Interpolation of extremely sparse geo-data by data fusion and collaborative Bayesian compressive sampling

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.