Effects of ongoing melting and buoyancy on melt band evolution in a compacting porous layer
Introduction
Melt bands are the result of the rearrangement of porosity into stripes of highs and lows caused by an instability when an external shear is imposed on a compacting system whose viscosity decreases with porosity. This phenomenon was first investigated by Stevenson (1989) who found that porosity aligned in stripes along the principal compressive stress axis.
Decompression melting occurs when mantle upwells, rapidly decreasing the lithostatic pressure but retaining heat, creating partial melt. This phenomenon occurs beneath mid-ocean ridges and is responsible for the melt production that feeds the formation of oceanic crust (Schubert et al., 2001). How this melt is transported from the mantle to the surface is not well understood. The volcanism associated with mid-ocean ridges is localized to within a kilometre of the ridge axis according to bathymetric and seismic data (Vera et al., 1990). Melt must be rapidly transported from depth in order to preserve isotopic signatures which are present at the surface (Kelemen et al., 1997). Seismic studies have interpreted melt to occur at approximately 60 km depth and up to a hundred kilometres from the ridge axis (Forsyth et al., 1998). As a result, a mechanism is required to rapidly transport melt laterally to the ridge crest.
Morgan (1987) and Stevenson (1989) theorized that anisotropic permeability could act as a melt focusing conduit. Stevenson (1989) further showed that a strain-rate driven, porosity localizing, instability exists when matrix viscosity decreases with porosity which could cause large-scale anisotropy. Holtzman et al. (2003) and Holtzman and Kohlstedt (2007) experimentally investigated the formation of strain-rate driven melt localization while Richardson (1998) and later Katz et al. (2006) modeled the bands numerically and all argued that bands might act as high permeability conduits in the mantle. A later study by Gebhardt and Butler (2016) showed that the background rotation in a mid-ocean ridge corner flow resulted in bands that were oriented towards the base of the plate which would not direct melt towards the ridge axis. However, bands in this orientation might transport melt more rapidly to a sublithospheric decompaction layer which could transport melt rapidly along the base of the plate (Sparks and Parmentier, 1991). Melt bands have also been suggested to be significant in the upper mantle in their role in reducing effective viscosity (Holtzman et al., 2012) and as being a possible cause of seismic (Holtzman and Kendall, 2010) and electrical anisotropy (Caricchi et al., 2011).
The consequences of the ongoing decompression melting in the upper mantle have not previously been taken into account in theoretical and numerical calculations of melt bands. Although previous numerical models have included ongoing melting (Katz, 2010), melt bands were not the focus of the study and the impact of internal melting on them was not quantified.
There are conflicting results for melt bands when the models include buoyancy. Katz (2010) included buoyancy, internal melting, and a corner flow geometry and found an absence of melt bands. However, Butler, 2009, Butler, 2010, Butler, 2012 produced melt bands in shear simulations including buoyancy. These studies used small boxes with periodic boundary conditions on the top and bottom boundaries, which means material circulated many times through the boundaries due to buoyancy. In this study we use an elongated box such that the material being analysed in the center did not recirculate.
In what follows, we will first review the compaction theory that describes melt bands including effects of melting and buoyancy. We will then derive the linearized equations and give solutions for the growth rate and oscillation frequency and then describe our numerical model. In a subsequent section we will present and compare our results from linear theory and numerical modeling and finally provide some discussion.
Section snippets
Governing equations
Continuum equations governing two phase fluid mixtures have been derived by McKenzie (1984), Scott and Stevenson (1984) and Bercovici et al. (2001). Here we use the form derived by McKenzie (1984) using mass and force balance of both phases. The dimensionless conservation of solid mass equation is expressed aswhere ϕ is porosity, Γ is melt rate per unit volume, t is time, is the solid velocity field while and are unit vectors in the horizontal and vertical
Growth rate
Instantaneous growth rates found using linear theory, Eqs. (11), (A.2), for angles between 0 and 90° from horizontal are plotted in Fig. 1 a) and b) against instantaneous angle at strains of 0 and 0.5. At strain 0, the growth rate is the same as when melting is absent while at a later time the effect of melting can be discerned. In the V cases the angle of maximum growth is split symmetrically about the angle of maximum growth for the corresponding C case, which is similar to splitting without
Discussion and conclusions
We analysed the growth and evolution of melt bands using linear theory and numerical simulations. There was close agreement between these two independent analyses giving us confidence in the correctness of both. The presence of a dimensionless melting rate of 0.075, which is our maximal estimate for the melting rate in the upper mantle, significantly decreases the maximum amplitude of the bands for the C cases but only minimally for the V cases. The largest effect of ongoing melting is the
CRediT authorship contribution statement
Z.E. Vestrum:Conceptualization, Methodology, Validation, Software, Formal analysis, Investigation, Data curation, Writing - original draft, Visualization.S.L. Butler:Conceptualization, Methodology, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We would like to thank John Rudge, Ben Holtzman and an anonymous reviewer whose helpful comments led to significant improvements of this manuscript. We also gratefully acknowledge funding from the Natural Sciences and Engineering Research Council of Canada.
References (50)
The effects of buoyancy on shear-induced melt bands in a compacting porous medium
Phys. Earth Planet. Inter.
(2009)Porosity localizing instability in a compacting porous layer in a pure shear flow and the evolution of porosity band wavelength
Phys. Earth Planet. Inter.
(2010)Numerical models of shear-induced melt band formation with anisotropic matrix viscosity
Phys. Earth Planet. Inter.
(2012)Shear-induced porosity bands in a compacting porous medium with damage rheology
Phys. Earth Planet. Inter.
(2017)- et al.
Experimental determination of electrical conductivity during deformation of melt-bearing olivine aggregates: implications for electrical anisotropy in the oceanic low velocity zone
Earth Planet. Sci. Lett.
(2011) - et al.
A computer simulation study of natural silicate melts. Part I: low pressure properties
Geochim. Cosmochim. Acta
(2007) - et al.
Effects of stress-driven melt segregation on the viscosity of rocks
Earth Planet Sci. Lett.
(2012) - et al.
Adiabatic temperature profile in the mantle
Phys. Earth Planet. Interiors
(2010) - et al.
Influence of melt on the creep behavior of olivine-basalt aggregates under hydrous conditions
Earth Planet. Sci. Lett.
(2002) - et al.
Melt extraction from the mantle beneath spreading centers
Earth Planet. Sci. Lett.
(1991)