Conditioning surface models to well and thickness data 



by Antoine Bertoncello, PhD
The PDF can be downloaded here. 
Modeling Uncertainty in Metric Space 



by Kwangwon Park, PhD
Modeling Uncertainty in metric space is a relatively new approach to Bayesian modeling with nonGaussian prior and computational complexity in the forward model. In this work, we provide an alternative approach to the traditional McMC framework for sampling the posterior, a framework that is not practical computationwise for most Earth Science problems. We reformulate the nonlinear inverse problem by defining distances between model outcomes to be equal to the difference in forward model response. A KarhoeneLoeve expansion is developed that allows creating new models from the prior that have zero distance to the field data (exact matching) or a specified likely distance (the traditional likelihood in Bayesian modeling). The problem of drawing models from the prior which have certain distance to other models is in image analysis termed the "preimage" problem and in this work we develop practical solution for highdimensional problem via multidimensional scaling and priorconsistent optimization.Ample examples demonstrate that the method has sampling properties similar to the rejection sampler but at a fraction of the computational cost.
The PDF can be downloaded here. 

Stochastic simulation of patterns using distancebased pattern modeling 



by Mehrdad Honarkhah, PhD
The PDF can be downloaded here. 
On the value of information for spatial problems in the Earth Sciences 



by Whitney Trainor, PhD
The value of information questions depends on three components 1) the prior, i.e. how much information is known prior to gathering the data/information, 2) the reliability of the data source in resolving what is unknown and 3) the decision question at hand. The VOI problem has been used in many fields of engineering, but for reasons of spatial and computational complexity, has not been developed much in the Earth Sciences. In this thesis we discuss several approaches to determine VOI for tackling real Earth modeling problems 1) the prior is often a geological constrained by what he Earth looks like geologically and can be modeled using geostatistical algorithms, 2) the reliability requires forward modeling on realistic geological models of the response of the (geophysical) data source in question and 3) the decision often involves making spatial decisions.
The PDF can be downloaded from the department database. 
