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On rotation of frames and physical vectors: an exercise based on plate tectonics theory

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Abstract

The mathematical interaction between the simultaneous rotation of both a coordinate frame and a set of physical vectors in that frame is covered and theoretically and empirically explained. A practical example related to the secular motion of the pole determined using recent GPS results is addressed. A least-squares adjustment is introduced to determine a possible displacement of the geodetic north pole of the frame caused by plausible changes in the coordinates of the observing stations defining the frame due to the rotation of the plates on which these stations are located. Two examples of GPS networks are investigated both referred to the latest definition of the IGS08 geodetic frame. The positioning and velocities of the points were exclusively obtained using GPS data as published by the International GNSS Service (IGS). The first case comprises the complete GPS/IGS network of global stations; the second one assumes the closest GPS/IGS stations to the now discontinued International Latitude Service network. The results of this exercise hints at the possibility that the secular global rotation of the frame caused by plate rotations should be accounted for in order to rigorously determine the true absolute velocities referred to the IGS frame before the actual velocities of the rotation of the plates using GPS observations are published.

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Acknowledgments

The authors thank their NGS colleagues S. Hilla, X. Li, and D. Smith for reviewing the draft of the manuscript and for their comments and suggestions. The improvements recommended by two anonymous reviewers and the Editor of the journal greatly enhanced the comprehension of the final version of the article and are sincerely appreciated.

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Authors and Affiliations

  1. Spatial Reference System Division, National Geodetic Survey, NOAA, Silver Spring, MD, 20910, USA

    Tomás Soler

  2. Department of Civil Engineering, National Taiwan University, No. 1, Sect. 4, Roosevelt Road, Taipei, 10617, Taiwan

    Jen-Yu Han

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  1. Tomás Soler
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  2. Jen-Yu Han
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Correspondence to Tomás Soler.

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Soler, T., Han, JY. On rotation of frames and physical vectors: an exercise based on plate tectonics theory. GPS Solut 21, 345–361 (2017). https://doi.org/10.1007/s10291-016-0521-5

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  • DOI: https://doi.org/10.1007/s10291-016-0521-5

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