Upper mantle seismic wave velocity: Effects of realistic partial melt geometries

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Abstract
We investigate seismic wave velocity reduction resulting from the presence of partial melt in the upper mantle. The amount of shear and bulk modulus reduction produced by the presence of a connected network of realistically shaped and naturally organized melt inclusions is found using finite element calculations. The geometries of the inclusions are taken directly from laboratory experiments of mantle melting, with finite element meshes constructed to conform to these shapes. The shear and bulk moduli of the composite material are found for both the unrelaxed (isolated inclusions) and relaxed (pressure equalized inclusions) cases by assigning appropriate material properties to the fluid. Modulus reduction from deformation simulations of a solid containing realistically shaped and ellipse‐shaped melt inclusions quantify the effect of melt pocket cuspateness and melt pocket organization on seismic velocity reduction. The three‐dimensional response is estimated from two‐dimensional distributions of the melt phase by determining the mode II and mode III components of elastic modulus reduction separately and summing their effects. In general, cuspate and naturally organized melt inclusions cause greater velocity reduction. It is shown that VP and VS reduction per percent partial melt are at least 3.6% and 7.9%, respectively. Even higher values for velocity reduction are possible above 1% melt fraction if melt exists only in tubules below 1% melt fraction. The lower, more conservative values of velocity reduction are ∼70% greater for VP and 84% greater for VS than the analytically determined values for ellipsoidal inclusions. Somewhat greater effects are possible if nonrandom organization of melt occurs on scales greater than our model.