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Estimating GPS velocity fields and strain-rate fields


Multiscale estimation of GPS velocity fields (pdf)
Geophysical Journal International, v. 179, p. 945-971, 2009
Carl Tape, Pablo Muse, Mark Simons, Danan Dong, Frank Webb

We present a spherical wavelet-based 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 time-dependent 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.


Horizontal velocity field in southern California, derived from continuous GPS time series.
These data were used in Tape et al. (2009) to estimate continuous velocity fields using spherical wavelets.


Vertical velocity field in southern California, derived from continuous GPS time series.
These data were used in Tape et al. (2009) to estimate continuous velocity fields using spherical wavelets.
The large blue circles in the Great Valley primarily represent hydrological subsidence.


Multiscale estimation of the three-component GPS velocity field in southern California.



Multiscale representation of the strain-rate field in southern California,
derived directly from the estimated multiscale velocity field.


Examples of spherical wavelet basis functions used in the estimation problem.

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