A single-chain-based multidimensional Markov chain model for subsurface characterization |
| |
Authors: | Weidong Li Chuanrong Zhang |
| |
Institution: | (1) Department of Geography, Kent State University, Kent, OH 44242, USA |
| |
Abstract: | Multidimensional Markov chain models in geosciences were often built on multiple chains, one in each direction, and assumed
these 1-D chains to be independent of each other. Thus, unwanted transitions (i.e., transitions of multiple chains to the
same location with unequal states) inevitably occur and have to be excluded in estimating the states at unobserved locations.
This consequently may result in unreliable estimates, such as underestimation of small classes (i.e., classes with smaller
than average areas) in simulated realizations. This paper presents a single-chain-based multidimensional Markov chain model
for estimation (i.e., prediction and conditional stochastic simulation) of spatial distribution of subsurface formations with
borehole data. The model assumes that a single Markov chain moves in a lattice space, interacting with its nearest known neighbors
through different transition probability rules in different cardinal directions. The conditional probability distribution
of the Markov chain at the location to be estimated is formulated in an explicit form by following the Bayes’ Theorem and
the conditional independence of sparse data in cardinal directions. Since no unwanted transitions are involved, the model
can estimate all classes fairly. Transiogram models (i.e., 1-D continuous Markov transition probability diagrams) are used
to provide transition probability input with needed lags to generalize the model. Therefore, conditional simulation can be
conducted directly and efficiently. The model provides an alternative for heterogeneity characterization of subsurface formations.
|
| |
Keywords: | Conditional independence Conditional simulation Pickard random field Subsurface formation Transition probability Transiogram |
本文献已被 SpringerLink 等数据库收录! |
|