Introduction

The Earth’s asthenosphere is characterized by a region of high electrical conductivity (> 0.05 S/m) (Shankland and Waff 1977), ~ 3–8% reduction of seismic wave velocity and high seismic attenuation (Anderson and Sammis 1970; Romanowicz 1995). A low degree of partial melting has often been considered as a viable explanation (partial melting hypothesis), because the magnitude of seismic and electrical anomalies cannot be explained by the temperature effect alone (Fischer et al. 2010). Alternative mechanisms based on solid state processes, such as anelastic relaxation (Goetze 1977; Stixrude and Lithgow-Bertelloni 2005) and hydrogen diffusion (Karato 1990) in mantle minerals have also been proposed (null hypothesis). However, the recent finding of young alkali basalt (< 10 Ma) on the 135 million-year-old Pacific plate (Hirano et al. 2006) provides strong physical evidence for partial melting at the top of the asthenosphere.

The criteria for melting in the asthenosphere have been discussed in a number of recent papers (Galer and O’Nions 1986; Plank and Langmuir 1992; Dasgupta and Hirschmann 2006). Volatile-assisted melting in the asthenosphere is favored as the mantle temperatures at the relevant depths are expected to be lower than the dry peridotite solidus (Dasgupta and Hirschmann 2006). The volatile contents of the primitive mantle samples suggest mantle abundances of ~ 150  ppm wt of H2O and ~ 100  ppm wt of CO2 (Saal et al. 2002), while CO2 contents of up to 1800  ppm wt have been reported in undegased sources (Cartigny et al. 2008). The recent discovery of young alkali basalt associated with volcanism along fractures in the lithosphere indicates up to 5 wt% CO2 and 1.0 wt% of H2O volatile contents (Okumura and Hirano 2013). However, the measurements based on melt inclusions in minerals and quenched glasses indicate a global average of about 3000  ppm wt of H2O and 170  ppm wt of CO2 in natural mid oceanic ridge basalt (MORB) (Naumov et al. 2014). A substantial contribution of volatiles to the melting can be expected at low temperature regions in the asthenosphere (Sifré et al. 2014; Yoshino et al. 2010).

The reduced seismic velocity and elevated electrical conductivity have been widely used as evidence for the presence of melt in the Earth’s interior (Anderson and Sammis 1970). The magnitudes of the seismic velocity and conductivity variations are directly linked to the melt fraction, therefore comparison of geophysical data with laboratory models has long been considered as the most plausible way to quantify the melt contents in partially molten regions of the Earth (Anderson and Sammis 1970; Shankland and Waff 1977). The accurate determination of melt volume fraction in the asthenosphere is a key constraint for the plate tectonics and mantle convection models (Schmerr 2012). Apart from identifying the partially molten regions and quantifying the melt fractions, the seismic and electrical methods can also be used to characterize their spatial distribution. For example, laboratory-based experiments (Caricchi et al. 2011; Zhang et al. 2014; Pommier et al. 2015) have been able to attribute the seismic and electrical anisotropies observed at spreading ridge environments to the shear localization of melt due to plate motion.

The presence of a melt significantly modifies the viscoelastic properties of mineral assemblages. The critical parameters are the volume fraction and the melt microstructures (Kohlstedt 1992). Unfortunately, experimental determinations of seismic velocity on realistic melt compositions are limited to a few studies. An early measurement of Vp and Vs in a melt-bearing peridotite reported no significant effect of melt fractions below 3.0 vol% (Sato et al. 1989). The measurements based on torsional forced oscillation of melt-bearing olivine indicate reduced seismic velocities, and high attenuation can be observed for melt fractions as low as 0.01 vol% (Faul et al. 2004), suggesting a possible melt fraction of 0.1–1 vol%, for the average grain size variation in the upper mantle from 1 to 10 mm, respectively. The recent experimental developments allow accurate determination of seismic velocity measurements of partially molten rocks at the pressure and temperature conditions expected at the Earth’s interior (Chantel et al. 2016) and predicted about 0.2 vol% melt content in the asthenosphere. On the contrary, the melt fraction estimations based on the acoustic velocity of analogue systems (Takei 2000) indicate significantly higher melt fractions than those predicted using realistic upper mantle melts (Faul et al. 2004; Chantel et al. 2016). For example, the 6.6% melt required to explain 10% Vs reduction in Borneol-diphenylamine analogue system (Takei 2000) is considerably higher than the about 1% melt required by basaltic melt to explain a similar velocity reduction (Chantel et al. 2016).

The dependence of acoustic wave velocities and attenuation upon melt fraction and grain-scale melt distribution has also been discussed in several theoretical studies. These studies were based on ideal melt geometries and explained using the oblate spheroid model (Schmeling 1986), tube model (Mavko 1980), the crack model (O’Connell and Budiansky 1974) and models based on grain boundary wetness or ‘‘contiguity’’ (Takei 1998, 2002; Yoshino et al. 2005; Hier-Majumder 2008). The calculations based on the finite element method on melt geometries led (Hammond and Humphreys 2000) to conclude more than 1% melt is required to explain 3.6% and 7.9% velocity reduction for Vp and Vs respectively, which is significantly lower than the 6.2% and 11% reductions observed in laboratory measurements for similar melt fractions (Chantel et al. 2016). The naturally occurring, randomly distributed melt (Faul et al. 2004; Chantel et al. 2016) is shown to have a significant effect on seismic velocity compared to the simplified melt textures assumed in theoretical models (Hammond and Humphreys 2000; Takei 2002; Yoshino et al. 2005) or analogue systems (Takei 2000). The considerably higher melt volume fractions required in theoretical models can be attributed to the idealized geometries, such as planar cracks, spheres, ellipsoids, or simplified cuspate forms, which may not represent the true melt geometries in naturally occurring melt (Kohlstedt 1992; Faul et al. 1994; Hammond and Humphreys 2000), limiting their applications to partially molten regions in the asthenosphere.

An early electrical conductivity measurements on basaltic melt suggested 5–10 vol% melt needed to account for the observed electrical anomalies in the asthenosphere (Tyburczy and Waff 1983; Maumus et al. 2005). However, recent studies suggest the presence of much lower volume fractions; 0.3–3.0 vol% for hydrous basaltic melt (Yoshino et al. 2010; Ni et al. 2011), or less than 0.3 vol% for carbonatitic melt (Gaillard et al. 2008; Yoshino et al. 2010). The electrical conductivity of volatile enriched basalt (15–35 wt% CO2 and about 2–3 wt% H2O) indicates about 0.1–0.15 vol% melt could explain the observed conductivity anomalies (Sifré et al. 2014). The development of melt interconnectivity in partially molten rocks is known to have a profound effect on electrical conductivity (Waff 1974; Maumus et al. 2005). However, the number of studies investigating the influence of melt microstructures on EC is extremely limited. The study by ten Grotenhuis et al. (2005) showed that a melt geometry evolving from isolated triple junction tubes at 0.01% of melt to a network of interconnected grain boundary melt layers at 0.1% of melt has a greater effect on electrical conductivity.

Various other experimental techniques have been used to constrain the melt fraction associated with the low velocity zone (LVZ) in the Earth’s asthenosphere. Geochemical constraints from trace elements partitioning suggest that low degree of melting (less than 1%) can be generated at greater depth (below than 100 km) (Salters and Hart 1989). Similarly, studies based on experimental petrology, such as volatile (H2O and CO2) effect on peridotite solidus, indicate the melt fraction in the asthenosphere LVZ has to be 0.1 vol% or less (Plank and Langmuir 1992; Dasgupta and Hirschmann 2007).

Both experimental and theoretical models acknowledge that the volume fraction and spatial distribution of melt play an integral part in modifying the seismic and electrical properties of partially molten rocks. However, large discrepancies still remain in the laboratory estimations (regardless of the technique) of the amount of melt volume fraction present in the asthenosphere (Pommier and Garnero 2014; Karato 2014). Due to the large number of studies addressing the electrical properties of melt, the disagreement between laboratory-based electrical conductivity measurements is highly visible (Karato 2014). The influence of volatile contents could be one of the key parameters controlling the conductivity of the resulting melt (Yoshino et al. 2010; Ni et al. 2011; Sifré et al. 2014). A model based on chemical variation in the melt has been proposed to explain the apparent disagreement on melt fraction estimations between electrical conductivity measurements and seismic models (Pommier and Garnero 2014). The discrepancy may primarily stems from the absence of systematic experimental investigation into the structural factors influencing the EC in partially molten systems. The effect of melt fraction on seismic velocity has been mostly limited to numerical models. Significant disagreement between these theoretical models is still present due to the choice of melt geometries (Yoshino et al. 2005). A comparison with recent laboratory-based seismic velocity measurements on realistic partially molten materials (Chantel et al. 2016) indicates a significant underestimation of seismic response by theoretical models (Takei 2000; Yoshino et al. 2005). The cross-correlation of melt fraction estimations based on theoretical seismic models and laboratory electrical conductivity is at present a highly uncertain exercise.

The effect of melt texture and chemical compositions (volatiles) have long been assumed for the observed inconsistency, but there has never been a systematic study on how the evolving melt textures influence the electrical conductivity and seismic velocity (SV). Similarly, melt textures and melt contents during high pressure, high temperature experiments are strongly affected by the stress field and the temperature distribution within the sample and it is highly unlikely that two experiments would yield identical melt distributions.

In this study, we aim to investigate the effect of ongoing textural modification of partially molten peridotite analog on both electrical conductivity and sound wave velocity. Here we have developed a novel high-pressure multi-anvil cell design to investigate simultaneously the seismic and electrical properties of partially molten samples. Acoustic wave velocity (Vp and Vs) and EC are measured on an identical sample presenting the same temperature gradient, stress field and the chemical impurities, which all influence the melt content and the melt texture in partially molten high pressure samples. This critical improvement enables us to compare the seismic and electrical responses to the onset of melting, to different melt volume fractions and to the evolution of melt interconnectivity of a partially molten sample. Based on our observations, we suggest possible scenario which may resolve the observed discrepancy of melt fraction estimations based on EC and SV measurements.

Methods

Sample preparation

Samples used in this study were a powder mixture of natural San Carlos (SC) olivine and volatile-rich natural MORB glass (location 6°44′N, 102°36′W, collected during the Searise-1 research cruise). The volatile content is estimated to be 2730 (± 140) ppm wt H2O and 165 (± 40) ppm wt CO2 (Andrault et al. 2014), comparable with the average H2O and CO2 levels observed in MORB from diverse geological settings (Naumov et al. 2014). The MORB glass and inclusion free, hand-picked, SC olivine crystals were crushed separately and reduced to fine grain powders (see grain size distribution in Fig. S1). The water content analysis of the San Carlos olivine indicates less than 1 ppm wt of water (Soustelle and Manthilake 2017). These powders were then mixed in predetermined weight proportions to obtain the desired melt fractions at high temperature. The accurate determination of melt fraction using the image analysis is an uncertain exercise. The mixing of MORB with olivine results in an accurate control of the melt fraction in the sample as the MORB component melts instantaneously above its melting temperature, which is significantly lower than the olivine solidus. This procedure has been extensively used to obtain a controlled melt fraction in high-pressure experiments (Faul et al. 1994; Cmíral et al. 1998; Maumus et al. 2005; Yoshino et al. 2010; Caricchi et al. 2011; Zhang et al. 2014; Chantel et al. 2016). While this technique is suitable for obtaining controlled melt fractions (nominal melt fractions) in laboratory experiments, it cannot be used as a substitute for the physical property measurements of incipient melting scenarios (Sifré et al. 2014). We prepared different starting materials with MORB volume fractions of 0.1, 0.5, 1 and 2 vol% mixed with San Carlos olivine. The powder mixtures were ground with an automatic agate mortar for more than 2 h to obtain a homogeneous distribution of the MORB component. The average grain size of the starting powder size was estimated to be 3.74 ± 3.32 µm (Fig. S1). To achieve high accuracy during weighting of the powder, we prepare more than 5 g for each composition. The resulting powder mixtures were then hot pressed at 2.5 GPa and 1100 K for 2 h using a 1500 ton multi-anvil apparatus. The low temperature for hot pressing experiments (below the melting temperature of MORB) ensures that the starting materials are melt free and thus that the evolution of melt texture occurs during the conductivity and velocity measurements.

High-pressure high-temperature experiments

High-pressure, high-temperature experiments were performed using a 1500 ton Kawai-type multi-anvil apparatus at Laboratoire Magmas et Volcans, Clermont-Ferrand, France. For experiments conducted at 2.5 GPa, we used octahedral pressure media composed of MgO and Cr2O3 (5 wt%) in an 18/11 multi-anvil configuration (octahedron edge length/anvil truncation edge length) (Fig. 1). The assembly was designed to accommodate the geometrical requirements for measurements of Vp, Vs and EC in a single high pressure cell. The pre-synthesized cylindrical sample was inserted into a hexagonal boron nitride (hBN) capsule. The use of high-purity hBN sintered at high temperature and pressure without binder (Type—BN HP, FINAL Advanced Materials) prevents the B2O3 reacting with the silicate melt. The hBN capsule also helps to electrically insulate the sample with respect to the furnace. The furnace is composed of a 25 µm thick cylindrical Re foil, with apertures for the electrode and the thermocouples wires. A zirconia sleeve was placed around the furnace to act as a thermal insulator. Oxygen fugacity of the sample was not controlled during the experiments, but should be below Re-ReO2 buffer.

Fig. 1
figure 1

Schematic cross section of the high pressure cell assembly for simultaneous acoustic velocity and electrical conductivity measurements. The assembly was designed to place the sample at the centre of the cell at high pressure due to differential compression of alumina and MgO pistons. The respective pistons lengths were calibrated in prior experiments

Full size image

We placed two electrodes made of Re discs (25 µm thick) at the top and bottom of the cylindrical sample. A tungsten-rhenium (W95Re5–W74Re26) thermocouple junction was placed at one end of the sample to monitor the temperature. On the opposite side it was connected to a single W95Re5 wire (see Fig. S2 for details on electrode connection). We collected impedance spectra between the two W95Re5 wires. Cylindrical MgO ceramic sleeves were used to insulate the electrode wires from the furnace. A dense Al2O3 buffer rod was placed between one of the tungsten carbide (WC) anvil truncations and the sample to enhance the propagation of elastic waves and to provide sufficient impedance contrast to reflect ultrasonic waves at the buffer rod-sample interface. Both ends of the anvil, the alumina buffer rod and the samples were mirror polished using 0.25 µm diamond pastes to enhance mechanical contacts. All ceramic parts of the cell assembly, including the pressure media, were fired at 1373 K prior to the assembling to remove any absorbed moisture.

Acoustic wave velocity measurements

Acoustic wave velocities of samples were measured using the ultrasonic interferometry technique (Chantel et al. 2016; Freitas et al. 2017). In this method, electrical sine wave signals of 20–50 MHz (3–5 cycles) with Vpeak-to-peak of 1–5 V were generated by an arbitrary waveform generator (Tektronix AFG3101C) and were converted to primary (Vp) and secondary (Vs) waves by a 10° Y-cut LiNbO3 piezoelectric transducer attached to the mirror polished truncated corner of a WC anvil. The resonant frequency of the transducer is 50 MHz for compressional waves (P-waves) and 30 MHz for shear waves (S-waves). Elastic waves propagated through the anvil, the alumina buffer rod (BR) and the samples, and were reflected back at the anvil-BR, BR-sample, and sample-electrode interfaces. We also consider possible reflections from the Re electrodes (Davies and O’Connell 1977; Jackson et al. 1981; Nielser and Jackson 1989) (Text S1c). The reflected elastic waves were converted back to electrical signals by the transducer and captured by a Tektronix DPO 5140 Digital Phosphor Oscilloscope at a rate of 5 × 109 sample/s. Signals at 20, 30, 40 and 50 MHz were recorded at each temperature step. The two-way travel time for the acoustic waves propagating through the sample can be determined by the time difference between the arrivals of the echoes from the BR-sample interface and the sample-electrode interface by the pulse-echo overlap method (Kono et al. 2012).

Electrical conductivity measurements

EC measurements were performed using the ModuLab MTS Impedance/Gain-phase analyzer in the frequency range of 106–101 Hz. Polyphasic samples are characterized by a combination of resister-capacitor/constant phase element (R-C/CPE) circuits and the resistance can be obtained by fitting the impedance spectra to appropriate equivalent circuits (Fig. S3). Once the sample resistance has been determined, conductivity can be calculated using the sample dimensions determined at each temperature using the thermal expansion of the constituent phases. The insulation resistance of the assembly was determined in a preliminary experiment using an hBN rod at similar pressure–temperature conditions and was observed to be lower than the sample resistance.

At the target pressure of 2.5 GPa, the sample was kept at 500 K for more than 12 h. While maintaining 500 K, the electrical resistance of the samples, measured at regular intervals, usually increases due to the removal of the moisture absorbed by the sample and surrounding materials. This step is crucial to prevent the moisture (H2O) being incorporated into the sample at higher temperatures (Manthilake et al. 2009). The next heating cycle started once the resistance reached a steady value, which is often 1–2 orders of magnitude higher than the resistance measured at the beginning of the heating cycle. We generally performed several heating–cooling cycles at temperature steps of 50–100 K, until sample resistance was reproducible between the heating and cooling paths. This procedure minimizes the uncertainty of EC measurements due to adsorbed moisture. Once the solid sample EC was reproducible, the temperature was gradually increased in smaller temperature steps (25 K) to initiate melting. Sample melting is characterized by a drastic decrease in the sample resistance (increase in conductivity). Finally, the temperature was kept constant at 1650 K and impedance spectra were collected at regular intervals for more than 1 h.

Melt textures and dihedral angle measurements

Micro-textures of the recovered samples were investigated with a Field Emission Gun Scanning Electron Microscope (FEG-SEM) with an accelerating voltage of 15 kV and working distance of 9–11.6 mm. High magnification back scattered electron (BSE) images were obtained to identify the degree of interconnectivity and the structure of the melt at the grain boundaries in partially molten samples after SV and EC measurements. The presence of the hard alumina piston may introduce differential stresses to the sample, resulting in a shape-preferred orientation (SPO) in partially molten samples (Bussod and Christie 1991). To characterize the possible melt alignment in an olivine matrix, we performed image analyses on BSE images along a section parallel to the axis of the cylindrical sample. The orientation of the long axis of melt pockets and area of the melt pockets were obtained by image processing techniques using Matlab software (Fig. S4).

Grain size and grain orientation distribution

The grain size of our samples was estimated using two different techniques: the intercept method, and using FOAMS software (Shea et al. 2010). The intercept method estimates the number of intersections of grain boundaries with a random line drawn across the sample. The length of the line is important to statistically cross enough grains. The FOAMS software measures every isolated particle from skeletonized images and estimates its morphological parameters: area, perimeter, shape from 2D ellipse with a long and short axis, etc. The program also calculates 2D parameters such as aspect ratio and elongations. From the binary images, the code can convert 2D morphological information into 3D information using the equivalent diameter for spherical geometry by means of stereological conversion equations from (Sahagian and Proussevitch 1998). This program works properly for all type of samples for 2D information. Volumetric estimations (2D–3D) can be performed when the grains are mostly rounded and do not show strongly elongated shapes. Results are given in Table S1.

Experimental uncertainties

Experimental measurements of Vp, Vs and EC are subjected to uncertainties originating from the estimation of temperature, pressure, sample dimensions and fitting errors. Errors have been estimated to be 2.5% for seismic velocities (2σ), 5% for velocities drops (2σ) and 5% for EC values (2σ). Errors on the melt fractions are less than 1% relative (ex: 1 ± 0.01% of MORB). Detailed sources of uncertainties for each technique and error propagation calculations are given in supporting information (Text S1) (Bouhifd et al. 1996; Gillet et al. 1991; Li et al. 2007). Error bars are reported in each figure when larger than the symbol size except Figs. 2 and 8a for visibility.

Results

Acoustic velocity

The acoustic wave velocities obtained for samples containing SC olivine and 0.1, 0.5, 1, and 2% nominal volume fractions of melt are shown in Fig. 2. Below the melting temperature, Vp and Vs decrease with increasing temperature, emphasizing the characteristic decrease of bulk and shear modules with temperature. Upon melting of the MORB component, which is at about 1590 K, both Vp and Vs decrease significantly for the samples with 0.5–2% MORB. The magnitude of the velocity drop is positively correlated to the MORB fraction in the sample, but no significant change is observed at the melting temperature for pure olivine and the sample with 0.1 vol% melt. After the initial decrease in response to the MORB melting, the acoustic velocities Vp and Vs remain unchanged while maintaining the sample at a constant temperature of 1650 K.

Fig. 2
figure 2

a S- and b P-wave velocities as a function of increasing temperature (left) and as a function of time at a constant temperature (right) for olivine- and melt-bearing samples investigated in this study. The uncertainty results from the estimations of temperature, pressure, sample dimensions and data fitting errors and are estimated to be lower than 2.6% (2σ) of the value. Errors are not represented for visibility. Temperature error [10 K (2σ)] is within the symbol for all data points

Full size image

Electrical conductivity

The electrical conductivity of samples containing 0.1, 0.5 and 2 vol% of nominal melt fractions are shown in Fig. 3. At the melting temperature of MORB (~ 1590 K), the samples with 0.5–2 vol% melt indicate sudden increases in conductivity (up to a factor of 5), compared to their solid counterparts. However, no immediate change in conductivity is observed for 0.1 vol% melt upon crossing the temperature threshold. EC of all melt-bearing samples continues to increase after the melting event, while being kept at a constant temperature of 1650 K. The rate of increase of conductivity gradually decreases with time (Fig. 3), probably approaching a steady-state with time, however, these 1-h duration experiments did not reached a stable EC value over time. The conductivity values after being kept at 1650 K for more than 30 min indicate an increase in conductivity of 0.6 log units, a factor of 3.98, for the 0.1% melt sample compare to the value obtained before melting. The conductivity variations after being kept for more than 50 min at 1650 K, are about 0.6 log units, a factor of 3.98, for the 0.5%, and a 0.4 log units, a factor of 2.51, for the 2% melt-bearing samples.

Fig. 3
figure 3

Electrical conductivity as a function of reciprocal temperature (left) and, as a function of time at a constant temperature (right), for the samples containing 0.1, 0.5 and 2 vol% melt fractions. Solid and dashed lines indicate the corresponding conductivities immediately after melting and after 1 h at constant temperature of 1650 K. The uncertainties associated with the electrical conductivity data measurements are less at high temperatures. The uncertainty results from the estimations of temperature, pressure, sample dimensions and data fitting errors and are less than 5% (2σ) of the value for EC. Error in temperature is 10 K (2σ)

Full size image

Textural analyses of samples and melt

The presence of melt is clearly visible for all samples, with melt distributing along the grains boundaries as well as triple junction tubes. Interconnected melt networks are visible over a large part of each sample including the sample with 0.1 vol% of melt (Fig. 4). Using the high resolution SEM images, we determined the wetting angles of the melt-solid interfaces, which indicate a median angle of 27° ± 4°.

Fig. 4
figure 4

Backscattered electron (BSE) images showing near equilibrium melt textures at melt-olivine interfaces at 1650 K. Well-developed interconnected melt channels in samples with a, b 2.0%, c, d 1.0%, e, f 0.5% and g, h 0.1% melt volume fractions. The bright particles attached on sample surface and holes are rhenium pellets coming from polishing (TC’s, furnace and electrodes are made of Re). Biggest particles are presents in samples holes and along sample/capsule interface (c, g) whereas smallest particles are attached to sample surface along polishing scratches (well visible in f)

Full size image

Table S1 presents the grain size and grain orientation parameters derived from both intercept and FOAMS software, samples average grain size are similar and between 7 and 15 µm. The eccentricity is calculated from the best fitting ellipse foci and circle centre. This parameter indicates how far the best fitting ellipse deviates from perfect circularity, the values from 0.76 to 0.84 in our samples indicate that grains are mainly rounded but not perfect spheres. Elongation parameter is expressed by ε = (a − b)/(a + b), which characterizes the difference between the long (a) and short (b) axes of the fitting ellipse; large values (close to 1) indicate elongated particles. Our average values trends from 0.25 to 0.36, meaning grains have an elliptic cross section which slightly deviates from circularity. Aspect ratio is expressed as A = b/a, and characterizes the shape of the particle; large aspect ratios (close to 1) indicate particles are rounded and not elongated; our high-intermediate values are in good agreement with this observation.

The analyses based on the orientation of the long axis of melt pockets indicate random distribution of melt within the olivine matrix (Fig. S4). The associated histogram indicates no significant preferential orientation.

Discussion

Effect of evolving melt texture on acoustic wave velocity and electrical conductivity

Upon melting, partially molten samples evolve toward textural equilibrium with time, thus improving the melt interconnectivity and melt redistribution within the olivine matrix (Fig. 4). The comparison of images of samples before melting and after keeping prolonged time above the melting temperature of MORB clearly demonstrate the evolution of Ol + MORB powder mixture from initial non-equilibrium state (MORB is randomly distributed) to the extensive wetting of crystal faces and the smoothly curved solid-melt interfaces (Fig. S5). The textural equilibrium depends on several factors such as melt fraction, melt chemistry and grain size distribution (Laporte and Provost 2000). The melt geometries in olivine-basalt systems consist of grain boundary melt layers, triple junction networks (Yoshino et al. 2005, 2009) and ellipsoïdal discs (Faul et al. 1994). The continuous increase of EC observed in our experiments can be attributed to the gradual development of an interconnected network of melt channels, which facilitate the movement of charge carried through the melt. In contrast, acoustic wave propagation in a partially molten media should be more affected by the presence of melt in its path (volume fraction), than its fine geometrical evolution subsequent to melt interconnection. We note that the EC increased rapidly in the first tens of minutes and appeared reaching near steady-state after about 1 h, indicating that the textural modifications that influence the interconnectivity of the melt can be mostly achieved within few hours. The melt takes its final like shape very rapidly (in the first hour), however complete equilibration between melt and host olivine matrix in both chemical and textural aspects require several weeks of annealing (Waff and Blau 1982; Laporte and Provost 2000).

Interpretation of acoustic wave velocity results

The magnitude of the drop in seismic wave velocity in response to melting is proportional to the melt volume fraction in the sample (Fig. 2). Compared to the higher melt fractions, the sample containing 0.1% melt does not show abrupt variations of acoustic wave velocity in response to the onset of melting of MORB components. This observation suggests that the volume fraction of melt has to be sufficiently large (higher than 0.1 vol%) to alter the seismic wave propagation through partially molten rock. Additionally, associated errors to seismic wave velocity measurements and fitting does not allow distinguishing significant drop for low melt fractions (~ 0.1%). Further, the relatively constant seismic velocity at a constant temperature of 1650 K, after the melting of MORB, suggests that the seismic velocity is less sensitive to the ongoing textural equilibration of the sample. The melt fraction in a partially molten rock with complete wetting properties is observed to be the key parameter controlling the magnitude of seismic velocity in geological systems. The secondary waves (Vs) are more sensitive to the presence of melt due to their near zero shear modulus, which further enhances their ability to detect and quantify melting in laboratory samples.

The comparison of present data with previous experimental and theoretical estimations of seismic velocity is shown in Fig. 5. While our results are consistent with that of Chantel et al. (2016), there are considerable deviations in our experimental values from those estimated based on theoretical approximations (Takei 2000). As explained previously, the disagreement may arise due to the simplified melt geometries assumed in theoretical models. This observation can be further corroborated by comparing two theoretical models, one based on natural melt geometries (Yoshino et al. 2005), and the other on ideal melt geometries (Takei 2000). The model with melt arrangements similar to naturally occurring melt record a significant velocity drop for a given melt fraction compared to the one assuming ideal melt distribution. However, the model based on grain boundary wetness (Yoshino et al. 2005) also predicts the seismic velocities are significantly affected by modifications on the pore geometry. It has been shown that the melt wetting properties vary significantly with increasing pressure and volatile content (Yoshino et al. 2007). The slight discrepancy between the present study and that of Yoshino et al. (2005) can be explained by the change in wetting properties, due to improved melt wetting properties at high pressure and the presence of both H2O and CO2 in our samples.

Fig. 5
figure 5

Comparison of reported acoustic velocities and electrical conductivities for partially molten systems. a Vp,s/Vp0,s0 ratios for various melt fractions. Experimentally determined velocities for the olivine-basalt system (Chantel et al. 2016) and theoretical estimations for olivine-basalt (Yoshino et al. 2005) and melt analogue systems (Takei 2000) are shown for comparison. Errors in SV ratio are 3.6% (2σ), errors in melt fraction are within the data symbol (1% relative). b Reported electrical conductivity values for olivine, MORB and olivine + MORB compositions. Open circles and filled circles indicate our conductivity data for our volatile-bearing partial melts at melting and data after 1 h at 1650 K. The conductivity values presented in the figure are C06 (Constable 2006), P72 (Presnall et al. 1972), TW83 (Tyburczy and Waff 1983), N11 (Ni et al. 2011), Y10 (Yoshino et al. 2010), Z14 (Zhang et al. 2014), C11 (Caricchi et al. 2011), M05 (Maumus et al. 2005) and L17 (Laumonier et al. 2017). The EC values reported in Zhang et al. (2014) indicate melt conductivity before (open circle) and after (solid circle) the textural modifications due to the shear deformation. Errors on our data points are 5% (2σ) on EC value and 10 K (2σ) in temperature

Full size image

Interpretation of electrical conductivity results

The electrical conductivity variation while kept at constant temperature (at 1650 K) provides valuable insights into the development of interconnected melt channels in partially molten samples. For larger melt fractions (above 0.1%), the melt network forms efficiently as shown by an order of magnitude conductivity increase observed at the onset of melting. However, after the onset of melting and the associated EC jump, while kept at constant temperature of 1650 K, the increase in electrical conductivity for larger melt fractions (2% with 0.4 log unit increase of EC) is smaller than the sample with a low melt fraction (0.1% with 0.6 log unit increase of EC). This potentially indicates that when the melt fraction is sufficiently large, the major portion of melt is already arranged into a well distributed network of melt channels. On the other hand, the subsequent modifications improving the melt interconnectivity have a significant effect on low melt fractions. It has been shown that the melt geometry in a mineral-melt aggregate is determined by the solid–solid and solid–liquid interfacial energies (Laporte and Provost 2000). The solid–liquid interfacial energies may control the interconnectivity of a partially molten medium at low melt fraction; the network of melt could be limited in its 3D extension between the olivine grains, with some surfaces remaining initially non-wetted due to surface tension.

As for acoustic velocity, a sharp variation in electrical conductivity was not immediately apparent for the sample with 0.1% melt fraction. However, when maintained at 1650 K, EC continued to increase for the 0.1% melt sample, after 1 h to 0.6 log unit higher than the conductivity of the sample before melting. This observation suggests that the electrical conductivity method can be used to detect melt fractions lower than 0.1% as long as the measurements are performed on texturally equilibrated samples. This indicates that EC is extremely sensitive to the onset of melting. Furthermore, the sample resistance measurement is instantaneous and can be a powerful tool to detect the onset of melting during an experiment.

The electrical conductivity of similar olivine-basalt systems has been investigated in previous experiments (Maumus et al. 2005; Yoshino et al. 2010; Caricchi et al. 2011; Zhang et al. 2014; Laumonier et al. 2017) (Fig. 5). While measured conductivities are located within the individual EC measurements of olivine (Constable 2006; Laumonier et al. 2017) and basaltic melt (Presnall et al. 1972; Tyburczy and Waff 1983; Ni et al. 2011; Laumonier et al. 2017), the partially molten systems do not display good agreement between different studies. The slightly higher EC observed for partially molten samples in Yoshino et al. (2010), compared to our study may have been due to their use of texturally equilibrated melt-bearing samples (pre-synthesized samples in a piston cylinder apparatus) in electrical conductivity measurements, which compare favourably with our observations. EC values comparable to texturally equilibrated samples can be obtained by extrapolation of our EC data for timescales of days and weeks (Fig. 6).

Fig. 6
figure 6

The comparisons of electrical conductivity before and after 1 h at 1650 K for studied melt fractions. The conductivity corresponding to the LVZ is shown by the blue shaded area. The vertical lines indicate the minimum melt fractions required to explain the high-conductivity zone in the asthenosphere. Extrapolated data using the logarithmic laws fitted from data in Fig. 3 were represented from relevant time-scales with squares. This slow increase shows that weeks of equilibration will be necessary to have half an order of magnitude increase of EC. Such an increase is compatible with measurements performed on equilibrated material after weeks of annealing. Errors on EC are 5% (2σ) and within the data symbol for melt fraction (1% relative). Errors on extrapolated values are 10% (2σ) and we not displayed for distinction with measured data points

Full size image

The source of discrepancy

The interpretation of seismic and electrical anomalies in terms of melt fraction often results in conflicting estimations as to the extent of melting in the asthenosphere (Pommier and Garnero 2014; Karato 2014). A conductivity model based on major element chemistry of melt attributed the apparent inconsistencies in conductivity measurements to possible chemical variations in the melt (Pommier and Garnero 2014). Their model predicts that low degree melting of peridotite produces melt that is more conductive than basaltic compositions. We find their approach is an important step towards unifying the seismic and electrical observations. However, the melt fractions estimations used in their study were based on theoretical models, which appear to underestimate the effect of melt fraction on seismic velocity.

Monitoring the behaviour of melt-bearing samples for an extended period of time at high pressure and high temperature remains a challenging exercise. Escape of melt during prolonged heating is one of the major sources of failure, and experimental studies often overcome this issue by shortening the duration of the in situ measurements at high temperature. However, our results demonstrate that the EC values can vary significantly with time within the first hour of measurements, and relatively stable EC values can be obtained once the 3D interconnected network has been established. Texturally non-equilibrium melt can lead to an underestimation of the total effect on EC of a given melt fraction (Fig. 6). Comparison of such measurements with geophysical profiles, therefore, results in an overestimation of the melt fraction in the corresponding region in the Earth’s mantle. Values here provided after 1 h at 1650 K are not fully stabilized as highlighted by the subtle slope of the fit. We also note that once the sample conductivity stabilized, as a result of improved melt interconnectivity, electrical conductivity values of samples containing 0.1, 0.5, and 2% are not considerably different (less than one order of magnitude). This difference becomes subtle, close to the uncertainty of measurements, for higher melt fractions according to the trend shown in Fig. 6. This implies that uncertainties on inferred melt fractions from EC can be very important if implied melt fractions are higher than few percents. This observation is particularly crucial for magnetotelluric (MT) profiles with low spatial resolution. For these reasons, EC values here provided will not be further used for geophysical implications. However, we note that the electrical conductivity measurements are superior over acoustic wave velocity for qualitative detection of low melt fractions for samples with evolved melt textures. If the wetting properties of the melt are modified by the presence of significant amounts of volatiles in the melt (H2O and CO2) the electrical response for low melt fractions is instantaneous (Sifré et al. 2014).

In this study, we observe real-time Vp, Vs and EC responses during melting and consecutive textural evolution of melt. The variation of electrical conductivity subsequent to the melting of MORB can also be caused by the chemical changes occurring at high temperatures for a prolonged period of time. The effect of change in chemical composition on electrical conductivity in melt has been investigated in previous studies (Roberts and Tyburczy 1999), with a general trend showing an increase in conductivity with increasing alkali and Fe + Mg contents and a decrease with increasing silica content. However, we observe that the melt composition stays similar to the starting MORB composition during the experiments, except for a minor decrease in Fe content (Table 1). The Na is an important charge carrier in silicate melt (Pfeiffer 1998; Gaillard and Marziano 2005; Ni et al. 2011) and Na contents in our melt remains similar to the starting composition. Based on the totals of chemical analyses of melt, we confirm that significant volatile enrichments may not occur in our melt. Therefore, the observed conductivity increase with time is not expected to be caused by any chemical modification to the melt. This observation also confirms that the final melt fraction in the sample stays similar to the starting material. Similarly, due to the low partition coefficient between olivine and melt (~ 0.004) (Novella et al. 2014), the water is mostly retained by the melt phase, so proton (H+) diffusion in olivine affecting the electrical conductivity at high temperature can also be ruled out. The constant velocity after the melting of MORB components also rules out the possible increase in melt fraction in the sample at constant temperature, which is also supported by image analysis and chemical mapping of the sample. Further, analyses on the orientation of the matrix and melt pockets in our samples indicate random shape-preferred orientation (SPO) ruling out melt channelling due to possible anhydrostaticity in the high-pressure cell assembly (Fig. S4).

Table 1 Chemical composition of MORB and olivine before and after the experiments.
Full size table

Applications of laboratory results to the Earth’s interior

The comparison between laboratory data and seismological signals requires experiments in which the molten phase is in textural equilibrium with the solid matrix. Due to time-limited laboratory experiments, transient conditions may affect the results of acoustic velocities. In this case, textural analysis is important for correct interpretation of experimental data and run products. In a partially molten system at given pressure and temperature, the melt network can evolve to minimize the energy of melt-solid interfaces. This equilibration process concerns the wetting angle θ at solid–solid melt triple junctions, the area-to-volume ratio of melt pockets at grain corners and the melt permeability threshold (Laporte et al. 1997). The small dihedral angles estimated for our partially molten samples ensures complete grain boundary wetting and melt interconnectivity even for extremely low melt volume fractions (von Bargen and Waff 1986; Laporte et al. 1997; Laporte and Provost 2000), which is crucial for propagation of seismic waves. The solid-melt dihedral angle is known to vary with pressure, temperature and with the composition of the melt phase (Minarik and Watson 1995; Yoshino et al. 2005). Experimental studies suggest that textural equilibration is a time-dependent process, which usually requires long annealing times (weeks or months) (Waff and Blau 1982; Laporte and Provost 2000; Maumus et al. 2005). Still, small dihedral angle (10°–30°), the extensive wetting of crystal faces and the smoothly curved solid-melt interfaces observed in our samples are strong indications that the microstructure has reached transient conditions and forming a melt-solid network close to equilibrium textures (Cooper and Kohlstedt 1984; Waff and Faul 1992; Cmíral et al. 1998) (Fig. 4). Further, after reaching the peak temperature, the acoustic velocity remains nearly constant (Fig. 2), suggesting that the samples are well relaxed, enabling a safe comparison of our seismic wave velocity measurements with geophysical observations.

In addition, the extrapolation of laboratory acoustic wave velocities measurements to natural observations require the consideration of both anelasticity and frequency effects. Laboratory experiments (when not torsional) are usually performed at the frequency range from 20 to 50 MHz. The choice of this frequency range is determined by both requirements on excitation frequencies for the piezo-electric transducer as well with the restricted size of the probed samples in HP-HT apparatus.

Both anelasticity and anharmonicity that are accounting for the temperature dependence of sound velocity could lower the observed velocities. These are functions of frequency, temperature, pressure, mineral/melt intrinsic properties (including the chemical composition) as well as grain size and grain boundaries micro-textures (Rivers and Carmichael 1987; Karato 1993; Jackson et al. 2002, 2004; Faul et al. 2004). In solids, anharmonic effects related to thermal expansion (∂ρ/∂T) were found to be important in high frequency (MHz) experiments. This process does not imply energy loss and remains nearly insensitive to frequency (Karato 1993). On the other hand, anelasticity is associated to energy loss and depends on frequency and relaxation effects. Relaxation effects are thermally activated, hence anelasticity must be accounting for a significant part of the attenuation at high temperatures. Anelasticity of partially molten system have been poorly studied (Faul et al. 2004; Jackson et al. 2004). Because our melt fractions are small (≤ 2%) and similar to melt fraction estimated in the mantle, the assumption of using anelastic values of pure olivine is reasonable (Jackson et al. 2002; Chantel et al. 2016), also partially molten systems were found to have similar grain boundary sliding process to solid (Jackson et al. 2002; Faul et al. 2004). Nevertheless, this process is more easily activated in melt-bearing samples, where weaker grain boundaries have been reported (Faul et al. 2004). In addition, most of silicate melts have very high absorption in this frequency range and signals are seriously attenuated (Rivers and Carmichael 1987). However, this study showed that the echo overlap technique is suitable for high-Q melts, and thus appropriate for MORB melts. This study also stressed that for low viscosity melts (< 1000 Pa·s), which is the case of MORB melts at high temperature (presence of volatiles will significantly increase this effects), velocities are independent from frequency, as expected when wave’s period is much smaller than the characteristic relaxation time (1/f ≪ τ). Relaxation time was estimated using the relation τ = 0.01 × η × β, where β is the inverse of adiabatic compressibility and η the melt viscosity, used for fitting of theoretical and experimental dispersion curves by Rivers and Carmichael (1987). Calculation using their parameters for the Kilauea basalt (1700 K) yields relaxation time of 0.467 nanoseconds for frequency of 30 MHz (used in our study). The product of angular frequency by relaxation time between 10−2 and 10−1 (0.088) can be converted into a C/C0 ratio (see Fig. 10 in Rivers and Carmichael 1987). It estimates the measured velocity to be similar to the relaxed one as the ratio is very close to unity (1 ≤ C/C0 < 1.10), pointing a very small effect of anelastic behavior. Our moderately hydrous MORB probably have a lower viscosity and accordingly a shorter relaxation time favoring our conclusions.

Detailed discussion on quality factor (Q) estimation by ultrasonic experiments, on similar compositions, has already been made by Chantel et al. (2016). However, our ∂ln(Vp)/∂T and ∂ln(Vs)/∂T values of − 4.95 and − 8.78 (× 10−5) K−1, of our olivine + MORB samples prior melting, are somewhat similar with temperature dependence values calculated by high-Q from Karato (1993), indicating a good agreement with pure olivine data up to melting point with anharmonic plus anelastic behavior.

Finally, the use of MHz frequencies tends to underestimate the effect of anelasticity. This increases the uncertainty on our measurements, but this uncertainty must be reasonable as shown by the small errors estimated in absorption calculations (4%) (Rivers and Carmichael 1987), as well with near relaxed sound speed found for melt. In this study, we thus report a minimal effect of the presence of partial melt on the acoustic wave velocities and consider similar bias as estimated for solids (anelasticity and anharmonicity) because small fraction of melt seems to have only a moderate effect. Our extrapolation suffers also from grain size considerations as detailed by Jackson et al. (2002), even though this process was found to be nearly frequency independent for attenuation at mantle conditions.

Geophysical implications

Our study demonstrates that the melt content in a partially molten media can be better quantified using the reduction of seismic velocity for melt fractions with a minimum detectable melt fraction between 0.5 and 0.1% (no seismic velocity drop seen for 0.1%). On the other hand, for the studied melt fractions of 0.1–2.0% with well-developed interconnectivity, electrical conductivity, varies within a strict range of about 0.5 log units even if transient values were only reached, too narrow to resolve fine melt structures without introducing significant uncertainties.

In this study, we specifically use the % drop in acoustic wave velocity as a measure to determine the melt fraction. Our study indicates that the 3–8% global reduction in seismic velocity (Vs) observed at the top of the asthenosphere (Anderson and Sammis 1970; Widmer et al. 1991; Romanowicz 1995) can be explained by 0.3–0.8% volatile-bearing melt (Fig. 7a). However, these values may vary laterally depending on the extent of melting at the corresponding temperatures and the volatile contents in the mantle (Sifré et al. 2014). Regional Vs variations of up to 10% observed below the Pacific plate (Schmerr 2012) indicate large melt fractions of up to 1% present in some parts of the asthenosphere, suggesting large heterogeneities in terms of melt distribution. Apart from the global reduction of seismic velocity, numerous studies report velocity perturbations in various geological settings such as spreading ridges, intraplate mantle plumes and subduction (e.g., Pommier and Garnero 2014). Assuming melt chemistry does not have any significant influence on acoustic wave velocity (Rivers and Carmichael 1987); we compare our melt fraction estimations to those reported using theoretical models (Table S2 and Fig. 7b).

Fig. 7
figure 7

a The % drop in P- and S-wave velocity as a function of the sample melt fraction. The geophysically observed S-wave velocity anomaly for the LVZ in the asthenosphere is shown by the shaded rectangle. Note that the 3–8% Vs drop observed for most of the asthenosphere can be explained by 0.3–0.8% melt. bVs velocity anomalies observed at various geological settings and the possible melt fraction estimations based on our model. The Vs anomalies presented in the figure are from EPR 17S (Toomey et al. 1998), EPR 8-11N (Toomey et al. 2007), Yellowstone-Snake River (Wagner et al. 2010), Hawaii (Laske et al. 2011), and the Pacific (Kawakatsu et al. 2009; Schmerr 2012). Errors on velocity drops are 5% (2σ) relative and within the symbol for melt fraction (1% relative)

Full size image

In addition to the use of absolute sound wave velocities and velocities drop, the use of Vp/Vs ratio can be of significant interest for comparison with seismological data. Bulk and shear moduli of a partial melt system (a solid containing pore spaces saturated with melt) varies as a function of melt volume fraction. Accordingly, the relative change of Vp/Vs ratio could indicate the presence of melt in deep mantle conditions. As detailed in Chantel et al. (2016), the absolute velocities values measured on analog systems do not compare well with real seismic velocities measurements. It is mainly due to the difference in mineralogy (e.g., pure olivine against peridotites) and relaxation effects due to differences in frequencies between natural and experimental seismic velocities estimations (see discussion therein). However, the use of Vp/Vs ratios and its variations allow a relevant comparison of our analog data to natural system as changes are relative and not based on absolute velocities values.

Our data indicate that below melting point, Vp/Vs ratio increases from 1.75 to 1.8 from room temperature up to 1650 K (Fig. 8). These values are consistent with values observed for solid upper mantle ranging from 1.7 to 1.8 given by standard models such as PREM (Dziewonski and Anderson 1981) or AK135 (Kennett et al. 1995). These values are also consistent with moderate Vp/Vs values obtained from upper mantle minerals, ranging also between 1.7 and 1.8 for olivine (1.8), clino and orthopyroxenes (1.72 and 1.74) at the same pressures (Li and Liebermann 2007). At melting, we observe a strong and sudden increase of the Vp/Vs ratio. The magnitude of the increase correlates positively with the melt fraction. Vp/Vs ratios above 1.9 are observed for sample with 2% melt fraction (Fig. 8c). Our Vp/Vs ratio values compare favorably with LVZ estimations with ratios given by global models ranging between 1.8 and 1.85 and requiring only moderate amount of melt (< 1% of melt). However, our data implies very high melt fractions involved in local anomalies where Vp/Vs ratios up to 2.5 or more have been reported (Schaeffer and Bostock 2010; Hansen et al. 2012). These very high anomalies imply higher melt fractions (12.5% for Vp/Vs ratio of 2.5, based on the trend defined in Fig. 8c) even if other physical processes such very high volatiles contents in melts could explain these anomalies.

Fig. 8
figure 8

aVp/Vs ratio of our experiments reported as a function of increasing temperature. The standard deviation on the data lies between 0.0305 and 0.0335 (lowest to highest temperature values) corresponding to an error majored by 1.75% of the Vp/Vs ratio (1σ). bVp/Vs ratio as a function of the volume melt fraction (MORB content). Values for solid sample before melting are represented by circles and values after partial melting occurred with squares. Vp/Vs ratios from seismological data: PREM (Dziewonski and Anderson 1981) and AK135 (Kennett et al. 1995) are represented in black dashed lines. Vp/Vs ratios from nominal minerals are represented by colored zones (green for Olivine, grey for OPX and gold for CPX), velocities data at 2.5 GPa were taken from (Li and Liebermann 2007). c Inset figure in aVp/Vs ratio increase at melting in function of melt fraction, quantifying the magnitude of increase of the ratio in response to partial melting

Full size image

In general, we find that the melt contents reported in previous geophysical studies are consistently higher than the estimations based on laboratory measurements of seismic wave velocities. The majority of these studies used the theoretical prediction of velocity reduction for partially molten rocks, which underestimate the effect of melt fraction on seismic velocity. The use of our laboratory measurements provides melt fractions that are consistent with petrological models. Further, we believe that the refined melt fraction estimations would provide a solid platform to constrain a meaningful cross-correlation between field-based seismic and electrical observations. The effect of the chemical composition of melt on acoustic wave velocity is one of the important aspects worth exploring in future studies.

Conclusions

This study presents the first simultaneous measurements of electrical conductivity and acoustic wave velocity of partially molten samples of geophysical importance. The results highlight how electrical conductivity and acoustic wave velocity respond to the evolving melt texture from a completely random melt distribution. The continuous increase of electrical conductivity at constant temperature, after melting of MORB, indicates that the melt interconnectivity evolves with time. In contrast, constant seismic velocity after the melting suggests acoustic velocity is sensitive to the melt volume fraction in the sample, but less affected by the evolving melt texture. Our results suggest that the electrical conductivity of partially molten materials measured before reaching the evolved melt interconnectivity can lead to an underestimation of the EC for a given melt fraction. This may result in an over-estimation of melt fraction in geological settings. Overall, the Vs measurements appear to be a more appropriate method for determining the melt fraction in a partially molten system with complete wetting properties. The previous approximations based on theoretical models of seismic velocity appear to overestimate the extent of melting in the mantle. This study demonstrates the importance of using electrical conductivity values from texturally equilibrated partially molten sample for comparison with geophysical data.