Journal of the Geodetic Society of Japan

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We derive the Euler vectors describing the relative plate motions from 558 rates of change of Global Positioning System (GPS) baseline lengths among 34 stations. These rates, which were obtained by Tsutsumi (1995), are for the period from July 1992 to August 1994. Fixing the Pacific plate, we seek for the Euler vectors describing the motions of the North America, Eurasia, Australia and Africa plates relative to the Pacific plate. We make two types of models, namely, rigid (R) and non-rigid (NR) models. In R-model intraplate deformations are not taken into account, whereas in NR-model they are considered by simultaneously estimating the local motions of 24 stations such as those located in plate boundary zones due to intraplate deformations. The GPS-derived Euler vectors obtained here describing the motions of the North America, Eurasia and Africa relative to the Pacific both in R-and NR-models are significantly different from the corresponding ones in NUVEL-1A. Our poles of these relative motions lie about 20°, at maximum, west-northwest-north-northwest of the corresponding NUVEL-1A poles. Our angular velocities of these relative motions are larger than the corre sponding NUVEL-1A velocities by approximately 02°/m.y. On the other hand, the Euler vectors for the Australia-Pacific relative motion both in R- and NR-model agree with NUVEL-1A within 95% confidence level, though their associated errors are larger than those of the Eulervectors for other relative motions. The local station motions due to intraplate deformations are generally consistent with those expected from the interactions among the plates . Some stations, however, exhibit large local motions, which indicate that significant intraplate deformations are taking place even in the regions far away from plate boundaries .

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All the parameters to be estimated in a geodetic observation model before the GPS era were continuous. Thus the conventional Gauss-Markoff model has been in the core of geodetic estimation theory. GPS carrier phase observables are very precise but contain integer unknowns—GPS carrier phase ambiguities. Although mixed geodetic observation models and integer programming have been implicitly used in GPS ambiguity resolution, they have never been established systematically as a challenging observation model for further theoretical investigation and as a mathematically solid optimization model in geodesy. The purposes of this paper are thus to: (ii) define various real-integral geodetic observation models; and (i) introduce integer programming as a theoretical basis to deal with estimation of real-valued and integer unknowns. Theoretically, the advantages of using integer programming include: (ii) searching for the solution is smartly carried out automatically so that many non-promising points will not be tested. Thus it should outperform any trial-and-error methods currently used in GPS ambiguity resolution; and (uA) a searching bounded box is not required so that the possibility of excluding the correct solution from the pre-selected bounded box is completely avoided. Preliminary results are given to demonstrate how integer programming works.

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