PhD defense by Sarouyeh Khoshkholgh

Title: Uncertainty Quantification in Seismic Subsurface Modelling by Informed Proposal Monte Carlo

Abstract: A key feature of optimizing subsurface resource exploration is accurate geophysical modelling. In this regard, associating, combining and integrating petrophysical, geological and geophysical data play a crucial role. To do so, solving probabilistic inverse problems of desired model parameters in the subsurface is used to describe reservoir properties. Subsurface uncertainty quantification is obtained through probabilistic solutions to corresponding geo- statistical and geophysical inverse problems. In geoscience, Monte Carlo sampling methods are widely used in producing solutions for nonlinear inverse problems. A fundamental problem when using Mont Carlo search or sampling algorithms is the inefficiency due to the high computational cost of forward calculations, particularly when dealing with large scale inverse problems. This thesis addresses this issue and describes a new methodology that significantly improves the performance of MCMC algorithms, resulting in more effective uncertainty analysis.

There are a number of algorithms that attempt to guide Monte Carlo sampling by exploring the target distribution while it is being performed. However, many of them are limited by the No-Free-Lunch theorem. According to the No-Free-Lunch theorem, the more information about the problem we add, the more efficient algorithm could potentially be. This study presents a new methodology for the Markov Chain Mont Carlo (MCMC) algorithm designed for highly nonlinear problems with computationally expensive forward calculations and a large number of model parameters.

In this thesis, we first explain Informed Proposal Monte Carlo, in which information about the target distribution is introduced to the sampling procedure by using a global proposal distribution. This can be achieved by finding an approximate posterior distribution and using it as global proposal in MCMC algorithm. This proposal distribution is problem dependent and typically calculated using simplified physics. Afterwards we review some of the most recent, blind and informed MCMC algorithms. Then the theoretical and methodological framework of our approach is presented. We introduce our specific strategy for generating prior models in which image warping is used to perturb the subsurface velocity. Finally, we apply our proposed methodology to the probabilistic problem of full-waveform inversion of seismic data with a large number of model parameters. The results indicate that injecting external information in the form of a global proposal can significantly reduce the convergence time and increase efficiency of the algorithm.

Supervisor
Prof. Klaus Mosegaard, Physics of Ice, Climate and Earth, Niels Bohr, University of Copenhagen

Assessment of Committee
Prof. Markus  Jochum, Physics of Ice, Climate and Earth, Niels Bohr, University of Copenhagen
Prof. Vasily Demyanov, Institute of GeoEnergy Engineering, School of Energy, Geoscience, Infrastructure and Society
Heriot-Watt University 
Lead R&D Geophysicist, Dr. Hanno Klemm, Total 

For at copy of thesis, please contact: Tina Bang-Christensen (tinabang@nbi.ku.dk)