大数据集条件模拟的半锥化策略
Half-tapering strategy for conditional simulation with large datasets
摘要：
高斯条件实现通常用于各种地球科学应用中的风险评估和规划。条件实现可以通过首先创建无条件实现，然后通过克里金法进行后置处理来获得。许多有效的算法可用于第一步，因此瓶颈在于第二步。我们建议仅在条件化步骤中使用锥度协方差（Half-Taper或HT方法），而不是使用期望协方差（F方法）或锥形协方差（T方法）进行条件模拟。这使得能够加速计算并减少调节步骤的存储器需求，而且还能够在实现中保持正确的短尺度变化。一个标准的基础上的模拟的均方误差，以帮助预测的相似性HT到F。此外，一个指数是用来预测的条件步骤的克里格矩阵的稀疏性。讨论了锥度函数选择的一些准则。一系列的1D，2D和3D标量响应函数的分布进行了比较F，T和HT方法。所得到的分布表明，与T相比，HT与F具有更好的相似性。
英文摘要：
Gaussian conditional realizations are routinely used for risk assessment and planning in a variety of Earth sciences applications. Conditional realizations can be obtained by first creating unconditional realizations that are then post-conditioned by kriging. Many efficient algorithms are available for the first step, so the bottleneck resides in the second step. Instead of doing the conditional simulations with the desired covariance (F approach) or with a tapered covariance (T approach), we propose to use the taper covariance only in the conditioning step (Half-Taper or HT approach). This enables to speed up the computations and to reduce memory requirements for the conditioning step but also to keep the right short scale variations in the realizations. A criterion based on mean square error of the simulation is derived to help anticipate the similarity of HT to F. Moreover, an index is used to predict the sparsity of the kriging matrix for the conditioning step. Some guides for the choice of the taper function are discussed. The distributions of a series of 1D, 2D and 3D scalar response functions are compared for F, T and HT approaches. The distributions obtained indicate a much better similarity to F with HT than with T.
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