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Welcome to my home page. I hope to provide here an overview of my research and teaching activities as well as some personal information. I have been on the Faculty at Stanford since 1998 and my research has evolved from geostatistics to working on inverse problems and modeling uncertainty in the Earth sciences. My approach is more engineering than mathematics, and therefore more practical than theoretical. Below I have provided a summary and link of the PhD Dissertations that I have advised. These dissertations provide a comprehensive overview of my work. Feel free to send any questions or comments to This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

 
Conditioning surface models to well and thickness data PDF Print E-mail

 

 

by Antoine Bertoncello, PhD

The PDF can be downloaded here.

 
Modeling Uncertainty in Metric Space PDF Print E-mail

by Kwangwon Park, PhD

Modeling Uncertainty in metric space is a relatively new approach to Bayesian modeling with non-Gaussian 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 computation-wise for most Earth Science problems. We reformulate the non-linear inverse problem by defining distances between model outcomes to be equal to the difference in forward model response. A Karhoene-Loeve 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 "pre-image" problem and in this work we develop practical solution for high-dimensional problem via multi-dimensional scaling and prior-consistent 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 distance-based pattern modeling PDF Print E-mail

by Mehrdad Honarkhah, PhD

The PDF can be downloaded here.

 
On the value of information for spatial problems in the Earth Sciences PDF Print E-mail

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.