Analysing non-coaxial folding effects in the Small Circle Intersection method

The Small Circle (SC) tools analyse the stereographic tracks (small circles) followed by the palaeomagnetic vectors during folding processes. Working with interfolding and synfolding remagnetizations, the Small Circle Intersection (SCI) method allows finding the best solution of grouping that should correspond with the remagnetization direction. Once this is known, it is possible to determine the magnetization age as well as the degree of bed tilting at this moment. The SC tools are based on some assumptions, among which the coaxiality between the different deformation events is the one addressed in this work (i.e. absence of vertical axis rotations, VARs, or differential horizontal axis rotations, dHARs). This assumption is based on the necessity of knowing the rotation axis for folding after the acquisition of the remagnetization, and SC tools consider the bedding strike as this axis, something that is only accomplished under coaxial folding. In order to explore how non-coaxiality affects the solutions derived from the SC methods, we first (i) identify the variables that control these errors through simple models that only consider two theoretical palaeomagnetic sites, after that it is possible (ii) to derive the mathematical relationships between them. Finally, we (iii) simulate errors derived from the use of SC tools using a population of 30 palaeomagnetic sites recreating different possible scenarios with VARs and dHARs in nature.