The influence of seasonal signals on the estimation of the tectonic motion in short continuous GPS time-series

TLDR: The methodology can be used to estimate for any station how much the accuracy of the linear trend will improve when one tries to subtract the annual signal from the GPS time- series by using a physical model and it is demonstrated that for short time-series the trend error is more influenced by the fact that the noise properties also need to be estimated from the data.

About: This article is published in Journal of Geodynamics.The article was published on 2010-04-01 and is currently open access. It has received 84 citations till now. The article focuses on the topics: White noise & Noise (signal processing).

Figures

Figure 1: The upper panel shows the North component of the GPS position time-series at CASC. The lower panel shows the same data set after subtraction of a linear trend and a yearly signal.

Figure 2: Power spectral density of the GPS residuals at CASC, North component. The circles denote the spectral density computed from the observations and the solid line is the fitted power-law plus white noise model.

Figure 6: The same as Fig. 5 but with α = 1.3 and σpl/σw = 3.3. Only σpl was estimated from the data.

Figure 4: The difference of the predicted trend errors shown in Fig. 3 computed with and without an annual signal in the design matrix for different noise models.

Frequently asked questions

Q1. What are the contributions in this paper?

In this paper, Bos et al. investigated how temporal correlated noise alters the conclusions of Blewitt and Lavallee ( 2002 ) and showed that the presence of an annual signal has no influence on the accuracy of the linear trend when the observation period is around 1.5, 2.5 and 3.5 years. 

Q2. How much influence do the authors find for power-law plus white noise?

for power-law plus white noise, which is found in most GPS time-series, the authors find minimal influence closer to integer plus a quarter year intervals. 

Q3. What is the likely explanation for the deterioration of the linear trend?

Blewitt and Lavallée (2002) demonstrated that an annual signal within the data deteriorates the accuracy of the estimated linear trend in time-series with an observation time span of a few years, even when this annual signal is taken into account during the estimation process. 

Q4. How can the authors reduce the trend error?

Finally the authors have shown that when the noise model can be simplified to a simple scaling of a priori known covariance matrix, Eq. 5, the underestimation of the trend error and the spread in the predicted trend error is significantly reduced. 

Q5. What is the effect of the power-law noise on the linear trend?

This underestimation caused by the fact that some of the power-law noise is considered to be part of the linear trend by the MLE method which results in smaller residuals. 

Q6. How can the authors estimate the accuracy of the linear trend?

Their results can be used to estimate how much the accuracy of the linear trend will improve when one tries to reduce the annual signal in short GPS time-series by, for example, subtracting atmospheric and hydrological loading values. 

Q7. What is the spectral index of the noise in GPS data?

Caporali (2003) and Williams et al. (2004), among others, have shown that the noise in GPS data can be well described as the sum of white and power-law noise.