Time Series Analysis Technique
The basic concept of the time series analysis technique, which is still under development, is to create a unique basis function for each data point. The function which is built contains an initial position a constant velocity function and a time dependent velocity. These basis function are then inverted to find their contribution to the smooth spline results. In this technique there is a damping factor which controls how much the time dependent velocity is allowed to vary over short time scales. This problem would consume incredible computing resources for even a small subset of CGPS stations due to the very large number of basis functions. One technique to improve computing performance is to generate ortho-normal basis functions from the original ones and to use only the most significant of these for the inversion. This can be employed for CGPS daily solutions because they do not generally vary dramatically over short time scales. The user is allowed to control both the damping and the ortho-normal cut-off used. For detailed studies the parameters can be allowed to vary and the best fitting solution to the observed data can be found using common inversion techniques.
This technique has several advantages:
- it does not assume a functional form for deformation a priori
- observations need not be regularly spaced in time
- it provides an easy decomposition of white noise and time-variable signal
- it provides a continuous representation of time-variable site motion.
TS Analysis Simple Example
Matlab images of a simple example of the TS Analysis
