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Smooth paths for a long track.

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posted on 15.12.2021, 18:24 by William S. D. Wilcock, Rose S. Hilmo

An example of smoothed paths that are fitted to a track comprising 355 call locations between 0021 UT and 1834 UT on December 13, 2011. (a) Smoothed tracks obtained using the method of Eq (15) with three choices of smoothing weight after discarding the 21 outlying locations. Call locations are shown as faint plus symbols with an ellipse illustrating the average location uncertainty. The mean squared normalized spatial misfit is 2.49, 2.07 and 1.81 for smoothing weights α = 108, 106 and 104, respectively. Also show is a smoothed track based on averaging locations temporally by weighting with a Gaussian function with a 20-minute standard deviation. (b) Tracks obtained using the double-difference method of Eq (19). The starting data set comprises 13,174 double-difference times and is constructed by linking each call to up to 8 calls within the next hour if there are four common stations. The solutions were obtained with 5 iterations at each smoothing weight and with poorly fitting double difference times discarded after 3 iterations if the absolute misfit exceeded three times the assumed uncertainty. Totals of 11,999, 11,683 and 11,625 difference times were used in the final solutions for smoothing weights of β = 10, 2, and 0.5, respectively. The mean variances of the double difference time misfits normalized to their assumed uncertainties are 0.58, 0.44, and 0.41. (c-d) Speed as a function of time corresponding to the tracks shown in (a) and (b), respectively.