Mathematical and geological approaches to minimizing the data requirements for statistical analysis of heterogeneity: summary technical progress report Page: 11 of 23
This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
to an MRF without resorting to such artifices as embedded variograms. Small-scale
continuous MRFs might also be superposed on large-scale discrete MRFs to reproduce
the effects of continuous variations in depositional processes that typically occur
between episodes of abrupt changes in depositional environment. For example, a
large-scale discrete MRF could be used to describe such events as changes in climatic
regime or tectonic activity, while small-scale continuous MRFs within each feature of
the large-scale field could characterize deposits produced by changes in stream
discharge. Examination of Figures 1 and 2 suggest that MRFs offer a promising
method of synthesizing realistic geologic structures.
C. Comparison of MRF Models to Other Stochastic Models
There are a number of advantages of MRF models over other stochastic models.
Unlike traditional stochastic models, which rely on subjective variogram analysis to
estimate correlation scale, Markov parameters can be determined objectively on the
basis of hypothesis testing using independent samples extracted from the observed field.
In addition, the pattern-generating process, although specified locally, gives rise to a
global pattern that can be easily controlled. Disadvantages of MRFs include the
intrinsic difficulty of using analytical methods to determine model characteristics
because of the combinatorial nature of the fields and the large fields typically required
to produce reliable estimates of the Markov parameters (Cross and Jain, 1983). Despite
these disadvantages, it is anticipated that MRFs will more realistically capture the
geologic characteristics of a field than would be possible using continuous random field
simulation architectural element analysis.
Cross, G.R. and A.K. Jain, 1983, 'Markov Random Field Texture Models', IEEE Trans.
Pattern Analysis and Machine Intelligence, v. PAMI-5, p. 25-39.
Metropolis, N., A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and
E. Teller, 1953, 'Equations of State Calculations by Fast Computing Machines', J.
Chem. Phys.,v. 21, p. 1087-1091.
Spitzer, F., 1971, 'Markov Random Fields and Gibb's Ensembles', Amer. Math. Mon.,
v. 78, p. 142-154.
Upcoming Pages
Here’s what’s next.
Search Inside
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
Mathematical and geological approaches to minimizing the data requirements for statistical analysis of heterogeneity: summary technical progress report, report, December 31, 1991; United States. (https://digital.library.unt.edu/ark:/67531/metadc683775/m1/11/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.