The Effect Of Earth's Lateral Inhomogeneity And Non-hydrostatic Prestress On Tidal Gravity

Tide is closely related to the human activities,and measured by various modern techniques.Tidal signal,on the one hand,is regarded as background field and removed from gravity or deformation observations.On the other hand,tidal response reflects the rheology properties of the Earth's internal materials,thus tidal analysis is a vital solution to investigate the internal structure of the Earth.The misfit between the theoretical and measured values of the tidal response,with the development of the measurement techniques,has been more and more emphasized.The misfit suggests that the tidal theory needs further development,which is based on accurate measurements.Tidal theory for a three-dimensional Earth model stipulates that non-hydrostatic pre-stress arises from the transition from a spherically-symmetrical model to an asymmetrical model when introducing asymmetrical density increments.Molodenskiy(1980)and Fu&Sun(2007)studied the effects of laterally inhomogeneous seismic wave velocity and density on tidal gravity,respectively.The contribution of non-hydrostatic pre-stress on tidal gravity has been neglected in previous studies since the effects of density increments are assumed to be smaller than those of rheology parameter increments.This study presents analytical expressions for calculating the effects of incremental stress on tidal gravity with a new approach and develops the tidal theory for a three-dimensional Earth model.The expressions are verified with the simple ocean-land model after which the effects of incremental stress are calculated using the real Earth model GyPSuM(Simmons et al.,2010).The results suggest that although the effects of non-hydrostatic pre-stress are less than those of seismic wave velocity disturbance,the contribution to final results is significant and should not be neglected.By considering the collective contributions of seismic wave velocity disturbance,density disturbance,and non-hydrostatic pre-stress,the global theoretical variation of semidiurnal gravimetric factors is obtained,and varies from-0.16%to 0.09%compared to those in a layered Earth model.M2 tidal gravimetric factors measured by superconducting gravimeters worldwide are collected and compared to the theoretical results of this study(Boy et al.,2003;Sun et al.,2019).Theoretical values generated by the three-dimensional tidal theory for 11 of 14 stations show an improved match to measurements compared to those of traditional theory,which further verifies the accuracy of the formulae presented by this study.One important procedure of gravity data processing is to make the tidal corrections.Sound tidal corrections rely on accurate tidal gravimetric factors.The present study selects data from 12 gPhone gravimeter stations and 3 superconducting gravimeter stations for the period between 2009 and 2015 distributed across the China's mainland.Based on these data,the distribution of M2 tidal gravimetric factors over China is obtained.The corresponding theoretical values of the M2 wave provided by the DDW99 solid Earth tide model(Dehant et al.1999)and the CSR4.0 ocean tide model(Eanes&Bettadpur 1996)are estimated.The results suggest that the measurements and theoretical values of the M2 wave are close,with an average misfit no greater than 0.6%for most regions of China 's mainland,although the misfit is relatively large,about 1.1%,in northeast China.According to the three-dimensional tidal theory and the correction effects on the M2 gravimetric factors at Lhasa,Lijiang,and Wuhan,where the 3 superconducting gravimeters are located,the current study selects the best fitting three-dimensional earth model,namely the GyPSuM,for China's mainland.The theoretical values of the tidal gravimetric factors while considering three-dimensional inhomogeneities are calculated.The results show that the changes of gravimetric factors caused by lateral inhomogeneity across China vary from-0.07%to 0.09%.