Bayesian Markov chain Monte Carlo inversion of geophysical data for the purpose of estimating the hydraulic properties of the unsaturated zone

Ground-penetrating radar (GPR) has the potential to provide valuable information on hydrological properties of the vadose zone because of their strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR data within a coupled geophysical-hydrological framework may allow for effective estimation of subsurface van-Genuchten-Mualem (VGM) parameters and their corresponding uncertainties. An important and still unresolved issue, however, is how to best integrate GPR data into a stochastic inversion in order to estimate the VGM parameters and their uncertainties, thus improving hydrological predictions. Recognizing the importance of this issue, the aim of the research presented in this thesis was to first introduce a fully Bayesian inversion called Markov-chain-Monte-carlo (MCMC) strategy to perform the stochastic inversion of steady-state GPR data to estimate the VGM parameters and their uncertainties. Within this study, the choice of the prior parameter probability distributions from which potential model configurations are drawn and tested against observed data was also investigated. Analysis of both synthetic and field data collected at the Eggborough (UK) site indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when these data are combined with a realistic, informative prior. A subsequent study explore in detail the dynamic infiltration case, specifically to what extent time-lapse ZOP GPR data, collected during a forced infiltration experiment at the Arrenaes field site (Denmark), can help to quantify VGM parameters and their uncertainties using the MCMC inversion strategy. The findings indicate that the stochastic inversion of time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions. In turn, this significantly improves knowledge of the hydraulic properties, which are required to predict hydraulic behaviour. Finally, another aspect that needed to be addressed involved the comparison of time-lapse GPR data collected under different infiltration conditions (i.e., natural loading and forced infiltration conditions) to estimate the VGM parameters using the MCMC inversion strategy. The results show that for the synthetic example, considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions. When investigating data collected at the Arrenaes field site, further complications arised due to model error and showed the importance of also including a rigorous analysis of the propagation of model error with time and depth when considering time-lapse data. Although the efforts in this thesis were focused on GPR data, the corresponding findings are likely to have general applicability to other types of geophysical data and field environments. Moreover, the obtained results allow to have confidence for future developments in integration of geophysical data with stochastic inversions to improve the characterization of the unsaturated zone but also reveal important issues linked with stochastic inversions, namely model errors, that should definitely be addressed in future research.

Main results of the Monte Carlo studies carried out for nuclear medicine practices within the ORAMED project

The aim of ORAMED work package 4 was the optimization of the medical practices in nuclear medicine during the preparation of radiopharmaceuticals and their administration to the patient. During the project a wide campaign of measurements was performed in the nuclear medicine departments of the collaborating hospitals. Such data were intrinsically characterized by a large variability that depended on the procedure, the employed techniques and the operator's habits. That variability could easily hide some important parameter, for example, the effectiveness of the adopted shielding (for syringe and vial) or the effect of the distances from the source. This information is necessary for a valuable optimization purpose of radiation protection. To this end a sensitivity analysis was carried out through Monte Carlo simulations employing voxel models, representing operator's hand during the considered practices. Such analysis allowed understanding at what extent the range of personal dose equivalent evaluated during measurements can be considered intrinsically related to the procedures. Furthermore, with the Monte Carlo simulations it was possible to study the appropriateness of the shielding usually utilized in these practices.

A semi-grand canonical Monte Carlo simulation model for ion binding to ionizable surfaces: proton binding of carboxylated latex particles as a case study

In this paper, we present a computer simulation study of the ion binding process at an ionizable surface using a semi-grand canonical Monte Carlo method that models the surface as a discrete distribution of charged and neutral functional groups in equilibrium with explicit ions modelled in the context of the primitive model. The parameters of the simulation model were tuned and checked by comparison with experimental titrations of carboxylated latex particles in the presence of different ionic strengths of monovalent ions. The titration of these particles was analysed by calculating the degree of dissociation of the latex functional groups vs. pH curves at different background salt concentrations. As the charge of the titrated surface changes during the simulation, a procedure to keep the electroneutrality of the system is required. Here, two approaches are used with the choice depending on the ion selected to maintain electroneutrality: counterion or coion procedures. We compare and discuss the difference between the procedures. The simulations also provided a microscopic description of the electrostatic double layer (EDL) structure as a function of p H and ionic strength. The results allow us to quantify the effect of the size of the background salt ions and of the surface functional groups on the degree of dissociation. The non-homogeneous structure of the EDL was revealed by plotting the counterion density profiles around charged and neutral surface functional groups.

Quantitative integration of high-resolution hydrogeophysical data through Monte-Carlo-type conditional simulations

Geophysical techniques can help to bridge the inherent gap with regard to spatial resolution and the range of coverage that plagues classical hydrological methods. This has lead to the emergence of the new and rapidly growing field of hydrogeophysics. Given the differing sensitivities of various geophysical techniques to hydrologically relevant parameters and their inherent trade-off between resolution and range the fundamental usefulness of multi-method hydrogeophysical surveys for reducing uncertainties in data analysis and interpretation is widely accepted. A major challenge arising from such endeavors is the quantitative integration of the resulting vast and diverse database in order to obtain a unified model of the probed subsurface region that is internally consistent with all available data. To address this problem, we have developed a strategy towards hydrogeophysical data integration based on Monte-Carlo-type conditional stochastic simulation that we consider to be particularly suitable for local-scale studies characterized by high-resolution and high-quality datasets. Monte-Carlo-based optimization techniques are flexible and versatile, allow for accounting for a wide variety of data and constraints of differing resolution and hardness and thus have the potential of providing, in a geostatistical sense, highly detailed and realistic models of the pertinent target parameter distributions. Compared to more conventional approaches of this kind, our approach provides significant advancements in the way that the larger-scale deterministic information resolved by the hydrogeophysical data can be accounted for, which represents an inherently problematic, and as of yet unresolved, aspect of Monte-Carlo-type conditional simulation techniques. We present the results of applying our algorithm to the integration of porosity log and tomographic crosshole georadar data to generate stochastic realizations of the local-scale porosity structure. Our procedure is first tested on pertinent synthetic data and then applied to corresponding field data collected at the Boise Hydrogeophysical Research Site near Boise, Idaho, USA.

Monte Carlo simulation of a clearance box monitor used for nuclear power plant decommissioning.

When decommissioning a nuclear facility it is important to be able to estimate activity levels of potentially radioactive samples and compare with clearance values defined by regulatory authorities. This paper presents a method of calibrating a clearance box monitor based on practical experimental measurements and Monte Carlo simulations. Adjusting the simulation for experimental data obtained using a simple point source permits the computation of absolute calibration factors for more complex geometries with an accuracy of a bit more than 20%. The uncertainty of the calibration factor can be improved to about 10% when the simulation is used relatively, in direct comparison with a measurement performed in the same geometry but with another nuclide. The simulation can also be used to validate the experimental calibration procedure when the sample is supposed to be homogeneous but the calibration factor is derived from a plate phantom. For more realistic geometries, like a small gravel dumpster, Monte Carlo simulation shows that the calibration factor obtained with a larger homogeneous phantom is correct within about 20%, if sample density is taken as the influencing parameter. Finally, simulation can be used to estimate the effect of a contamination hotspot. The research supporting this paper shows that activity could be largely underestimated in the event of a centrally-located hotspot and overestimated for a peripherally-located hotspot if the sample is assumed to be homogeneously contaminated. This demonstrates the usefulness of being able to complement experimental methods with Monte Carlo simulations in order to estimate calibration factors that cannot be directly measured because of a lack of available material or specific geometries.

Bayesian Markov-chain-Monte-Carlo inversion of time-lapse cross hole ground-penetrating radar data to characterize the vadose zone at the Arrenaes field site, Denmark

The ground-penetrating radar (GPR) geophysical method has the potential to provide valuable information on the hydraulic properties of the vadose zone because of its strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR traveltime data can allow for a significant reduction in uncertainty regarding subsurface van Genuchten-Mualem (VGM) parameters. Much of the previous work on the stochastic estimation of VGM parameters from crosshole GPR data has considered the case of steady-state infiltration conditions, which represent only a small fraction of practically relevant scenarios. We explored in detail the dynamic infiltration case, specifically examining to what extent time-lapse crosshole GPR traveltimes, measured during a forced infiltration experiment at the Arreneas field site in Denmark, could help to quantify VGM parameters and their uncertainties in a layered medium, as well as the corresponding soil hydraulic properties. We used a Bayesian Markov-chain-Monte-Carlo inversion approach. We first explored the advantages and limitations of this approach with regard to a realistic synthetic example before applying it to field measurements. In our analysis, we also considered different degrees of prior information. Our findings indicate that the stochastic inversion of the time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions compared with the corresponding priors, which in turn significantly improves knowledge of soil hydraulic properties. Overall, the results obtained clearly demonstrate the value of the information contained in time-lapse GPR data for characterizing vadose zone dynamics.

Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.

Strategisten reaalioptioiden mallintaminen Monte Carlo -simulointimenetelmällä, case Voest Alpine Stahl Ag

Tutkielman päätavoitteena oli selvittää, miten Monte Carlo –simulointi soveltuu strategisten reaalioptioiden arvonmääritykseen. Tutkielman teoriaosuudessa käytiin läpi reaalioptioteoriaa ja Monte Carlo –simulointimenetelmää toiminta-analyyttisella tutkimusotteella. Tuloksena todettiin, että simulointimenetelmää on reaalioptioiden yhteydessä yleensä käytetty, kun muu menetelmä ei ole ollut mahdollinen. Tutkielman pääpaino on tapaustutkimukseen pohjautuvassa empiriaosuudessa, jossa rakennettiin päätöksentekometodologista tutkimusotetta seuraten simulointimalli, jolla tutkittiin Voest Alpine Stahl Ag:n vaihtoehtoisten hinnoittelustrategioiden taloudellista vaikutusta. Mallin rakentaminen perustui yrityksen tilinpäätösaineistoon. Havaittiin, ettei yritys ole valitsemansa strategian vuoksi juurikaan menettänyt tuottoja, mutta toisaalta pelkkä tilinpäätösaineisto ei riitä kovin luotettavaan tarkasteluun. Vuosikertomusten antaman tiedon pohjalta analysoitiin lisäksi yrityksen toiminnassa havaittuja reaalioptioita. Monte Carlo –simulointimenetelmä sopii reaalioptioiden arvonmääritykseen, mutta kriittisiä tekijöitä ovat mallin rakentaminen ja lähtötietojen oikeellisuus. Numeerisen mallin rinnalla on siksi aiheellista suorittaa myös laadullista reaalioptioanalyysia.

Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

Étude des artefacts en tomodensitométrie par simulation Monte Carlo

En radiothérapie, la tomodensitométrie (CT) fournit l’information anatomique du patient utile au calcul de dose durant la planification de traitement. Afin de considérer la composition hétérogène des tissus, des techniques de calcul telles que la méthode Monte Carlo sont nécessaires pour calculer la dose de manière exacte. L’importation des images CT dans un tel calcul exige que chaque voxel exprimé en unité Hounsfield (HU) soit converti en une valeur physique telle que la densité électronique (ED). Cette conversion est habituellement effectuée à l’aide d’une courbe d’étalonnage HU-ED. Une anomalie ou artefact qui apparaît dans une image CT avant l’étalonnage est susceptible d’assigner un mauvais tissu à un voxel. Ces erreurs peuvent causer une perte cruciale de fiabilité du calcul de dose. Ce travail vise à attribuer une valeur exacte aux voxels d’images CT afin d’assurer la fiabilité des calculs de dose durant la planification de traitement en radiothérapie. Pour y parvenir, une étude est réalisée sur les artefacts qui sont reproduits par simulation Monte Carlo. Pour réduire le temps de calcul, les simulations sont parallélisées et transposées sur un superordinateur. Une étude de sensibilité des nombres HU en présence d’artefacts est ensuite réalisée par une analyse statistique des histogrammes. À l’origine de nombreux artefacts, le durcissement de faisceau est étudié davantage. Une revue sur l’état de l’art en matière de correction du durcissement de faisceau est présentée suivi d’une démonstration explicite d’une correction empirique.

Étude de la formation et de l'évolution de nanostructures par méthodes Monte Carlo

Cette thèse, composée de quatre articles scientifiques, porte sur les méthodes numériques atomistiques et leur application à des systèmes semi-conducteurs nanostructurés. Nous introduisons les méthodes accélérées conçues pour traiter les événements activés, faisant un survol des développements du domaine. Suit notre premier article, qui traite en détail de la technique d'activation-relaxation cinétique (ART-cinétique), un algorithme Monte Carlo cinétique hors-réseau autodidacte basé sur la technique de l'activation-relaxation nouveau (ARTn), dont le développement ouvre la voie au traitement exact des interactions élastiques tout en permettant la simulation de matériaux sur des plages de temps pouvant atteindre la seconde. Ce développement algorithmique, combiné à des données expérimentales récentes, ouvre la voie au second article. On y explique le relâchement de chaleur par le silicium cristallin suite à son implantation ionique avec des ions de Si à 3 keV. Grâce à nos simulations par ART-cinétique et l'analyse de données obtenues par nanocalorimétrie, nous montrons que la relaxation est décrite par un nouveau modèle en deux temps: "réinitialiser et relaxer" ("Replenish-and-Relax"). Ce modèle, assez général, peut potentiellement expliquer la relaxation dans d'autres matériaux désordonnés. Par la suite, nous poussons l'analyse plus loin. Le troisième article offre une analyse poussée des mécanismes atomistiques responsables de la relaxation lors du recuit. Nous montrons que les interactions élastiques entre des défauts ponctuels et des petits complexes de défauts contrôlent la relaxation, en net contraste avec la littérature qui postule que des "poches amorphes" jouent ce rôle. Nous étudions aussi certains sous-aspects de la croissance de boîtes quantiques de Ge sur Si (001). En effet, après une courte mise en contexte et une introduction méthodologique supplémentaire, le quatrième article décrit la structure de la couche de mouillage lors du dépôt de Ge sur Si (001) à l'aide d'une implémentation QM/MM du code BigDFT-ART. Nous caractérisons la structure de la reconstruction 2xN de la surface et abaissons le seuil de la température nécessaire pour la diffusion du Ge en sous-couche prédit théoriquement par plus de 100 K.

Spectrum simulation of rough and nanostructured targets from their 2D and 3D image by Monte Carlo methods

Corteo is a program that implements Monte Carlo (MC) method to simulate ion beam analysis (IBA) spectra of several techniques by following the ions trajectory until a sufficiently large fraction of them reach the detector to generate a spectrum. Hence, it fully accounts for effects such as multiple scattering (MS). Here, a version of Corteo is presented where the target can be a 2D or 3D image. This image can be derived from micrographs where the different compounds are identified, therefore bringing extra information into the solution of an IBA spectrum, and potentially significantly constraining the solution. The image intrinsically includes many details such as the actual surface or interfacial roughness, or actual nanostructures shape and distribution. This can for example lead to the unambiguous identification of structures stoichiometry in a layer, or at least to better constraints on their composition. Because MC computes in details the trajectory of the ions, it simulates accurately many of its aspects such as ions coming back into the target after leaving it (re-entry), as well as going through a variety of nanostructures shapes and orientations. We show how, for example, as the ions angle of incidence becomes shallower than the inclination distribution of a rough surface, this process tends to make the effective roughness smaller in a comparable 1D simulation (i.e. narrower thickness distribution in a comparable slab simulation). Also, in ordered nanostructures, target re-entry can lead to replications of a peak in a spectrum. In addition, bitmap description of the target can be used to simulate depth profiles such as those resulting from ion implantation, diffusion, and intermixing. Other improvements to Corteo include the possibility to interpolate the cross-section in angle-energy tables, and the generation of energy-depth maps.

An efficient scheme for the evaluation of coding performance of high speed links incorporating joint error behaviour based on Monte Carlo Method

While channel coding is a standard method of improving a system’s energy efficiency in digital communications, its practice does not extend to high-speed links. Increasing demands in network speeds are placing a large burden on the energy efficiency of high-speed links and render the benefit of channel coding for these systems a timely subject. The low error rates of interest and the presence of residual intersymbol interference (ISI) caused by hardware constraints impede the analysis and simulation of coded high-speed links. Focusing on the residual ISI and combined noise as the dominant error mechanisms, this paper analyses error correlation through concepts of error region, channel signature, and correlation distance. This framework provides a deeper insight into joint error behaviours in high-speed links, extends the range of statistical simulation for coded high-speed links, and provides a case against the use of biased Monte Carlo methods in this setting

Modelo de gestión de la red de distribución tercerizada segmento tiendas región central, en productos de consumo masivo, mediante datos de panel y simulación de Monte Carlo.

El proyecto de investigación parte de la dinámica del modelo de distribución tercerizada para una compañía de consumo masivo en Colombia, especializada en lácteos, que para este estudio se ha denominado “Lactosa”. Mediante datos de panel con estudio de caso, se construyen dos modelos de demanda por categoría de producto y distribuidor y mediante simulación estocástica, se identifican las variables relevantes que inciden sus estructuras de costos. El problema se modela a partir del estado de resultados por cada uno de los cuatro distribuidores analizados en la región central del país. Se analiza la estructura de costos y el comportamiento de ventas dado un margen (%) de distribución logístico, en función de las variables independientes relevantes, y referidas al negocio, al mercado y al entorno macroeconómico, descritas en el objeto de estudio. Entre otros hallazgos, se destacan brechas notorias en los costos de distribución y costos en la fuerza de ventas, pese a la homogeneidad de segmentos. Identifica generadores de valor y costos de mayor dispersión individual y sugiere uniones estratégicas de algunos grupos de distribuidores. La modelación con datos de panel, identifica las variables relevantes de gestión que inciden sobre el volumen de ventas por categoría y distribuidor, que focaliza los esfuerzos de la dirección. Se recomienda disminuir brechas y promover desde el productor estrategias focalizadas a la estandarización de procesos internos de los distribuidores; promover y replicar los modelos de análisis, sin pretender remplazar conocimiento de expertos. La construcción de escenarios fortalece de manera conjunta y segura la posición competitiva de la compañía y sus distribuidores.

Error and complexity of random walk Monte Carlo radiosity

The author studies the error and complexity of the discrete random walk Monte Carlo technique for radiosity, using both the shooting and gathering methods. The author shows that the shooting method exhibits a lower complexity than the gathering one, and under some constraints, it has a linear complexity. This is an improvement over a previous result that pointed to an O(n log n) complexity. The author gives and compares three unbiased estimators for each method, and obtains closed forms and bounds for their variances. The author also bounds the expected value of the mean square error (MSE). Some of the results obtained are also shown