A method for bounding uncertainties in combined plate reconstructions

We present a method for calculating uncertainties in plate reconstructions that does not describe the uncertainty in terms of uncertainties in pole positions and rotation angles. If a fit of magnetic anomalies of the same age and fracture zones that were active as transform faults at that time can be found, such a reconstruction can be perturbed and degraded by small rotations about each of three orthogonal axes (partial uncertainty poles). If the uncertainty in the reconstruction is a consequence of independent, small, but acceptable, rotations about these axes, then the uncertainties in reconstructed points will be elliptical in shape. The dimensions and orientation of such ellipses will depend upon the magnitudes of the perturbing rotations and upon the relative geometry of the partial uncertainty poles and the points in question. In a sequence of rotations, each rotation will contribute an elliptical region of uncertainty for each reconstructed point, and these ellipses can be combined as independent statistical quantities to obtain a confidence ellipse for the sequence of rotations. As a test, we calculated uncertainties for three points on the Pacific plate with respect to North America at the time of anomaly 6 (20 Ma). The computed uncertainties are similar in shape to those that we previously obtained for a sequence of marginally acceptable rotations, but the major axes of the ellipses presented here are about 25% shorter.