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

Abstract

S U M M A R YA 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.

Cenozoic evolution of the Tan–Lu Fault Zone (East China)—Constraints from seismic data

“…14B), the Hawaiian, Foundation, Cobb and Marquesas chains all reflect this change in their geometry. This change was also noted and discussed by many investigators (e.g., Cox and Engebretson, 1985;Andrews et al, 2006).…”

Plate Tectonics

“…By using combined evidence from preserved magnetic lineations, and geologic data from accreted terranes such as 'Argo Land' and the rules of plate tectonics (Cox and Hart, 1986), it is possible to constrain the overall geometries of Tethys mid-ocean ridges quite well, as demonstrated by Heine et al (2004). As mentioned earlier, Molnar and Stock (1987) first showed that the hot spots in the Pacific appear to have moved relative to the set of hot spots used to determine Indo-Atlantic APM; however, Andrews et al (2006) found that this relative motion is only significant prior to 68 Ma. In their model, the breakup of the supercontinent Pangaea occurs in the central North Atlantic around 200 Ma (Labails et al, 2010) followed by the formation of the Pacific Plate about 190 Ma .…”

Abyssal hill deflections at Pacific‐Antarctic ridge‐transform intersections

“…We made an attempt to evaluate the effects of absolute plate motion on the stress field at the Menard and Pitman RTIs. In Appendix C we show that this effect, if any, on changes in size and number of J-shaped abyssal hill curvatures at the intermediate spreading PAR cannot be quantified due to the limited multibeam bathymetry data set and significant uncertainty in the considered absolute Pacific plate motion models [Andrews et al, 2006;Koppers et al, 2001;Wessel and Kroenke, 2008].…”

“…Figure C1. (a) The absolute Pacific plate motion relative to a fixed spot in the mantle according to three models (brown, blue, and red lines) [Andrews et al, 2006;Koppers et al, 2001;Wessel and Kroenke, 2008] and migration of the PAR relative to the mantle (orange, green, and purple lines) calculated by combining the finite rotations of the three absolute Pacific plate motion models with the rotations for the motion of the PAR relative to the Pacific plate (black lines representing synthetic flow lines plotted relative to the Pacific and Antarctic plates annotated with magnetic anomaly isochrons) [Croon et al, 2008] [43] The azimuth of the absolute Pacific plate migration relative to a fixed spot in the mantle according to the Koppers et al [2001], Andrews et al [2006] and WK08-A [Wessel and Kroenke, 2008] models is similar to the azimuth of the Pacific plate relative to the Antarctic plate [Croon et al, 2008] during most of the evolution of Menard FZ (Figure C1b). The significant change in azimuth of Pacific absolute plate motion was placed at 43 Ma at the landmark Hawaii-Emperor chain bend by Koppers et al [2001].…”

“…We assumed symmetric spreading of the PAR and summed the relative plate motion model [Croon et al, 2008], using half-angle rotations, with the absolute Pacific plate motion rotations of Koppers et al [2001], Andrews et al [2006] and WK08-A [Wessel and Kroenke, 2008] ( Figure C1a). The ridge migration rate at the latitude of Menard FZ has been fast at about 40 to 50 mm/yr since 48 Ma (∼chron C21o).…”