T-distributed Random Fields: A Parametric Model for Heavy-tailedWell-log Data1
T-distributed Random Fields: A Parametric Model for Heavy-tailedWell-log Data1
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DOI：
10.1007/s11004-006-9050-z
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发表时间：
2007-01
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影响因子：
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通讯作者：
J. Røislien;H. Omre
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文献类型：
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作者：
J. Røislien;H. Omre
空间现象观测值的直方图通常比高斯分布具有更重的尾部，这使得高斯随机场模型不适合。定义了具有重尾边缘概率密度函数的AT分布随机场模型。该模型是熟悉的 Student-T 分布的推广，并且可以给出贝叶斯解释。增加的可变性表现为交叉实现，与内实现相反，因为所有实现都是类似高斯的，并且实现之间的方差不同。 T-分布随机场模型易于分析处理，并发展了条件模型，为条件模拟和预测提供了算法，即所谓的T-克里金法。该模型与大多数先前定义的随机场模型相比具有优势。高斯随机场模型是 T 分布随机场模型的特殊极限情况。当随机场的多个稀疏采样实现可用时，该模型特别有用，并且在这种情况下显然有利于高斯模型。 T 分布随机场模型的特性在北海 Gullfaks 油田的测井观测中得到了证明。这些预测对应于传统的克里金预测，而相关的预测方差更具代表性，因为它们是特定于层的，并且包括因使用方差估计而引起的不确定性。
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. AT-distributed random field model with heavy-tailed marginal probability density functions is defined. The model is a generalization of the familiar Student-Tdistribution, 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. TheT-distributed random field model is analytically tractable and the conditional model is developed, which provides algorithms for conditional simulation and prediction, so-calledT-kriging. The model compares favourably with most previously defined random field models. The Gaussian random field model appears as a special, limiting case of theT-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 theT-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.