Determination Of Ocean Tide Loading Displacements In New Zealand Using GPS Technique

The gravitational attractions of the Sun and the Moon cause the periodic redistribution of ocean mass,and the elastic response of the solid earth derived from mass variation on surface called the ocean tide loading(OTL)displacement.The OTL displacement can be computed by convoluting global ocean tide model with Green's function which calculated from Earth model,the OTL displacement can reach up to tens of centimeters and is closely related to the internal structure of the Earth at the load point.Meanwhile,the Global Navigation and Satellite System(GNSS)can measure OTL displacements with sub-millimeter accuracy.Thus,the contemporary observation techniques can be used not only as a supplement(or judging criteria)to current ocean tide models,but also to explore the internal structure of the Earth.Based on the above background,measurements from the tide gauge stations in New Zealand are used to validate the modeling accuracy of the global ocean tide models,which include FES2014 b,TPXO9-Atlas,DTU10,EOT11 A,and HAMTIDE11 a.The results show that the five ocean tide models in New Zealand are consistent with the measured results.Subsequently,the five global ocean tide models mentioned above and three Earth models,including PREM,STW105 and AK135,are used to calculate the OTL displacement.We compare and analyze the OTL displacements calculated by different combined models.The results of comparisons show that the FES2014 b and TPXO9-Atlas models not only agree better with the tide gauge results,but also have the smallest differences in OTL displacements,so it can be proved that the accuracy of the above two models is the highest in New Zealand.For the M2 tide constituent,the differences of OTL displacements between different Earth models are more complicated than that between ocean tide models,and the differences of models have no significant influence on O1 tide constituent,which need further discussion in the future.At the same time,the accuracy of GNSS observation technology for OTL displacement has reached sub-millimeter level.In this paper,the OTL displacement parameters of eight tidal constituents are solved according to the “static method” with more than 12 years of continuous global positioning system(GPS)data at 188 stations,and the vector differences are calculated and statistically analyzed from the model values.Except for the K1 and K2 constituents,which are affected by GNSS-related orbit errors,the root-mean-square(RMS)error of the remaining six constituents is less than 0.5 mm in the horizontal components,the RMS error between the FES2014 b and the measurements in the vertical component is the smallest,which only about 0.4 mm,and the RMS error of the Q1 constituent in the three components is only 0.2 mm.The residuals between modeled and predicted OTL displacements also show that FES2014 b have the smallest residuals in the three components.For the Hauraki Bay,which has the complex coastline,the residuals reduced by 3 mm when use the latest model FES2014 b and TPXO9-Atlas,indicating that the modeling accuracy and the resolution of ocean tide models have an important influence on the OTL displacement.The spatial consistency in different components for different models can be found according to the residuals.In addition to the comparative analysis of tidal models,the effects of different Earth models on the OTL displacement had also been analyzed based on the residuals.For the M2 constituent,the Earth model which considering the lateral isotropy has a minimum RMS error of only 0.3 mm in the east component,while the maximum RMS error exceeds 0.4 mm in the north component,and the RMS of AK135 is the largest in the vertical component while the RMS size of the other three models is comparable.For the remaining seven tide waves,there is no significant difference between different earth models.The residuals between observations and the different models show that the residuals not only differ in magnitude but also in phase for each station in the horizontal components,while the residuals only differ in magnitude in the vertical components,which may be due to the lateral anisotropy of the Earth's upper mantle.At the same time,when the mean regional OTL displacement residuals are substracted,the RMS reduction of the O1 constituent is consistent with the theoretical modeling error of the solid tide.Therefore,this regional spatial consistency may be due to the solid tide modeling error.Finally,considering the anelastic characteristics of the real earth,the residual least squares principle is used to constrain the shear modulus and thickness of the asthenosphere using the OTL displacement observations.When the asthenosphere shear modulus decreases by about 10% and the thickness increases to 70-275 km,the minimum RMS between the modeling value calculated by the constrained model and the observed value is only 0.39 mm.In addition,the residuals of OTL displacement at some stations along the western coast become larger after considering the asthenosphere anelasticity.This may be due to the differences in the internal structure of the two plates in New Zealand,but further verification is needed.