In geotechnical or geological engineering, geo-data interpolation based on measurements is often needed for engineering design and analysis. However, measurements are sometimes extremely sparse (e.g., several, or even just a few, data points) because of limited access to the subsurface and the cost of tests. It is, therefore, difficult to properly interpolate the measurements. On the other hand, multiple data sources (e.g., standard penetration tests, SPT, and cone penetration tests, CPT) often exist in engineering practice, and data fusion methods (e.g., cokriging) have been developed to leverage the correlation among multiple data sources for interpolation of sparse geo-data. Performance of cokriging depends on proper modeling of spatial variability using variogram models. However, the construction of proper variogram models requires many measurement data points. Therefore, it is very challenging to properly interpolate extremely sparse geo-data due to the difficulty in obtaining suitable variogram models. In this study, a novel data fusion method, called collaborative Bayesian compressive sampling (Co-BCS), is proposed to tackle this problem. Equations of the proposed Co-BCS method are derived, and the method is illustrated using real data. The results show that the proposed method not only properly interprets extremely sparse geo-data by integrating correlated secondary data sources but also quantifies the associated interpolation uncertainty simultaneously.

在岩土工程或地质工程中，工程设计和分析通常需要基于测量的地理数据插值。然而，由于对地下的有限访问和测试成本，测量有时极其稀疏（例如，几个或什至几个数据点）。因此，难以适当地对测量值进行插值。另一方面，工程实践中经常存在多个数据源（例如，标准渗透测试，SPT和圆锥渗透测试，CPT），并且已经开发了数据融合方法（例如，cokriging）以利用多个数据源之间的相关性。用于稀疏地理数据的插值。共克里金的性能取决于使用变异函数模型对空间变异性进行正确建模的能力。然而，适当的变异函数模型的构建需要许多测量数据点。因此，由于很难获得合适的变异函数模型，因此很难对非常稀疏的地理数据进行适当的插值非常困难。在这项研究中，提出了一种称为协作贝叶斯压缩采样（Co-BCS）的新型数据融合方法来解决此问题。推导了所提出的Co-BCS方法的方程，并使用实数据说明了该方法。结果表明，该方法不仅可以通过集成相关的二次数据源来正确解释极稀疏的地理数据，而且可以同时量化相关的插值不确定性。在这项研究中，提出了一种称为协作贝叶斯压缩采样（Co-BCS）的新型数据融合方法来解决此问题。推导了所提出的Co-BCS方法的方程，并使用实数据说明了该方法。结果表明，该方法不仅可以通过集成相关的二次数据源来正确解释极稀疏的地理数据，而且可以同时量化相关的插值不确定性。在这项研究中，提出了一种称为协作贝叶斯压缩采样（Co-BCS）的新型数据融合方法来解决此问题。推导了所提出的Co-BCS方法的方程，并使用实数据说明了该方法。结果表明，该方法不仅可以通过集成相关的二次数据源来正确解释极稀疏的地理数据，而且可以同时量化相关的插值不确定性。