Time Dependent Velocity Estimation

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 average position a constant velocity function and a time dependent velocity. These basis function are then esitmated using a damped least squares inversion to find a model for a specific damping parameter. The damping parameter controls the width of the averaging kernel following the Backus and Gilbert method. This provides a physical basis for selecting a damping parameter appropriate for model estimation of time varying velocities.

This technique has several advantages:
  1. it does not assume a functional form for deformation a priori
  2. observations need not be regularly spaced in time
  3. it provides an easy decomposition of any type (color) noise and time-variable signal
  4. it provides a continuous representation of time-variable site motion.