Regression Techniques in Plate Tectonics

Abstract

We discuss a linearized model to analyze the errors in the reconstruction of the relative motion of two tectonic plates using marine magnetic anomaly data. More complicated geometries, consisting of several plates, can be analyzed by breaking the geometry into its stochastically independent parts and repeatedly applying a few simple algorithms to recombine these parts. A regression version of Welch’s solution to the Behrens-Fisher problem is needed 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 statistical techniques have led to more sophisticated models for the Indo-Australian plate.

We propose an influence­based regression diagnostic for tectonic data. A generalization of the standardized influence matrix of Lu, Ko and Chang is applied 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 to analyze the influence of the blocks on the estimated treatment effects.