On the application of non-linear optimization algorithms for an advanced estimation of Local Solid Earth Tides (LSET) by GNSS solutions to be used as possible precursors of seismic events

In this  work  we plan to study local deviations from  Solid Earth Tides (L-SET) adopted by the IERS-2010 model. The study is  performed exploiting the coordinates of about 100 stations worldwide estimated by GNSS technique. The coordinates solutions, expressed both in XYZ and  local NEU, is achieved over a time series 20 years long at least and with a sampling rate in turn of 1 day (1D) and 3 hours (3H). The computations were performed in Precise Post Processing mode (PPP), switching off the IERS-2010 tides model. In practice, the study consists of estimating the Love and Shida numbers of (L-S) SET, station by station. The 1D  were used to estimate L-S of long periodic tides: 18.6, half-year, monthly 13.6 and 13.3 days; while 3H data were helpful for diurnal and semi-durnal tides. The L-S estimation is done using two different numerical approaches: the nonlinear Levenberg-Marquardt least squares and the Gradient Descent and the Gauss-Newton algorithms. This investigation is proving to be particularly compelling because, since L-S define the level of rigidity of the Earth layers. For these reasons they could be deemed as potential seismic precursors. The comparison between the two types of approaches needs to understand what is the more reliable numerical approach   in terms or robustness and solution stability.