Effects of lateral inhomogeneity in a spherical Earth on gravity Earth tides

Abstract

Molodenskiy (1977, 1980) presented the disturbance method to deal with the effect of a lateral inhomogeneous structure on tidal gravimetric factors. Those studies introduced expressions to calculate the effects caused by seismic waves, but ignored the contribution of lateral density changes. The present study develops the theory by reformulating the expressions with new notation and calculation. We present novel expressions for computing the effects of lateral density inhomogeneity and introduce a new three‐dimensional lateral inhomogeneous Earth model (Zhao, 2001) to compute these effects. Our numerical results show that the effects of density are of the same level as those of seismic waves: they are not negligible. The effects of the lateral inhomogeneous structure calculated for the real three‐dimensional inhomogeneous model are much less, by a factor of about 0.2, than those of the simple Ocean‐Land model presented in Molodenskiy and Kramer (1980). Collecting contributions from the seismic wave and density models, we obtain the completed total effect of the real three‐dimensional inhomogeneous Earth structure on semidiurnal gravimetric factors, with a magnitude of about −0.16 to 0.1%. This result is less than, but almost of the same order as that of Earth’s elliptical effect (ca. 0.7%; Dehant, 1995). Finally, we calculate the corresponding effects on tidal gravity for all three kinds of Earth tide: semidiurnal, diurnal, and long period ones. Compared to the tidal gravity changes, the gravity variations caused by the increments are about 0.15% for the semidiurnal tide and 0.1% for the diurnal and long period tides.