Numerical models on the influence of partial melt on elastic, anelastic and electric properties of rocks. Part I: elasticity and anelasticity

Abstract

With the aim of a simultaneous interpretation of elastic, anelastic and electric in situ data from the asthenosphere a comprehensive set of numerical models is developed for partial melt in different geometrical configurations. For the elastic and anelastic modulus use is made throughout of the melt squirt mechanism. Frequency dependence is not treated in detail but estimated from the limiting cases of the relaxed and unrelaxed modulus. This has the advantage that quantitative values of viscocity and flow path dimensions are not required. In the models melt can be assumed to occur in the form of tubes, films, and triaxial ellipsoidal inclusions of arbitrary aspect ratio. The conditions in which the solutions for triaxial ellipsoidal inclusions can be approximated by simpler ones for spheroidal inclusions are discussed. It is then shown up to which aspect ratio a published model on melt films is applicable. The problem of interconnection of inclusions is treated with a statistical numerical approach. It is found that a reduced degree of interconnection may have a significant influence on anelastic relaxation at melt fractions corresponding to a moderate modulus decrease. A useful representation of the anelastic melt models is introduced by plotting the relaxation strength against the effective modulus, both of which depend on the state of melting. Such diagrams allow a clear distinction between the different melt geometries and may be used for the interpretation of observed data. Finally, different melt geometries are superimposed and it is found that under certain conditions bulk dissipation may reach the order of that for shear.