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Geomathematics is extremely important in geosciences, particularly in the geology. The key for any geomathematical analysis is the definition of a typical model to be applied for further prognosis, either through deterministic or stochastic approaches. The selection of the appropriate procedure is presented in this paper. Two different geomathematical subfield datasets were used in subsurface geological mapping and palaeontology and different biostatistics applications, representing important geomathematical subfields in the Croatian geology. The different subsurface interpolation methods tested, validated and recommended for application were used to obtain the best possible outcome in reservoir modelling, in the cases with small datasets. Cross-validation may be chosen as the main selection criteria, applied to the Croatian part of the Pannonian Basin System (CPBS). Recent advances in biostatistics applied in palaeontology and case studies from Croatia are also presented, where biometric studies are of significant importance in fossil biota. Data, methods and problems in geosciences are vast subjects, and address a wide spectrum of fundamental science. Because geology includes subsurface and surface geology, and very different datasets regarding variable and number of data, we have chosen here two representative case study groups with original samples from Northern Croatia. Subsurface mapping has been presented on limited petrophysical datasets from the Northern Croatian, Miocene, hydrocarbon reservoirs. Biostatistics have been presented on very different samples, allowing us to achieve paleoenvironmental reconstructions of the size of relevant fossils, such as dinosaurs or other species and their paleoenvironments. All examples highlight examples of the valuable application of geomathematical tools in geology. The results, cautiously validated and correlated with other, non-numerical (indicator, categorical) geological knowledge, are of enormous assistance in creating better geological models.

Recent Advances in Geomathematics in Croatia: Examples from Subsurface Geological Mapping and Biostatistics