High-temperature anelasticity and elasticity of mantle peridotite

An apparatus has been devised which allows precise creep and relaxation measurements to be made on minerals and rocks at temperatures up to 1600°C and at very low deviatoric stresses (1 < σ < 300 bar). This paper is concerned with measurements on mantle peridotite (lherzolite) from Balmuccia (Zone of Ivrea, Italy).The reaction of the sample to a step-like increase in stress is called its “creep function”. It is shown that the creep function contains all the necessary information to derive the spectra of the quality factor Q(ω) and of Young's modulus E(ω), within the seismic range of frequencies, provided the material behaves as a linear system. This has been proven up to a strain of 5 × 10^?5.The Q^?1-spectra at 1200 and 1300°C, obtained by Fourier inversion from the creep function, show no pronounced peak in the frequency band 0.01 < tf < 1 Hz and exhibit a general tendency to decrease slightly with frequency. The creep function: ?(t) = ?_u · 1 + 3.7 · q · {(1 + 50t)^0.27 ? }], where q is related to Q, satisfactorily describes the data at high temperatures and leads to $\text{Q}{}^{\mathrm{?1}}\text{(ω, T) = 3 × 10}{}^3\text{· ω}{}^{\mathrm{<mtext>?0.27\; ·\; </mtext><mtext>exp</mtext>}}\text{(}\text{?30}\text{RT}\text{)}$E(ω) is related to Q(ω) by the material dispersion equation. Above 1100°C the unrelaxed Young's modulus decreases rapidly with temperature according to an activation energy of about 20 kcal/mole. A lowering of short period S-wave velocity by 40% and P-wave velocity by 10% occurs below the solidus. Therefore, no partial melting is required in the asthenosphere.Steady-state creep at low axial stresses (20 < σ < 100 bar), obtained from the same rock, follows the relation $\text{?}\text{?}\text{= 3 × 10}{}^7\text{· δ}{}^{1.4}\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ indicative of grain boundary diffusion or superplasticity. At higher stresses a power law $\text{?}\text{?}\text{= 45 · δ}{}^4\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ typical of dislocation creep, is found.The frequency dependence of Q and the ratio of the activation energies of Q and are indicative of so called “high-temperature background absorption”, as the dominant mechanism, and of a diffusion-controlled dislocation mobility common to both absorption and creep. From a, b, and c, relations between the effective viscosity η_f and Q of the form: $\text{log}\text{η}{}_{\mathrm{e??}}\text{=}\text{1}\text{α}\text{·}\text{log}\text{Q ? (n ? 1) ·}\text{log}\text{ω +}\text{log}\text{D}$ are derived, where α ～ 0.25, n is the power of σ, and D is a constant.