Lanzano P. Deformations of an Elastic Earth

International Geophysics Series, 1982, Volume 31. Academic Press, New York, London, 1982. – 244 pp.
To study the real Earth from a dynamical point of view, we must take into account (1) its internal constitution, i.e., the Earth's density profile and elastic parameters, (2) its external shape, (3) its gravity field, and (4) various perturbing potentials. Such a study would then be related to the fields of seismology, geodesy, and astronomy. Let us begin by considering a few basic facts about these four characteristics.
Our knowledge of the interior of the Earth is provided by seismic studies that have been responsible for determining the velocity of propagation of seismic waves and for measuring the spheroidal and toroidal oscillations experienced by the Earth subsequent to seismic events. From this knowledge a rheological profile of the Earth comprising the variation of its density and of the Lame elastic parameters along various layers can ultimately be determined. The external shape of the Earth is the geoid, the determination of which can be achieved by the gravimetric or the astrogeodetic method of physical geodesy, or both, and by satellite geodesy. The Earth's gravity field is the result of two forces: the gravitational attraction exerted by the whole Earth at each point according to Newton's law and the centrifugal force due to the Earth's rotation. The magnitude of the vector field is the intensity of gravity, whereas its direction at a point provides the direction of the vertical at that point.Concepts of Physical Geodesy
Hydrostatic Equilibrium and Earth Density Models
Elastic Deformations of a Rotating Earth Caused by Surface Loads
Solution of the Linearized Navier-Stokes Equations
Precessional and Nutational Motions of a Rigid Earth
Ocean Tides