Abstract
It is an indisputable fact that the GNSS time series contain colored noise. However, we find that colored noise greatly affects parameter estimation of general linear trajectory models. For the post-seismic timescale parameters, ignoring the colored noise will increase the iteration times of the calculation parameters by 10–11 times. For parameters of coefficients, ignoring colored noise will obviously increase the deviation of parameter estimates. To overcome the above problems, we first estimate colored noise by maximum likelihood estimation. Then, the nonlinear least square algorithm with colored noise as the stochastic model is used to calculate timescale parameters. Finally, general linear trajectory models are constructed by using the calculated timescale parameters, and their optimal parameters are estimated by maximum likelihood estimation. The method is validated by lots of simulation experiments. The results show that the number of iterations is reduced by 90% compared with the traditional method; the deviation for parameters of coefficients decreased significantly. These methods are applied to the 2011 Tohoku-Oki earthquake. The results show that a nonlinear least square algorithm based on an appropriate stochastic model can provide strong constraints for timescale parameters. Among them, the timescale parameters of logarithmic terms decay exponentially with the increase in the distance from the epicenter; timescale parameters of exponential terms increase linearly northward. On the other hand, colored noise is an important factor affecting the extraction of seismic signals. For co-seismic displacement, ignoring colored noise will seriously underestimate small amplitude co-seismic signals. In the northern of Tohoku with the smallest co-seismic displacement, ignoring the colored noise will underestimate the co-seismic displacement by 20 mm. For post-seismic displacement, the float caused by ignoring colored noise is up to 500 mm, and the larger float (> 200 mm) is randomly distributed in the spatial domain. Therefore, it is necessary to consider the influence of colored noise on post-seismic deformation.
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Data Availability
The GNSS data used in this research have been obtained from Nevada Geodetic Laboratory at http://geodesy.unr.edu/.
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Acknowledgements
The research is supported by the National Natural Science Foundation of China (41774041); We thank the Nevada Geodetic Laboratory for providing GNSS data. Some figures are plotted using the public domain Generic Mapping Tools (GMT).
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Ren, A., Xu, K., Shao, Z. et al. Effect of the 2011 Tohoku-Oki earthquake on continuous GNSS station motions. GPS Solut 27, 50 (2023). https://doi.org/10.1007/s10291-022-01386-1
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DOI: https://doi.org/10.1007/s10291-022-01386-1