Lower crustal earthquakes in the East African Rift System: Insights from frictional properties of rock samples from the Malawi rift

Earthquakes in the southern part of the East African Rift System (EARS) occur at depths up to 45 km in the lower crust, unusually deep for an extensional regime. Typically, earthquakes in continental crust nucleate at temperatures less than 350°C, the temperature at which crystal plastic creep in quartz becomes efficient, corresponding to a depth of ~15 km with an average continental geothermal gradient. Several hypotheses have been proposed to explain the deep seismicity in the EARS, including the presence of high-viscosity mafic material, an abnormally low geotherm, locally elevated strain rates, or high fluid pressures. Here, we provide frictional properties of simulated fault gouges to address the seismic behavior of felsic and mafic crystalline basement rocks from the amagmatic Malawi Rift at the southern, propagating end of the EARS. Rotary shear experiments are conducted at 100, 200, and 250 MPa effective normal stress, a fluid pressure of 100 MPa and from room temperature to 700 °C. The friction of the felsic sample (58% plagioclase) is fairly constant up until 400 °C, after which it decreases. At temperatures of 600 °C and above, the relation between shear stress and effective normal stress deviates from linearity. The friction coefficient of the mafic sample is nearly constant in the considered range of temperature and normal stress and the sample shows a linear relation between normal stress and shear stress. The mafic sample also has negative, and decreasing, (a-b) values at temperatures > 400°C. These results are consistent with earthquake nucleation in mafic material, if present, at lower crustal P-T conditions. On the other hand, the data indicate that earthquake nucleation is unlikely in felsic material at temperatures above 500 °C, unless effective normal stress is low and strain rate is elevated by several orders of magnitude.

Several explanations have been proposed for a deep seismic-aseismic transition in the EARS.It has been suggested that the depth of the transition is influenced by the presence of old, cold, anhydrous, strong and thick crust and lithosphere (e.g.Shudofsky et al., 1987;Jackson & Blenkinsop, 1993;Nyblade & Langston, 1995;Jackson et al., 2004;Craig et al., 2011).Craig et al. (2011) suggest that thick conductive lithosphere acts as a thermal insulator for the crust from the mantle, which lowers the geotherm, thereby allowing for a larger depth extent of seismogenesis.In order for quartz-rich rocks to generate earthquakes at 35-40 km depth, an average geothermal gradient of 7.5-10 C/km would be needed.It is also possible that mafic material is present in the EARS lower crust and can account for brittle seismogenic behavior to a deeper level than would be expected for felsic rocks (Shudofsky et al., 1987;Nyblade & Langston, 1995;Albaric et al., 2009;Fagereng, 2013).This is because of the greater viscous strength of mafic rocks (Mackwell et al., 1998).An increased fluid pressure due to the presence of magma or other volatiles could cause local and transient embrittlement within viscous lower crust (Corti et al., 2003), but increased fluid pressures have been considered unlikely in the amagmatic southern EARS where lower crustal earthquakes occur (Craig et al., 2011).
Another mechanism to increase strain rate is by strain localization.The anisotropy of the crust causes weak zones where deformation localizes, increasing the stain rate in these zones (Kirby, 1985).This can allow frictional failure to occur at significantly greater depths than with a homogeneously distributed strain.A condition for these weak zones hosting seismicity at great depths, is that the surrounding rock must be strong and store sufficient elastic strain to generate seismic slip in these weak zones.Fagereng (2013) suggests that seismic behavior at great depths within strong, possibly mafic, lower crust can take place within weak shear zones, where deformation is localized, and strain rate is elevated.This hypothesis agrees with Handy & Brun's (2004) model of earthquakes being signs of transient rheology, and observations of lower crustal pseudotachylytes within mylonites in anhydrous, strong rocks (e.g.Sibson, 1980;Menegon et al., 2017).
Here, we report results from hydrothermal rotary shear experiments on gouges derived from a mafic and a felsic rock from the Malawi rift, an amagmatic segment of the EARS where lower crustal earthquakes have been observed (e.g.Jackson and Blenkinsop, 1993;Nyblade and Langston, 1995;Yang & Chen, 2010;Craig et al., 2011).The samples were tested to analyze trends in friction and friction rate parameters (a-b) with temperatures and effective normal stresses going up to 700°C and 250 MPa, respectively.The aim is to obtain frictional properties of the felsic and mafic end member components to identify whether either of the samples could be capable of hosting deep earthquakes.Also, since localization on weak planes may play a crucial role in increasing the strain rate and shifting the brittle-viscous transition deeper, the experimental microstructures were studied to investigate the deformation processes and any evidence for strain localization.

Materials
For these experiments, we selected two end member rock types from the Malawi region, one sample a quartzofeldspathic gneiss (sample M01) and the other a retrogressed, mafic basement gneiss (sample M17).The locations of these samples are indicated in Figure 1.Both samples are crystalline basement rocks with a schistose to gneissic fabric (Figure 2a,b), from high strain zones within outcrops mapped as Paleoproterozoic metamorphic rocks.The mineralogy was analyzed using semi-quantitative XRD as well as by total dissolution in HF and subsequent ICP-MS analysis (Supplementary Table 1).The relative mineral abundances were calculated on the basis of the minerals identified in the XRD, by optical microscopy, and the whole rock chemistry determined in the ICP-MS analysis and is shown in Table 1.
The felsic sample M01 contains more than 50 % plagioclase with substantial amounts of muscovite and quartz and minor garnet, ilmenite and sphene.It can be classified as a quartzofeldspathic gneiss and was collected adjacent to the Mughese shear zone.The rock contains a well-developed foliation defined by compositional domains (Fig 2a,c), with a superimposed but weakly interconnected micaceous foliation (Fig. 2c).The microstructure is characterized by dynamically recrystallized quartz showing a consistent grain size of tens of micrometers, and a weak shape preferred orientation (Fig. 2c).Feldspar porphyroclasts are present within the pervasively recrystallized quartz matrix, but also have a relatively small grain size which rarely exceeds 100 µm.
Mafic sample M17 consists of hornblende (> 50%) with plagioclase, quartz, and accessory phases.At the outcrop scale, the rock is pervasively lineated and has a foliation defined by feldspar and amphibole rich domains (Fig. 2b).Hornblende crystals show a well-developed shape preferred orientation, also weakly developed in the feldspar layers (Fig. 2d).
Malawi basement rocks are typically Neo-to Paleoproterozoic in age, but the rift valley follows orogenic belts that have been deformed in up to three events at metamorphic grades from amphibolite to granulite (Fig. 1; Versfelt and Rosendahl, 1989).Both samples chosen here contain amphibolite facies minerals, such as hornblende and white mica.They therefore represent rocks that either only reached amphibolite facies temperatures, or that experienced some rehydration subsequent to higher grade metamorphic conditions.Retrograde hydration has long been established as typical of deforming zones in the mid-to lower crust (e.g.White & Knipe, 1978;Wintsch et al., 1995).The rocks are therefore representative of materials that would deform preferentially within granulite facies felsic and mafic gneisses, or of typical felsic and mafic amphibolite facies rocks.There is inevitably variation throughout the Malawi rift around the chosen compositions, but we identify the rocks chosen for the experiments as pervasively sheared (Fig. 2a,b) and likely to have accommodated localized shear strain at mid-to lower crustal conditions.They are therefore suitable for general hypothesis tests on the frictional properties of rocks at mid-to lower crustal conditions in the Malawi rift.

Methods
The samples were crushed with a pestle and mortar and sieved until all particles were smaller than 0.5 mm.This material was subsequently crushed using a Retsch XRD-Mill McCrone to obtain a narrow particle size distribution with an average grain size of 5 μm.Grain size analysis was done with a laser diffraction particle size analyzer.Results can be found in supplementary figure S1.
In order to obtain a reproducible starting layer thickness and porosity, about 0.65 grams of powder with ~0.05 grams of D.I. water was pre-pressed in a dye at a stress of 208 MPa into ring-shaped samples (see also Den Hartog et al., 2012).A hydrothermal ring shear apparatus as described by Niemeijer et al. (2008) and Den Hartog et al. (2012) was used to perform a series of rotary shear experiments (supplementary figures S2 and S3).In these experiments, the ring-shaped sample is sandwiched between two pistons placed inside a pressure vessel.Normal load is then applied to the sample by an Instron loading frame and controlled to within 0.05 MPa.Fluid pressure and temperature inside the vessel can be controlled to within 0.1 MPa and 1°C, respectively.The piston sealing assembly is equipped with a pressure compensation chamber, so that applied fluid pressure does not affect the effective normal stress on the sample.We used demineralized water as the pore fluid which can access the sample through small gaps between the piston and confining rings.While the top piston is kept stationary, the bottom piston is rotated by a motor in a clockwise direction, creating a dextral shear on the sample.Two load cells in the upper forcing block measure the torque applied to the system by the rotational movement which is then converted into shear stress (resolution of 0.006 MPa for the 1.2 kN loadcells, 0.0249 MPa for the 5 kN loadcell, and 0.0997 MPa for the 20 kN loadcells).Rotary displacement is measured on the base of the vessel using a potentiometer with a resolution of 0.12 m.
Three types of experiments were done: (1) Constant velocity and constant normal load experiments to create microstructures at selected conditions.In these experiments, the samples were sheared at 1 μm/s for 5000 seconds; (2) velocity stepping experiments at varying temperature; and (3) normal stress stepping experiments at varying temperature (600, 650 and 700°C) and normal stress conditions (50 -250 MPa), to investigate the dependence of shear stress on effective normal stress, all with a constant pore pressure of 100 MPa.To achieve steady state in these experiments, a run-in was performed at 1 μm/s for 3000 seconds.After this, velocity or normal load was stepped up.The experimental data were inverted to obtain values for a, b, (a-b) and d c by using an iterative least squares method (e.g.Reinen & Weeks, 1993;Blanpied et al., 1998;Ikari et al., 2009).The normal load stepping tested the dependence of shear stress on normal stress to establish any divergence from purely linear dependence, indicating deviation from frictional deformation behavior.The data were acquired at 900 Hz using a 18-bit National Instrument A/D converter and averaged and logged at rates of 1-300 Hz using LabView.Analysis of the data was done using Xlook, in which the data were corrected for the seal friction (normal and shear stress) and the stiffness of the machine (displacement).The apparent friction coefficient of the samples in these experiments was then calculated as ⁄ , thereby ignoring cohesion.Data were analyzed based on the RSF theory (Dieterich, 1978;Ruina, 1983;), which describes the sliding behavior of a fault with a set of constitutive equations, using the slowness version of the state evolution (e.g.Marone, 1998): In these equations, a and b are material properties for describing friction, in which a is seen as the direct effect and b as the evolutionary effect.At steady state, the state variable does not change, so equation (1) reduces to ∆ ln In this equation, ∆ is the difference between steady state friction before and after a velocity step, V 0 is the sliding velocity before the step, and V 1 is the sliding velocity after the step.
The velocity dependence of steady state friction, which determines the stability of sliding, results from an interplay between a and b (e.g.Scholz, 2002).If (a-b) > 0, the material is velocity strengthening, which will always lead to stable sliding.If (a-b) ≤ 0, a frictional instability can occur at a critical value of effective normal stress ( ).For a given system stiffness, sliding is unstable under quasistatic loading if .If , it is in the conditionally stable regime, meaning sliding is stable under quasistatic loading, but unstable under dynamic loading if subjected to a jump in velocity exceeding ΔV (Ruina, 1983, Gu et al., 1984, Scholz, 1998).
After the experiment, the samples were dried and impregnated with epoxy resin.The samples were then cut so that the inside of the sample, normal to the shear plane and subparallel to the shear direction, could be studied (Supplementary Figure S4, Verberne et al., 2015).

Results
The evolution of the apparent friction coefficient with displacement at different temperatures and normal stresses is shown in Figure 3 for both samples.All the experiments are characterized by an initial increase in friction which rolls over into a steady level of friction, except for the experiments at 400 and 600 ºC for the mafic sample and at 600 and 700 ºC for the felsic samples.In these cases, an initial increase to peak friction occurs with subsequent weakening, which is larger in the felsic sample.Regardless of temperature, subsequent velocity-steps show the typical response to upward changes in driving velocity; an instantaneous increase in friction followed by a decay towards a new steady state level.At a temperature of 200 ºC (Fig. 3a), unstable slip events or stick slips appear for both samples during the runin at 1 m/s and persist during the velocity-steps up to a velocity of 10 m/s (felsic) or 30 m/s (mafic) at which point friction stabilizes.At temperatures of 300°C and 400°C (Fig. 3b), strength increases from ~0.6 to ~0.7 for the felsic sample, whereas the friction coefficient for the mafic sample remains relatively stable at ~ 0.7.Some stick slips induced by velocity steps can also be seen for the felsic sample at 300 °C and 400 °C (see Figure 5 for model inversions for two of these steps).
Figure 3: Plots of the evolution of friction with displacement.Temperature and effective normal stress as indicated.Sliding velocity was stepped through the range 1-3-10-30-100 with a displacement for each individual step of 3-0.9-0.9-0.9-0.9 mm, respectively.
Stick slips develop at velocities of 30 m/s and higher for the mafic sample at 300°C, and at 400°C for the felsic sample.At 500 °C and 600 °C (Figure 3c), the felsic sample at 100 MPa is clearly weaker than at lower temperatures, but the sample has a much higher apparent friction at 200 MPa where it is stronger than the mafic sample.Elevating the effective normal stress to 250 MPa did not increase friction further.The friction coefficient of the mafic sample remains near 0.7 at 500 °C and 600 °C temperatures and 100 and 200 MPa normal stresses.The data for the experiments at 700 °C are shown in Figure 3d.While the mafic sample is again around the same value of friction of ~0.7, the felsic sample shows considerable weakening with displacement, from a peak friction of ~0.55 to 0.45 and subsequently shows strong transient increases in friction as a result of the velocity-steps.
Values of steady state friction for the different samples at different temperatures and normal stresses are presented in Table 2.The steady state friction values were determined after about 3 mm displacement at 1 μm/s.In figure 4, this steady state friction is plotted vs. temperature.At 500 °C and 600 ºC, the values for the mafic sample at 100 MPa and the felsic sample at 250 MPa are very similar.For the mafic sample, the friction coefficient seems to be relatively independent of normal stress and temperature and is around 0.7 for all conditions.The felsic sample has a friction of around 0.55 at low temperatures, then increases to 0.6-0.7 between 200 °C and 400 °C, after which it decreases again.At 200 MPa, apparent friction is considerably higher, up to 0.81 at 600°C.
Figure 6 shows how (a-b) values at 100 MPa vary with temperature and velocity.At low (<100 °C) temperatures, (a-b) values for both samples are positive, indicating stable sliding behavior.At temperatures larger than 100 °C, (a-b) values for both samples are predominantly negative.While the felsic sample has negative (a-b) values both for low and high velocities, the mafic sample shows a clear trend with positive (a-b) values for high velocities, going towards negative values at low velocities, with the exception of the experiment at 200 °C (Figure 6d).At 700 °C, the felsic sample shows strongly positive (a-b) values, that are an order of magnitude larger than typical room temperature values.In comparison, the mafic sample shows a more gradual variation in (a-b) values, and still has negative (a-b) values at low velocities at 600 ºC.In general, the transitions from negative to positive values for the mafic sample occur at lower velocities with higher temperatures.At constant temperatures of 500 and 600 ºC, higher effective normal stress yields more positive values of (a-b), irrespective of sliding velocity (Figure 7).Values for the individual RSF parameters could not be obtained for all velocity-steps because sliding was frictionally unstable, which makes it impossible for the inversion to find solutions.In these cases, we used the peak friction and the steady state solution (equation 2, see also He et al., 2003) to obtain values for (a-b) that are shown in Figures 6 and 7 (see also Tables 3 and 4). Figure 8 shows that the a-value shows a mild increase with temperature for the mafic sample, whereas it increases exponentially for the felsic sample at a temperature of > 500 ºC, showing extremely large values of a of ~0.1 at a temperature of 700 ºC.
As the felsic sample showed variations in apparent friction with effective normal stress, normal load stepping experiments were performed for this sample.For samples that show purely frictional behavior, shear stress is linearly dependent on normal stress.Figure 9 shows the shear stress (a) and apparent friction (b) as a function of effective normal stress for the felsic sample.At 600°C and 650°C, shear stress at high normal stress is less than predicted by a linear relationship.List of experiments and corresponding conditions.Steady state friction at the end of the run-in at 1 mm/s at each temperature is given.The normal stress given is the applied normal stress which is approximately equal to the effective normal stress due to the design of the top block which allows for a compensation of pore fluid pressure (see Niemeijer et al., 2008 for details).
* After this experiment, the piston teeth were deformed and excessive weakening was observed at high normal stress which is most likely related to the deformation of the teeth.While the slopes of the linear fits at 600°C and 650°C are the same, the slope at 700 °C is much shallower.Overall, shear stress clearly becomes a more non-linear function of normal stress with increasing normal stress and temperature for the felsic sample.

Microstructural observations
Upon disassembly of the piston pair and removal of the confining rings, almost all samples fragmented into numerous small pieces.Typically, these pieces fracture along inclined and curved planes from the inner side of the annulus to the outer one.This results in a variable thickness of the recovered gouge layers.A notable exception is the sample deformed at a constant velocity of 1 m/s and 700 °C (u716), of which several pieces were recovered to span the full gouge layer thickness.In the following, we only discuss the microstructures of the experiments performed at a constant sliding velocity, to avoid the issue of a complicated velocity and temperature history (see Table 2).Note that these experiments were sheared for 5 mm only.The mafic sample sheared at room temperature and a constant velocity of 1 m/s (Figure 10a) has developed a few subtle shears at low angle to the sample top and base.These shears are recognized from tabular zones of relatively finer grain size (indicated in red).The contrast in grain size is not large and is most obvious by the general absence of larger grains (~10 m).The amount and length of localized shears increases in the sample deformed at 500˚C (Figure 10b).Here the shears are recognized both as cracks that opened after sample removal from the apparatus, and by locally reduced grain size within thin, tabular zones.These shears lie at an angle of about 15°, clockwise and anti-clockwise, to the base of the sample as expected for R and P shears.There is no clear shape-preferred orientation of grains in either the mafic sample deformed at room temperature, or in the mafic sample deformed at 500˚C.Grains have locally developed intragranular fractures at both room temperature and 500˚C.
A weakly developed, preferred orientation of muscovite can be seen in the felsic sample deformed at room temperature (Figure 11a,c).In the felsic sample sheared at 500 °C, however, a clearer foliation has developed locally (Figure 11b,d,e), dipping to the left in a section cut parallel to the dextral shear direction, as expected for S planes in an S-C configuration.The sample deformed at room temperature also has a weak foliation, but in the opposite direction to that expected for S planes.whereas tabular zones of reduced grain size (indicated in red) dip in both P and R-shear orientations (Figure 11a,c).In both samples, cracks (indicated in blue) have opened in the Riedel orientation as well as in a non-planar horizontal orientation, presumably upon unloading of the sample.These unloading cracks may have opened along either brittle R-shears reflecting grain comminution, or along a well-developed foliation, as they are also in the S orientation (Figure 11d,e).These cracks are more continuous and more frequent in the sample deformed at 500˚C, consistent with the better-developed foliations in this sample.
In the samples deformed in normal stress stepping experiments at temperatures of 600, 650 and 700 °C (Figure 12), a well-developed muscovite preferred orientation is visible in the microstructure, in an S plane orientation (Figure 13).However, this shape-preferred orientation becomes less clear with increasing temperature.The long axes of the muscovite grains in the sample deformed at 700 °C are either horizontal or dipping into an S plane orientation (Figure 13c).All samples have areas of higher density, reflected by lighter color in the backscatter images, what may be interpreted as lower porosity (Figures 12,13) The grain boundaries in these areas are not sharp and seem somewhat smeared out.These areas cover larger parts of the samples with increasing temperature.Also, some of these areas seem to follow a boundary-parallel or R-shear orientation, particularly at 700 °C.

Frictional Properties of the felsic sample
Our felsic sample is somewhat similar in composition to Rhode Island Westerly granite (where Westerly granite has 30% quartz, 30% microcline, 30% oligoclase and 5-10 % biotite, Tullis and Yund, 1977), but contains less quartz and more muscovite.In general, steady state friction is comparable to experiments on gouges of Westerly granite (e.g.Blanpied et al., 1991Blanpied et al., , 1995)), tested at similar conditions.At less than 400˚C friction at 100 MPa is between 0.55 -0.6, and increases to 0.7 at 400 °C.At temperatures over 400°C, friction decreases significantly (Figure 4).The results up to a temperature of 400 ºC are comparable to those obtained by He et al. (2013) on wet plagioclase gouges (=0.73),but these authors did not observe weakening at temperatures above 400 ºC.A decrease in friction to 0.5 was observed by Blanpied et al. (1995) at 600 ºC and a sliding velocity of 0.1 m/s, which is comparable to the decrease we observed at an order magnitude faster velocity and at 500 ºC.
The velocity dependence of friction is also similar to that of Westerly granite.The values are positive at a temperature below 100 ºC, then transitions to negative, to return to strongly positive values again at high temperatures.This aseismic-seismic-aseismic pattern has been recognized by many authors (e.g.Chester & Higgs, 1992;Blanpied et al., 1995;Chester, 1995;Den Hartog et al., 2012).Results of pure plagioclase gouge, on the other hand, show only mild variations of the values of (a-b) with increasing temperatures, with values showing mildly velocity-weakening behavior with values clustering around -0.005 (He et al., 2013).A particular noteworthy observation of our experiments is the strong increase in the a-value with increasing temperature, in particular at 700 ºC (Figure 8).Typically, the direct effect is linked to the inherent rate-dependence of contact strength (e.g.Beeler et al, 2007).Therefore, any significant changes in the value of a should be the results of a change in the dominant deformation mechanism.An additional observation is that the shear stress dependence on normal stress begins to deviate from linearity at temperatures of 600 ºC and higher, in particular for high effective normal stress (> 200 MPa), similar to what has been observed for calcite (Verberne et al., 2017) and dry salt with increased confining pressure (Shimamoto, 1986).One possible explanation is that the pore fluid within the sample is no longer drained to the pressure-controlled reservoir due to a strong decrease in porosity, which could cause a decrease in the actual effective normal stress on the sample (Faulkner et al., 2018).However, if this was the case, dilatant hardening would be observed upon doing velocity steps (Faulkner et al., 2018), which we did not observe.
Another possibility is that temperature-dependent variations in frictional properties of the felsic sample are caused by an increase in the contribution of crystal-plastic behavior at temperatures from 600 ºC and higher.We can calculate the flow strength of the individual minerals using flow laws of dislocation creep of the type (e.g.Ranalli, 1995): exp ∆ (4) This equation can easily be rewritten to obtain shear stress (e.g.Niemeijer et al., 2016).Using parameters for quartz or anorthite (Ranalli, 1995), we obtain values that are in the GPa range and are thus far too high to explain the observed weakening and non-linearity in the normal stress dependence.On the other hand, we observe a weak foliation defined by the preferred orientation of muscovite (Figure 11), which should deform much easier by dislocation glide (Shea andKronenberg, 1992, Mariani et al., 2006) following a flow law of the exponential type according to: exp exp ∆ (5) The peak shear stresses after velocity-steps for the experiments at 600 and 700 ºC are shown in figure 14 both in log-log space to derive the stress exponent n (as in equation 4) and in log-linear space to obtain the pre-exponential factor c (as in equation 5).The fits to the (limited) data show that at 600 ºC and 100 MPa effective normal stress, both equations fit poorly with slopes that are meaningless.In contrast, the data at 700 ºC can be fit with equation ( 4) with a stress exponent of 23 or alternatively with equation ( 5) with a pre-exponential factor c of 0.41.This value is in between the values of the two end-member flow laws for muscovite (c=0.15 and c=0.55) obtained by Shea & Kronenberg (1992).We have only a very limited number of data points so this resemblance could be completely fortuitous.At the same time, we observe a weak shape preferred foliation of muscovite so we might speculate that the rapid increase in the a-value is a result of the increased contribution of dislocation glide within muscovite grains.

Frictional properties of the mafic sample
The mafic sample behaves completely differently from the felsic sample at our experimental conditions.It shows a consistent friction coefficient of about 0.7 at all tested temperatures and effective normal stresses.This sample contains mostly hornblende, of which not much is known.Although recognizing that there are likely differences in frictional properties of amphiboles (hornblende) and pyroxenes, as a mafic rock, the results could be compared to gabbro.He et al. (2007He et al. ( ) & (2013) ) find steady state friction values for gabbro of between 0.7 -0.75 for temperatures between room temperature and 600°C and normal stress up to 300 MPa, which are similar to our results here.
The (a-b) values for the mafic sample generally decrease with decreasing velocity, showing more negative values at the lower velocities.The low-velocity (a-b) values are still in the unstable regime at temperatures up to the tested 700 °C.The results from the pyroxene gouges from He et al. (2013) show similar (a-b) trends.The mafic sample does not show any significant changes in microstructures with temperature, with some zones of fracture development and grain size reduction and without a clear fabric development.
The friction coefficient of the mafic sample is independent of temperature and normal stress and shows linear behavior.This potentially indicates that the controlling deformation mechanism in the mafic sample does not change in the range of temperatures, effective normal stresses, and strain rates tested here.This is likely due to a high viscous strength of mafic material (Mackwell, 1998), meaning that the material is easier to deform brittlely than plastically up to higher temperatures.This interpretation is consistent with the absence of clear microstructural evidence for plasticity in the mafic sample.Through the entire P-T range tested, it therefore seems to behave by granular or cataclastic flow.

Implications for lower crustal earthquakes
Several explanations have been proposed for deep crustal earthquakes in general, and in the EARS specifically.With their greater viscous strength, mafic rocks can account for a deeper brittleviscous transition than felsic rocks (Fagereng, 2013;Albaric et al., 2009;Shudofsky et al., 1987;Nyblade & Langston, 1995).Also, the thick, conductive lithosphere will act as a thermal insulator for the crust from the mantle, which lowers the geotherm (Craig et al., 2011), and deepens the brittle-viscous transition.However, even with the coldest thermal structure calculated for the rift environment, temperature at the depth of the lower crustal earthquakes (35-44 km) would still be on the order of 600-700°C (Fagereng, 2013).In our experiments, while the felsic sample behaves as expected of a rock going from dominantly brittle to viscous deformation, deformation behavior in the mafic sample remains exclusively brittle and frictional.The friction parameters found for the mafic sample show that it is in the unstable regime at high temperatures and at lower velocities, indicating that it is capable of generating unstable (earthquake) slip under these laboratory conditions, whereas the felsic sample is firmly in the velocity-strengthening regime.Therefore, the felsic sample, which represents the quartzofeldspathic gneisses that dominate Malawi basement geology (Fig. 1; Bloomfield, 1966;Carter andBennett, 1973, Chapola andKaphwiyo, 1992), is likely to accommodate steady creep at depths where lower crustal earthquakes occur in the southern EARS.Of the two samples tested here, the only sample that might be able to host the nucleation of deep earthquakes is the mafic sample.Note that this inference requires an extrapolation over several orders of magnitude in loading velocity or strain rate (Figure 14).Shear zones with mafic components may be a particularly good candidate for lower crustal earthquakes, as has previously been suggested by Brodie and Rutter (1987) based on field observations in the Ivrea Zone of northern Italy.
Nucleation of deep earthquakes in rocks that are represented by our felsic samples is highly unlikely, since we observe strongly velocity-strengthening behavior at the highest temperature tested and at 600 ºC, the sample becomes more velocity-strengthening with increasing effective normal stress.This implies that in order to obtain velocity-weakening behavior, we need an elevated strain rate due to strain localization as well as an elevated pore fluid pressure that decreases effective normal stress (e.g.Sibson, 1980), such as CO 2 that has previously been suggested to modulate seismicity on normal faults (Parry and Bruhn, 1990;Miller et al., 2004).In the Magadi-Natron basin of the Kenya-Tanzania border region, surface CO 2 anomalies have been explained by flow of mantle fluids along major faults that penetrate the lower crust (Lee et al., 2016).However, such examples of potential deep fluid flow in the southern EARS are few, and more data are required to determine whether this is a widespread process.Equally, magmatic activity could potentially trigger seismicity, as it does in the northern EARS.In Tanzania, an early stage of magmatism may be a locally possible explanation for a long-lasting deep earthquake sequence (Albaric et al., 2010).No evidence has, however, been presented for active magmatism south of the Rungwe Volcanic Province in southern Tanzania, and thus it is difficult to invoke magmatic triggers of earthquakes anywhere in Malawi.
One could envisage that a lower crustal high strain zone with mixed felsic-mafic composition could host earthquakes if the distribution and size of mafic and felsic parts allows for propagation of earthquakes through the felsic proportions of the fault (Figure 14).Numerical simulations and linear stability analysis using rate-and-state friction equations with double spring-slider configurations have demonstrated that seismic slip can be hosted on faults that are composed of a mixture of velocityweakening and velocity-strengthening materials (Skarbek et al, 2012;Luo & Ampuero, 2018).The size and proportion of velocity-weakening patches (i.e.mafic bodies in this case) that are needed to generate a fault-spanning seismic event, depend on the values of (a-b) and d c of both the velocity weakening and velocity strengthening materials, the effective normal stress within the two materials and the stiffness of the fault.Luo & Ampuero (2018) formulated three terms that control the mode of slip in a heterogeneous fault: (6) Here, the subscript w denotes the property of the velocity-weakening material and s is for the velocity-strengthening material and G is the shear modulus.In the limiting case of a large  and a small     ), there is a value for  above which the fault will rupture in a fault spanning event.This limiting value  TC is proportional to the ratio of fault area of velocity weakening material over velocitystrengthening material, f, defined as L w /L s .Assuming a high effective normal stress at 40 km depth, we expect  to be much larger than 1.The critical or character slip distance d cs we determined for the felsic material at 700 ºC was on the order of several 100s of µm and about one order of magnitude higher than d cw of the mafic material, considering d c1 , fulfilling the requirement of a small  2 .Taking the (a-b)-values for both materials at 700 ºC and 1 m/s, we get a value for  of 0.2, which would indicate that f is 5, or that fault area taken up by velocity-weakening mafic material has to be 5 times larger than the area with felsic material in order for an earthquake to propagate through the felsic patches.In order to obtain a more accurate estimate of the size of mafic bodies that would be needed for fault-spanning ruptures to occur on mixed felsic-mafic faults, numerical simulations beyond the 2-D simulations of Luo & Ampuero (2018) are needed which is beyond the scope of the present work.Note also that in this simple calculation, we have disregarded any possible velocity-dependence of the rate-and-state friction parameters, in particular of (a-b).A velocity dependence of (a-b) is expected when thermally activated, time-dependent mechanisms contribute to the deformation (Chen & Spiers, 2016).For our felsic sample at 700 ºC (Figure 6) or 600 ºC and high normal stress (Figure 7), we observe either no velocity dependence of (a-b) or an increasing (a-b) with decreasing velocity.We therefore expect that at natural strain rate, the felsic sample is strongly velocity-strengthening, with (a-b)-values that are inversely proportional to the stress exponent of the controlling deformation mechanism.On the other hand, particularly our data for the mafic sample at 600 ºC (Figure 7) shows a loglinear decrease in (a-b) with sliding velocity.Extrapolating this to the loading rates inferred in the EAR of 2-3 mm/year or 0.1 nm/s, we obtain a value of -0.03 (Figure 15).Our simplified extrapolation without a microphysical model basis still suggests that the proportion of velocityweakening mafic material must be at least 1.5 times larger than the area of velocity-strengthening material.Here, we implicitly assume that deformation occurs within a 1 mm-thick zone, but the actual slip zone could be thinner in nature.In this case, the strain rate is higher and the difference with the experimental strain rates is thus smaller.To summarize, under natural loading conditions we would expect different (a-b)-values than those we obtained at our experimental loading rates.At the same time, what trends we have in our experimental data indicate that the two rock types change behavior in opposite directions: with decreasing velocity, the felsic sample becomes more velocity-strengthening, whereas the mafic sample becomes more velocity-weakening (Figure 15) The calculation indicates, overall, that seismicity on faults embedded in a compositionally heterogeneous, hydrostatically pressurized, lower crust requires the faults to be volumetrically dominated by mafic rocks, at least given the boundary conditions and materials considered in this study.

Conclusions
In order to evaluate which rock types are most likely involved in the deep crustal earthquakes (35-45 km) that occur in the southern, amagmatic, East African Rift System, we performed a series of hydrothermal friction experiments on fault gouge prepared from felsic and mafic samples from Malawi.Experiments were done at effective normal stresses of 100 to 250 MPa, a fluid pressure of 100 MPa and temperatures ranging from 20 to 700 °C.To establish the velocity dependence of friction, quantified via the parameter (a-b), sliding velocities were instantaneously stepped in the range of 1 to 100 m/s in 3 and 3.5-fold steps.We can conclude the following: 1) Apparent friction of the fault gouge derived from the mafic sample is 0.7 and does not show much variation with temperature up to the maximum temperature tested (700 ºC).
2) The apparent friction of fault gouge derived from the relatively feldspar-rich felsic sample increases slightly with temperature from ~0.55 at room temperature to 0.7 at a temperature of 400 °C and decreases at temperatures above that.This behavior is similar to that established for granites.3) Both samples show frictionally unstable behavior and negative (a-b) values over a broad range of temperatures and sliding velocities.The felsic sample, however, becomes strongly velocitystrengthening at temperatures from 600 ºC.4) Sliding shear strength of the felsic sample shows deviations from a perfect linear dependence on effective normal stress at temperatures of 600 ºC and above.5) We infer that the onset of ductility of one of the phases in the felsic sample is the cause of both the non-linearity in normal stress dependence and the weakening.The most likely mechanism, at laboratory conditions, is fluid-assisted diffusion creep because an estimate of dislocation creep flow strength far exceeds the measured shear stress unless all deformation is accommodated by dislocation glide in the muscovite.6) The frictional properties of felsic and mafic samples suggest that deep earthquakes in the East African Rift System are most likely to nucleate in mafic rocks.This means that either the lower crust contains significant volumes of mafic material, or earthquakes nucleate in mafic rocks but are then capable of propagating into surrounding crust.7) An ideal candidate for lower crustal earthquakes is mafic shear zones in which deformation is localized and strain rates elevated, in rocks that are capable of hosting earthquake slip.Similarly, shear zones with mixed mafic and felsic materials are good candidates if the mafic component is sufficient for earthquake propagation through felsic volumes.We estimate that a critical volume fraction of mafic material is on the order of 80% but acknowledge uncertainties in this calculation which requires more detailed modelling.
Figure 2: a) Photo of the outcrop from which sample M01 (felsic) was obtained.See text for description.Compass for scale is ~15x15 cm.b) Photo of the outcrop from which sample M17 (mafic) was obtained.See text for description.Pen for scale is 15 cm long.c) Micrograph of a thin section from the hand specimen from which sample M01 was obtained.d) Micrograph of a thin section from the hand specimen from which sample M17 was obtained

Figure 4 :
Figure 4: Apparent coefficient of friction (=shear stress / effective normal stress, ignoring cohesion) at the end of the step at 1 m/s as a function of temperature.Measurement errors are smaller than the symbol size, reproducibility was not tested.

Figure 5 :
Figure 5: Examples of model fits to the experimental data from experiment u559, which was done on the felsic sample M01 at temperatures of 300 and 400 ºC.The largest standard deviations of the misfits to the models are always on the critical displacement(s) and can be up to 30%, as in the case of the example shown in a), whereas standard deviations on the values of a, b 1 and b 2 are generally less than 1%.

Figure 6 :
Figure 6: Plots of (a-b) as a function of temperature (a,b) as well as sliding velocity (c,d) for all experiments performed at 100 MPa effective normal stress (see Tables 2, 3 and 4).a, c) Felsic sample b, d) Mafic sample Figure 7: a) Plots of (a-b) as a function of sliding velocity for experiments performed at effective normal stresses of 100, 200 and 250 MPa as well as 500 and 600 ºC for the felsic sample b) Plots of (a-b) as a function of sliding velocity for experiments performed at effective normal stresses of 100, 200 and 250 MPa as well as 500 and 600 ºC for the mafic sample

Figure 9
Figure 9: a) Plot of shear stress as a function of effective normal stress with linear fits to the data for temperatures of 600, 650 and 700 ºC b) Plot of apparent friction as a function of effective normal stress for temperatures of 600, 650 and 700 ºC

Figure 10 :
Figure 10: Overview microstructures of the mafic samples deformed at a constant velocity of 1 m/s for 5 mm at an effective normal stress of 100 MPa and at (a) room temperature and (b) 500 ºC.Cracks are indicated by blue lines, zones of grain size reduction are indicated by red lines.Sample thickness in both cases is about 800 m and shear sense is top-to-the-right.

Figure 11 :
Figure 11: Overview microstructures of the felsic samples deformed at a constant velocity of 1 m/s for 5 mm at an effective normal stress of 100 MPa and at (a) room temperature and (b) 500 ºC.Cracks are indicated by blue lines, zones of grain size reduction are indicated by red lines.Sample thickness in both cases is about 800 m and shear sense is top-to-the right.White boxes indicate the location of the close-ups shown in (c) for the relation between cracks, zones of finer grain size, and poorly developed foliation in the room temperature sample, and in (d) and (e) for the 500˚C sample.

Figure 12 :
Figure 12: Microstructures obtained in normal-stress-stepping experiments using the felsic sample at 1 m/s and temperatures of 600 (a), 650 (b) and 700 ºC (c).A faint foliation defined by aligned muscovite is present and denser zones are visible as lighter areas.These areas appear to increase in size with increasing temperature.White boxes indicate the locations of the close-ups, shown in Figure 13.Shear stress is topto-the-right in all cases.

Figure 13 :
Figure 13: Details of the microstructures of the felsic sample deformed at 1 m/s and temperatures of 600 (a), 650 (b) and 700 ºC (c).Shear sense is top-to-the-right in all cases.

Figure 14 :
Figure 14: Plots of the peak shear stress for the three different up-step velocities (3-10-30 m/s) which have been converted to strain rates by dividing over the gouge layer thickness of 1 mm.a) Plot in log-log space, showing the stress exponent in a power flow law as the slope b) Plot in semi-log space, showing the preexponent constant in an exponential flow law as the slope.

Figure 15 :
Figure 15: Schematic of the envisioned fault zone structure at depth, with transposed and dismembered layers of mafic/velocity-weakening material (grey) within a felsic/velocity-strengthening matrix (white with dashed lines denoting foliation).The mafic layers are inferred to have been transposed within a ductile shear zone; the timing of transposition and the original orientation of the layers is not inferred nor implied.a) Dominantly felsic/ductile/velocity-strengthening, deforming through distributed deformation b) Contains substantial transposed mafic/velocity-weakening layers, along which a discontinuity (thick dashed line) can form and involve more than 80 % velocity-weakening material.c) Log-linear extrapolations of experimental data obtained at 600 ºC and 100 MPa effective normal stress and inferred amount of mafic (velocity-weakening material) needed to nucleate an earthquake that ruptures the entire fault (i.e. that ruptures through the velocity-strengthening felsic material).

Table 1 :
Mineral composition (wt%)of the felsic and mafic sample studied in this research.

Table 3 -
Rate-and-state parameters for the mafic sample.Experimental conditions can be found in Table1.The standard deviations (s.d.)of the fitted parameters are only given for the critical slip distances d c1 and d c2 .The standard deviations of the other parameters are smaller than 0.1% of the value.The last column displays the linear hardening or weakening trend (linear term, l.t.) which was used to detrend the data of that particular velocity step.Steps denoted with * result in stick-slips or transient stick-slips.Most of these cases could not be modeled and the values are not available (n/a).Values from the manual calculation (see main text) are given where they result in negative values.

Table 4 -
Rate-and-state parameters for the felsic sample, same as in Table3.