Fusion of sparse non-co-located measurements from multiple sources for geotechnical site investigation

A profile of geotechnical properties is often needed for geotechnical design and analysis. However, site-specific data might be characterized as MUSIC-X (i.e., Multivariate, Uncertain and Unique, Sparse, Incomplete, and potentially Corrupted with "X" denoting the spatial/temporal variability), posing a significant challenge in accurately interpreting geotechnical property profiles. Different sources, or types, of data are commonly available from a specific site investigation program, and they are usually cross-correlated, and thus can provide complementary information. This leads to an important question in geotechnical site investigation: how to integrate multiple sources of sparse data for enhancing the profiling of different geotechnical properties. To address this issue, this study proposes a novel method, called fusion Bayesian compressive sampling (FusionBCS), for integrating sparse and non-co-located geotechnical data. In the proposed method, the auto- and cross-correlation structures of different sources of data are exploited in a data-driven manner through a joint sparse representation. Then, profiles of different geotechnical properties are jointly reconstructed from all measurements under a framework of compressive sampling/sensing. The proposed method is illustrated using simulated and real geotechnical data. The results indicate that the accuracy of the interpreted geotechnical property profiles may be significantly improved by integrating multiple sources of site investigation data.