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Abstract. Three-dimensional (3D) stratigraphic modelling is capable of modeling the shape, topology, and other properties of strata in a digitalized manner. The implicit modeling approach is becoming the mainstream approach for 3D stratigraphic modelling, which incorporates both the off-contact attitudes and the on-contact occurrence information of stratigraphic interface to estimate the stratigraphic potential field (SPF) to represent the 3D architectures of strata. However, the magnitudes of SPF gradient controlling variation trend of SPF values cannot be directly derived from the known stratigraphic attribute or attitude data. In this paper, we propose an Hermite-Birkhoff radial basis function (HRBF) formulation, AdaHRBF, with an adaptive gradient magnitude for continuous 3D SPF modeling of multiple stratigraphic interfaces. In the linear system of HRBF interpolant constrained by the scattered on-contact attribute points and off-contact attitude points of a set of strata in 3D space, we add a novel optimizing term to iteratively obtain the true gradient magnitude. The case study shows that the HRBF interpolants can consistently establish accurate multiple stratigraphic interfaces and fully express the internal stratigraphic attribute and attitude. To ensure harmony of the variation of stratigraphic thickness, we adopt the relative burial depth of stratigraphic interface to the Quaternary as the SPF attribute value and propose a new stratigraphical thickness index (STI) to represent the variation trend of stratigraphic thickness in SPF. In addition, the proposed stratigraphic potential field modeling by HRBF interpolants can provide a suitable basic model for subsequent geosciences numerical simulation.

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The growth, sintering, and interaction of cobalt with ceria were studied under ultrahigh vacuum conditions by vapor-deposition of Co onto well-defined CeOx(111) (1.5 < x < 2) thin films grown on Ru(0001). Charge transfer from Co to ceria occurs upon deposition of Co on CeO1.96 and partially reduced CeO1.83 at 300 K. X-ray photoelectron spectroscopy studies show that Co is oxidized to Co2+ species at the cost of the reduction of Ce4+ to Ce3+, at a lesser extent on reduced ceria. Co2+ is the predominant species on CeO1.96 at low Co coverages (e.g., ≤0.20 ML). The ratio of metallic Co/Co2+ increases with the increase in the Co coverage. However, both metallic Co and Co2+ species are present on CeO1.83 even at low Co coverages with metallic Co as the major species. Scanning tunneling microscopy results demonstrate that Co tends to wet the CeO1.96 surface at very low Co coverages at room temperature forming one-atomic layer high structures of Co–O–Ce. The increase in the Co coverage can cause the particle growth into three-dimensional structures. The formation of slightly flatter Co particles was observed on reduced CeO1.83. In comparison with other transition metals including Ni, Rh, Pt, and Au, our studies demonstrate that Co on ceria exhibits a smaller particle size and higher thermal stability, likely arising from strong metal–support interactions. The formed particles upon Co deposition at 300 K are present on the ceria surface after heating to 1000 K. The Co–ceria interface can be tuned by varying the Co metal coverage, the annealing temperature, and the nature of the ceria surface.