Comparison of the Results of Stabilization by Tikhonov and TSVD Methods in Three-Dimensional Strain Analysis Using Time Series of Permanent Station GPS (Case Study: Washington)

The simultaneous analysis of the horizontal and vertical of the Earth's crust is one of the achievements of new methods of positioning. This possibility, along with the time series of the GPS permanent stations, makes it easy to understand any changes in the shape of the crust in different directions. In this paper, 19 permanent GPS stations in the region of Washington have been used. By fitting a linear Trend and q periodic signal to these series, the displacement rates were estimated in three directions. According to the results, the accuracy of the horizontal displacement rate is 3.5 times better than the vertical component. Rates are invariant quantities, hence they are used as inputs of the iosoparametric model to provide an accurate interpretation of the tectonic behavior of the region. Using the Picard condition and adding noise to observation, the instability of the problem was proved in this case. TSVD and TSVD were used for stabilization. In TSVD mode, Truncation Number was considered as 5, and only the smallest amount of singular solubility was eliminated. In the Tikhonov model, the stabilization parameters were estimated between 0.022 and 0.61. With the continuation of the calculation process, we see a difference in the results between the two-dimensional and 3D-stabilized. Part of this difference can be due to the fact that the vertical component is not considered, and the other part can be the result of the bias due to the stabilization.