Regression techniques in plate tectonics

We discuss a linearized model to analyze the errors in the reconstruction o f the relative motion of two tectonic plates using marine magnetic anomaly data. More complicated geometries, consisting of several plates, can be ana lyzed by breaking the geometry into its stochastically independent parts an d repeatedly applying a few simple algorithms to recombine these parts. A r egression version of Welch's solution to the Behrens-Fisher problem is need ed in the recombination process. The methodology is illustrated using data from the Indian Ocean. Through a historical perspective we show how improving data density and improving sta tistical techniques have led to more sophisticated models for the Indo-Aust ralian plate. We propose an influence-based regression diagnostic for tectonic data. A ge neralization of the standardized influence matrix of Lu, Ko and Chang is ap plied to study the influence of a group of data points on a subparameter of interest. This methodology could also be used in treatment-block designs t o analyze the influence of the blocks on the estimated treatment effects.