Spatial distribution estimation by considering the cross-correlation between components with indirect data using Gaussian process regression

Generally, soil properties are measured only at limited locations. To rationally estimate the spatial distribution of soil properties, it is preferable to effectively use all available measurement data, including indirect data. We propose a Gaussian process regression with multiple random fields that considers the cross-correlation between one of the random fields of direct data and indirect data, and show the application to simulated data and actual measured data. In the application, the direct data are of CPT tip resistance (qc), which was obtained within a narrow area, and the indirect data are of shear wave velocity (Vs) obtained by surface wave exploration, which were obtained over a wide area. We estimate the spatial distribution of qc from the limited qc and wide area Vs data. The estimation accuracy of the proposed method is evaluated by cross-validation, and its effectiveness is discussed.