Errors in plate rotations as described by covariance matrices and their combination in reconstructions

Abstract

We use covariance matrices to describe the errors in plate rotations and to combine the contrbutions of individual plate pairs for plate reconstructions. First, for the rotation of a pair of plates the covariance matrix which describes the errors in the rotation is defined. Then we show how individual covariance matrices can be combined in a circuit of successive plate rotations to assess the errors in a plate reconstruction. Using the covariance matrix for accumulated errors from a sequence of rotations, we can determine the uncertainties in the position of selected points on one plate in the plate circuit to another that is assumed to be fixed. As an example, the position of the Pacific plate relative to North America is reconstructed at chron 6 (20 Ma). This choice is made to allow a direct comparison with published error assessments. Using the accumulated covariance matrix, we find similar uncertainties in the positions of their selected points on the Pacific plate. As a further test, this reconstruction is repeated using seafloor spreading data that directly relate Antarctica to Africa, bypassing the link of India. This eliminates the largest source of error in the plate circuit, that due to the short ridge segment between Africa and India. This revised, shortened circuit results in generally smaller errors in the positions of points on the Pacific plate. The covariance matrices of the two alternative circuits are used to construct the optimal estimate and its associated error. The optimal estimate and its error region intersect the two alternative reconstructions and their error regions.