Numerical Modelling of Instantaneous Plate Tectonics

TLDR

The study aims to derive a self‑consistent model of instantaneous relative motions for eleven major plates by jointly inverting spreading rates, fracture‑zone trends, and earthquake slip vectors under the assumption of rigid lithospheric plates. They linearize the inverse problem and solve it iteratively with a maximum‑likelihood method, using linear theory to compute uncertainties in angular velocity vectors and to analyze information distribution, and they also invert island‑chain and ridge trends to assess hot‑spot stability. The analysis shows that Gaussian statistics are adequate, the model satisfies all data thereby supporting the rigid‑plate assumption, resolves slow North–South America motion, and indicates that hot spots have remained stationary relative to each other over the past 10 Myr.

Abstract

Assuming lithospheric plates to be rigid, we systematically invert 68 spreading rates, 62 fracture zones trends and 106 earthquake slip vectors simultaneously to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set. The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable. We then invert the trends of 20 linear island chains and aseismic ridges under the assumptions that they represent the directions of plate motions over a set of hot spots fixed with respect to each other. We conclude that these hot spots have had no significant relative motions in the last 10 My.