Multiscale estimation of GPS velocity fields (pdf) Geophysical Journal International, v. 179, p. 945971, 2009 Carl Tape, Pablo Muse, Mark Simons, Danan Dong, Frank Webb We present a spherical waveletbased
multiscale approach for estimating a spatial velocity
field on the sphere from a set of irregularly spaced
geodetic displacement observations. Because the adopted
spherical wavelets are analytically differentiable,
spatial gradient tensor quantities such as dilatation
rate, strain rate and rotation rate can be directly
computed using the same coefficients. In a series of
synthetic and real examples,we illustrate the benefit of
the multiscale approach, in particular, the inherent
ability of the method to localize a given deformation
field in space and scale as well as to detect outliers
in the set of observations. This approach has the added
benefit of being able to locally match the smallest
resolved process to the local spatial density of
observations, thereby both maximizing the amount of
derived information while also allowing the comparison
of derived quantities at the same scale but in different
regions.We also consider the vertical component of the
velocity field in our synthetic and real examples,
showing that in some cases the spatial gradients of the
vertical velocity field may constitute a significant
part of the deformation. This formulation may be easily
applied either regionally or globally and is ideally
suited as the spatial parametrization used in any
automatic timedependent geodetic transient detector.

Code available for
download: The Matlab codes associated with this estimation procedure are part of the compearth repository on github. They can be downloaded from github as a zipped file or using git from the command line. Please email me with corrections or suggestions. 