基于训练图像马尔可夫网格先验的贝叶斯岩性/流体类预测模型
A Bayesian model for lithology/fluid class prediction using a Markov mesh prior fitted from a training image
摘要：
我们认为，贝叶斯模型的观测振幅随偏移距变化（AVO）数据反演成岩性/流体类，并特别研究如何选择的先验分布的岩性/流体类的影响反演结果。两个不同的先验分布被认为是，一个简单的手动指定的马尔可夫随机场前与一阶邻域和马尔可夫网格模型与一个更大的邻域估计从训练图像。它们被选择来模拟水平连通性和岩性/流体类的垂直厚度分布，并在北海的海上碎屑岩油藏进行比较。我们结合先验与相同的线性高斯似然函数的基础上卷积线性Zoeppritz关系和估计的属性，由此产生的两个后验分布从这些分布与梅特罗波利斯-黑斯廷斯算法模拟。先验对岩性/流体类的边缘后验概率的影响是明显可观察的，但适度。然而，在后验实现中，先验对连通性的重要性要强得多。马尔可夫网格先验的较大邻域使其能够比一阶邻域马尔可夫随机场先验更好地识别和建模连通性和曲率。因此，我们得出结论，后实现的马尔可夫网格先验的基础上出现更高的横向连接，这是地质上合理的。
英文摘要：
We consider a Bayesian model for inversion of observed amplitude variation with offset (AVO) data into lithology/fluid classes, and study in particular how the choice of prior distribution for the lithology/fluid classes influences the inversion results. Two distinct prior distributions are considered, a simple manually specified Markov random field prior with a first order neighborhood and a Markov mesh model with a much larger neighborhood estimated from a training image. They are chosen to model both horisontal connectivity and vertical thickness distribution of the lithology/fluid classes, and are compared on an offshore clastic oil reservoir in the North Sea. We combine both priors with the same linearised Gaussian likelihood function based on a convolved linearised Zoeppritz relation and estimate properties of the resulting two posterior distributions by simulating from these distributions with the Metropolis-Hastings algorithm. The influence of the prior on the marginal posterior probabilities for the lithology/fluid classes is clearly observable, but modest. The importance of the prior on the connectivity properties in the posterior realisations, however, is much stronger. The larger neighborhood of the Markov mesh prior enables it to identify and model connectivity and curvature much better than what can be done by the first order neighborhood Markov random field prior. As a result, we conclude that the posterior realisations based on the Markov mesh prior appear with much higher lateral connectivity, which is geologically plausible.
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