Intersections of remanence small circles: new tools to improve data processing and interpretation in palaeomagnetism

Abstract

S U M M A R YIntersections of remanence small circles are increasingly used in palaeomagnetism to determine the palaeofield direction from synfolding remanences. The approach ['small circle intersection (SCI) method'] presupposes that remanence small circles from sites tilted to different directions intersect in a common point, which is assumed to represent the palaeofield direction. The SCI method is not restricted to synfolding remanences. It can be applied also to derive the palaeofield direction from pre-folding remanences, in addition to tilt correction and as a cross-check for fold tests. However, the SCI method has specific requirements and does not work in all cases. The suitability of data sets and reliability of palaeofield estimates have to be assessed carefully and always against the background of local geology. This paper examines the occurrence and distribution of SCI as a tool of judgement: first, a data set is most suitable and a palaeofield estimate by SCI most reliable, when most of the theoretically possible intersections are realized and, in addition, clearly grouping in a narrow region. Second, the small circles that greatly determine the result of SCI, are identified by the highest number of intersections they have with the others. These criteria allow a systematic investigation of SCI estimates upon stability and dependencies. Moreover, SCIs can be an indicator of irregular, unexpected tectonic settings. When the intersections disperse strongly although significant bedding strike differences are given, relative rotations or other unexpected displacements are likely to have occurred. If so, the SCI estimate will be invalid and probably biased, however, also Fisher mean calculation and most fold tests will be affected. In this case, the SCIs can help to separate the data into subsets valid for Fisher statistics and SCI methods. The other possibility is to use tentative reconstructions to infer the true sequence of tilts and rotations and correct the data adequately.

Widespread Cretaceous secondary magnetization in the High Atlas (Morocco). A common origin for the Cretaceous remagnetizations in the western Tethys?

“…The 95% confidence circle is also represented. Further explanation has been given by Waldhör & Appel (2006). The curve in the A contours shows the expected palaeomagnetic directions at the Imilchil area from the GAPWP in Africa coordinates ).…”

“…Because the secondary magnetization is broadly syntectonic, directions obtained before or after tectonic correction cannot be directly used. The small circle intersection (SCI) method of Shipunov (1997) and Waldhör & Appel (2006) allows us to calculate the characteristic direction of a synfolding remagnetization. This method assumes that during tilting, the direction of magnetization rotates around a horizontal axis parallel to the bedding strike and then the magneti- zation vector follows a small circle trajectory in its rotation around the bedding strike.…”

“…Furthermore, the method assumes that no vertical-axis rotations occurred. The statistical solution is obtained by minimizing the sum A= Σ│α M │ of the angular distances (α M ) between the direction and each small circle (see Waldhör & Appel 2006). This method has been successfully used for finding the remagnetization characteristic direction in Mesozoic basins in Iberia (Soto et al 2008(Soto et al , 2011Casas et al 2009;Gong et al 2009).…”

Pre‐Cenomanian vs. Cenozoic folding in the High Atlas revealed by palaeomagnetic data

“…() in Bathonian to Albo‐Cenomanian red beds, the ChRM component in the Central High Atlas corresponds to a widespread Cretaceous remagnetization that occurred between 80 and 110 Ma, most likely at 100 Ma. This age was calculated by comparing the remagnetization direction obtained by the small circle intersection (SCI) method (Waldhör and Appel, ) with the global apparent polar wander path (GAPWP) in Africa coordinates (Moussaid et al ., ; Torres‐López et al ., ), while also considering the normal polarity of remagnetization within the Cretaceous superchron. The hysteresis parameters of the analysed limestones are in the Superparamagnetic‐Single domain mixing zone of the Day plot (Torres‐López et al ., ), typical of chemically remagnetized limestones (Dunlop, ).…”

Introduction: Palaeomagnetism in fold and thrust belts: new perspectives

“…Tauxe & Watson 1994;McFadden 1998;Enkin 2003), but mathematical approaches to the fold test do not consider phenomena such as folding kinematics. While some authors have already considered this problem (Cairanne et al 2002;Delaunay et al 2002;Waldhör & Appel 2006;Villalaín et al 2015), further advances in this regard need to be accomplished. † Understanding the architecture of rotated areas -understanding of the spatial and temporal variability of rotational patterns in fold and thrust belts is still in its infancy.…”