Accessing power-law properties of post-seismic deformation in land movements

The International GNSS Service (IGS) Tide Gauge Benchmark Monitoring (TIGA) Working Group aims at providing accurate positions and long-term rates of change (velocities) of Global Navigation Satellite System (GNSS) stations at or close to tide gauges (GNSS@TG) around the world. These positions and velocities are applied to separate vertical land movements from the mean sea level records derived from tide gauge observations. Therefore, the exact vertical and horizontal velocity components and associated uncertainties are fundamental in sea-level studies where they are employed as vertical and horizontal land movement estimates, respectively.

The University of Luxembourg carried out a reprocessing of a global network of GNSS stations. This was done as part of the activities of the IGS BLT TIGA (British Isles continuous GNSS Facility and University of Luxembourg Tide Gauge Benchmark Monitoring) Analysis Center. This study will focus on the estimation of vertical and horizontal velocities for GNSS stations from the BLT multi-year repro2 solution for which post-seismic deformation was noticed. Besides the linear velocity we also added the post-seismic term in form of logarithmic and exponential functions to the model in order to describe the post-seismic decay as a part of entire time series. This removed the need to exclude the epochs affected by an earthquake prior to the analysis. The indisputable novelty of the applied approach is that the magnitude of post-seismic deformation is being estimated simultaneously with the data model (velocity, seasonal signals and noise) using a Maximum Likelihood Estimation (MLE) approach. If all parameters are determined together artificial biases can be avoided, which may be introduced if the parameters where estimated separately. Moreover, with this approach we obtain the most probable values for the vertical and horizontal velocities and associated uncertainties as well as, the non-linear position changes before and after an earthquake. The Tohoku Mw 9.0 undersea megathrust earthquake off the coast of Japan, which took place on 11 March 2011 was investigated as it caused post-seismic deformation to be seen in the position time series of 20 TIGA stations. We noticed that a long-term velocity, describing the motion of a station, can be significantly affected before and after the earthquake. In this presentation we will introduce how post-seismic deformation should be modeled with a combination of logarithmic and exponential functions while the power-law properties of the time series are also taken into consideration to obtain reliable velocity and uncertainty estimates.