A Method for Bounding Uncertainties in Combined Plate Reconstructions

We present a method for calculating the radial axis. Other pole positions about which uncertainties in plate reconstructions that does finite rotations bring magnetic anomalies and not describe the uncertainty in terms of fracture zones from one plate into near uncertainties in pole positions and rotation coincidence with those of the other plate will angles. If a fit of magnetic anomalies of the surround the point describing this "best" pole and same age and fracture zones that were active as angle. (Although the best rotation and its transform faults at that time can be found, such a uncertainty can be described in this way, one reconstruction can be perturbed and degraded by cannot, however, treat the best pole and angle as small rotations about each of three orthogonal a vector, even if it seems to be represented as axes (partial uncertainty poles). If the one.) The angles associated with those pole uncertainty in the reconstruction is a consequence positions close to the positions of the 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 reconstructed magnetic anomalies and fracture zones will be larger than those for pole positions far from these data [e.g., Stock and Molnar, 1983]. Thus the family of rotations representing the uncertainties in the pole position and rotation angle will form a plunging blimp-shaped volume in latitude-longitude-angle space. The point representing the "best" rotation should lie toward the center of the blimp but may not be exactly the center. All other acceptable pole positions and angles would then lie within the blimp. The uncertainty of a rotation, as represented by this three-dimensional blimp-shaped region of the Pacific plate with respect to North America at latitude-longitude-angle space, is difficult to 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.