Inversion Methodology

  • A. John HainesEmail author
  • Lada L. Dimitrova
  • Laura M. Wallace
  • Charles A. Williams
Part of the SpringerBriefs in Earth Sciences book series (BRIEFSEARTH)


We explain the theory and implementation of the inversion methodology. Our initial grid is based on the locations of the GPS sites resulting in VDoHS rates dependent only on nearby values of observed GPS velocities. We create VDoHS rate basis functions on this grid and refine the grid to solve for the corresponding velocities. These velocity responses are used to invert the observed GPS velocities using Bayesian methodology based on the maximum entropy principle. We constrain the VDoHS rates to be as small as consistent with the observations, while limiting the short wavelength variations in the VDoHS rates. The resultant solution fits the statistically significant variations in GPS observations while ignoring the noise-dominated short wavelengths. The primary issues affecting the quality of the inversion for discrete GPS data are observational uncertainty and sample spacing.


Inversion methodology Theory Implementation VDoHS rate basis functions Localized VDoHS rates Finite elements Boundary conditions Bayesian methodology Maximum entropy principle Solution resolution 


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • A. John Haines
    • 1
    Email author
  • Lada L. Dimitrova
    • 2
  • Laura M. Wallace
    • 2
  • Charles A. Williams
    • 3
  1. 1.GNS ScienceDunedinNew Zealand
  2. 2.Institute for GeophysicsUniversity of TexasAustinUSA
  3. 3.GNS ScienceAvalonNew Zealand

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