dc.description.abstract | We have been given a two-dimensional image of a geological
structure. This structure is used to construct a three-dimensional
statistical model, to be used as prior knowledge in the analysis
of seismic data. We consider two classes of discrete lattice
models for which efficient simulation is possible; sequential
Markov random field (sMRF) and Markov mesh random field (MMRF). We
first explore models from these two classes in two dimensions,
using the maximum likelihood estimator (MLE). The results indicate
that a larger neighbourhood should be considered for all the
models. We also develop a second estimator, which is designed to
match the model with the observation with respect to a set of
specified functions. This estimator is only considered for the sMRF
model, since that model proved to be flexible enough to give
satisfying results. Due to time limitation of this thesis, we
could not wait for the optimization of the estimator to converge.
Thus, we can not evaluate this estimator. Finally, we extract
useful information from the two-dimensional models and specify a
sMRF model in three dimensions. Parameter estimation for this model
needs approximative techniques, since we only have given
observations in two dimensions. Such techniques have not been
investigated in this report, however, we have adjusted the
parameters manually and observed that the model is very flexible
and might give very satisfying results. | |