A MATLAB/GNU Octave toolbox for computation of velocity and strain rate field from GNSS coordinate time series

A MATLAB toolbox, also compatible with GNU Octave, was developed in order to allow a user not necessarily expert in programming to calculate the strain rate field of an area by means of a procedure with a high level of automation starting from coordinate time series. The results can be used to investigate the crustal tectonic deformations of the studied area. These steps are implemented:

• time series download from a data repository, e.g. the Nevada Geodetic Laboratory (NGL), or another similar database (the download function can be easily edited to allow the use of input time series having different format);
• calculation of the station velocities by means of the Maximum Likelihood Estimation (MLE) method, including modeling of offsets, outliers, noise and periodic components. The MLE modeling is carried out by using the external package Hector (Bos et al., 2013. J. Geod., 87, 351-360), automatically called by means of a specifically developed MATLAB function;
• estimation of Common Mode Error and, if necessary, its removal from time series of some stations and recalculation of the corresponding velocities.
• calculation of the strain rate field on a regular grid with the modified least squares method, in which a scale factor can be introduced to define the locality of the deformation analysis. Besides the strain rate field, the toolbox provides the corresponding uncertainty estimation and geometric evaluation of the significance of the results;
• visualization of the results for their interpretation for scientific purposes, including the map of principal strain and the contour plots of change in area (or dilatation), engineering shear normalized to the change in area, second invariant of the strain, prevailing eigenvalue, corresponding uncertainties and geometric significance.

The toolbox, which is available free of charge to any interested user, is characterized by considerable flexibility, and can be easily adapted to different data sources.

The toolbox was recently used in order to refine the rates of active crustal deformation in the upper plate of subduction zones in the specific case of the E-dipping West Crati fault (Calabria) and to evaluate the convergence rate in the Main Thrust Fault (also called Sicilian Basal Thrust) north to Hyblean Plateau (South-Eastern Sicily).