Inelastic Processes in the Shell

Abstract

It has been known for some thousands of years that the Moon keeps a nearly constant face to the Earth. Only one explanation has been offered of how this state can have come about, namely tidal friction in the interior of the Moon. Darwin made an extensive study of the effects of tidal friction in the Earth and other planets, with special reference to the apparent secular acceleration of the Moon. Mercury and known satellites appear to keep constant faces to their primaries (there seems to be some d,oubt now about Mercury, but the rotation still appears to be slow). Turbulence in tidal currents in shallow seas seems to account for most of the friction for the Earth; but the other bodies have probably never had shallow seas, and we must infer some imperfection of elasticity at strains of the order of It is very hard to detect such imperfection in the laboratory. Other types however are very conspicuous. Fracture in igneous rocks and well compacted metamorphic ones such as quartzites occurs at strains of the order of and there is a complicated non-linear behaviour when the elastic strains are somewhat less than this; this may lead to permanent deformation far exceeding the direct elastic one. It was shown by various geodesists that mountains produce far smaller disturbances of gravity than would be expected if they were simply added loads. An explanation was given by Airy, who postulated a lower layer of denser but weaker matter. Extra load on a thin crust would push the interface down, and the resulting lack of heavy matter would largely compensate for the extra attraction of the mountain. Later Suess made the crucial inference on geological grounds that most surface rocks are essentially derived from granite or similar rocks with densities about 2.7, and overlie a layer with a density of 3-0 or so. Then A. MohorovilSiC in 1909 detected a duplication of earthquake pulses, as if one pair, Pg and Sg, travelled in an upper layer but another, Pn and Sn, in a lower one with higher velocities. Curiously, none of the continental seismologists at the time appear to mention Suess or Airy. The first mention in geophysics of the geological inference was, I think, in the paper by Winch and me in 1922 on the Oppau explosion. Later comparison with experiment confirmed these early results except that the lower layer seemed to need a density more like 3.3 and the upper was a great deal more complicated. But this is still too simple. Hayford’s survey of the United States assumed exact uniformity of mass per unit area and greatly reduced the residuals in comparison with the hypothesis that extra mass on the surface is not accompanied by defect below. But Helmert noticed that successive residuals along a survey line tended to keep the same sign, and on this ground multiplied Hayford’s uncertainties by about 3. Barrel1 inferred hence that the lower layer cannot be completely weak; he supposed a layer about lOOkm down where the strength is much less than that of surface rocks, but still appreciable. He called this the asthenosphere. Again confirmation came from Turner’s discovery of deep-focus earthquakes in 1921. Earthquakes comparable with the strongest shallow ones occur to depths of about a tenth of the Earth‘s radius. They send out strong S pulses. This is definite evidence that a discontinuous change occurs in the stress-difference and the material must have been able to stand that until the earthquake took place. (Incidentallyl it is hard to