Residual Deformation of Real Earth Models with Application to the Chandler Wobble

Abstract

By using Volterra's relation, it is shown that a tangential dislocation in a gravitating radially inhomogeneous sphere can be characterized by discontinuities in the stress and displacement fields across the source surface r = r,,. This representation of the source facilitates the numerical evaluation of the displacement field.It is found that at the free surface of the Earth the six simultaneous linear differential equations governing the spheroidal field associated with the Legendre polynomial of the first degree (I = 1) degenerate into five.The two equations corresponding to the toroidal field for 1 = 1 degenerate into one. Therefore, when dealing with the case 1 = 1, one must incorporate additional conditions, namely, that the angular momentum of the sphere about its centre is zero and that the centre of mass of the sphere is not displaced.The changes in the inertia tensor due to an earthquake of arbitrary depth and orientation are calculated with the assumption that the Adams-Williamson condition holds at the core. No difference in the numerical results are obtained if the Adams-Williamson conditions does not hold. Comparison with homogeneous, non-gravitating Earth model shows that, in general, real Earth models render a smaller value for the changes in the inertia tensor. It appears from our results that earthquakes are insufficient to maintain the Chandler wobble.

Global plate tectonics and the secular motion of the Pole

“…where to the first order of f Sul Several models for the computation of the contribution to the moments and products of inertia due to earthquake faulting or slip displacements are available in literature [Mansinha and Smylie, 1967], [Dahlea, 19731, i [Israel et al, 1973], but up to now only analytical solutions of the Lagrange-Liouville equations using the approximations established in [Munk and Mac--Donald, 1966, p. 38] have been investigated.…”

Coseismic Excitation of the Earth’s Polar Motion

“…That prompted a series of investigations of seismic excitation of polar motion: Mansinha and Smylie (1967), Smylie and Mansinha (1968;1971), Mansinha et al (1970;1979), Ben-Menahem and Israel (1970), Israel et al (1973), Israel and Ben-Menahem (1975), Rice and Chinnery (1972), Dahlen (1971;1973), O'Connell andDziewonski (1976), Smith (1977). Unfortunately the search for signatures left by large earthquakes {e.g., the great 1960 Chilean event and the 1964 Alaskan event) in polar motion was essentially inconclusive: the quality of the polar motion data at the time was insufficient for that purpose both in accuracy and temporal resolution.…”

On the static deformation of the earth.

“…(9). Then Saito's formulation is equivalent to that of SMYLIE andMANSINHA (1971) andISRAEL et al (1973). OKUBO and SAITO (1983) derived the variational equation for the static deformation.…”

“…Boundary conditions at the core-mantle boundary (r=b) are (ISRAEL et al, 1973;CROSSLEY and GUBBINS, 1975) …”

“…We rederive the variational equation using the formulation of SMYLIE andMANSINHA (1971) andISRAEL et al (1973). In the solid mantle, using Eq.…”