1. Comment concerning ‘The rotation group in plate tectonics and the representation of uncertainties of plate reconstructions’ by T. Chang, J. Stock and P. Molnar
- Author
-
Michael Stefanick and Donna M. Jurdy
- Subjects
Plate tectonics ,Geophysics ,Geochemistry and Petrology ,Pacific Plate ,Mathematical analysis ,Covariance ,Ellipse ,Geodesy ,Pseudovector ,Ellipsoid ,Stock (geology) ,Mathematics ,Rotation group SO - Abstract
We wish to make a few comments on Chang et al.’s paper. The use of covariance matrices or their geometric counterpart error ellipses to describe rotation errors is not a new idea. For present-day plate motion models Chase (1978) and Minster & Jordan (1978) used this description with angular variables, but these are easily converted to lengths. We believe that we (Jurdy & Stefanick 1987, referred to as J&S) were the first to treat the full three-dimensional problem of representing and combining rotation errors as tensors including optimal estimates. Chang et al.’s paper does not discuss any of these contributions. Moreover, the authors factor rotations into a mean rotation followed by a set of perturbing rotations and the latter are treated statistically. This separation is artificial and obscures the geometric content of a description of errors and does not allow a comparison of alternative estimates or the formation of an optimal estimate if they are independent. We wish to go into detail on these points. We defined our fit of rotations so that there would be an exact fit for one rotation (Stock & Molnar 1983) and then found those rotations which would correspond to an rms misfit of 10 km at the endpoints of the common boundary or at a sequence of points along the common boundary. (The results would be slightly different in the two cases.) This was done so that we could compare our method for combining errors with Stock & Molnar’s method of partial uncertainty rotations which, for combining errors, was combinatorial and required 74 rotation combinations. The agreement was very good. That was our purpose. We made no attempt to make real picks of magnetic anomalies and to estimate the individual errors and make a x 2 fit. If this were done there would be no exact fit and we would have found the rotation which gave the best fit as well as the set of rotations which gave acceptable values for x2. A rotation or a set of rotations is most intuitively represented by an axial vector or set of axial vectors ending in some error ellipsoid. If we have several estimates of a rotation due to alternative chains or different authors then we can imagine several ellipsoids (hopefully intersecting) and if the estimates are independent we can combine the results and obtain an optimal estimate and corresponding error ellipsoid which will roughly coincide with the intersection of the original ellipsoids. Geometrically this is straightforward. Representing the reconstruction of Stock & Molnar (1983) and Molnar & Stock (1985) in our description (J&S), we illustrated the combination of errors for two different chains of reconstructions for the Pacific plate relative to the North American for chron 6, 20 Ma
- Published
- 1992
- Full Text
- View/download PDF