Table 5 – Tabulation of parameters used for timescale
calculations presented in Fig. 14 .
a. φ0 refers to starting porosity or melt fraction used
in simulations.
b. Units of log10(Pa s) for the entire column.
c. Extrapolation using grain size dependence exponent of n = 0.
d. Extrapolation using grain size dependence exponent of n = 1.9,
a value obtained in Fig. 7 of this manuscript.
e. Extrapolation using grain size dependence exponent of n = 3.
f. The composition of melt in C423 is Li-sil. while C372 is MORB melt.
g. Here \(\eta_{s}\) has been scaled from 1012.51 to
1020.32 Pa s assuming a grain size dependence of n =
3.
When extrapolating the effective matrix viscosities to geologic
conditions, the results differ significantly given the grain size and
temperature dependence of repacking and GBD (Fig. 14 ). The
grain size and temperature dependence of GBD are well established with a
grain size exponent of 3 and an Arrhenius relationship for temperature.
Shear cell and avalanche experiments on aggregates of a variety of
materials suggest that the repacking rheological law (eq. (16)) at
ambient conditions is largely grain size independent and any temperature
dependence is unclear (Boyer et al. , 2011, Cassar et al. ,
2005, Dijksman et al. , 2010, Jop et al. , 2006). At high
temperature and pressure, however, there are multiple deformation
mechanisms that can accommodate grain translation and rotation past each
other, and grain boundary sliding can be frictional or viscous. Thus,
the reference viscosity constrained in this study may have grain size
and temperature dependence informed by how sliding is partitioned
between viscous and frictional sliding. A better characterization of
grain boundary sliding as applied to repacking together with
microstructural analyses of repacked samples would be warranted to
improve the present formulation of the repacking rheology in the future.
Nonetheless, calculating the timescales required to reduce the initial
height of a compacting layer and form a melt layer suggest that
repacking provides an efficient melt extraction mechanism at
intermediate melt fractions using a relatively broad range in grain size
exponents (from n = 0 to n = 3 in Fig. 14 ). Such results
support the lack of textural evidence for viscous compaction processes
in preserved magma chambers (Holness, 2018, Holness et al. , 2017)
and would be further supported upon detection of fabric development
perpendicular to paleogravity of early crystallized matrix-forming
phenocrysts (Fiedrich et al. , 2017, Garibaldi et al. ,
2018).