Regular spacing of salt structures as a Rayleigh–Taylor signature: edge-corrected point-pattern and structure-factor analysis of the U.S. Gulf Coast and North German basins

This record contains the manuscript, analysis code, derived datasets, figures and numerical results for a study of the map-view spatial arrangement of salt structures in two salt provinces: the U.S. Gulf Coast (USGS gcdiapirg) and the North German Basin (BGR InSpEE). Using edge-corrected spatial point-pattern statistics (Clark–Evans nearest-neighbour index, pair correlation function g(r), Ripley's L) together with the structure factor S(k) and number variance, and testing against complete-spatial-randomness and density-gradient (inhomogeneous-Poisson) null models, the study shows that within coherent loading-driven provinces salt-structure populations are significantly regularly spaced (Clark–Evans R = 1.10–1.47, p ≈ 0.002), with hard-core exclusion and a 12–15 km characteristic spacing — the map-view signature of Rayleigh–Taylor wavelength selection combined with salt-withdrawal exclusion. Regularity strengthens with salt thickness (Glückstadt Graben > central basin > Gulf shelf). The order is robust at short and intermediate range; long-range hyperuniformity cannot be confirmed because the intrinsic basin density gradient masks the long-wavelength limit. Pooling across a whole basin, or selecting only the mature-diapir sub-class, both spuriously return clustering, so correct inference requires single-province analysis of the complete structure population. Contents: analysis code (Python / NumPy / SciPy / Matplotlib), derived coordinate datasets (CSV), figures (PDF/PNG), numerical results, and the manuscript (PDF + LaTeX source). Development repository: https://github.com/Ruqing1963/salt-structure-spacing Data sources and licences: U.S. Gulf Coast salt diapirs — USGS data release "Salt Diapirs in the Gulf Coast" (gcdiapirg), doi:10.5066/P9KH3WB4 (public domain). North German salt structures — BGR "InSpEE-Salzstrukturen" (© BGR, Hannover, 2015; open geodata licence / geonutzv; base mapping after Reinhold, Krull & Kockel 2008). Only derived structure centroids are redistributed. Analysis code is released under the MIT licence.