Static deformations and dislocation theory - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 482

9

Static deformations and dislocation theory

In addition to generating seismic waves, tsunamis and free oscillations of the Earth,
earthquakes generate static displacements, strains and tilts both locally and at tele-
seismic distances. The nearly global extent of these static deformations was brought
out clearly by Press (1965) following the great Alaska earthquake of 27 March
1964. The basis for modelling the displacement fields is Volterra's theory of
elastic dislocations, published in 1907, dealing with the elasticity theory of sur-
faces across which displacements are discontinuous. The theory was revived by
Steketee (1958a), and applied to geophysical problems by him (Steketee, 1958b)
and his student at the time (Rochester, 1956). The surprising extent of the displace-
ment fields demonstrated by Press led to a re-evaluation of their e

ect on the polar
motion (Mansinha and Smylie, 1967). In this chapter, we first present the elasticity
theory of dislocations , as it is now known, in an infinite uniform elastic half-space,
and then in realistic Earth models. We conclude with the calculation of the e

ff

ff ects

of earthquakes on the polar motion.

9.1 The elasticity theory of dislocations

The starting point for the elasticity theory of dislocations is the reciprocal theorem
of Betti (1.266) (Sokolniko

, 1956, pp. 390-391). This states that for two sys-
tems of surface tractions and body forces the work done by the first system, acting
through the displacements caused by the second system, is equal to the work done
by the second system, acting through the displacements caused by the first system.
With t i and t i

ff

representing the surface tractions per unit area, F i and F i

represent-

ing the body forces per unit volume, and u i and u i

representing the displacements

they cause, the theorem reads

t i u i dS F i u i dV t i u i dS F i u i dV . + = + (9.1)

S V S V