Some elementary relations between mass distributions inside the Earth and the geoid and gravity field

The influence of mass distributions inside the Earth on the gravity field and geoid at the earth surface is computed by means of spherical harmonic expansions. The general formulas are applied to compute the effect of topography and isostatic compensation on the gravity field and geoid. The rigidity of the earth crust is taken into account. The thickness of the crust can be estimated from the spherical harmonic coefficients of topography and geoid. In geophysical textbooks (e.g. Turcotte, G. and Schubert, G. 1982. Geodynamics. Wiley, New York.) a formula is used to compute the geoid height from mass density disturbances. The approximations and assumptions in this formula are derived.