Statistical tests for closure of plate motion circuits

Abstract

The standard method of testing whether data describing the relative motion of three plates meeting at a triple junction are consistent with rigid plate tectonics uses the condition of plate circuit closure: the Euler vectors or angular velocities describing the relative motion of each plate pair must sum to zero. Deviations from closure suggest that the data are systematically in error, or that the plate boundaries have been identified incorrectly, or that the plates are non‐rigid. We examine two methods, one based on a chi‐square test and the other based on an F‐ratio test, of testing whether plate motion circuits close. We find the latter test is useful, but the former is of limited value because of the common practice of systematically overestimating errors in plate motion data. We apply the F‐ratio test to Minster and Jordan's data for the boundaries dividing the Pacific, Cocos, and Nazca plates, which prove consistent with plate circuit closure. Application of the test to their data for the boundaries dividing the Australian, Antarctic, and African plates shows nonclosure even after deletion of data from the Carlsberg Ridge, which recently has been suggested to divide the African plate from an Indo‐Arabian plate. This nonclosure suggests systematic errors in the data or internal deformation of one or more of the plates meeting at the Indian Ocean Triple Junction.