Statistical tools for estimating and combining finite rotations and their uncertainties

and the uncertainties in the data. Using a heuristic description of non-linear least squares, we show how the methodology is analogous to standard linear regression. We generalize the method for reconstructing a single plate boundary to solve for the closure of a triple junction, and we present a simple way to combine the covariance matrices of individual rotations to estimate the uncertainties in their product, and show how to derive the uncertainties in the reconstructed points. Since any statistical analysis depends upon assumptions about the errors in the data, we discuss the assumptions inherent in the proposed methodology, and the limitations which result from these assumptions. One of them (referred to as the ‘equal-kappas’ assumption) is especially troublesome when two or more rotations, based on di V erent data distributions, are combined. From similar problems arising in linear regression, we propose a method to solve the plate reconstruction problem when the equal-kappas assumption is not tenable. Finally, we briefly review the sources of error in the magnetic anomaly and fracture-zone crossings that are inverted to derive plate reconstructions, and show how their uncertainties can be evaluated. A series of examples illustrates how these tools, implemented in software, can be used to solve or to test various plate geometries involving a single plate boundary, a triple junction and a combination of both.

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