T -distributed Random Fields: A Parametric Model for Heavy-tailedWell-log Data1 |
| |
Authors: | Jo R?islien and Henning Omre |
| |
Institution: | (1) Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology, Oslo, Norway;(2) Department of Mathematical Sciences, Norwegian University of Science and Technology, Oslo, Norway |
| |
Abstract: | Histograms of observations from spatial phenomena are often found to be more heavy-tailed than Gaussian distributions, which
makes the Gaussian random field model unsuited. A T-distributed random field model with heavy-tailed marginal probability density functions is defined. The model is a generalization
of the familiar Student-T distribution, and it may be given a Bayesian interpretation. The increased variability appears cross-realizations, contrary
to in-realizations, since all realizations are Gaussian-like with varying variance between realizations. The T-distributed random field model is analytically tractable and the conditional model is developed, which provides algorithms
for conditional simulation and prediction, so-called T-kriging. The model compares favourably with most previously defined random field models. The Gaussian random field model
appears as a special, limiting case of the T-distributed random field model. The model is particularly useful whenever multiple, sparsely sampled realizations of the
random field are available, and is clearly favourable to the Gaussian model in this case. The properties of the T-distributed random field model is demonstrated on well log observations from the Gullfaks field in the North Sea. The predictions
correspond to traditional kriging predictions, while the associated prediction variances are more representative, as they
are layer specific and include uncertainty caused by using variance estimates. |
| |
Keywords: | random fields hierarchical models sampling kriging parameter estimation |
本文献已被 SpringerLink 等数据库收录! |
|