Variogram, Correlation and Kriging Estimation (VarioCorreKrigE)

VarioCorreKrigE is a Python-based geostatistical toolkit developed for simple to advanced spatial analysis, with particular emphasis on earthquake engineering and natural‑hazard applications rather than full geophysical forward modelling. The framework integrates experimental variogram and correlogram estimation, parametric model fitting, auto‑ and cross‑dependence analysis, grouped and multivariate workflows, and kriging-based spatial interpolation within a consistent and extensible environment. While engineered primarily for analysing spatially distributed variables such as ground‑motion intensities, residuals, site-condition proxies, and other engineering-relevant datasets, the package also accommodates both distance‑based and angular dependence structures. Importantly, VarioCorreKrigE also supports traditional geophysical spatial‑estimation techniques including cokriging, collocated cokriging, and related multivariate interpolation methods which can be used as exploratory tools or as part of more formal dependence‑modelling workflows. In addition, the framework incorporates advanced statistical capabilities such as variogram and correlogram bootstrapping for pseudo‑posterior parameter estimation, as well as a full implementation of empirical Bayesian kriging (EBK) for propagating parameter uncertainty into spatial predictions. By combining robust estimation procedures, flexible covariance and correlation modelling, and practical visualisation tools, VarioCorreKrigE provides a reproducible platform for characterising spatial variability, quantifying dependence, and supporting engineering decision‑making in seismic and broader natural‑hazard contexts.