Effects of Lateral Inhomogeneity and Non-hydrostatic Pre-stress of Earth
on Tidal Gravity
Abstract
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. 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 for the first time presents
expressions for calculating the effects of non-hydrostatic pre-stress on
tidal gravity 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 non-hydrostatic pre-stress are
calculated using the real Earth model GyPSuM. 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 M2 semidiurnal gravimetric factors is obtained, and varies
from −0.16% to 0.09% compared to those in a layered Earth model. M2
gravimetric factors measured by superconducting gravimeters worldwide
are collected and compared to the theoretical results of this study.
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.