Browsing Department of Mathematics by Document Types "Doctoral thesis"
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4D Seismic History Matching Using the Ensemble Kalman Filter (EnKF): Possibilities and Challenges
(Doctoral thesis, 20100527)This research endeavor presents a 4D seismic history matching work flow based on the ensemble Kalman filter (EnKF) methodology. The objective of this work is to investigate the sensitivity of different combinations of ... 
Analysis and Approximation of Coupled 1D3D Flow Models
(Doctoral thesis, 20200318)In this thesis, we consider a specific instance of mixeddimensional partial differential equations (PDEs) commonly referred to as the coupled 1D3D flow model. The model itself consists of the Poisson equation defined on ... 
Analysis of multibeam sonar echos of herring schools by means of simulation
(Doctoral thesis, 20130531)The synchronized behavior of large schools of fish can be a fascinating sight and has caught the attention of researchers for decades. Schools of thousands, or even millions of fish can seemingly function as a single entity, ... 
Analytical Methods for Upscaling of Fractured Geological Reservoirs
(Doctoral thesis, 20151016)Numerical simulations have become an essential tool for planning well operations in the subsurface, whether the application is petroleum production, geothermal energy, groundwater utilization or waste disposal and leakage. ... 
Analytical, combinatorial and topological properties of quadratic differentials and their applications
(Doctoral thesis, 20171213)Quadratic differentials ﬁrst appeared in 1930s in works of Teichmuller in connection with moduli problem for Riemann surfaces. Later it was revealed that quadratic differ entials and their trajectories give solutions to ... 
An approximate hybrid method for modeling of electromagnetic scattering from an underground target
(Doctoral thesis, 20101209)The detection of a potential petroleum reservoir is achieved through inversion of electromagnetic data acquired in sea floor receivers. Inversion of electromagnetic data requires a number of repeated solves of the ... 
Assessment of Sequential and Simultaneous Ensemblebased History Matching Methods for Weakly Nonlinear Problems
(Doctoral thesis, 20150213)The ensemble Kalman filter (EnKF) has, since its introduction in 1994, gained much attention as a tool for sequential data assimilation in many scientific areas. In recent years, the EnKF has been utilized for estimating ... 
Bayesian and frequentist computation with application to data from the Medical Birth Registry of Norway
(Doctoral thesis, 20190425)In chapter 1, the field of statistics is discussed in general terms. Then, Bayes’ theorem is presented together with the posterior distribution. Finally, we consider maximum likelihood estimation and its relation to ... 
Bayesian Variational Methods in Carbon Storage Monitoring
(Doctoral thesis, 20210119)This thesis explores the use of deep learning and variational inference in Carbon Capture and Storage (CCS) monitoring. It consists of an introductory part and three scientific papers. The first chapter introduces CCS and ... 
Brauer groups of bielliptic surfaces and classification of irregular surfaces in positive characteristic
(Doctoral thesis, 20210527)In this work we tackle three problems about surfaces. In Part I (Chapter 2) we study the Brauer groups of bielliptic surfaces in characteristic zero. More precisely, given a bielliptic surface X, we give explicit ... 
Brauer Groups of Bielliptic Surfaces and Twisted Derived Equivalences
(Doctoral thesis, 20210830)This thesis focuses on two interrelated projects. The first project concerns the study of bielliptic surfaces, their Brauer groups and the pullback maps from their Brauer groups to those of their canonical covers. We prove ... 
Classical and Stochastic Slit Löwner Evolution
(Doctoral thesis, 20141010) 
Coherence for Monoidal and Symmetric Monoidal Groupoids in Homotopy Type Theory
(Doctoral thesis, 20211203)Homotopy Type Theory (HoTT) is a variant of MartinLöf Type Theory (MLTT) developed in such a way that types can be interpreted as infinitygroupoids, where the iterated construction of identity types represents the different ... 
Compositional reservoir simulation with emphasis on the IMPSAT formulation
(Doctoral thesis, 20060407) 
Computeraided proofs and algorithms in analysis
(Doctoral thesis, 20130614)The computational power has increased dramatically since the appearance of the first computers, making them a vital tool in the analysis of dynamical systems. We present further applications of those two basic ideas, namely ... 
Conditioning reservoir models on vast data sets
(Doctoral thesis, 20210909)History matching is a valuable process to obtain better models and a more reliable forecast in oil reservoir applications. In such processes, one conditions the simulation models on the observed data from the field. One ... 
Conforming Discretizations of MixedDimensional Partial Differential Equations
(Doctoral thesis, 20180601)Mixeddimensional partial differential equations (PDEs) are coupled equations defined on connected manifolds of different dimensionalities. Two main examples of mixeddimensional PDEs are considered in this dissertation, ... 
Continuous Updating of a Coupled ReservoirSeismic Model Using an Ensemble Kalman Filter Technique
(Doctoral thesis, 20070329)This work presents the development of a method based on the ensemble Kalman filter (EnKF) for continuous reservoir model updating with respect to the combination of production data, 3D seismic data and timelapse seismic ... 
Convective mixing in geological carbon storage
(Doctoral thesis, 20111125)The industrial era has seen an exponential growth in the atmospheric concentration of carbon dioxide (CO2), resulting mainly from the burning of fossil fuels. This can cause changes in the climate that have severe impacts ... 
Derivation and numerical solution of fully nonlinear and fully dispersive water wave model equations
(Doctoral thesis, 20170609)The water wave theory is a classical part of Fluid Mechanics. It has a long scientific history with a great number of mathematical results [10, 32]. The first studies in this field were done by Stokes in 1847 [34]. He ...