Constraints on melt distribution from seismology: a case study in Ethiopia

Abstract Low seismic velocities and/or strong seismic anisotropy are often interpreted as being caused by partial melt. To better understand this, we used numerical modelling, varying the shape and amount of melt, to show how seismic phases are affected by melt. We observed that seismic waves are more sensitive to the shape than to the amount of melt. Rayleigh wave velocities were almost always reduced in the presence of melt, while Pn/wide-angle P-wave refraction and Love wave velocities showed low velocity anomalies for vertically aligned melt, but little anomaly for horizontally aligned melt. These data can therefore be used to determine the alignment of melt. Shear wave splitting/receiver functions showed strong anisotropy and can be used to constrain the strike of vertically aligned partial melt. We showed that melt in the mantle beneath Ethiopia is probably stored in low aspect ratio disc-like inclusions, suggesting that the melt is not in textural equilibrium. We estimated that 2–7% of the vertically aligned melt is stored beneath the Main Ethiopian Rift, >6% of the horizontally and vertically aligned melt is stored beneath the Red Sea Rift and 1–6% of the horizontally aligned melt is stored beneath the Danakil microplate. This supports the idea of strong shear-derived segregation of melt in the narrow Main Ethiopian Rift compared with that observed beneath Afar.

Volcanism at the Earth's surface is driven by the partial melting of rocks in the upper mantle and the buoyancy-driven ascent of melt to the surface. The presence of melt in the mantle can affect the strength of mantle rocks (Takei & Holtzman 2009) and thus affects mantle dynamics in tectonically active regions (Holtzman & Kendall 2010;Pommier et al. 2015). However, melt follows complex pathways to the surface (e.g. Kelemen et al. 1997;Holtzman & Kohlstedt 2007) and can pond at many depths before eruption (Annen et al. 2006). If we are to understand the processes that form the crust, drive tectonic plates and give rise to volcanoes, then we must understand the mechanisms by which melt is stored and transported.
In this study, we considered the sensitivity of a number of seismic phases (body waves and surface waves) commonly measured in volcanic settings to the presence of partial melt. This allowed us to determine the seismic attributes that are most sensitive to the presence of melt, thus guiding future studies about how to interpret seismic data. We applied this new understanding to unravelling the nature of melt distribution in the mantle beneath the Main Ethiopian and Red Sea rifts in Ethiopia.

Seismic images of melt
Laboratory experiments at high frequencies (.MHz) have shown that partial melt strongly affects seismic parameters (Faul et al. 1994) such as velocity and attenuation. More recent studies have suggested that these laboratory experiments can be extrapolated to field-scale seismic frequencies (1-10 23 Hz) (Garapic et al. 2013). Relationships have been derived to extract melt fractions from seismic velocity anomalies (e.g. Hammond & Humphreys 2000) and, although these are often used to interpret melt volumes (West et al. 2001;Goes & van der Lee 2002;Stixrude & Lithgow-Bertelloni 2005;Stork et al. 2013), they are only valid for specific melt geometries and must be treated with caution. In addition, isotropic velocities are sensitive to variations in temperature (Jackson et al. 2002), composition (Karato & Jung 1998) and attenuation (Goes et al. 2012), all parameters that are expected to be anomalous in the presence of partial melt. Unravelling the nature of melt storage from isotropic velocities alone therefore remains difficult. Furthermore, seismic properties vary strongly with melt geometry (Kendall 1994;Hammond & Humphreys 2000;Takei 2013), which further complicates the interpretation of isotropic velocity. Observations of seismic anisotropy have been used to characterize melt beneath volcanic settings where it shows particular sensitivity to the aspect ratio (the shape of the melt pockets/inclusions) and any preferential alignment of the melt (Kendall 1994;Hammond & Humphreys 2000;Bastow et al. 2010;Holtzman & Kendall 2010;Keir et al. 2011;Hammond 2014). Thus, although seismology clearly has the capability to image regions of melt in the crust and mantle, unravelling these signals requires careful analysis of both their isotropic and anisotropic signals.

Effects of melt on seismic velocities
To model the effects of melt on seismic properties, we calculated the elastic constants (using the Matlab toolbox MSAT; Walker & Wookey 2012) for aligned isolated melt pockets in a matrix material using effective medium modelling. We used the theory of Tandon & Weng (1984), which is based on the assumption that an applied stress is perturbed by inclusions, which, in general, can be either faster or slower than the surrounding medium. Tandon & Weng (1984) built on the formalism of Eshelby (1957), who determined the strain perturbation due to an ellipsoidal inclusion that may be either prolate or oblate in shape. Tandon & Weng (1984) generalized the theory to consider the effects of multiple aligned inclusions, together with the effects of the inclusion aspect ratio on the composite elastic moduli. A limitation of their theory is that, although the volume fraction of the inclusions can be very high, the inclusions cannot interact with each other. A more generalized theory can be used to model the effects of interconnected, low wetting angle inclusions (e.g. Chapman 2003), but this theory assumes penny-shaped inclusions and therefore cannot be used for higher wetting angle inclusions. Furthermore, frequency-dependent effects, which are sensitive to the size of the inclusion, are neglected and it is assumed that the melt inclusions are significantly smaller than the seismic wavelength (Al-Harrasi et al. 2011). Nevertheless, we were able to test a broad range of melt geometries using this theory to understand how different amounts and geometries of melt affect seismic waves.
The elastic constants were calculated using P-and S-wave velocities of 8.0 and 4.5 km s 21 and a density of 3.3 kg m 23 for the matrix material and 2.7 and 0.0 km s 21 and a density of 2.7 kg m 23 for the melt. We tested the effects of melt stored in isolated oblate spheroidal inclusions and tubules, analogous to melt stored along grain faces or grain boundaries, respectively (Schmeling 1985) (Fig. 1).
In our models, we varied: (1) the amount of partial melt; (2) the aspect ratio (a) of the melt (a , 1 for aligned discs, a ¼ 1 for spherical inclusions, a . 1 for tubules); and (3) the direction of alignment (vertical or horizontal) of melt inclusions. The effective medium models produced elastic constants for each model (Fig. 1), from which it was possible to determine the velocity reduction and anisotropy that would be observed for a seismic phase travelling through a medium characterized by these elastic constants (Figs 2 & 3).
For typical melts in the upper mantle (e.g. silicate or carbonate melts), the dihedral angle is ,348 (Minarik & Watson 1995;Holness 2005). At these low dihedral angles, melt is mobile and will wet grain boundaries (Garapic et al. 2013). As melt moves, it forms larger channels of melt through reactive transport, which increases the permeability further, allowing melt to move (Kelemen et al. 1997). A further mechanism to facilitate the ascent of melt is through the formation of melt-rich bands where the strain rates are high (e.g. Holtzman & Kohlstedt 2007). The modelling approach used here was analogous to any of these models of melt storage as long as the length scales of the melt structures were much smaller than the seismic wavelength. In this study, we only modelled vertically and horizontally aligned melts. This is valid as many melt transport and storage mechanisms are subhorizontal (e.g. sills, ponding at the base of the lithosphere) or subvertical (dykes, reactive transport). However, for more complex mechanisms (e.g. the shear-derived segregation of melt), the melt may be inclined (Holtzman & Kendall 2010). In these cases, we expect more complex relationships between the melt and seismic velocities/ anisotropies than those explored here.
This simple modelling approach probably underestimates the effect of melt on seismic properties. For example, it does not account for the cuspate nature of the melt inclusions, which will cause stronger velocity reductions for each melt fraction (Hammond & Humphreys 2000). Also, this approach assumes that the inclusions are isolated and therefore no attenuation effects due to the interconnectivity of melt are considered. This can also act to increase the effect of melt on seismic velocities as a result of melt squirt flow, where the pressure gradients caused by the passage of the seismic wave cause fluid to flow along grain boundaries (Hammond & Humphreys 2000;Jakobsen & Chapman 2009;Garapic et al. 2013). As a result, the estimated melt fractions in this study are possibly too high, but this approach can help us to understand the relationships between melt and seismic velocity/ anisotropy, yield useful estimates of the geometry of melt segregation and help us to understand the relative variations in melt segregation.  Figures 2 and 3 show the expected velocities and anisotropies for melt fractions from 0 to 15% and aspect ratios from 0.01 to 100 for horizontal and vertically aligned melts, respectively. We investigated the seismic phases that are commonly measured to understand mantle structure, such as horizontally travelling Pn, wide-angle refraction waves, surface waves (both Rayleigh and Love waves), and vertically travelling shear wave splitting and receiver functions.

Pn and wide-angle refraction data
Waves refracted at the Moho (Pn) are commonly used to infer seismic velocities in the uppermost mantle. They can be determined from impulsive, Fig. 2. Effect of horizontally aligned melt on different seismic waves. (a) Pn/refraction velocity (horizontally propagating P-wave (averaged from all back azimuths)); (b) Pn/refraction azimuthal anisotropy (azimuthal anisotropy in horizontally propagating P-wave); (c) Rayleigh wave velocity (horizontally propagating, vertically polarized shear wave (averaged from all back azimuths)); (d) Rayleigh wave azimuthal anisotropy (azimuthal anisotropy in horizontally propagating, vertically polarized shear wave); (e) Pn/refraction velocity/Rayleigh wave velocity (ratio of (a) and (c)); (f ) Pn/refraction velocity/Rayleigh wave velocity azimuthal anisotropy (azimuthal anisotropy in ratio of (a) and (c)); (g) Love wave velocity (horizontally propagating, horizontally polarized shear wave (averaged from all back azimuths)); (h) Love wave velocity azimuthal anisotropy (azimuthal anisotropy in horizontally propagating, horizontally polarized shear wave); (i) Pn/refraction velocity/Love wave velocity (ratio of (a) and (g)); ( j) Pn/ refraction velocity/Love wave velocity azimuthal anisotropy (azimuthal anisotropy in ratio of (a) and (c)); (k) (Love wave velocity/Rayleigh wave velocity) 2 (square of ratio of (g) and (c)); (l) shear wave splitting (time difference between fast and slow shear waves in vertically propagating shear waves); (m) V P /V S from Hk stacking from receiver functions (ratio of vertically travelling P-wave velocity and vertically propagating, dominant (fast or slow shear wave that has largest amplitude) vertically polarized shear wave (averaged from all back azimuths)); (n) azimuthal anisotropy in V P /V S from Hk stacking from receiver functions (azimuthal anisotropy in (m)). artificial sources or measured from natural earthquakes. In active tectonic settings, the presence of low upper mantle P-wave velocities and azimuthal anisotropy have been used as evidence for the presence of melt (e.g. Ethiopia - Mackenzie et al. 2005;Maguire et al. 2006;Stork et al. 2013;Corbeau et al. 2014;Tibet -Hearn et al. 2004;Pei et al. 2007; the western USA -Hearn 1996;Buehler & Shearer 2014;and Turkey -Hearn & Ni 1994). Pn and wide-angle refracted waves spend the majority of their time propagating horizontally in the mantle, thus we investigated the effects of melt on horizontally propagating P-waves. As a comparison with Pn tomography studies, we took the average P-wave (a) Pn/refraction velocity (horizontally propagating P-wave (averaged from all back azimuths)); (b) Pn/refraction azimuthal anisotropy (azimuthal anisotropy in horizontally propagating P-wave); (c) Rayleigh wave velocity (horizontally propagating, vertically polarized shear wave (averaged from all back azimuths)); (d) Rayleigh wave azimuthal anisotropy (azimuthal anisotropy in horizontally propagating, vertically polarized shear wave); (e) Pn/refraction velocity/Rayleigh wave velocity (ratio of (a) and (c)); (f ) Pn/refraction velocity/Rayleigh wave velocity azimuthal anisotropy (azimuthal anisotropy in ratio of (a) and (c)); (g) Love wave velocity (horizontally propagating, horizontally polarized shear wave (averaged from all back azimuths)); (h) Love wave velocity azimuthal anisotropy (azimuthal anisotropy in horizontally propagating, horizontally polarized shear wave); (i) Pn/refraction velocity/Love wave velocity (ratio of (a) and (g)); ( j) Pn/refraction velocity/Love wave velocity azimuthal anisotropy (azimuthal anisotropy in ratio of (a) and (c)); (k) (Love wave velocity/Rayleigh wave velocity) 2 (square of ratio of (g) and (c)); (l) shear wave splitting (time difference between fast and slow shear waves in vertically propagating shear waves); (m) V P /V S from Hk stacking from receiver functions (ratio of vertically travelling P-wave velocity and vertically propagating, dominant (fast or slow shear wave that has largest amplitude) vertically polarized shear wave (averaged from all back azimuths)); (n) azimuthal anisotropy in V P /V S from Hk stacking from receiver functions (azimuthal anisotropy in (m)). velocity across all back-azimuths. The first observation was that the expected P-wave velocity was strongly dependent on the geometry of the melt. For horizontally aligned inclusions (Fig. 2a), low velocities occurred for large melt fractions stored with any inclusion shape, whereas for vertically oriented inclusions (Fig. 3a) the lowest velocities were seen for melt fractions in thin discs (low aspect ratios). Thus observations of low Pn velocity in the mantle suggest either high melt fractions or vertically aligned melt in disc-like inclusions. Interestingly, these models show that the absence of a Pn anomaly does not preclude the fact that melt is present. Significant amounts of melt can be stored as horizontally aligned low aspect ratio inclusions and give small (,0.2 km s 21 ) reductions in P-wave velocity. A strong azimuthal anisotropy would be expected for aligned vertical discs or horizontally aligned tubular inclusions (Figs 2b & 3b), but this would not be observed for horizontally aligned low aspect ratio melt or vertically aligned high aspect ratio melt (Fig. 2b).

Surface wave data
The best estimates of upper mantle S-wave velocities come from surface wave studies. Many studies have highlighted low S-wave velocities in the crust and mantle as evidence for the presence of melt (e.g. Ethiopia - Sebai et al. 2006;Bastow et al. 2010;East Pacific Rise -Forsyth et al. 1998;Gulf of California -Wang et al. 2009). Typically, these studies use both Rayleigh waves (vertically polarized) and Love waves (horizontally polarized). As for the Pn velocities in the previous section, we averaged across all back-azimuths to estimate the average S-wave velocity. For Rayleigh waves, a strong velocity reduction was seen for both horizontally and vertically aligned melts (Figs 2c & 3c); however, the reduction was strongest for low aspect ratio horizontally aligned melts. For Love waves, a strong velocity reduction was only seen for vertically aligned low aspect ratio or horizontally aligned high aspect ratio melts. Little reduction was evident for horizontally aligned low aspect ratio or vertically aligned high aspect ratio melts (Figs 2g & 3g). For vertically aligned low aspect ratio melts, both Rayleigh (Fig. 3d) and Love waves (Fig. 3h) showed strong azimuthal anisotropy, but with stronger anisotropy for the Rayleigh waves. This difference in azimuthal anisotropy gave rise to a weak radial anisotropy for low aspect ratio vertically aligned melt (Fig. 3k). If data are available from only selected back-azimuths, then different azimuthal anisotropies for Love and Rayleigh waves could give rise to an apparent strong radial anisotropy. For example, a Rayleigh wave travelling sub-parallel to the strike of aligned low aspect ratio melt will propagate with a relatively fast seismic velocity, whereas a Love wave travelling the same path will propagate with a relatively slow velocity, giving rise to the apparent radial anisotropy. For horizontally aligned low aspect ratio melt, the radial anisotropy is strong with V SH . V SV , particularly at low aspect ratios (Fig. 2h), but no azimuthal anisotropy is expected (Fig. 2d, h).
A parameter that can be used to distinguish the geometry of melt is the ratio of Pn velocity to surface wave velocity. For horizontally aligned melt, a large V P /V SV would be expected for moderate amounts of melt with aspect ratios ,1 (Fig. 2e). However, if melt is aligned vertically, on average little anomaly in V P /V SV is observed (Fig. 3e), although V P /V SV exhibits a strong azimuthal anisotropy (Fig. 2f). Conversely, for horizontal low aspect ratio melts little anomaly was expected for V P /V SH (Fig. 2i), but an increase in V P /V SH was observed for vertically aligned low aspect ratio melts (Fig. 3i).

Shear wave splitting
Shear wave splitting in subvertically propagating body waves is one of the most common techniques used to estimate S-wave anisotropy in the crust and mantle. It has excellent lateral resolution and, with the use of earthquakes from many depth ranges (e.g. crustal earthquakes, teleseismic earthquakes), it can place depth constraints on the origin of the anisotropy. Shear wave splitting in horizontally travelling body waves is difficult to measure due to free surface and near-surface effects (Booth & Crampin 1985), so we only investigated the effect of melt on vertically propagating shear waves. The presence of aligned melt has been used to explain high shear wave splitting results (e.g. Ethiopia - Ayele et al. 2004;Kendall et al. 2005;Gao et al. 2010;Keir et al. 2011;Hammond et al. 2014;Japan -Wirth & Long 2010). Much like previous studies investigating the efficacy of melt to generate anisotropy (e.g. Blackman & Kendall 1997), we showed that vertically aligned melt with low aspect ratios can generate significant shear wave splitting for vertically travelling phases (e.g. SKS splitting) (Fig. 3l). Horizontally aligned low aspect ratio melt will produce very little anisotropy in vertically travelling phases (Fig. 2l). However, high aspect ratio horizontally aligned melt can produce small amounts of splitting for high melt fractions (Fig. 2l).
studies have suggested that the presence of V P / V S . 1.85 provides evidence for significant melt in the crust (e.g. Ethiopia - Dugda et al. 2005;Stuart et al. 2006;Hammond et al. 2011;Tibet -Xu et al. 2007) and, more recently, Hammond (2014) showed that anisotropy in V P /V S can be explained by the presence of aligned melt. The presence of vertically oriented low aspect ratio melt (and, to a lesser degree, horizontally aligned high aspect ratio melt) will generate a split Ps phase as it enters the anisotropic medium. This gives rise to two values of V P /V S , one attributed to the fast S-wave and the other to the slow S-wave. The former will give rise to lower values of V P /V S , while the latter will be much higher. The relative amplitude of the split shear waves is controlled by the incoming back-azimuth, with back-azimuths close to the fast direction having a dominant fast shear wave and thus lower V P /V S than those events with a backazimuth close to the slow axis. This manifests itself in a strong azimuthal anisotropy in V P /V S (Fig. 3n). No azimuthal anisotropy was seen for low aspect ratio horizontal inclusions or high aspect ratio vertical inclusions (Fig. 2n), but V P /V S can be elevated across all back-azimuths (Fig. 2m).

Summary
It is clear that the presence of melt, depending on the amount and geometry, can provide a wide range of seismic observations. If melt is stored in tubules or spherical inclusions, this does not reduce seismic velocities efficiently and produces minimal seismic anisotropy, meaning that higher melt fractions of a few per cent are required to explain most seismic anomalies. This suggests that, in the presence of observed strong anisotropy or reductions in velocity, melt is most likely to be stored in geometries more similar to aligned discs. It is easy to envisage scenarios where this may be the case, such as melt stored in dykes or sills, preferentially aligned shear bands in the mantle (Holtzman & Kendall 2010), or due to the melt wetting grain boundaries (Garapic et al. 2013). Conversely, this shows that the absence of a velocity anomaly does not mean that melt is not present, rather it may suggest that the melt network or storage characteristics are not efficient at producing a seismic anomaly.
To determine how different melt scenarios affect seismic data, we first placed some estimates on the errors in the different seismic datasets (based on estimates from studies beneath Ethiopia). For absolute velocities, we assumed that an anomaly .0.2 km s 21 would be observable above error (e.g. Bastow et al. 2010;Stork et al. 2013). For V P /V S estimated from receiver functions, an anomaly .0.05 km s 21 is required (e.g. Hammond 2014). An anisotropy of at least 2% is needed for us to consider it to be observable. This equates to c. 0.3 s of splitting for a 70 km thick layer ), but anisotropy is often a path-averaged effect, so lower amounts of anisotropy over a large region may be observable. Radial anisotropy was estimated using the approach of Sebai et al. (2006): where V SV is the S V velocity and V SH is the S H velocity. Using errors for absolute velocity of 0.2 km s 21 resulted in errors in j of c. 0.1. With these estimates of error, we constructed Table 1. This can be used as a guide to determine the range of plausible melt scenarios that can be detected using different seismic phases. Seismically, one of the best indicators of melt is the Rayleigh wave velocity. This shows an observable velocity reduction for all scenarios except near-spherical/vertically aligned tubular inclusions with a low melt fraction (although these scenarios produce little observable anomaly in any dataset). At low melt fractions (,2%), Pn and Love waves are very sensitive to vertically aligned low aspect ratio melt, but show little anomaly in the presence of horizontally aligned low aspect ratio melt. This makes a combined analysis of Rayleigh and Love/ Pn waves very useful in determining the likely geometry of the melt. Indeed, this has been observed beneath Toba, Sumatra, where Jaxybulatov et al. (2014) argued that low Rayleigh wave velocities and normal Love wave velocities showed that melt must be stored in sills in the lower crust beneath Toba volcano. One note of caution is that Rayleigh, Love and Pn wave velocities are typically determined for a path average, so may be limited in being able to distinguish smaller bodies of melt or spatial changes in melt storage. This example of strong radial anisotropy in the presence of horizontally aligned melt shows how measuring anisotropy is a powerful tool to determine melt storage characteristics. Vertically aligned low aspect ratio melt will give rise to strong azimuthal anisotropy, which would manifest in back-azimuthal variations in most seismic datasets and in shear wave splitting for vertically travelling shear waves and receiver functions. An example of this comes from the Main Ethiopian Rift (MER), where strong shear wave splitting together with azimuthal variations in Rayleigh and Love waves show that aligned melt is present in the mantle beneath the MER Bastow et al. 2010) and strong shear wave splitting together with azimuthal variations in V P /V S from receiver functions suggest aligned melt in the crust beneath Afar, Ethiopia Hammond 2014). Horizontally aligned high aspect ratio melt (tubes) will also result in some azimuthal anisotropy, but with lower magnitude. However, high melt fractions with tubular geometries can cause observable splitting or azimuthal anisotropy in surface waves and observable velocity reductions for Pn, Love and Rayleigh waves. In the presence of strong azimuthal anisotropy, care must be taken in interpreting absolute velocity variations. If a dataset is biased towards events from one azimuth, then this could lead to the inference of larger/smaller anomalies than may be expected for an average across all azimuths.

Melt in the mantle beneath Ethiopia
Ethiopia is host to the meeting of three tectonic rifts: the Red Sea, Gulf of Aden and Main Ethiopian rifts ( Fig. 4). It is an ideal natural laboratory to study the final stages of continental break-up. Over the last two decades, many projects have focused on imaging the uppermost mantle to determine the driving processes of rifting beneath the region (Nyblade & Langston 2002;Maguire et al. 2003;Belachew et al. 2011;Hammond et al. 2011Hammond et al. , 2013  , suggesting that the injection of magma into the lithosphere plays a key role in accommodating the strain associated with tectonic break-up . However, to date, our understanding of the details of melt segregation has remained unclear. For example, estimates from Pn tomography suggest that c. 3% melt is present at uppermost mantle depths beneath the Dabbahu-Manda-Hararo (DMH) rift segment in Afar (Stork et al. 2013); however, magnetotelluric studies suggest upwards of 12% melt is present (Desissa et al. 2013). Pommier & Garnero (2014) suggested that the composition of the melt could partly explain this discrepancy because peridotitic melts are more conductive than basaltic melts, meaning that lower melt fractions (3-13%) could explain the magnetotelluric data. There is much evidence from measurements of anisotropy to suggest that melt is aligned beneath Ethiopia Sebai et al. 2006;Sicilia et al. 2008;Bastow et al. 2010;Hammond et al. 2010Hammond et al. , 2014Keir et al. 2011;Hammond 2014). As shown here and discussed previously (Kendall 1994;Hammond & Humphreys 2000), this alignment, together with the shape of the melt, can change the sensitivity of seismic waves to melt. For example, 1% melt stored at low aspect ratios could, in fact, give a larger seismic anomaly than 10% melt in spherical or tubule-shaped inclusions (Figs 2 &  3). This raises the question: what range of models of melt can explain the observed seismic anomalies?
In this study, we focused on the nature of melt storage in the uppermost mantle. Estimates of the depth of melt initiation vary from 75 to 90 km beneath the MER and Afar (Rooney et al. 2005;Hammond et al. 2010;Rychert et al. 2012;Ferguson et al. 2013;Armitage et al. 2015 (Makris & Ginzburg 1987;Dugda et al. 2005;Hammond et al. 2011). As a result, we looked for estimates of seismic velocity and anisotropy at c. 50 km depth as representative of melt in the mantle beneath the MER and Afar. We choose three areas that have been suggested to be underlain by melt, but which are related to different stages in the rifting process: (1) the MERan area of late-stage continental break-up; (2) the DMH rift segment in Afar -an area where incipient ocean spreading is thought to occur; and (3) the Danakil microplate (DM) in Afar -a suspected microplate located between the current location of rifting in Afar and the Red Sea between Eritrea and Yemen (Fig. 4). Table 2 shows the constraints used for the various regions. The P-wave velocities are from wideangle refraction studies in the MER (Mackenzie et al. 2005;Maguire et al. 2006) and a Pn tomography study in Afar (Stork et al. 2013). The S-wave velocities are from the surface wave model of Fishwick (2010). This study inverted Rayleigh waves, so these estimates are for the S V velocities. Estimates of shear wave splitting are from Hammond et al. (2014). This study used multi-layer inversions to identify an upper layer of anisotropy, probably related to melt in the uppermost mantle underlain by anisotropy due to flow in the mantle. We used the upper layer estimates of anisotropy only. To obtain estimates of anisotropy in the mantle, we removed the 0.1-0.4 s of splitting estimated for the crust from the receiver function studies 1.0-1.2 Sebai et al. (2006) 0.6-1.0 Bastow et al. (2010) beneath the DMH rift segment, Afar (Hammond 2014) and assumed that a similar amount existed in the crust beneath the MER, a reasonable assumption given the high splitting for upper crustal earthquakes . Finally, we used estimates of radial anisotropy (equation 1) from the regional surface wave study of Sebai et al. (2006) in Afar and the detailed local study of the MER of Bastow et al. (2010). The Sebai et al. (2006) study was at low resolution (c. 500 km lateral resolution), so care must be taken in using these constraints to infer lateral variations between the three locations presented here. For the Bastow et al. (2010) constraint for the MER, the best-resolved ray paths were rift-parallel and the inferred orientation of melt pockets was obtained from shear wave splitting and surface waves Bastow et al. 2010).
In comparing different parts of the rift system, we assumed that the properties of the mantle were unchanged. In reality, thermal structure, geodynamic flow, lithospheric topography and the composition of the mantle will all affect the rock matrix properties, the depth of melt initiation and the amount of melting. Also, realistic melting models show that the style of melting will vary from its initiation at depth to storage at shallower depths. Despite this, this simple modelling exercise can place some first-order constraints on the distribution of melt beneath Ethiopia.
A first assessment can be made qualitatively using Table 1. Extremely low P-wave and Rayleigh wave velocities were observed beneath the DMH rift segment, together with high shear wave splitting and a suggestion of j . 1 (V SH . V SV ) (although estimates of j are poorly constrained). Ignoring the estimates of j, melt scenarios 2, 9,11,13,16,18 and 20 fitted these data, suggesting moderate to high melt fractions with predominantly vertically aligned low aspect ratio melts or a very high melt fraction with a horizontally aligned high aspect ratio melt. Only a small Pn anomaly was observed beneath the DM. However, a strong V SV anomaly was present. Little shear wave splitting was observed and there was a suggestion of j . 1. Again, ignoring j, melt scenarios 1 and 3 fit these data, suggesting low melt fractions preferentially aligned horizontally. Finally, beneath the MER, strong P-and SV-wave anomalies were present, with strong splitting and j , 1 for rift-parallel paths. Melt scenarios 9, 16 and 18 fit these data, suggesting vertically aligned moderate to high melt fractions with low/moderate aspect ratios.
These results make sense intuitively, with strong vertical alignments of melt beneath the narrow MER and Afar rifts, as suggested by studies using individual datasets Bastow et al. 2010;Hammond et al. 2010Hammond et al. , 2014, although Hammond et al. (2014) suggested that the low degree of splitting away from the rift in Afar showed that horizontal melts were probably present. The next step was to see whether it was possible to perform a more quantitative approach and place better constraints on the range of melt models that can fit these data.

Melt segregation inversions
To invert the data, we used the same approach as outlined in the modelling section. However, we constrained our models using the observations summarized in Table 2. We varied the melt fraction (0-15%) and the aspect ratio (0.01-100) of vertical and horizontal inclusions and used a Voight-Ruess-Hill average to generate a composite medium. We also tested cases where only horizontal or vertical inclusions were present. This is similar to the approach used to invert receiver function estimates of V P /V S for melt geometries in the crust beneath Afar, Ethiopia (Hammond 2014). An important consideration is that we ignored any effects from preferred lattice orientations or other shapepreferred orientations from fine-scale layering and also any thermal or compositional effects, thus we may have overestimated the effects of melt-related anisotropy and an overall reduction in velocity.
We estimated P-wave and S-wave velocities for horizontally travelling waves (equivalent to Pn, refraction and surface wave studies) by averaging the velocities across all back-azimuths (an approach similar to surface wave and Pn inversions). For the S-wave velocity we used the vertically polarized wave for comparisons with Rayleigh wave inversions and horizontally polarized waves for comparisons with Love waves. We estimated the amount of shear wave splitting for a vertically propagating wave through a layer 70 km (DMH and DM) or 60 km (MER) thick. This is based on a likely depth of initial melting of ,90 km (Rooney et al. 2005;Hammond et al. 2010;Rychert et al. 2012;Ferguson et al. 2013;Armitage et al. 2015) and a crust 20 km (Afar; Hammond et al. 2011) and 30 km (MER; Maguire et al. 2006) thick. Finally, radial anisotropy was estimated using equation (1).
For Afar, we estimated the average V SV and V SH across all back-azimuths before calculating j. This is because Sebai et al. (2006) based their estimates on V SV and V SH inversions from all back-azimuths. However, as this model lacks detailed resolution, we also tested the Afar results without the Sebai et al. (2006) constraint. For the MER we estimated j using melt-parallel ray paths only, similar to the ray path coverage of (Bastow et al. 2010) (assuming melt is aligned in the orientation of the rift; Kendall et al. 2005).

MER
A number of observations were made beneath the MER (Fig. 5, Table 3).
(1) Low aspect ratio (0.02-0.2) vertically oriented melt must be present. (2) Melt solely stored in spheres or tubules cannot explain the data.
(3) If only vertically aligned melt is present, then it must have an aspect ratio ,0.2 (for 7% melt) and ,0.05 (for 2% melt). (4) Horizontally aligned melt is not required, but if it is present, then melt fractions are between 2 and 7% and the vertically aligned melt has aspect ratios between 0.02 and 0.10. There is no constraint on the aspect ratios of any horizontally aligned melt.    Light grey region shows all the models that fit the seismic constraints. Dark grey region is a projection of the models that fit the seismic constraints. (c) Light grey region includes constraints on radial anisotropy from Sebai et al. (2006), dark grey regions exclude constraints on radial anisotropy.

Afar: DMH rift segment
Beneath the DMH rift segment, a number of observations were made (Fig. 6, Table 4).
(1) Both low aspect ratio and high aspect ratio melts can explain the seismic observations. (2) If melt is stored in discs (a , 1), then melt fractions are .6%; both horizontal and vertical melt must be present. (3) If melt is stored in tubes (a . 1), then melt fractions are .11%. Horizontal high aspect ratio melts alone can explain the seismic observations. (4) If melt fraction ¼ 6%, then vertical melt has aspect ratios of 0.1-0.13 and horizontal melt has aspect ratios between 0.05 and 0.1. (5) If melt fraction ¼ 15%, then vertical melt has aspect ratios between 0.25 and 100 and horizontal melt has aspect ratios between 0.16 and 0.40 or 3 and 100. The results do not change considerably if the radial anisotropy constraints are not included in the inversion. The main difference is that we cannot rule out the possibility that more higher aspect ratio melts at high melt fractions may be present (Fig. 6, Table 5).
(2) If only horizontally aligned melt is present, then it has aspect ratios between 0.13 (4% melt) and 0.2 (6% melt). (3) Vertically aligned melt is not required, but if it is present then melt fractions are constrained between 1 and 5% and horizontal inclusions have aspect ratios ,0.1 and vertical inclusions have aspect ratios .0.08. Again, removing the radial anisotropy constraint does not change these observations. It allows models of horizontal melt with lower aspect ratios and lower melt fractions to fit the data (Fig. 7, Table 7).  (c) Light grey region includes constraints on radial anisotropy from Sebai et al. (2006), dark grey regions exclude constraints on radial anisotropy.

Discussion
To a first order, the inversion results support the qualitative assessment discussed earlier. Moderate to large amounts of melt, predominantly aligned vertically, are found beneath the MER and DMH, but away from the rift beneath the DM the melt is predominantly aligned horizontally and can be explained by relatively small amounts of melt. This supports previous observations in both the MER Bastow et al. 2010;Hammond et al. 2010Hammond et al. , 2014 and Afar . However, with this study we can now place some constraints on the likely shapes and amounts of melt in these regions. The MER must have significant vertically aligned melt with an aspect ratio ,0.2. Melt beneath the Red Sea Rift in Afar requires more melt (.6%) than the MER (2-7%), with a mixture of horizontal and vertically aligned melt. The mantle beneath the DM does not need particularly large amounts of melt (1-5%), but this must be stored in low aspect ratio horizontally aligned structures (a , 0.2). Melt present in the mantle (at fractions less than a few per cent) under isotropic stress conditions would be expected to reach textural equilibrium (Takei 2013). This would probably form a homogeneous network of interconnected tubules (Takei 2013). Our inversions show that this is probably not the case beneath the MER and much of Afar. Melt stored in low aspect ratio disc-like inclusions fits the data better than spheres or tubes (Tables 3-7). This means that if melt is stored at the grain scale, it is probably wetting the grain boundaries rather than the grain edges, similar to that seen in laboratory experiments (Garapic et al. 2013). Laboratory experiments on rocks show that, in the presence of uniaxial compression and shear, melt aligns on the grain boundary sub-parallel to the maximum compressive stress (Daines & Kohlstedt 1997;Zimmerman et al. 1999;Takei 2010). In addition, in shear experiments, melt-rich bands form at small strain rates, sub-parallel to the shear plane (Holtzman et al. 2003a, b;Takei & Holtzman 2009). Our results showed that low aspect ratio vertically aligned melt is present beneath the MER and the Red Sea Rift. Interestingly, the aspect ratios for vertically aligned melt beneath the MER are lower (0.02-0.2) than that for the Red Sea Rift (.0.1). Independent estimates of the amounts of melt beneath  the DMH rift segment come from magnetotelluric studies (Desissa et al. 2013). These models of conductivity structure estimate that up to 13% melt is present in the uppermost mantle. In our models, this suggests that melt is stored in high aspect ratio (.1) tubular-like inclusions.
Our results support the idea of lateral variations in melt storage beneath Ethiopia. In the narrow MER and, to a lesser degree, the DMH rift segment, where seismic evidence shows very steep gradients in the lithosphere-asthenosphere topography (Rychert et al. 2012), mantle flow can cause large strain rates at the rift margins, resulting in significant shear-derived segregation of melt. This generates subvertical alignment of the melt bands. Beneath the DM, melt (1-6%) is stored in horizontally aligned low aspect ratio (0.013 2 0.2) structures. In this region, little topography is inferred on the lithosphere-asthenosphere boundary (Rychert et al. 2012), thus any shear due to mantle flow will act to align the melt in horizontal sheets.

Conclusions
It is evident that seismology provides limited constraints on the amount of melt, but can estimate the location, the orientation of any alignment and the probable shape of any melt present. This is particularly true when using multiple seismic attributes, showing that joint inversions for anisotropy in multiple seismic phases are needed (e.g. Brisbourne et al. 1999;Obrebski et al. 2010). Future studies incorporating other geophysical (e.g. magnetotelluric), geodetic (e.g. global positioning system or interferometric synthetic aperture radar) and geological (experimental petrology) techniques to try and place constraints on the amount of melt in the crust and mantle will assist seismic constraints on the geometry of melt. We cannot distinguish between the different mechanisms of melt segregation (e.g. dykes and sills, melt on grain boundaries, shear-derived segregation of melt) with the modelling approach used here as any alignment of melt on length scales smaller than the seismic wavelength will cause similar anisotropy. Studies investigating frequency dependence in anisotropy measurements in hydrocarbon reservoirs have shown that the size of fractures can be identified (Maultzsch et al. 2003;Al-Harrasi et al. 2011). Applying this to earthquake data to understand the size of melt inclusions has the potential to place more constraints on the mechanism of melt segregation in the crust and mantle.
We have shown how the presence of partial melt in the crust and mantle affects a variety of different seismic waves. This is summarized in Table 1, which provides a guide to future seismic studies aiming to identify melt from the analysis of seismic waves. We applied this improved understanding to place constraints on the nature of the partial melt present beneath the MER and Afar Depression, Ethiopia. We showed that low aspect ratio melts stored in vertical inclusions are present beneath the MER and Red Sea Rift, with larger melt fractions beneath the Red Sea Rift than the MER, whereas low aspect ratio melt in horizontal inclusions was found beneath the DM. This supports the idea of the shear-derived segregation of melt being a major component for the transport of melt from its place of generation to shallow depths.