Using a combination of the self consistent scheme [Hill, J.
Mech. Phys. Solids, 1965, Budiansky, J. Mech. Phys. Solids,
1965] and differential effective medium theory [Boucher, Rev.
Metall., 1976 and McLaughlin, Int. J. Eng. Sci., 1977]
in a similar way to Mainprice [Tectonophys, 1997] we examine the
effect of introducing inclusions of melt into a solid matrix on the elastic
constants (and hence shear and compressional velocities), attenuation,
and anisotropy of the resulting medium. We consider both a homogeneous
distribution of spherical inclusions and either aligned or randomly oriented
elliptical inclusions. The effect of assuming an isotropic or anisotropic
background matrix material is also considered. From this we are able
to place some bound on the melt fraction and possible microstructure of
magma chambers that is consistent with parameters from seismic inversions.
In particular we hope to apply this technique to the data from the 1996
and 1997 land and sea reflection surveys at Mount Vesuvius [Gasparini,
EOS, 1998].