Uncertainties in plate reconstructions relative to the hotspots; Pacific-hotspot rotations and uncertainties for the past 68 million years

Abstract

SUMMARY A method previously used for estimating the uncertainty in rotation of a plate relative to the hotspots is shown to be insufficient because of the neglect of the uncertainty in one of the three degrees of freedom of a rotation. Two new methods for estimating best-fitting rotations and associated uncertainties for the rotation of a plate relative to the hotspots are presented. Both methods require a priori estimates of the uncertainties in the locations of individual hotspots and their ancient tracks for a particular age. The use of a priori uncertainties permits the hypothesis of hotspot fixity to be tested. The first method, the two-hotspot method, leads to simple geometrical interpretations of best-fitting rotations and of the eigenvectors and eigenvalues of the appropriate covariance matrix. This simplicity comes at the cost of using only two hotspots and their associated tracks with assumed equal circular uncertainties. The second method, the N-hotspot method, allows use of an arbitrary number of hotspots (≥2), with unequal elliptical uncertainties. This generality and power comes at the cost of losing the simple geometrical interpretation of the first method. Elliptical uncertainties are generally more appropriate because hotspot tracks are less well known along-strike than across-strike because of gaps and uncertainties in ages along the tracks. When both methods are applied to the estimate of the Pacific-hotspot rotation since the age of the Hawaiian‐Emperor elbow, using the tracks of both the Hawaiian and Louisville hotspots, they produce similar rotations and similar uncertainties. The N-hotspot method is further applied to estimate Pacific-hotspot motion at six additional ages from 10.9 Ma to 67.7 Ma, corresponding to the ages of key magnetic anomalies used in global plate reconstructions. The goodness of the resultant fit shows that the assigned uncertainties and assumption of hotspot fixity are mutually consistent. The pre-elbow (i.e. pre-47.9 Ma or Emperor) pole of rotation is shown to differ significantly from the post-elbow (i.e. post-47.9 Ma or Hawaiian) pole of rotation. Moreover, rotation over the past 47.9 Ma is shown to have occurred in at least three statistically distinct stages, from 47.9 to 20.1 Ma, from 20.1 Ma to ≈6 Ma, and from ≈6 Ma to the present. The change in pole position at 20.1 Ma is accompanied by a highly significant 50 per cent increase in the rate of rotation of the Pacific plate relative to the hotspots. These encouraging results suggest that the new methods can be used to improve and to quantify plate motions relative to the hotspots for a wide variety of applications.