Creep in the earth and planets

Abstract

Evidence of imperfectly elastic behaviour in the earth and planets is provided by the following phenomena: 1. (1) damping of the earth's free nutation; 2. (2) damping of elastic waves passing through the earth; 3. (3)secular acceleration of the moon; 4. (4) figure of the moon; 5. (5) figure of the earth; 6. (6) rotations of satellites of the planets; 7. (7) free oscillations of the directions of the moon's axes; 8. (8) eigenfrequencies of the earth; and 9. (9) damping of the S wave as a function of frequency. Darwin attempted to explain the secular acceleration of the moon by viscosity in the body of the earth. This was shown to be unsatisfactory in 1915. A logarithmic law of creep, containing one relevant constant, agrees with some laboratory tests and approximately with a large quantity of seismological data. But it was found that if the constant is chosen to fit the damping of the free nutation (Eulerian nutation or Chandler wobble) the beginning of a transverse seismic wave at distance 80° would be spread over about 70 sec and be unreadable. I propose a law of creep by which for a constant shearing stress P the response is a shearing strain ϵ given by: ϵ = P μ [1 + q α {(1 + at) α − 1 ]} where t is time and μ, q, a, α are constants. This is a particular case of imperfection of elasticity. In it, for disturbances lasting a second or more, there are essentially only two creep parameters to be fixed, α and qa α . These may be determined by the two data: 1. (1) that the relaxation time of the free nutation is 30 ± 20 yyears; 2. (2) that S at 80° reaches half its ultimate value in 2 sec. We obtain α as probably between 0.14 and 0.21, with 0.19 as the most probable value. We then proceed to show that this law of creep, with α = 0.19, can account for approximately the right amount of damping (or internal friction) in all the other phenomena listed above. Laws with α = 1 (elastico-viscous law) and α = 0 (logarithmic law) fail to do so. A consequence of this law of creep is that where it holds convection cannot take place.