Sigseg: a tool for the detection of position and velocity discontinuities in geodetic time-series

The detection of discontinuities in geodetic data is an ever more important topic due to both the influence of discontinuities on the results of models and analyses, and to the very meaning of discontinuities in physical phenomena. We consider and describe a mathe- matical model, originally formulated for the approximation of images by smooth functions, in one dimension (1D). The model had been designed to smooth the data while pre- serving and detecting its discontinuities following a vari- ational approach. A second and more complex model for the approximation of images by functions with smooth first derivatives is also available. This second model had been designed to smooth the data while preserving and detecting the discontinuities of the data, but also those of the first derivative. Such interesting features suggest the chance to apply this second model to 1D geodetic data, in particular for the detection of discontinuities and velocity changes in position time-series rather than for signal smoothing. The sigseg (signal segmentation) program implements the two variational models in 1D and is presented with applications to geodetic data. The essential mathematical elements are sketched, and some details on the numerical implementa- tion are given.