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

Interferometric synthetic aperture radar (InSAR) is a cost-effective method for displacement measurement at dams and reservoir banks, and is especially relevant for structures without embedded equipment or rarely monitored. However, the lack of redundant observations prevents the determination of a posteriori variances for InSAR measurements, which limits the uptake of the InSAR technology for structure monitoring. This paper presents a methodology for the integration of persistent scatterer interferometry (PSI) and Global NavigationSatellite System (GNSS) displacement measurements. Double differences between PSI and GNSS data are used as observations in a redundant network connecting the points of interest, with GNSS data used to constrain PSI measurements. This procedure allows the determination of adjusted displacements and a posteriori variances at all network points. Maximum uncertainty of 3 mm was achieved for displacementsalong the SAR sensor line-of-sight at both the dam and its surrounding slopes. The proposed method is of interest for monitoring purposes, because it allows displacement measurement at both the structure and its surroundings, together with the displacement uncertainty, which aids decision makers in the planning of maintenance operations for the whole area influenced by the dam.

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

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

Les ports et autres infrastructures construits sur des côtes exposées à de fortes houles ont besoin d

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.

After a large set of GNSS tests carried out on a 325 m baseline, with different length observation sessions, we assessed the quality of GNSS with short-length sessions to monitoring the displacements of a large embankment dam, in south of Portugal. The GNSS campaigns were performed at the same time of classic geodetic observation campaigns, with Leica TCA2003 tacheometer and Leica NA2 optical level, and the results were compared: the standard deviations of the differences of the two methods for horizontal and vertical displacements were 3.6 mm and 5.7mm, respectively. These values are in agreement with those which we obtained on a 325 m baseline with GNSS using sessions of 5 minutes length. The results of this test show that the GNSS with short-length sessions has enough precision to monitoring large embankment dams.

The pathologies of structures that cause changes of surface temperatures can be detected by the analysis of the temperature of walls and other surfaces. The measurement of the surface temperatures can be easily performed with the use of thermal imaging cameras which work like an ordinary digital camera and give, instantly, a colour image where the colours are related with the temperature of the surface. This paper presents a study of the use of this methodology in the monitoring of concrete dams, specifically on the detection of resurgences of water on the downstream face, usually related with the transfer of water.Three concrete arch dams were used to test this methodology: Alto Ceira, Cabril and Alto Ceira II. On the day on which the images were taken (4th of June of 2013), Alto Ceira and Cabril were under normal operation. Both structures presented important cracks. These dams were used to test if, under normal conditions, namely with the thermal camera more than 100 m away from the dam, it was possible to detect colder areas. Alto Ceira II was, at that day, near the end of the construction. As it has several thermometers inside the concrete, the temperatures measured by these were used to validate the information on the thermal images.

Drone or UAV (unmanned aerial vehicle) are the most common names used to refer light aircrafts without human pilots aboard. This paper presents one application that explores its use as a carrier of digital cameras, allowing the acquisition of images at distances of a few meters of a dam.Dams, and especially large dams, are structures that usually present high risk. For this reason they are subject to surveillance to evaluate its safety. Visual inspections contribute to the knowledge of the structure and are irreplaceable since some problems can only be detected, and their evolution followed, by this method. If to make a photographic reportage inside galleries or in other accessible areas is easy, when one must evaluate the state of the exterior walls or other inaccessible locations on dams, the only method available to inspect the surface was to set the camera/binoculars on the banks of the river.Drones can easily overcome this problem, since they can be guided near the structure, at distances of a few meters This paper presents the results of an experience made at Bouçã dam: it is described the UAV system used, the dam, the flights, the photogrammetric products generated (orthomosaic and point cloud), the problems faced. In Figures 1 and 2 are presented two photographs of Bouçã dam taken during this experiment by a digital camera carried by a drone octocopter.

This paper presents a methodology for aided visual inspections of rock slopes based on change detection techniques usually used in remote sensing. This methodology, that uses photographs taken by an ordinary digital camera, has undergone several field tests during the excavation works of Foz Tua dam. Its main goal is to detect displacements of the visible rock blocks that can lead to rock falls and to mitigate the ensuing risks.

Lisbon Downtown presents unique geomorphologic properties which makes it an area prone to terrain instability. Serious accidents have occurred there, namely, during the 1755 earthquake and a flooding event at the extension of a subway line, demanding a frequent monitorization for safety reasons and expense minimization. In this study, Permanent Scatterers technique is applied. The calculated displacement velocities are compared to those obtained from levelling operations. Possible causes for the discrepancy are presented in the paper. Besides a subsidence trend, a seasonal behaviour is also detected, probably related to aquifer recharge or tides.

A fusão de dados é uma técnica que combina dados obtidos de diferentes sensores com o objectivo de melhorar a precisão desses dados e possibilitar inferências que não seriam possíveis utilizando um único tipo de sensor.Através dum filtro de Kalman é possível fazer a fusão de deslocamentos com acelerações, sendo os primeiros medidos com o GNSS e as segundas medidas com acelerómetros. Esta fusão tira partido da precisão do GNSS em baixas frequências e da grande sensibilidade dos acelerómetros em altas frequências, originando uma série temporal de deslocamentos de longa e de grande resolução, independentemente de os dados terem sido registados com diferentes frequências de amostragem. Realizaram-se ensaios no LNEC para testar a fusão destes dois tipos de sensores num modelo estrutural simples correspondente a um edifício de três pisos, instrumentado com antenas GNSS e acelerómetros. Apresentam-se os resultados obtidos nestes ensaios, discute-se a incerteza dos deslocamentos medidos e a generalização da sua aplicação a grandes estruturas.

The low price and the quality of the products derived from photographs taken by cameras mounted on unmanned aerial vehicles (UAV) turn them very attractive to be used in several situations, namely when the area that needs to be covered hasn

The low price and the quality of the products derived from photographs taken by cameras mounted on unmanned aerial vehicles (UAV) turn them very attractive to be used in several situations, namely when the area that needs to be covered hasn

A utilização de VANT (Veículos Aéreos Não Tripulados) como plataformas para a obtenção de fotografias destinadas à aquisição de informação geográfica tem despertado um interesse crescente por poder ser, em certos domínios, uma alternativa interessante aos métodos aéreos tradicionais. Na comunicação é apresentado o controlo da qualidade de um ortomosaico e de um modelo digital de superfície de uma zona central de Coimbra seguindo duas metodologias de análise: a habitual, baseada na análise da estatística

As cheias constituem 40% de todos os desastres naturais mundiais e, na última década do século XX, foram responsáveis pela perda de 100 mil vidas humanas, afetando mais de 1400 milhões de pessoas. Nos últimos cem anos têm sido o fenómeno natural mais mortífero em Portugal, sendo o Baixo Tejo o local onde ocorrem as maiores cheias em termos de área inundada, com intervalo médio de 2,5 anos. A elevada frequência de cheias torna o Baixo Tejo adequado como região piloto para um trabalho sistemático de calibração de modelos de inundação. Este artigo centra-se na calibração de modelos 2D de simulação de cheias para eventos de 2001 e 2006, no troço de 70 km do Rio Tejo entre Tramagal e Ómnias, recorrendo ao modelo numérico Tuflow, que resolve as equações bidimensionais de superfície livre em águas pouco profundas.Os modelos de inundação foram baseados num modelo digital de terreno (MDT) adquirido em 2008 por técnicas de radar (resolução espacial de 5 m), em medições in situ de nível de água em Ómnias (condição-fronteira a jusante) e no caudal em Tramagal e Zêzere (condições-fronteira a montante). Cinco diques foram introduzidos nos modelos. Todos os modelos têm as mesmas condições-fronteira e resolução da malha de 30 m. Um estado estacionário inicial foi garantido. Utilizaram-se classes de ocupação do solo CORINE Land Cover 2006, combinadas com coeficientes de rugosidade obtidos na literatura.Mapas de inundação obtidos a partir da segmentação de imagens de radar de abertura sintética (SAR) nas classes água/terra permitiram a calibração dos modelos para as cheias de 2001 e 2006. Estes mapas foram comparados com os mapas de inundação simulados e os coeficientes de Manning (rugosidade) foram alterados em conformidade. Os modelos foram também calibrados pelo nível de água medido na estação hidrométrica de Almourol, a 12 km a jusante de Tramagal. Obtiveram-se, assim, mapas de coeficientes de rugosidade. E foi efetuada uma simulação para a maior cheia do século XX (fevereiro de 1979), para a qual não existe imagem de radar de abertura sintética; neste caso, a validação do modelo foi feita usando os valores de nível de água na estação de Almourol e as marcas de cheia distribuídas pela planície de inundação.As imagens de radar de abertura sintética foram fornecidas pela Agência Espacial Europeia ao abrigo do projeto CAT

O calendário Gregoriano não é mais do que uma reforma do calendárioJuliano, devido a Júlio César, que adaptou os formalismos romanos a uma antigaestrutura solar de origem egípcia. Este ensaio descreve a história do calendárioGregoriano 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.

Este relatório apresenta uma metodologia para controlo dos erros instrumentais e avaliação da incerteza de medição dos distanciómetros eletromagnéticos (DEM) usados na observação geodésica de barragens de betão. A metodologia, que é baseada numa base de teste existente no campus do LNEC, é ilustrada com a análise de seis medições da base, entre 2010 e 2014, com os dois DEM utilizados pelo Núcleo de Geodesia Aplicada.

The monitoring systems have two main objectives: (i) to evaluate the safety conditions and durability of the infrastructures and to develop a better understanding about their day-to-day behaviour; (ii) to detect the occurrence of special events that might jeopardize the safety of the structure. To reach the first objective it is mandatory to create a database as most extensive as possible to support an analysis of the structural behaviour. Regarding the second objective near real-time automatic systems must be created in order to analyse the recorded data and establish limits of alert with alarm warnings when those limits are exceeded. This R&D project aims to develop a measurement system, based on GNSS (Global Navigation Satellite Systems), suitable to monitor large scale civil engineering structures and infrastructures, particularly bridges and dams. This monitoring system final objective is to measure the displacements of some selected points of the structures. These points should be the most important ones to characterize the general behaviour of the monitored structure. The advantages of using a GNSS system are undeniable: this equipment is robust, operates under all weather conditions, does not require intervisibility between the monitored points and the reference points, uses an external tridimensional reference systems, and provides an extremely accurate time-reference frame. The GNSS positioning is affected by a numerous set of errors due to natural and artificial phenomena. These errors should be reduced as much as possible, in order to obtain good estimated distances between the observed satellites and the antenna of the receivers. There are well known observation and observation combination techniques (phase differences measurements, relative positioning and Precise Point Positioning - PPP) that allow to strongly reduce, or sometimes even eliminate, most of the errors. Using carefully selected observation and processing techniques it is possible to obtain high-precision GNSS positioning. The RTK (Real Time Kinematics) is the more recent high-precision positioning GNSS technique. It allows us to obtain high quality coordinates in almost real-time. When used in conjunction with top grade receivers (able to do observations at high frequencies) the RTK seems to be able to monitor high frequencies displacements of structures. Unfortunately the positioning precision is only at the centimetre level. To reduce this uncertainty it will be used short baselines and processing techniques based on the use of various filters and methodologies for multi-sensor observations fusion. It is precisely in the development of these techniques that the actual research project is focused. After the monitoring system specification, several techniques will be developed and tested in order to be included in a reliable measurement system that will meet the specified requirements. To define the monitoring system demands the following items have been addressed: - Requirements of the monitoring system in view of the behaviour of the selected structures; - Acquisition of know-how on data acquisition systems and in-site monitoring equipment; - Identification, characterization and analysis of software available for data processing.

A inspeção visual assistida pode ser utilizada para a monitorização de ensaios de flexão atéà rotura de vigas de madeira, tendo sido usado um sistema de observação com fotografia evídeo. Foi desenvolvido um programa para identificação automática das imagens da viga,que registaram alterações significativas, tendo a fratura sido delineada através de técnicasde análise de imagem orientada por objetos.

A extração de informação a partir de imagens digitais tem-se tornado numa prática comum em váriasáreas do conhecimento. Foi desenvolvido um programa em MATLAB para permitir a um utilizador nãoespecializado a realização de tarefas simples de processamento digital sobre imagens adquiridas porvários géneros de sensores.

O relatório apresenta os princípios gerais da termografia e a sua aplicação prática no levantamentotérmico de paramentos de barragens de betão para apoio ao acompanhamento da evolução depatologias. Apresentam-se aplicações relativas ao levantamento térmico dos paramentos de jusantedas barragens do Alto Ceira II, Alto Ceira e Cabril. O levantamento realizado na primeira barragem,que se encontrava na fase final de construção e ainda vazia, permitiu a avaliação da qualidade dosresultados obtidos (temperaturas superficiais do paramento) por comparação com valores medidospor termómetros embebidos no betão. Nas outras duas barragens, ambas apresentando problemasde infiltrações, permitiu avaliar a aplicabilidade das imagens térmicas na deteção de ressurgimentosde água na superfície do betão, geralmente indicativas da existência de repasses de água.

O presente relatório apresenta uma experiência de aquisição de fotografias aéreasutilizando um veículo aéreo não tripulado (VANT) para recolha de informação geográfica doquebra-mar da Ericeira, com o objetivo de testar a capacidade destes dados para produçãode ortofotomapas e modelos numéricos de superfície para monitorização de infraestruturasao longo do tempo. A experiência foi realizada numa colaboração entre o LNEC e aempresa SINFIC, SA

Neste relatório faz-se a síntese dos métodos disponíveis para realizar a Inspecção Visual Assistida(IVISA) de paramentos de barragens de betão, no que diz respeito às várias fases envolvidas: aquisiçãode imagens, processamento, monitorização temporal e arquivo. Apresentam-se os recursos existentesno LNEC e a adquirir, assim como os custos associados.

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Este relatório apresenta um procedimento para a avaliação da incerteza de medição de equipamento de nivelamento geométrico de precisão e ainda regras para o teste estatístico de hipóteses sobre essa incerteza de medição, preconizadas na segunda parte da norma ISO 17123, exemplificados com um ensaio comparativo de um nível automático numérico Wild NA 3003 e de um nível automático Wild NA2, com um micrómetro óptico acoplado.

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 regularizaçãode problemas inversos lineares mal colocados e a sua aplicação às redes altimétricas eplanimétricas usadas na monitorização de deslocamentos de pontos notáveis de grandesbarragens por métodos da Geodesia Aplicada. A metodologia é ilustrada por intermédiode três casos de estudo.

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

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

The work presents the theoretical definitions of the gamma, multi-gamma, digammaand trigamma functions as well as operational approximations to compute their values.A more precise alternative, due to Robert Windschitl, to the traditional approximationof the gamma function by the Stirling

O trabalho descreve os princípios da análise Bayesiana, usando como caso deestudo a amostra aleatória normal identicamente distribuída. Após um curto preâmbulohistórico, são resumidos, na Secção 2, os conceitos mais importantes da análise frequencista.Nas secções seguintes, são abordados os temas Bayesianos mais importantes, taiscomo a estimação, pontual e regional (Secção 5), e o teste de hipóteses sobre osparâmetros da distribuição da amostra (Secção 6). As distribuições anteriores de Laplace,Jeffreys e conjugada normal-gama invertida são apresentadas na Secção 4. O problemada 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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