Abstract Site characterization based on measurements is essential for geological and geotechnical engineering. However, measurements are usually limited and sparse because of many limitations, which can hardly be utilized to perform a well site characterization. Therefore, some data fusion methods are commonly utilized to integrate correlated data to improve the performance of site characterization. Among data fusion methods, cokriging is widely utilized to improve the performance of site characterization by integrating measurements of correlated variables. The correlation between correlated variables is expressed by a cross-variogram, which can only be calculated using co-located measurements between correlated variables. However, the measurements in geological and geotechnical engineering are commonly obtained by destructive sampling, which are usually not co-located and cannot be utilized to calculate the cross-variogram. In this study, a Bayesian inference method is developed to tackle this difficulty. The proposed method is illustrated and validated by two real datasets. The results show that the proposed method can estimate a well cross-variogram model, no matter whether the measurements of correlated variables are co-located or not. Moreover, the uncertainty of variogram models and cokriging estimation can be quantified by the proposed method. The proposed method can improve the wide utilization of the cokriging method, which can help characterize geology conditions of geological and geotechnical engineering.

中文翻译：

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基于贝叶斯推理的交叉变异函数概率估计

摘要 基于测量的场地特征对于地质和岩土工程至关重要。然而，由于许多限制，测量通常是有限和稀疏的，很难用于进行井场表征。因此，通常使用一些数据融合方法来整合相关数据以提高站点表征的性能。在数据融合方法中，协同克里金法被广泛用于通过整合相关变量的测量来提高场地表征的性能。相关变量之间的相关性由交叉变异函数表示，该交叉变异函数只能使用相关变量之间的同位测量来计算。然而，地质和岩土工程中的测量通常是通过破坏性采样获得的，它们通常不在同一位置，不能用于计算交叉变异函数。在这项研究中，开发了一种贝叶斯推理方法来解决这个难题。所提出的方法通过两个真实数据集进行了说明和验证。结果表明，无论相关变量的测量值是否共存，所提出的方法都可以估计出良好的交叉变异函数模型。此外，变异函数模型和协同克里金法估计的不确定性可以通过所提出的方法进行量化。该方法可以提高协同克里金法的广泛应用，有助于表征地质和岩土工程的地质条件。所提出的方法通过两个真实数据集进行了说明和验证。结果表明，无论相关变量的测量值是否共存，所提出的方法都可以估计出良好的交叉变异函数模型。此外，变异函数模型和协同克里金法估计的不确定性可以通过所提出的方法进行量化。该方法可以提高协同克里金法的广泛应用，有助于表征地质和岩土工程的地质条件。所提出的方法通过两个真实数据集进行了说明和验证。结果表明，无论相关变量的测量值是否共存，所提出的方法都可以估计出良好的交叉变异函数模型。此外，变异函数模型和协同克里金法估计的不确定性可以通过所提出的方法进行量化。该方法可以提高协同克里金法的广泛应用，有助于表征地质和岩土工程的地质条件。变差函数模型和协同克里金法估计的不确定性可以通过所提出的方法进行量化。该方法可以提高协同克里金法的广泛应用，有助于表征地质和岩土工程的地质条件。变差函数模型和协同克里金法估计的不确定性可以通过所提出的方法进行量化。该方法可以提高协同克里金法的广泛应用，有助于表征地质和岩土工程的地质条件。