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Published June 2014 | Published
Journal Article Open

Detecting transient signals in geodetic time series using sparse estimation techniques


We present a new method for automatically detecting transient deformation signals from geodetic time series. We cast the detection problem as a least squares procedure where the design matrix corresponds to a highly overcomplete, nonorthogonal dictionary of displacement functions in time that resemble transient signals of various timescales. The addition of a sparsity-inducing regularization term to the cost function limits the total number of dictionary elements needed to reconstruct the signal. Sparsity-inducing regularization enhances interpretability of the resultant time-dependent model by localizing the dominant timescales and onset times of the transient signals. Transient detection can then be performed using convex optimization software where detection sensitivity is dependent on the strength of the applied sparsity-inducing regularization. To assess uncertainties associated with estimation of the dictionary coefficients, we compare solutions with those found through a Bayesian inference approach to sample the full model space for each dictionary element. In addition to providing uncertainty bounds on the coefficients and confirming the optimization results, Bayesian sampling reveals trade-offs between dictionary elements that have nearly equal probability in modeling a transient signal. Thus, we can rigorously assess the probabilities of the occurrence of transient signals and their characteristic temporal evolution. The detection algorithm is applied on several synthetic time series and real observed GPS time series for the Cascadia region. For the latter data set, we incorporate a spatial weighting scheme that self-adjusts to the local network density and filters for spatially coherent signals. The weighting allows for the automatic detection of repeating slow slip events.

Additional Information

© 2014 American Geophysical Union. Received 26 FEB 2014; Accepted 22 MAY 2014; Accepted article online 27 MAY 2014; Published online 10 JUN 2014. We thank two anonymous reviewers for improving the quality of this paper. Bryan Riel is supported by a NASA Earth and Space Science Fellowship. GPS data used in this paper can be found at the SOPAC data archive, http://sopac.ucsd.edu/dataArchive/, and the Central Washington University archive, http://www.geodesy.cwu.edu/.

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