Effects of ongoing melting and buoyancy on melt band evolution in a compacting porous layer

Highlights

• Ongoing melting included in linear theory and numerical models of melt bands.

• Melting does not inhibit band growth when bulk viscosity decreases with porosity.

• Buoyancy causes oscillations but does not inhibit band growth.

• Melt driven expansion can drive a porosity segregating instability.

Abstract

We analyze a two-phase porous medium whose permeability and solid viscosity are dependent on porosity. It has been established experimentally and numerically that when such a medium is subjected to shear, the porosity rearranges into stripes of high and low porosity known as melt bands (Holtzman et al., 2003; Katz et al., 2006; Butler, 2009). This study uses linear theory and numerical simulations to analyze the effect of ongoing melting and buoyancy forces on the formation and evolution of melt bands. Previously, the consequences of internal melting have not been quantified and studies including buoyancy forces have conflicting interpretations (Katz, 2010; Butler, 2009). In this study, we show that the inclusion of internal melting significantly decreases the amplitude of these bands if the bulk viscosity is constant, but has a minimal effect on the amplitude when the bulk viscosity decreases with porosity. Most recent studies indicate that bulk viscosity likely strongly decreases with porosity, indicating that ongoing melting does not preclude the existence of significant melt bands in Earth's upper mantle. Buoyancy forces are shown to induce an oscillation of the bands with no effect on amplitude. We also show that isotropic expansion driven by melting and density differences between the solid and liquid can drive a porosity localizing instability.

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.