Statistical comparison of palaeomagnetic directional records from lake sediments

Summary. This paper presents three statistical methods for testing the reproducibility or compatibility of palaeomagnetic directional records in undated cores of sediment. These methods are based on: (a) the intrinsic equations (curvature and torsion as functions of arc‐length) of the curve defining changes in direction; (b) an F ‐test derived from multiple linear regression theory and (c) the construction and comparison of confidence bands. All methods utilize a projection of palaeomagnetic unit vectors on to the tangent plane to their mean direction. Since preliminary alignment to a common depth scale is necessary both for method (b) and for subsequent pooling of data, some theoretical results are presented for this problem, allowing for the possibility of missing segments in either core. Methods (b) and (c) are applied to two cores from Loch Lomond, Scotland. Both methods show that, after suitable relative rotation and alignment, these palaeomagnetic directional records are indeed compatible, demonstrating that the Loch Lomond sediments can provide reliable palaeosecular variation data of igh quality.