzikálneho poľa samostatne. V tejto práci predstavíme štyri 2D integrované modely litosféryv karpatsko–panónskej oblasti a okolitých jednotiek. Ako posledné, predstavíme geofyzikálnemodely litosféry študovanej oblasti na základe modelovania použitím 3D inverzie. Algoritmus jeschopný vypočítať hustotnú distribúciu v litosfére na základe Bayesianského prístupu zospoločnej inverzie tiažovej anomálie na voľný vzduch, geoidu a topografie. Tieto modely súvypočítavané na základe rôznych vstupných datových setov a a priori informácií. Na základenášho modelovania nemôžeme potvrdiť extrémne stenčenie (menej ako 70 km) litosférypanónskej panvy. Na druhej strane naše výsledky poukazujú na narastajúci trend litosférickéhohrubnutia Karpatského oblúka od Západných Karpát smerom do Východných, čo potvrdzujepredchádzajúce teórie o postupnom procese subdukcie. V oblasti Južných Karpát sme dosiahliprotichodné výsledky. Výsledky získané na základe 3D inverzie poukazujú na extrémne stenčenúlitosféru na druhej strane 2D integrované modelovania takéto extrémne stenčenie v danej oblastinepodporuje. Napriek tomu je pravdepodobnejšie, že moezíjska platforma je ohnutá a podsunutápod Južné Karpaty. Ďalšia zaujímavá vec sa ukazuje v juhovýchodnej oblasti panónskej panvy,kde výsledky 3D inverzie odhaľujú taktiež výrazné stenčenie litosféry. Táto oblasť môže byťpotenciálne zaujímavá a bolo by vhodné ďalej pokračovať vo výskume danej oblasti.

O principal objetivo deste trabalho foi avaliar um procedimento de campo para testar o comprimento mínimo que fraturas devem ter para construir uma rede de fluxo em escala de dezenas de metros ao longo de maciços cristalinos. O comprimento mínimo é determinado a partir do limite de percolação, definido por modelos baseados na Teoria da Percolação e a densidade de fraturas no poço, determinada pela perfilagem ótica. Para testar o valor de 3,9 metros que foi encontrado, foram realizados bombeamentos em dois poços próximos enquanto o nível estático era registrado no poço de observação. O método apresenta facilidades em termos de operação e para obter-se o número de fraturas que interceptam o poço, no entanto o registro do nível estático é afetado por fatores externos, como presença de efeitos de maré e variação da pressão atmosférica, e correções são necessárias para permitir identificar a interferência proveniente somente do bombeamento. / The objective of this work is to develop a field procedure to determine a minimum characteristic length forming a connected fracture network in crystalline rocks. This minimum length is determined as a percolation threshold defined by models based on Percolation Theory and fracture density data determined from borehole imaging with well-logging probes. The characteristic length (3.9 meters) once estimated for a testing well was evaluated by monitoring its water head meanwhile nearby wells at different distances were pumped. The water head variation recorded in the testing well was disturbed by interfering effects associated to earth tides and atmospheric pressure, requiring further corrections to isolate effects induced by pumping. The results of these tests validate the percolation limit determined from logging data suggesting a rock mass with very low connectivity. The proposed test can be regarded as simple and easy to apply in many practical situations, for example when evaluating groundwater resources or geotechnical properties in fractured crystalline rocks.

O principal objetivo deste trabalho foi avaliar um procedimento de campo para testar o comprimento mínimo que fraturas devem ter para construir uma rede de fluxo em escala de dezenas de metros ao longo de maciços cristalinos. O comprimento mínimo é determinado a partir do limite de percolação, definido por modelos baseados na Teoria da Percolação e a densidade de fraturas no poço, determinada pela perfilagem ótica. Para testar o valor de 3,9 metros que foi encontrado, foram realizados bombeamentos em dois poços próximos enquanto o nível estático era registrado no poço de observação. O método apresenta facilidades em termos de operação e para obter-se o número de fraturas que interceptam o poço, no entanto o registro do nível estático é afetado por fatores externos, como presença de efeitos de maré e variação da pressão atmosférica, e correções são necessárias para permitir identificar a interferência proveniente somente do bombeamento. / The objective of this work is to develop a field procedure to determine a minimum characteristic length forming a connected fracture network in crystalline rocks. This minimum length is determined as a percolation threshold defined by models based on Percolation Theory and fracture density data determined from borehole imaging with well-logging probes. The characteristic length (3.9 meters) once estimated for a testing well was evaluated by monitoring its water head meanwhile nearby wells at different distances were pumped. The water head variation recorded in the testing well was disturbed by interfering effects associated to earth tides and atmospheric pressure, requiring further corrections to isolate effects induced by pumping. The results of these tests validate the percolation limit determined from logging data suggesting a rock mass with very low connectivity. The proposed test can be regarded as simple and easy to apply in many practical situations, for example when evaluating groundwater resources or geotechnical properties in fractured crystalline rocks.