PlatEMotion: a Matlab® Tool for Geodetic Reference Frame Definition

Abstract

An important concept related to plate tectonics theory is the internal rigidity of tectonic plates together with Euler’s theorem, which allows modelling the relative motion of plates quantitatively. Roughly speaking, plates can be viewed as rigid caps on the surface of a sphere. The motion of a plate on a sphere can be described by a rotation about a virtual axis that passes through the centre of the sphere (Euler’s theorem). This implies that an angular velocity vector originating at the centre of the Earth can describe motions of plates. The most widespread parameterization of such a vector is using latitude and longitude to describe the location where the rotation axis cuts the surface of the Earth, and a rotation rate that corresponds to the magnitude of the angular velocity. Formally, the latitude and longitude of the angular velocity vector constitute the so called ‘Euler pole’. Here, we describe the main features of the developed software tool, called PlatE-Motion (PEM), which allows calculating both the expected velocity value for any point located on the Earth providing a Euler pole (direct problem) and inferring the Euler pole parameters by inverting the observed velocities at a set of sites located on a rigid block (inverse problem). PEM is developed in Matlab® framework and is designed for easy-to-use file exchange with the GAMIT/GLOBK software package [Herring et al., 2006], and has a user-friendly graphical user interface (GUI). The file formats of the data used by PEM are not only restricted to the GAMIT/GLOBK file formats, but they can also be simple ASCII files generated from other kind of software. The tool is available for the scientific community. The interested user can freely obtain it by simply contacting the author