Upper mantle seismic wave attenuation: Effects of realistic partial melt distribution

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Abstract
Frequency dependence of seismic velocity and attenuation resulting from viscoelastic relaxation of partially molten mantle is estimated. We consider the contribution of the melt squirt mechanism, through which pressure differences between disk‐shaped inclusions are equalized by melt passing through connecting tubes. The pressure differences arise as a result of shear strain compressing disk‐shaped pores differently on the basis of disk orientation with respect to the applied shear. The frequencies over which the transition from the unrelaxed to the relaxed states occurs are determined by representing the melt as a network of tubes connecting oblate ellipsoidal pores. The pressure equalization process is modeled by a system of first‐order linear differential equations, whose eigenvalues are the characteristic frequencies for melt squirt relaxation. It is shown that in this framework the set of frequencies is invariant to the absolute scale of the system but is sensitive to melt bulk modulus and viscosity, as well as distribution of melt inside pores and conduits. Use of realistic solid and melt physical properties and pore and conduit geometries demonstrates that it is the relaxed modulus that is most likely excited in the seismic band and that melt mobility has little effect on seismic attenuation. Some conceivable melt distributions, however, would result in detectable attenuation in the seismic band. In all cases investigated, attenuation increases with frequency, indicating that melt squirt is not responsible for global upper mantle Q observations.

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