Publications

Interferometric Synthetic Aperture Radar (InSAR) has proved its efficiency for displacementmonitoring in urban areas. However, the large volume of data generated by this technology turnsthe retrieval of information useful for structure monitoring into a big data problem. In this study, anew tool (SARClust) to analyze InSAR displacement time series is proposed. The tool performs theclustering of persistent scatterers (PSs) based on dissimilarities between their displacement time seriesevaluated through dynamic time warping. This strategy leads to the formation of clusters containingPSs with similar displacements, which can be analyzed together, reducing data dimensionality, andfacilitating the identification of displacement patterns potentially related to structural damage. Aproof of concept was performed for downtown Lisbon, Portugal, where ten distinct displacementpatterns were identified. A relationship between clusters presenting centimeter-level displacementsand buildings located on steep slopes was observed. The results were validated through visualinspections and comparison with another tool for time series analysis. Agreement was found inboth cases. The innovation in this study is the attention brought to SARClust

The hydrostatic-season-time (HST) model is a widely used method in the safety assessment of dams and for the estimation of reversible and irreversible deformations due to different load scenarios. After implementing an optimal HST-model to observational data, the residual time series can still expose some underlying periodicities. In our contribution, the underlying periodicities and their contribution to residual minimisation are further analysed by the Lomb–Scargle normalised periodogram frequency method. The extended HST-model, obtained by adding additional sinusoidal terms for the statistically most significant frequencies, presents a slight statistical improvement on the optimal HST-model. Statistically significant frequencies may not be justified or correlated to some physical process of the dam, but they make it possible to identify a pattern in the analysed period. The analyses are performed for the radial direction of long-term displacement time series measured at the topmost reading station of an inverted pendulum system in the central cantilever of the Alqueva concrete arch dam

The three authors of this paper work at the Applied Geodetic Division of the National Laboratory for Civil Engineering (LNEC), in Lisbon, Portugal. LNEC is a state owned research and development institution founded in 1946. It works in the various domains of civil engineering (structures, hydraulic, geotechnics, environment, materials, among others), giving it a unique multidisciplinary perspective in this field. The main goals of the LNEC are to carry out innovative research and development and to contribute to the best practices in civil engineering. The Applied Geodetic Division nowadays develops works in two domains: the geodetic surveying of large dams and other engineering structures for monitoring purposes, and the processing of digital images with applications in several domains, which includes the study of the evolution of pathologies in engineering works. Originally the processing of digital images made use mostly of the chromatic information included in the images (from satellite images to close range photographs). But recently it has evolved to extract information of the geometry of the objects by the generation of point clouds. This use of close range photographs (from distances of decimetres to a few meters), which started in the summer of 2014, looks very promising and we, the authors, are identifying possible areas where the use of point clouds and orthomosaics that can be of interest to our colleagues of LNEC, civil engineers mostly. This paper presents the first examples where point clouds and orthomosaics, generated from close range photographs, can help civil engineers on their studies. The photogrammetic products were all generated using the free open-source software Micmac (Multi-Image Correspondances, Méthodes Automatiques de Corrélation) from IGN (Institut National de l’Information Géographique et Forestière, France).

Les ports et autres infrastructures construits sur des côtes exposées à de fortes houles ont besoin d’être protégés. Une telle protection peut être obtenue par des digues ou brise-lames. Les digues à talus ont en général une meilleure résilience pendant les événements les plus agressifs. Un endommagement des digues affaiblit la structure et peut entraîner la perte de la capacité de protection, ce qui peut avoir des conséquences environnementales et économiques très graves. Pour cette raison, les brise-lames doivent être soumis à une surveillance régulière pour la détection des anomalies. Cet article présente quelques exemples de l'utilisation de drones dans la surveillance de la sécurité de ces structures, et décrit en particulier deux vols menés avec des drones et quelques possibilités d'extraction de données pour obtenir des informations d'intérêt pour les responsables de la sécurité.

This work presents several approaches in the validation of the hydrodynamic model Tuflow on the simulation of flood extents and water levels, based on satellite SAR imagery. A methodology that uses a simplified bathymetry in the river main course is employed, which proves to be reliable and accurate for high-flow events. This was made possible as the digital terrain model was acquired in a dry period, accounting for large dry areas in the river bed, avoiding in this way the need of expensive river bathymetry surveys. Also, two methods are applied to the SAR imagery to extract the flood boundaries: visual interpretation followed by manual delimitation and an object-based algorithm approach. The hydraulic model is tested on a reach of the Tagus River, Portugal, where the largest flood inundation areas occur, using a historical flood event to verify its robustness and reliability. The accuracy of model prediction is done through comparisons of water levels at a hydrometric station and the determination of commission and omission errors of flood extent, between the reference SAR image and the predicted inundation. It was concluded that the methodology followed in this work is well suited for the hydraulic model validation.

This article describes the implementation of a monitoring system on the breakwater at the Funchal Port (Madeira Island, Portugal) for the purpose of understanding its dynamic behavior and the temporal evolution of structural health. The monitoring system focuses on the breakwater superstructure and aims to identify the evolution of damage on the breakwater and analyze the impact of cruise ships docking and undocking. The system includes the measurement of displacements through geodetic techniques using global navigation satellite systems and the measurement of vibrations using accelerometers. Ten observation campaigns were performed over almost 3 years. As the measured displacements during this period were less than 7.5 mm it can be concluded that, despite some visible cracks, the breakwater superstructure did not suffer significant structural changes. It was shown from the measured acceleration records that some of the main modal parameters could be identified, namely the main natural frequencies of the superstructure. Through an analysis of the natural frequencies progression over time, it will be possible to identify deterioration effects on the foundation and/or the superstructure. The comparison of natural frequencies identified could be useful to evaluate the impact of these events on structural health.

A fusão de dados provenientes de diferentes tipos de instrumentos pode dar uma informação mais completa para a monitorização do comportamento de estruturas de engenharia civil, em particular nas pontes de grande vão. O objectivo da fusão de deslocamentos medidos com o GNSS e de acelerações, é tirar partido da precisão conseguida com o GNSS, em baixas frequências, e da grande sensibilidade dos acelerómetros, em altas frequências, e obter uma única série temporal de deslocamentos, longa e de grande resolução. Através dum filtro de Kalman será possível integrar deslocamentos medidos, com uma frequência de amostragem de, por exemplo, 1 Hz, e acelerações medidas, com uma frequência de amostragem de, por exemplo, 100 Hz, de modo a obter uma série temporal de deslocamentos de longa duração e com uma resolução de 100 Hz. Nesta comunicação apresentam-se os resultados preliminares dum ensaio realizado num modelo estrutural simples correspondente a um edifício de três pisos, instrumentado com antenas GNSS da Topcon e acelerómetros da Kinemetrics, modelo Episensor ES-U2, e da Nanometrics, modelo Titan SMA, tendo em vista a futura aplicação desta metodologia em pontes de grande vão.

There is an increasing trend to apply GNSS continuous observation of short baselines to the monitoring of engineering works, such as bridges and dams, for their structural analysis and safety control. In the case of large dams, one important application of the GNSS continuous observation is the establishment of early warning systems that demand accurate, frequently updated information and where the analysis of the baseline time series, in order to separate signal from noise is mandatory. The paper presents a study on the performance of linear filters of the asymmetric moving average (AMA) type to smooth baseline time series. The transfer function of the AMA is adopted as a smoothing criterion to define an adequate order for the AMA, in face of the spectral density function of the baseline time series. One series of measurements of a short test baseline (325 m), materialized in the campus of the National Laboratory for Civil Engineering, is used as an example of the proposed strategy.

Summary: A Bayesian estimator with informative prior distributions (a multi-normal and an inverted gamma distribution), adequate to displacement estimation at dam monitoring net-works, is presented. The hyper-parameters of the prior distributions are obtained by Bayesian empirical methods with non-informative priors. The performances of the Bayes estimator and the classical generalized lest squares estimator are compared using two measurements of the horizontal monitoring network of a concrete gravity dam: the Penha Garcia dam (Portugal). In order to test the robustness of the two estimators, gross errors are added to one of the measured horizontal directions: the Bayes estimator proves to be significantly more robust than the generalized least squares estimator.

Results from the application of Persistent Scatterers Interferometry in Lisbon Metropolitan Area revealed two previously unknown subsiding urban areas: one (Laranjeiras) is located in the center of Lisbon; another (Vialonga) is to be found toward the North, in an industrial region crossed by Lisbon's main highway and railway lines. The two subsiding sectors are bordered by sharp velocity gradients, and the subsidence pattern appears partially delimited by mapped geologic faults. Surface geology and urbanization alone are unable to explain the phenomena. In the Vialonga area, the historical record of water pore pressure shows a clear decline of the levels (up to 65 m in 27 years), providing evidence of over-exploitation of groundwater resources. Limited information from wells drilled inside and outside the subsidence area points to a spatial correlation between the subsidence and the water pressure levels, and suggests that faults could be acting as hydraulic barriers in the aquifer system. The surface subsidence detected is probably caused by compaction of a clay-rich Oligocene-aged aquitard, led by over-exploitation of adjacent aquifers. The same Oligocene aquitard layer is present in the Laranjeiras area, immediately bellow a multi-layered sand–clay–limestone Miocene aquifer, but further work is needed to diagnose the possibility of over-exploitation of groundwater here. In this work we were able to independently confirm the PSI results, by comparing autonomous PSI results processed for the same geographical areas, and by comparing PSI with leveling and continuous GPS derived subsidence velocities, whose close match provided further ground validation of the space-borne PSI technique.

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Atmospheric effects are still a limitation to the application of InSAR techniques for displacement measurement. In this study, zenith total delay (ZTD) values derived from global navigation satellite system (GNSS) are used to correct interferograms from tropospheric effects. Displacement measurements are obtained from the corrected interferograms through a persistent scatterer interferometry approach. The influence of different interpolation methods on the construction of ZTD maps is tested through two different algorithms: cubic spline and ordinary kriging. Differences are observed between the cumulative displacement maps obtained with both interpolators, but atmospheric effects are still present, possibly due to the small number of available GNSS stations.

A comunicação apresenta uma análise preditiva Bayesiana das medições de uma base “permanente” GNSS, muito curta, levadas a cabo durante cerca de dois meses com recetores de duas frequências e antenas geodésicas. Para avaliar a estabilidade temporal da base foram usadas as possibilidades preditivas posteriores de novas observações contra um conjunto de observações iniciais. As possibilidades preditivas posteriores da nova observação são dadas pela razão do máximo da densidade preditiva posterior pela densidade preditiva posterior da nova observação. A análise de cerca de 1500 medições da base mostrou que apenas 5% apresentam erros de observação significativos.

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MEO Arena building is one of the largest indoor arenas of the European Union and the largest one in Portugal. Due to its large capacity and unique structural characteristics, being composed of an inner wooden structure covered by a metallic roof, displacement measurements for structural health monitoring of the building is of utmost importance. This paper presents a method for displacement analysis of its metallic roof based on displacements acquired through Persistent Scatterer Interferometry and on geodetic measurements of the inner wooden structure. Regression models are used to estimate geodetic measures for the time of the SAR observations. Displacements of the metallic roof show a high correlation with temperature.

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During the design process of a rubble mound breakwater, in order to evaluate its effectiveness, scale model tests are required to study the hydraulic and structural behaviour of the proposed structure under predefined sea-wave conditions. The main goal of such tests is to study the structure overtopping and infer on damage progression by quantifying movements and displacements of the armour layer units. Scale model tests results can be also used to calibrate numerical models. Scale models of rubble-mound breakwaters are built in wave flumes (two-dimensional models, 2D) or in wave basins (three-dimensional models, 3D), enabling to simulate sea-wave conditions to study wave-structure interaction. A wave characterization and simulation software package is used to reproduce the prototype wave conditions, namely the significant wave height as well as the associated wave period. This makes possible to generate different sea states and therefore to study the rubble-mound breakwater behaviour and to identify possible weak areas in the armour layer. In order to characterize the armour layer envelope, recent applications of photogrammetric surveys were used, making it a promising technique. This method makes use of orthomosaics and clouds of points created from the photogrammetric survey. In this paper the first conclusions from the use of this technique are presented. The results of this analysis are extended to in situ breakwaters monitoring campaigns.

Ground displacements are a key factor to assess the safety and serviceability of any structure. A cost-effective technology for regional displacement monitoring, considering both the structure and its neighbourhood, would enable anomaly identification at an early stage and prevention actions. The objective of this work is to evaluate the stability of a segment of the Lisbon regional outer circular (circular regional exterior de Lisboa - CREL) through displacement measurements on the road and its surroundings using persistent scatterers interferometry (PSI). Synthetic aperture radar interferometry is a technology that uses satellite images acquired in the microwave band of the electromagnetic spectrum. PSI is one of the most used techniques, which allows measuring displacements at the Earth surface with millimetre accuracy. Man-made structures usually have stable reflective properties to microwaves, which turn them into good targets for displacement measurement through this technique. Therefore, it is possible to obtain a high density of measurements in urban areas. CREL is one of the most used roads to access Lisbon. The road has a length of 35 km and is fully operational since 1995. A displacement analysis using PSI was performed over an area of 50 km2, centred at Caneças (Odivelas municipality), which contains 8 km of CREL. Displacement measurements were computed for 1340 points/km2, every 11 days, between December 2011 and July 2013. Two areas close to CREL were identified presenting subsidence, with approximate areas of 0.6 km2 and 0.2 km2. Superimposed on this trend, an oscillatory behaviour was also detected. In conclusion, PSI is a useful technique to monitor displacements in urban areas and allowed the identification of possible unstable regions close to CREL, which may cause settlements at the road and damages at buildings nearby.

The protection of ports in coastal areas exposed to the action of the sea is carried by sea hydraulic structures (breakwaters) which are exposed to the influence of sea waves. The monitoring of the surface plates movement, constituting the protective mantle and the superstructure (concrete structure) is made by visual comparison of images obtained during follow-up visits. No quantification of these shifts is yet performed. In the design phase of a port protection structure, models are built to study the effect of waves on the protection blocks. During the testing phase waves are generated and periodically are measured the effects of waves in the model. Presently, photogrammetric monitoring of the model ports is being held, including the use of orthophotos and point clouds to measure displacements of protection blocks. With these methods there were obtained results of the change in overall topography of the model structure. However the real 3D motion of each block is indeterminate due to the absence of data on the geometry of the blocks. The extraction of these geometric data from the images, along with the spatial data of the point cloud, will deepen knowledge of the intended movement. This work presents an alternative monitoring solution based on image segmentation in order to obtain displacements of the model protection blocks so to monitor its development over time. Time sequence orthogonal images were obtained during the action of blocks movement. In this study, blocks are identified in the image and shifts are quantified. Validation is held by crossing image segmentation results with point clouds data obtained in laboratory by photogrammetric methods at the same moment images were taken. The present study intends to show the positive contribution of image processing techniques for the laboratory monitoring of breakwater models.

Da utilização do GNSS em contínuo para monitorizar fenómenos geofísicos, nomeadamente a vigilância vulcânica, sísmica e tectónica, e as respostas dinâmicas e quase estáticas das grandes estruturas de engenharia civil resultam séries temporais que devem ser convenientemente filtradas em função do tipo de sinal (frequência e amplitude) que se pretende monitorizar. Com o GNSS e utilizando o mesmo tipo de equipamento, mas empregando modos de posicionamento diferentes, é possível monitorizar numa banda muito larga. Com efeito, o GNSS em modo estático relativo é mais adequado para vigilância de longo período porque este tipo de posicionamento caracteriza-se por detectar deslocamentos de baixa frequência com exactidão milimétrica. Por outro lado, para a monitorização de movimentos rápidos, deslocamentos de curto período e vibrações recorre-se a um posicionamento GNSS mais expedito, como o modo de posicionamento cinemático em tempo real ou o posicionamento cinemático pós-processado. Sendo estes últimos mais afectados pelos efeitos de multipath e, por essa razão, menos precisos do que o modo estático. A aplicação de filtros digitais permite melhorar a precisão do posicionamento GNSS pela mitigação do ruído das séries temporais. Nesta comunicação, aplicam-se dois filtros digitais, a média móvel simples e a média móvel exponencial, que são do tipo passa-baixo, a uma série temporal GNSS obtida duma base curta instalada no campus do LNEC.

O calendário Gregoriano não é mais do que uma reforma do calendário Juliano, devido a Júlio César, que adaptou os formalismos romanos a uma antiga estrutura solar de origem egípcia. Este ensaio descreve a história do calendário Gregoriano e dos calendários da bacia do Mediterrâneo e do Oriente Próximo, com ele mais ou menos aparentados.

Interferometric synthetic aperture RADAR is an applied geodesy technique, which enables displacement measurement through satellite images. A literature review of the technique principles and of previous studies regarding its application to structural health monitoring allowed the identification of a few bottlenecks to the operational usage of this cost-effective technology for monitoring purposes.Three research lines were defined. First, a data mining strategy was developed to extract structural behaviour information from displacement time series from thousands of points on the region of interest, with tens of observation epochs each. Second, displacements from this technique were integrated into a previously existing monitoring system and were used to expand it to a larger number of points on the structure and to its surroundings. Third, an experimental infrastructure was deployed in order to perform several tests for displacement validation and uncertainty assessment. The infrastructure included a new model of artificial reflector to the satellite signals, purposefully developed in the scope of this study.The developed methods enabled the successful monitoring of different types of civil and geotechnical structures. Slope behaviour around water reservoirs was assessed during both the reservoir first impoundment and regular operation. Differential displacements were detected on building-blocks at a cultural heritage urban area and concrete arch dam responses to temperature loads were identified. The experimental work showed the achieved displacements agreed with those of other geodetic techniques and uncertainties around 2 mm were obtained for the measurements.In conclusion, interferometric synthetic aperture RADAR is a promising technique, able to provide useful information for structure monitoring, such as aiding in the planning of in situ monitoring activities and in identifying space-time patterns in structural behaviour. Thanks to its spatial coverage, observation period of a few days and achieved displacement uncertainty, it is advantageous to complement existing monitoring systems with data from this technique.

O Simulador de Cenários Sísmicos, LNECloss, é uma ferramenta computacional que permite avaliar perdas em consequência de um cenário sísmico especificado [LESSLOSS, 2007]. Esta ferramenta automática compreende vários módulos, como sejam, a modelação da acção sísmica no substrato rochoso e à superfície, a avaliação dos danos no edificado e a avaliação das perdas económicas e humanas. O Simulador foi integrado como aplicação externa num Sistema de Informação Geográfica (SIG) [Sousa, 2006]. Foram identificadas algumas necessidades de desenvolvimento no Simulador, que compreendem, por um lado, o alargamento do seu domínio geográfico para além do território de Portugal Continental, nomeadamente para o Arquipélago dos Açores, que possui uma taxa de ocorrência de sismos muito elevada e, por outro, a sua disponibilização através da Web, com um carácter autónomo, ou seja, que não necessite de alguma plataforma de informação geográfica tendo no entanto as suas capacidades no que respeita ao mapeamento e à síntese gráfica e tabular dos efeitos de um cenário sísmico. De entre as características deste simulador WebSIG, saliente-se uma interface gráfica de fácil operação, permitindo a sua utilização por agentes da protecção civil, no que respeita ao planeamento e à gestão da emergência na eventualidade de ocorrência de um sismo.

Neste relatório apresenta-se, de forma sucinta, a atividade de investigação realizada no âmbito do projeto ImEngine no período 2014-2023. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto INFRASAR no período 2014-2023. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto MEGA no período 2015-2023. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos.

Este relatório apresenta os procedimentos do levantamento fotogramétrico, realizado com um drone, assim como as ações complementares, destinados a obter informação de carácter geométrico da praia da Cova Gala em 2020. Este documento inclui ainda uma análise da qualidade dos produtos gerados e uma comparação com o levantamento realizado em 2019, cerca de um ano antes.

Este relatório apresenta os resultados da campanha de nivelamento geométrico das bocas de furos de captação de água na proximidade da Base das Lajes, realizada pelo Núcleo de Geodesia Aplicada do Departamento de Barragens de Betão do LNEC, em outubro de 2020. Os resultados são as cotas, num referencial local, das bocas dos furos de captação de água.

Este relatório apresenta os procedimentos dos levantamentos fotogramétricos, realizados com um drone, assim como as ações complementares, efetuadas em 2019, destinados a obter informação de carácter geométrico das praias de Cova - Gala, Vieira e São Pedro de Moel.

Neste relatório apresenta-se, de forma sucinta, a atividade de investigação realizada no âmbito do projeto ImEngine no período 2014-2017. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos, sendo proposta uma extensão do projeto, e respetiva revisão do plano de atividades, para os próximos dois anos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto INFRASAR no período 2014-2017. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos, sendo proposta uma extensão do projeto e revisão do plano de atividades para os próximos dois anos.

Neste relatório apresenta-se, de forma sucinta, a descrição da atividade de investigação realizada no âmbito do projeto MEGA no triénio 2015-2017. Os resultados da atividade são analisados e avaliados, em face dos objetivos inicialmente previstos, sendo proposta uma revisão do plano de atividades para os próximos dois anos.

O relatório apresenta uma proposta de plano de estudos para a tese de doutoramento da bolseira Dora Roque, a realizar no Núcleo de Geodesia Aplicada do Departamento de Barragens de Betão do Laboratório Nacional de Engenharia Civil. O objetivo principal do estudo é contribuir para a operacionalização da geodesia InSAR na determinação de deslocamentos para o controlo de segurança de estruturas.

O trabalho aborda simultaneamente a distribuição do desvio padrão da amostra aleatória normal e a distribuição do desvio padrão do modelo de Gauss-Markov, designados genericamente por desvio padrão empírico. Após mostrar que o desvio padrão empírico é um estimador excêntrico que subestima o desvio padrão da amostra ou do modelo, conforme o caso, são apresentadas correções de excentricidade. É também tratada a estimação do desvio padrão da amostra e do modelo em cenário Bayesiano, com diferentes distribuições anteriores. O trabalho é rematado por casos de estudo baseados na simulação de amostras normais e por um exemplo concreto relacionado com o controlo da precisão de um distanciómetro eletromagnético.

O presente trabalho apresenta uma metodologia genérica para a regularização de problemas inversos lineares mal colocados e a sua aplicação às redes altimétricas e planimétricas usadas na monitorização de deslocamentos de pontos notáveis de grandes barragens por métodos da Geodesia Aplicada. A metodologia é ilustrada por intermédio de três casos de estudo.

This paper deals with the beta-binomial model, which is an important stochastic model within the scope of the Bayesian statistical inference. After a short review of the binomial and beta distributions, the paper presents the closed formulae for the posterior probability density function of the binomial trial parameter and for the prior predictive and for the posterior predictive probabilities of the successes in binomial experiments. A description of the Bayesian methodology to test different hyper-parameters for the conjugate prior probability density functions of the beta family is also presented. Finally, the beta-binomial model is illustrated with a study case related to the quality control of the geodetic observation of large dams.

O presente trabalho, além de uma revisão sintética da abordagem frequencista, trata da abordagem Bayesiana da análise de regressão linear multivariada. É apresentada uma compilação de procedimentos e fórmulas para a estimação dos coeficientes da regressão, sob três cenários de informação anterior. Finalmente, o trabalho ocupa-se dos problemas da predição de respostas e da comparação de modelos de regressão.

The work presents the theoretical definitions of the gamma, multi-gamma, digamma and trigamma functions as well as operational approximations to compute their values. A more precise alternative, due to Robert Windschitl, to the traditional approximation of the gamma function by the Stirling’s series, is reported. The work is completed with a study case, related to the geodetic monitoring of large dams, that illustrates the previous concepts and definitions.

O trabalho descreve os princípios da análise Bayesiana, usando como caso de estudo a amostra aleatória normal identicamente distribuída. Após um curto preâmbulo histórico, são resumidos, na Secção 2, os conceitos mais importantes da análise frequencista. Nas secções seguintes, são abordados os temas Bayesianos mais importantes, tais como a estimação, pontual e regional (Secção 5), e o teste de hipóteses sobre os parâmetros da distribuição da amostra (Secção 6). As distribuições anteriores de Laplace, Jeffreys e conjugada normal-gama invertida são apresentadas na Secção 4. O problema da eliciação paramétrica das distribuições anteriores conjugadas é tratado na Secção 7. Palavras Chave: distribuições anteriores e posteriores, divergência de Kullback-Leibler, eliciação paramétrica, factor de Bayes, fórmula de Bayes, verosimilhança.

Este trabalho define uma estratégia, apoiada o mais possível nas disponibilidades do LNEC, para a calibragem dos distanciómetros electromagnéticos (DEM) usados pelo Núcleo de Geodesia Aplicada na observação geodésica de barragens.

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