Geometrical analysis of structural data collected at high South latitude: A modular arithmetic method that addresses meridional convergence

Abstract

The convergence of meridians toward the South Pole causes unique problems for geometrical comparison of structural geological and geophysical datasets from Antarctica. The true North reference direction ordinarily is used for measuring and reporting vector data (strike, trend) in Antarctica, as elsewhere. However, over a latitude distance of just 100 km at 85° South, the angular difference in the true North direction exceeds 10°. Consequently, when performing a regional tectonic analysis of vector data (strike, trend) for structures such as faults, dike arrays, or geophysical lineaments oriented with respect to North at different sites, it is necessary to rotate the data to a common reference direction. A modular arithmetic function, performed as a spreadsheet calculation, offers the means to unify data sets from sites having different longitude position, by rotation to a common reference direction. The function is SC ≡ SM + ∆L (mod 360), where SC = converted strike; SM = measured strike; ∆L = angle in degrees longitude between reference longitude and study site; and 360, the divisor, is the number of degrees in Earth's circumference. The method is used to evaluate 1) paleomagnetic rotation of the Ellsworth-Whitmore Mountains with respect to the Transantarctic Mountains, and 2) orogenic curvature of the Ross Orogen. Citation: Siddoway C. S. and M. F. Siddoway (2007), Geometrical analysis of structural data collected at high South latitude: A modular arithmetic method that addresses meridional convergence, in Antarctica: A Keystone in a Changing World - Online Proceedings of the 10 th ISAES, edited by A. K. Cooper and C. R. Raymond et al., USGS Open-File Report 2007-1047, Short Research Paper 061, 5 p.; doi: 10.3133/of2007-1047.srp061