Seismicity released during lateral dike intrusions in the Manda Hararo–Dabbahu Rift (Afar, Ethiopia) provides indirect insight into the distribution and evolution of tensile stress along this magma-assisted divergent plate boundary. In this paper, 5 dike intrusions among the 14 that form the 2005–present rifting episode are analyzed with local and regional seismic data. During dike intrusions, seismicity migrates over distances of 10–15 km at velocities of 0.5–3.0 km/h away from a single reservoir in the center of the rift segment, confirming the analogy with a slow spreading mid-ocean ridge segment. Comparison with geodetic data shows that the reservoir is located 7 km down rift from the topographic summit of the axial depression. Dikes emplaced toward the north are observed to migrate faster and to be more voluminous than those migrating southward, suggesting an asymmetry of tension in the brittle-elastic lithosphere. Seismicity during dike injections is concentrated near the propagating crack front. In contrast, faults and fissures in the subsurface appear to slip or open aseismically coeval with the intrusions. The seismic energy released during dike intrusions in the Manda Hararo Rift appears to be primarily modulated by the local magnitude of differential tensile stress and marginally by the rate of stress change induced by the intrusion. The low level of seismic energy accompanying dike intrusions, despite their significant volumes, is likely an indicator of an overall low level of tension in the lithosphere of this nascent plate boundary.
Dike intrusion is one of the main processes of crustal accretion along divergent plate boundaries, in particular at mid-ocean spreading ridges [e.g., Delaney et al., 1998; Curewitz and Karson, 1998]. At slow spreading mid-ocean ridges (full spreading rate: 2–5 cm/yr), magma ascending from the asthenosphere is often focused in the middle of the second-order spreading segments [e.g., Lin et al., 1990; Smith and Cann, 1999]. After a temporary storage in a crustal reservoir, melts are then redistributed along the rift by diking, consisting in the horizontal migration of magma [e.g., Callot and Geoffroy 2004] along a laterally propagating rupture [e.g., Abdallah et al., 1979; Einarsson and Brandsdóttir, 1980]. Dike intrusions are clustered in time, and are typically concentrated in periods of intense magmatic and tectonic activity called “rifting episodes”, that last for several months or years, and are separated by long recurrence times (102–103 yr) [Björnsson, 1985]. During an individual rifting episode, several dikes may be emplaced at intervals of a few weeks/months, progressively accommodating the tectonic strain deficit accumulated since the previous rifting episode [Arnott and Foulger, 1994; Buck et al., 2006; Grandin et al., 2010b].
From a mechanical point of view, magma is intruded in a dike in response to the existence of a differential tensile stress in the uppermost, brittle part of the lithosphere, and dike intrusions result in a reduction of this differential stress [e.g., Pollard et al., 1983; Rubin and Pollard, 1987; Buck, 2006; Grandin et al., 2010b, also Elastic thickness control of lateral dyke intrusion at mid-ocean ridges, submitted to Earth and Planetary Science Letters, 2011]. Intrusion dynamics reflect an imbalance between magma pressure within the dike Pm and the magnitude of the least compressive principal stress σ3, corresponding usually to the component of the stress tensor normal to the dike. Locally, the difference between the two terms is defined as the driving pressure Pd = Pm − σ3, whose initial (positive) value at the onset of intrusion should control the swiftness of the intrusion.
When magma is intruded into a dike, a swarm of small- to moderate-sized earthquakes (i.e., with M < 6) is commonly observed, which provides indirect evidence for occurrence of a rifting event [e.g., Sykes, 1970; Solomon et al., 1988]. Because rupture propagation generally occurs unidirectionally along a vertical plane, the process of Mode I opening during a dike intrusion is in many aspects similar to that of Mode II fracture during a strike-slip earthquake [Pollard and Segall, 1987; Rubin, 1992]. The major difference with “dry” seismogenic rupture is that dike intrusions are slow events, because the velocity of propagation (of the order of 1 km/h versus 1 km/s for earthquake rupture) is limited by viscous resistance of magma during transport from the source reservoir to the crack tip [Spence and Turcotte, 1985; Lister and Kerr, 1991]. As a consequence, propagation of a dike can be considered nearly aseismic. Also, the lack of large seismic events coeval with a dike intrusion is partly related to the high geothermal gradient within volcanic areas, such as at magma-assisted divergent plate boundaries, where the crustal seismogenic layer is thin.
Nevertheless, stress perturbation within the host rock surrounding the dike releases a small amount of seismic energy, which may be monitored in order to indirectly capture the dynamics of dike emplacement. Using such a method, the first convincing examples of horizontal dike migration were derived from observations made during the Krafla 1975–1984 rifting episode (Iceland), in an oceanic rift segment along the Icelandic section of the mid-Atlantic ridge [Brandsdóttir and Einarsson, 1979; Einarsson and Brandsdóttir, 1980]. Migration velocities of ∼1–2 km/h directed away from a single crustal magma reservoir located at the center of the segment, sustained for a few tens of hours, were deduced from seismic data [e.g., Tryggvason, 1984; Björnsson, 1985].
More recently, examples of a lateral propagation of seismicity linked with dike emplacement at the axes of various mid-ocean ridge segments with different spreading rates have been reported: in the intermediate spreading Juan de Fuca and Gorda ridges (NE Pacific) [e.g., Fox, 1995; Tolstoy et al., 2006; Dziak et al., 2007], the slow spreading mid-Atlantic ridge [Dziak et al., 2004], and possibly in the Gakkel (Arctic Ocean) and Mohns (Norwegian sea) ultraslow spreading ridges [Blackman et al., 2000; Tolstoy et al., 2001]. Unfortunately, the remoteness of oceanic environments has so far hindered deployment of multidisciplinary monitoring devices in these regions, limiting the information content of these small dike-induced earthquakes that could only be recorded by sparse hydrophone or ocean bottom seismometer networks [e.g., Tolstoy et al., 2006]. Nevertheless, the issue of a large distance between a seismically active region and available seismic sensors is not limited to oceanic environments, and was also faced during the two recent and unexpected dike intrusions of short duration (a few days/weeks) that occurred in the continental contexts of Tanzania (2007 Gelai) [Calais et al., 2008; Baer et al., 2008], and Saudi Arabia (2009 Harrat Lunayyir) [Baer and Hamiel, 2010; Pallister et al., 2010]. Resolving this problem by focusing on specific spreading segments where dike intrusions are likely to occur in the future, is currently one of the objectives of various research programs (e.g., Ridge 2000 program, 2000, http://www.ridge2000.org; MoMAR project, 2005, http://www.ipgp.fr/rech/lgm/MOMAR/).
Following Grandin et al. [2010b], dike intrusions are numbered from d0 (initial megadike of September 2005), to d13 (last observed dike of May 2010). The migration of seismicity away from a central magma chamber coeval with the two dikes of June and July 2006 (d1 and d2) was reported by Keir et al. . In this paper, we present new seismic data recorded by a small local seismological network that has captured earthquakes associated with three additional dike intrusions in July 2008 (d9), October 2008 (d10) and February 2009 (d11). Our earthquake locations and magnitudes, together with those reported by Keir et al.  for the d1 and d2 dikes, and the preliminary results of Belachew et al.  for the November 2007 dike (d7), allow us to draw preliminary conclusions on how the variability of the elastic potential energy stored as differential tensile stress along the plate boundary of the MHR may control dike intrusions, and to assess the evolution of tectonic stress throughout the duration of the current rifting episode.
2. Data Set and Method
In November 2007, the Institut de Physique du Globe de Paris (IPGP) and the Institute of Geophysics, Space Science and Astronomy (IGSSA) of the University of Addis Ababa, deployed a telemetered seismological network over the southern tip of the zone affected by the repeated dike intrusions of the MHR (Figure 1a). This network consisted in four short-period stations (bandwidth 0.5–50 Hz) installed as close as possible to the rift axis in order to detect small earthquakes. Unfortunately, the field conditions did not allow us to extend our monitoring network into the inner floor of the rift. Two three-component stations, SM1 and SM4, are located on the western rift shoulder, whereas another three-component station, SM2, lies on a volcano, on the eastern shoulder. A fourth vertical-component station, SM5, is located in the town of Semera. The seismic signals are sent by analog FM radio to Semera where they are continuously digitized and recorded at a sampling rate of 100 Hz.
With this network, numerous volcano-tectonic (VT) events were recorded at the time of three dike intrusions (d9, d10 and d11). Figure 2 shows an earthquake recorded by the network during the sequence related to the July 2008 dike (d9). Phase pickings were performed manually. Estimated uncertainty on phase pickings ranges from 0.02 s for the best defined P phases, to 0.20 s for the least constrained arrivals (0.05 s and 0.30 s, respectively, for S phases).
For earthquakes with magnitude higher than 2.5, a local magnitude ML was computed using the amplitude of S waves at SM2 and SM4 stations, with the formula ML = a0 + log(k × Ad) + a1 log(Δ), where k is a static magnification equal to 2800, Δ is the epicentral distance (unit: km), and Ad is the amplitude of ground motion (unit: μm), estimated from Ad = Av/ω, where Av is the amplitude of S waves read on the horizontal velocity components (unit: μm/s), and ω is the dominant pulsation of S waves (unit: rad/s) [Richter, 1958]. Values of parameters a0 and a1 are derived from seismological studies in Djibouti (a0 = −3.2 and a1 = 1.6) [Mohamed, 2009]. For earthquakes with magnitudes higher than 3.5, as the signal was generally saturated at SM2 and SM4, we used the signals recorded at permanent short-period stations of the Geophysical Observatory of Djibouti. For the remaining earthquakes with magnitudes smaller than 2.5, we calculated duration magnitudes MD using the formula MD = b0 + b1 log D + b2 Δ, where D is signal duration (unit: s), and b0, b1 and b2 are parameters derived from Real and Teng  (b0 = −1.01, b1 = 1.89 and b2 = 0.0009). The duration magnitude law was then calibrated against local magnitudes for the earthquakes recorded both by our local network and the Djibouti network. Our network detected events with magnitudes ranging from 1.2 to 4.6, which is slightly less than the magnitude of the events recorded by the regional network discussed by Keir et al. .
2.2. Location Method
We proceed to a two-step location inversion in order to assess the impact on earthquake location estimates induced by the unfavorable network geometry used in this study. First, we used a “classical” inversion method, Hypo71 [Lee and Lahr, 1975]. We used a 1-D velocity model derived from the seismic refraction profile shot in Ethiopia, between Assaïta and Lake Afdera, in March 1972 (profile V in the study by Berckhemer et al. ). We used the central part of the seismic profile, which runs less than 50 km from the zone where the dikes intruded (Model A in Figure S1 in the auxiliary material). A VP/VS ratio of 1.77 is estimated following the method described by Chatelain  (see also Appendix A by Jacques et al. ).
Second, we invert the hypocentral locations directly from the S-P phase delays available at the three closest stations (Figure 3). We follow the probabilistic approach of Tarantola and Valette . In this scheme, the a posteriori probability density function (p.d.f.) of hypocentral location is calculated by mapping the a priori estimated p.d.f. of the data (i.e., phase picking and associated uncertainty) into the parameter space (i.e., earthquake epicentral location). Travel time of seismic waves (the forward model) is assumed to be perfectly known (perfect theory). Because we invert for three parameters (latitude, longitude and depth), and we use three data points for each earthquake (S-P phase delays), the problem is mathematically evenly determined, and the inversion always yields a “best” solution. However, the result is very sensitive to errors on the velocity model, particularly for those earthquakes occurring outside the network (dikes d10 and d11), so we chose to limit our analysis to the inversion of two parameters (latitude and longitude, or depth and location along the dike, as explained below). Here, the chosen velocity model consists in a smoothed version of the velocity model used for Hypo71 earthquake locations, with two layers with a gradient of velocity, overlying a half-space of homogeneous velocity (Model B in Figure S1). This method provides a quantification of the errors affecting the estimated earthquake locations, with a result depending both on the assumed errors on phase pickings and the network geometry.
2.3. Epicentral Location Estimate
In a first step, earthquakes were located with Hypo71. Only events recorded at three or more stations and including at least 6 picked arrival times (P and S phases) were selected for the location inversion. Following this procedure, a total of 326 events have been identified over the period 2008–2009. Among these, 255 events show clear P and S phases in signals recorded at all three stations SM1, SM2 and SM4 (i.e., three S-P phase delays are available for these events). Following [Keir et al., 2009], due to the lack of stations directly above the active area, we first constrained the earthquake depth to be fixed to 5 km. We also tested a scenario where the depth of the earthquakes was not constrained, and we found that the results were more stable, with less outliers. This may presumably indicate that at least some earthquakes are located at a depth significantly different from 5 km. In the following, the result of the Hypo71 inversion with unconstrained depth are discussed, with no impact on our conclusions as far as epicentral locations are concerned.
In the second step, we use the probabilistic approach described above, with constraints on epicentral locations deduced solely from the 255 available S-P phase delays. Epicentral locations are computed with a depth fixed at 5 km to provide a rough estimate of the errors in the earthquake locations, given the geometry of the network, the assumed velocity model, and the estimated errors on phase pickings. The probabilistic approach sheds light on the confidence on the location estimates in the across- and along-dike directions (Figure S2). For the two northerly dikes d10 and d11, the earthquake locations along the strike of the dike (NNW-SSE direction) are estimated to be constrained within less than ±2 km for all earthquakes, and the uncertainty is less than ±1 km in most cases. The uncertainty on the lateral position of earthquakes across the strike of the dikes (WSW-ENE direction) is comparatively larger (±3–4 km on average, and up to ±5 km in the worst cases). In contrast, earthquakes occurring coeval with dike intrusion d9 (July 2008) are better constrained laterally (generally ±2 km).
The locations deduced from the two approaches can be readily compared (Figure S3). Although the assumptions between the two methods differ slightly (inversion with Hypo71 was performed with a nongradient layered velocity model, free hypocentral depth, and with occasional data from the additional station SM5), we find a very good agreement between the results of the two methods. For the July 2008 dike which occurred less than 10 km from the northern station SM4, 96% of the earthquake locations determined with Hypo71 (i.e., 143 earthquakes out of 149) fall within the 90% confidence region computed solely with S-P phase delays in the probabilistic approach. The values are 85% (51/60) and 93% (43/46) for the October 2008 and February 2009 dikes, respectively (Figure S2). Overall, the earthquake location errors deduced from the probabilistic method are likely overestimated, as the breadth of the earthquake swarm deduced from Hypo71 is less than 4 km, suggesting that a ±2 km would be a better suited value for the lateral uncertainty. In contrast, the difference in the along-strike location of earthquakes deduced from the two approaches appears to be smaller (near to ±1 km).
2.4. Hypocentral Depth Estimate
For the two distal dikes of October 2008 (d10) and February 2009 (d11), station-earthquake distances are too large for hypocentral depths to be reliably constrained (epicentral distance to the closest station, SM4, is greater than 15 km, whereas earthquakes are expected to occur above 10 km depth, see Table S1). However, for the July 2008 dike (d9), because the closest station (SM4) is located at an epicentral distance ranging between 6 km and 12 km, we may be able to determine the depth of the earthquakes with some accuracy. To perform this task, we use the probabilistic approach defined above, except that we now invert for the depth of the earthquakes, and, in order to stabilize the inversion, we force the earthquakes to occur exactly along the dike plane determined by the inversion of InSAR data (the two inverted parameters are now the depth and the location along the dike plane).
These results may then be compared with hypocentral depth locations obtained with Hypo71 with the constraint on depth relaxed (Figure 4a). First, as stated above, relaxing the constraint on earthquake depth with Hypo71 gives nearly the same solutions for the epicentral locations as previously found with a fixed depth. Also, the distribution of hypocentral depths with Hypo71 yields an average depth of earthquakes near 5 km, whereas the probabilistic method places the earthquakes at a slightly greater depth, near 6–7 km on average. Accumulation of earthquakes near 5 km obtained with the probabilistic method suggests that the change of the gradient in velocity model B at that depth has an strong impact on the inversion. For the least constrained earthquakes occurring near the northern dike tip, the probabilistic inversion oscillates between two groups of solutions near 7–11 km and 1–2 km depth, whereas Hypo71 converges to an intermediate solution near 6 km depth (Figure 4b), a depth also corresponding roughly to an interface in velocity model A. The shallowest solution with the probabilistic inversion at 1–2 km depth seems to correspond spatially with the locus of maximum opening deduced from InSAR. Yet, earthquakes occurring at that depth, if real, would be poorly constrained (distance to the closest station SM4 is 6 km). In contrast, the rest of the earthquake population seems to be located below the dike, in apparent disagreement with InSAR, although the associated hypocentral depth estimates are more reliable from a geometrical point of view. A crude interpretation could be that most earthquakes are located below the dike, with a few earthquakes located near to the locus of maximum dike aperture.
However, the depth of the dike estimated from InSAR is poorly constrained, and the absolute depth of dike intrusions may well be located several kilometers deeper (although the relative depth of individual dike intrusions is well constrained) [Grandin et al., 2010b]. If dike opening in July 2008 actually occurred 2–4 km deeper, a spatial matching between seismicity and the distribution of dike opening would be observed. In that case, the shallow patch of seismicity near 1–2 km depth would likely be interpreted as a spurious result of the inversion, and these earthquakes may be actually located near the region defined by the other group of solutions, at 9 km depth, some 3–4 km toward the north (as suggested by the shape of the contour of 90% confidence on hypocentral depth of event 1 in Figure 4b). The distribution of hypocentral depths deduced from the comparison of Hypo71 and the probabilistic method could therefore be compatible with the alternative interpretation that most earthquakes have occurred at the depth of the dike intrusion, which was likely underestimated by Grandin et al. [2010b]. This spatial matching between the dike shape and the location of dike-induced earthquake activity is also supported by the greater depth of earthquakes found near the northern dike tip of the dike (∼8 km) than near its southern tip (∼5 km), which is consistent with the shallowing of the dike toward the south deduced from InSAR.
3. Results and Discussion
Due to different problems, including disruptions in power supply, we have only been able to use the local seismic network described above to record and locate earthquakes related to three dike intrusions: July 2008 (d9), October 2008 (d10) and February 2009 (d11). Earthquakes induced by the June 2006 (d1) and July 2006 (d2) dike intrusions studied by Keir et al.  are also included in this paper for comparison. The epicentral locations associated with each of the five dike intrusions are shown in Figure 5.
3.1. Time Evolution of Seismic Activity
Earthquake activity in the MHR in 2005–2010 appears to be clustered in time and space. During the periods between dike intrusions, little seismicity is detected, and no earthquake could be located near the axis of the MHR. However, this lack of observation does not preclude that small undetected earthquakes may actually occur between dike intrusions, as suggested by observations of continued seismic activity along the rift axis between November 2005 and May 2006 reported by Ebinger et al. , as well as evidence for significant microseismicity above the inferred central reservoir of the Asal rift during the current interdiking period reported by Doubre et al. [2007b]. Nevertheless, our observations suggest that seismic activity is mainly concentrated during dike intrusions, and is organized in swarms lasting for 24–48 h. The evolution of cumulative Benioff strain released by earthquakes during individual dike intrusions shows a gradual increase of the rate of energy release, followed by a slow decay, with no clear mainshock-aftershock succession (Figure 6). This symmetrical distribution of seismic energy release as a function of time is typical of earthquake swarms, and is compatible with a magmatic origin of seismicity [e.g., Sykes, 1970]. The simultaneity between dike opening and seismic activity has already been clearly demonstrated by the abrupt ground displacement measured by continuous GPS stations for dikes d1 and d2 [see Keir et al., 2009, Figure 3]. Furthermore, a dense SAR archive acquired by the ENVISAT satellite has also allowed Grandin et al. [2010b] to show that deformation associated with other dike intrusions is likely restricted to a period shorter than ∼4 days. These independent constraints strongly suggest that the earthquake swarms are tightly related to the dike intrusions detected with InSAR and GPS.
3.2. Spatial Clustering of Earthquakes
Epicentral locations show that seismicity associated with each dike intrusion is concentrated in an elongated band along the axis of the MHR. Individual swarms have a length of 10–13 km, and a width of 2–4 km (Figure 5). Superimposition with InSAR data shows that the across-axis width of the seismically active region does not extend laterally beyond the limits of the surface ruptures associated with normal faulting above the dike [Grandin et al., 2010b] (Figures 7 and 8). Beyond confirming that dikes are emplaced with a nearly vertical dip, this observation strongly suggests that our absolute epicentral locations are well constrained. This also indicates that seismicity is directly related to stress perturbation in the host rock occurring in the vicinity of the opening dike.
In map view, we observe that, during dike intrusions, earthquakes are concentrated in spatially restricted regions along the dikes. The clusters occur at specific locations along the MHR (Figure 5): (1) two clusters at −9 km and −2 km to the north of the source reservoir are active near the two extremities of dikes d1 and d11, and (2) one cluster near 8 km to the south, is located near the southern end of d2 and the northern end of d9 (Figures 7 and 8). We note a great similarity between patterns of strain energy release for dikes d1 and d11, where two regions of significant seismic energy release along the dike length (−2 km and −9 km) have retained the same location. In contrast, the cluster located at −5 km, which was very active coeval to d1, and may have been involved in generating the seismicity in the first 2 h of intrusion d10, has disappeared in d11. Another possible cluster may be located near −15 km, at the northern tip of dike d10.
A similar clustering of seismic activity during dike intrusions is also observed at Kilauea (Hawaii), and is attributed to the existence of “barriers” caused by local stress concentrations and/or geometric complexities such as jogs or en échelon steps between dike subsegments, separated by shadows of seismicity interpreted as inferred magma reservoirs, or zones of weakness [Hill, 1977; Klein et al., 1987]. In the MHR, among the different clusters identified here, the one located near −9 km (12.38°N) seems to correspond to the location of prominent normal faults dissecting the remnants of the Ado'Ale Volcanic Complex (Figure 5). In contrast, the gap in seismic energy release near 0–2 km (∼12.29°N) matches with the inferred source magma reservoir for the dikes, and a relative minimum of seismic energy release near −3 km (12.34°N) may be related to the caldera imprinting the summit of the axial topography, a possible indication of an underlying magma reservoir (Figure 5). Similarly, the fissural eruptions of August 2007 (d6), June 2009 (d12) and May 2010 (d13) seem to be located in relative minimas of seismic energy release (the location of the eruptions is indicated by stars in Figures 7c, 7f, 8c, 8f, and 8i). Future studies of the behavior of faults imaged by InSAR during and between dike intrusions should provide more constraints on the relationship between seismicity, magmatism, topography and rift segmentation.
3.3. Migration of Earthquakes
A migration of seismicity along the axis of the MHR is observed during dike intrusions, as witnessed by the progressive change of S-P phase delays at individual stations during the swarms (Figure 3). Epicentral determinations show that migration is directed away from a region located around the latitude 12.29 ± 0.015°N. This latitude does not correspond to the prominent summital caldera at the top of the axial relief, but is rather located ∼7 km down rift, toward the SSE (Figure 1). This area coincides with the locus of maximum subsidence deduced from InSAR, associated with the intrusion of the two most distal dikes d7 and d10, which were emplaced to the south and to the north, respectively (Figure 8) [Grandin et al., 2010b]. This area also matches with the location of the inflation signal observed by InSAR in the periods between successive dike intrusions [Grandin et al., 2010a]. These observations strongly suggest that dikes are fed from a single source situated at the center of the rift, which is subsequently refilled with magma during interdiking intervals [Keir et al., 2009; Grandin et al., 2010b].
Migration is generally unidirectional, and occurs both down rift and up rift during the current rifting episode, thus contradicting the hypothesis that the directivity of lateral dike migration is controlled by the topographic gradient along the axis of the segment, which would otherwise force the dikes to migrate down rift [Rubin and Pollard, 1987; Fialko and Rubin, 1998; Buck et al., 2006]. Rather, the along-axis thinning of elastic-brittle lithosphere near the segment center, induced by the thermal weakening of the lithosphere due to midsegment focusing of melt, may play a more important role in driving lateral dike injections (Grandin et al., submitted manuscript, 2011). This hypothesis of a thickening of the axial elastic-brittle lithosphere toward segment ends is supported by an analogy with geophysical observations made at similar mid-ocean ridge segments [e.g., Whitehead et al., 1984; Lin et al., 1990; MacDonald et al., 1991; Hayward and Ebinger, 1996; Magde et al., 1997; Doubre et al., 2007a; Grandin et al., submitted manuscript, 2011].
A possible indication of an along-axis variation of seismogenic thickness in the MHR may be deduced from the seismic data gathered in the period October 2005–April 2006 (between megadike d0 and d1) by Ebinger et al. , who report a decrease in earthquake depths from Dabbahu toward the segment center (see their Figure 7). Unfortunately, as discussed above, difficult access to the field hindered an optimal network configuration, with the consequence that the depths of the earthquakes captured in the MHR are currently not sufficiently constrained to define systematic variations of the seismogenic thickness. In particular, because the closest stations used by Ebinger et al.  are located at epicentral distances larger than 30 km for events occurring in the region of emplacement of dikes d1 to d13, hypocentral depth estimations are particularly sensitive to uncertainty on the “average Afar” velocity model used in this study and that of Jacques et al. .
One exception to unidirectional propagation may be dike d2, which lies above the source reservoir (Figure 1). In that case, intrusion was likely to be both vertical and horizontal, and possibly horizontally bidirectional, with the earthquakes occurring in the first 4 h hinting at a ∼1–2 km northward migration (Figure 7). Unfortunately, interpretation of the migration pattern for this dike is difficult, because only distant stations were operating at the time of the intrusion, so that only 18 small-magnitude earthquakes (M < 3.5) could be located [Keir et al., 2009].
During individual earthquake swarms, most of the seismic energy is released during the first 5–20 h of seismic activity, when migration of earthquakes is observed, which we interpret as the duration of the magma intrusion (Figure 6). The average migration velocities for the five dikes studied here are in the range of 0.5–3.0 km/h (Figures 7 and 8), which is consistent with the migration of earthquakes associated with the September 2005 megadike (d0), reported by Ayele et al.  (Table 1). These values are similar to those deduced from the study of other dike intrusions in the Krafl Rift during the 1975–1984 rifting episode (∼1.6 km/h) [Brandsdóttir and Einarsson, 1979; Einarsson and Brandsdóttir, 1980], or at the slow and intermediate spreading segments of the mid-ocean ridge system, where such observations have been reported (∼1–2 km/h) [Dziak et al., 2007], and are likely to reflect the low viscosity of basaltic melts involved in these intrusions.
Table 1. Dates of the Dikes Discussed in the Text, With Corresponding Volumes V, Maximum Magnitude in the Earthquake Swarm Mmax, Cumulative Seismic Moment Released During the Swarm M0, Seismic Efficiency e, Direction of Migration, Length of Swarm l∞, Characteristic Time Scale of Seismicity Migration τW, and Characteristic Velocity of Migration v1/2 (Equation (1))
Migration velocities are not constant during intrusions, but rather decrease during the intrusion, until the final length of the dike is reached. This suggests a progressive decrease of the horizontal gradient of driving pressure as the dike grows, resulting from a combination of many factors, including pressure decrease in the magma as the material is withdrawn from a source reservoir of finite size [e.g., Ida, 1999; Buck et al., 2006; Rivalta, 2010], decrease of the magnitude of elastic stress at the crack front as the shape of the dike changes during its growth [e.g., Taisne and Tait 2009], and/or an increasing tendency to freezing in the tip region as the dike lengthens and duration of magma transport, and hence heat loss, increases [e.g., Spence and Turcotte, 1985; Fialko and Rubin, 1998]. Therefore, migration of seismicity provides important constraints on the dynamics of dike intrusions.
To compare quantitatively the different dike intrusion velocities, we assume that the distribution of seismicity follows an exponential law of time:
where l is dike length measured from the location of the onset of seismicity migration, t0 is the time of initiation of dike propagation, l∞ is the asymptotic dike length and τW is the characteristic time scale of dike propagation. This law is appropriate to describe the coupling between an overpressurized source reservoir and a laterally growing planar intrusion, assuming conservation of mass [e.g., Dvorak and Okamura, 1987; Lengliné et al., 2008; Rivalta, 2010]. With the assumption of a constant dike height and thickness during propagation, the dike volume, like the seismicity, follows an exponential evolution. From the above relation, and following an analogy with half-life in radioactive decay, we estimate a characteristic velocity of migration v1/2 = l∞/(τW * 2 ln(2)), which corresponds to the time taken by the dike to reach its half-length. We performed a least squares adjustment of the parameters in equation (1) using our data set (Figures 7 and 8). The values of l∞, τW and v1/2 are reported in Table 1.
Of particular interest are the characteristic velocities v1/2, which range from 1.0 to 2.3 km/h (Table 1). Among the five dikes presented in this study, these velocities appear to be loosely correlated with dike volume (Table 1). This may be attributed to different magnitudes of the driving pressure for the different dikes, with the fastest, most voluminous dikes, corresponding to the greatest magma pressure at onset of dike intrusion [Lister and Kerr, 1991; Mériaux and Jaupart, 1995]. Yet, preliminary analysis of seismicity associated with dike d7 (November 2007) that propagated toward the south, suggests a slow velocity for this dike [Belachew et al., 2011], despite a volume comparable to that of dike d10, one of the fastest of the migrating dikes. Therefore, the apparent correlation between dike volume and migration velocity highlighted here may be biased by the fortuitous sampling of dikes available for this study, and may not have general significance.
Nevertheless, a key observation is that dikes migrating northward (d1, d10 and d11) are more voluminous and migrated faster than those emplaced southward (d2 and d9). This is in keeping with the observation of Grandin et al. [2010b], who showed that during the 2005–2009 sequence of 13 intrusions, dikes emplaced toward the south were generally smaller than those emplaced toward the north, with the notable exception of dike d7 (November 2007), which migrated up to 25 km southward, the greatest distance for all dikes since d0 (September 2005). The asymmetry in opening includes the September 2005 megadike, with a larger peak opening toward the north (6–8 m) than the south (<5 m) [Grandin et al., 2009] (Figure 1c). The authors interpreted this observation as being caused by to the combination of (1) an overall increase of tension stored in the elastic lithosphere at increasing distance from the central magma reservoir and (2) an asymmetry of the distribution of tension, with more differential tensile stress stored in the lithosphere in the north than in the south. The origin of the asymmetry may be related to the history of rifting episodes in the past [Grandin et al., 2009], as observed in Iceland [Björnsson, 1985], and/or differences in thickness of the elastic-brittle lithosphere north and south of the magma reservoir (Grandin et al., submitted manuscript, 2011).
3.4. Seismic Moment Release Associated With Dike Intrusions
For each dike, the cumulative seismic moment M0 released during dike emplacement can be estimated using local magnitudes ML and duration magnitudes MD that we have estimated for dikes d9, d10 and d11 on the one hand, and local magnitudes ML provided by Keir et al.  for dikes d1 and d2 on the other hand. Body wave magnitudes mb or moment magnitudes Mw calculated by NEIC (National Earthquake Information Center) for the largest earthquakes are also available. When comparison is possible, these magnitudes agree within 0.3 units of magnitude. Conversion from magnitudes M (whether Mw, mb, ML or MD) to seismic moment M0 (expressed in Nm) is performed using the formula M = 2/3 × log M0 − 6.03 [Hanks and Kanamori, 1979].
As could be expected, the maximum magnitude of earthquakes accompanying dike intrusions is larger for the most voluminous dikes d0, d1 and d10, and lower for the smaller dikes d2 and d9 (Table 1). Yet, as is commonly observed for magma intrusions, most of the deformation during the dike injections of the MHR occurs aseismically [e.g., Foulger and Long, 1984; Pedersen et al., 2007]. This includes the megadike d0 of September 2005, which involved a volume of magma in excess of 1 km3 [Wright et al., 2006; Ayele et al., 2007; Grandin et al., 2009; Ayele et al., 2009]. Seismic moment release among the five dikes presented here spreads across 2 orders of magnitude, whereas dikes volumes differ by a factor less than 4. Including the megadike d0 (September 2005) increases this discrepancy, with a volume greater than that of dike d9 by a factor 39, and a seismic moment release greater by a factor 10,000. This tendency is highlighted by the “seismic efficiency” e, defined here as the ratio between the geodetic moment release Mg and the cumulative seismic moment M0 released during dike emplacement (multiplied by 100 if expressed in percent). The geodetic moment Mg is here defined as the product of the volume of the dike V and Young's modulus E. Here, we use E = 30 GPa, following Grandin et al. [2010b].
Despite uncertainty on the value of the elastic modulus and the possible bias on the estimation of the total seismic moment release resulting from the inhomogeneous seismic data set, we observe that seismic efficiency is very small, with Mg/M0 spanning between 6% for the September 2005 megadike (d0) and 0.03% for the d2, d9 and d11 dikes (Table 1). This compares well with the July 1978 Krafla dike intrusion (Iceland), which had a seismic efficiency of 0.6% [Einarsson and Brandsdóttir, 1980; Pedersen et al., 2007]. In contrast, a seismic efficiency of 40% is observed for the 2000 dike intrusion offshore the Izu peninsula (Japan) [Toda et al., 2002; Pedersen et al., 2007], 55% for the 2007 Gelai dike intrusion (Tanzania) [Calais et al., 2008; Baer et al., 2008], and 14–25% for the 2009 Harrat Lunayyir dike intrusion (Saudi Arabia) [Baer and Hamiel, 2010; Pallister et al., 2010].
The overall low seismic efficiency of dike intrusions in the MHR means that most of the strain change induced by intrusion of the dikes does not lead to brittle seismogenic rupture of host rock, and is accommodated by a combination of aseismic slip, tensile opening, ductile deformation, and/or elastic strain not exceeding brittle resistance of rocks. This low seismic efficiency likely reflects host rock that is initially relatively far from the brittle failure envelope, which is consistent with the low background seismic activity observed in the volcanic rift zones of the Afar region [Rubin and Gillard, 1998; Pedersen et al., 2007; Hofstetter and Beyth, 2003]. Such a low level of tectonic stress may be possibly related to the maturity of this proto-oceanic plate boundary, where plate strength is lower and magma supply rate is higher than in the less evolved continental rift environments mentioned in the above examples [Solomon et al., 1988; Baer and Hamiel, 2010].
Among the dikes intruded in the MHR, an apparently greater seismic efficiency is observed for the most voluminous dikes, and a comparatively lower efficiency for smaller intrusions (Table 1). This suggests that the rate of stress perturbation plays an additional role in modulating the amount of seismic energy released during a dike intrusion, which is compatible with the hypothesis that rate-and-state constitutive laws govern the process of earthquake generation [Dieterich et al., 2000; Toda et al., 2002].
Nevertheless, the case of dikes d1 and d11, which exhibit significantly different seismic efficiencies (1.58 % and 0.03 %, respectively) despite similar rates of stress change (within a ratio of 1–2, as inferred from the proxy V × v, where V is dike volume and v is migration velocity), and a location in nearly the same region of the plate boundary (see also section 3.6), may suggest that the importance of the rate of stress change in our data set should be toned down. Rather, the progressive decrease of background tensile stress is more likely to have caused the dramatic decrease of seismic efficiency observed from June 2006 (d1) to February 2009 (d11). This can be deduced from the evolution of normal stress on the vertical plane of the plate boundary during the 2005–present rifting episode in response to the d0-d12 dike injections, as discussed by Grandin et al. [2010b] [see also Hamling et al., 2010]. Intrusion of dike d1 has induced a reduction of the magnitude of the normal tensile stress reaching −5 MPa in the region of emplacement of d1 and d11. Occurrence of subsequent dikes d2-d9 did not significantly change the magnitude of tensile stress in that region, because most of these dikes occurred more than 5 km to the south (Figure 1c). Dike d10 then induced an additional decrease of tension by −2 MPa in the d1-d11 area, again reducing the propensity for more dike intrusions there. Therefore, a cumulative decrease of background tension of −7 MPa occurred between June 2006 (prior to d1) and February 2009 (prior to d11) in the area where d1 and d11 were emplaced. The earthquakes accompanying the dike intrusions are likely to be related to slip on faults located in the vicinity and/or beyond the propagating crack tip [Rubin, 1992]. Slip on these faults is promoted by the stress perturbation induced by the crack tip (approximately the same for d1 and d11) and the background tensile stress field (more tensile before d1 than before d11), explaining the lower seismic efficiency for d11 than for d1.
Nevertheless, occurrence of dike intrusion d11 demonstrated that the stress state was still tensile in this area in February 2009. Observation of eruptions coeval with the two last observed dike intrusions of June 2009 (d12) and May 2010 (d13) may indicate that most of the tensile stress has now been relieved in the vicinity of the magma reservoir, thus increasing the likelihood for future eruptions there (Figure 1).
3.5. Time-Space Variation of Strain Energy Release
As discussed above, earthquakes accompanying magma intrusion seem to migrate at a decaying velocity during dike growth. To infer the distribution of strain released by brittle seismic rupture as a function of time and space, we propose to follow the evolution of the cumulative Benioff strain release during propagation (Figure 6). When Benioff strain is plotted as a function of distance along the dikes from the source reservoir, we observe that strain release is not uniformly distributed spatially (Figures 7 and 8), and is neither correlated with the amount of opening along the dike body (Figure 1c). For dike d1, energy release as a function of dike length is triangular in shape, with the bulk of the energy released in two distinct peaks near the distal dike tip, and little seismicity near the region of first occurrence of seismicity, which likely corresponds to the point of magma injection from the source reservoir (Figures 7a–7c). The same first-order observation is repeated for d10 and d11, which also propagated toward the north (Figure 8d–8i). However, the triangular shape of seismic energy release with distance is less clear in the case of dike d10, mainly because two earthquakes of magnitude 4–4.5 occurred behind the crack front (i.e., near the midlength of the dike) after the end of propagation. Excluding these two shocks, a triangular shape of seismic energy released near the propagating dike front is also found.
For the best constrained dike d9, seismicity is organized in two successive stages (Figures 8a–8c). First, a leading series of small magnitude earthquakes migrates rapidly away from the source. Then, a trail of earthquakes with larger magnitudes follows (Figure 8). The majority of seismic energy during intrusion of d9 was released at its southern extremity, but a significant fraction was also released near its injection point, mainly in the 4 h preceding onset of southward propagation of seismicity. The case of dike d2 is more difficult to interpret, as only 18 earthquakes are available for this dike, but the pattern of seismicity nevertheless resembles that of d9: accumulation of events near the entrance point, then a propagation of earthquakes, and finally sustained seismicity near the dike end.
Overall, we notice that most of the seismic energy is released near the propagating tip of the dike, including in the period when the swarm has reached its final length. This indicates that little seismic energy is released along the dike body at any time, and that seismicity mostly reflects resistance involved in deforming host rock in a process zone surrounding the crack tip [Ukawa and Tsukahara, 1996; Roman and Cashman, 2006]. This confirms that perturbation of the ambient tensional stress field in the vicinity of the opening dike tip is capable of triggering seismicity, by raising the level of shear stress on optimally oriented faults located near the crack periphery [Rubin, 1992] (see also Hayashi and Morita  for similar observations during a dike intrusion of 1998 in the Izu peninsula).
Furthermore, simultaneous migration and growth of this process zone may explain other features of the distribution of seismic energy during dike propagation, such as the observed triangular shape of seismic energy release in the direction of migration, as shown in Figure 9. For a simple crack of length l loaded with a uniform driving pressure, Linear Elastic Fracture Mechanics (LEFM) predicts that the magnitude of maximum stress perturbation at distance r from the crack tip scales like l1/2, with a decay proportional to r−1/2 [e.g., Rice, 1968]. If we define the process zone as the region where stress conditions have been brought to the level defined by the shear failure envelope, then the size of the process zone may increase as l if off-dike irreversible deformation within the process zone is assumed to reflect damage of host rock in response to the stress singularity in the vicinity of the crack tip [Andrews, 1976; Cowie and Scholz, 1992; Manighetti et al., 2004]. Alternatively, when fluid flow is considered, the damage zone could also scale with the length of the fluid lag zone behind the crack tip, which might increase quasi-linearly with l (so that process zone size is controlled by the fluid flow part of the problem and is not an intrinsic rock property) [Rubin and Gillard, 1998]. In both cases, the effect of dike propagation and growth results in the expansion of a region affected by crack tip–related seismicity, with the rate of seismic energy released near the propagating dike front being proportional both to dike length and to the inflation rate of the dike, hence the velocity of propagation of the dike (Figure 9).
Accordingly, this model assumes that the dike retains a constant shape during its growth. This is reasonable if fracture resistance is unimportant, and viscous pressure loss in the dike interior is low. However, this is not a good assumption if the shortest in-plane dimension is the dike height h. For the larger dikes in the MHR (e.g., d0 or d10) it seems likely that l > h. In that case, one could expect (given one of the above scenarios in which damage zone increases with dike size) the damage zone will increase with dike length l until l approaches h, at which point a steady state would probably be reached. Decrease of the pressure in the magma source may also lead to a variable length:thickness ratio during dike growth. Nevertheless, the model of migration and expansion of the process zone during dike growth may be still relevant to explain the first-order observation that little seismic energy is released in the first hour of the intrusions during the fast growth of the short dike, whereas more seismicity is generated in the later stages, when dike length increases at a slower rate.
Alternatively, other mechanisms may explain the observed “triangular” increase of seismic moment release with distance from the source. One such mechanism is stopping of a dike due to inelastic deformation (e.g., fault slip, probably the clearest example of which was the first intrusion at Krafla in 1975 [Björnsson, 1985]). If so, one can expect significant seismicity at the distal end of the intrusion, and even continuing seismicity if fault slip and inflation by continued magma influx are coeval. In addition, one can expect a deeper brittle-ductile transition farther form the source, as supported by empirical evidence that (statistically) there are larger extensional tectonic stresses farther from the source (increase in fault scarp height in active rifts; increase in average dike thickness in eroded rifts [see Rubin, 1995; Grandin et al., submitted manuscript, 2011, and references therein]).
In fact, both scenarios are plausible, and they may even combine in the following way: during dike propagation away from the central reservoir, the dike tip moves toward a region where stress is closer to the failure envelope, or where a larger volume of rock is potentially near the failure envelope, and, simultaneously, the stress perturbation is progressively greater due to lengthening of the dike, hence generating more seismicity.
Whichever interpretation is preferred, the lack of significant seismicity behind the crack front is clearly observed for the five dikes studied here. This first-order observation is compatible with (1) stress conditions being brought closer to lithostatic, and further from conditions for brittle rupture, off to the side of the dike body due to dike inflation and (2) deformation occurring above and below the dike during dike inflation in a largely aseismic fashion. The main deformation process at the base of the dike (∼10 km) is likely to be ductile flow, due to the high temperature at that depth [e.g., Benn et al., 1988]. Above the dike, slip on faults, associated with a substantial tensile component, which is abundantly described for the Manda Hararo dikes [Rowland et al., 2007; Grandin et al., 2009, 2010a], as well as in the Krafla rift [e.g., Opheim and Gudmundsson, 1989] and the Asal rift [e.g., Doubre and Peltzer, 2007], appears to occur mostly aseismically, presumably due to the combination of low confining stress conditions, and soft forcing exerted by the slowly inflating dike. Finally, the absence of seismic energy released near to the dike injection point during propagation/growth of the dike may support the hypothesis that stress conditions are nearly lithostatic there, possibly due to thermal weakening caused by the underlying midsegment focusing of melt and/or more frequent dike intrusions near the magma source (Grandin et al., submitted manuscript, 2011).
3.6. Multiple Dikes
A key observation made during the 2005–present rifting episode in the MHR is that, in two instances (and probably three), a newly intruded dike has been emplaced at the same location as a previous dike in the sequence [Grandin et al., 2010b]. These “multiple” events are d1 and d11 on the one hand, and d6 and d12 (and possibly d2), on the other (Figure 1c). Figure 10 shows the proportionality between the line-of-sight displacement fields induced by pairs d1-d11 and d6-d12, deduced from InSAR. The high coefficient of correlation between displacement fields suggests that variations in the strain field among the two pairs may be solely explained by the differing volumes of the dikes, while the geometry of the dikes was identical [Grandin et al., 2010b]. In addition, seismicity associated with dike intrusions d1 and d11 indicates that the evolution of seismic energy release in time and space was very similar for the two dikes, with nearly equal migration velocities, bringing further support for the “multiple dike” hypothesis (Figures 7a–7c, Figures 8g–8i, Figure 6, and Table 1).
Using a simple linear regression between the phase vectors, we find that the volume of dike d11 is about 62% of the volume of dike d1, whereas the volume of dike d12 is about 85% of the volume of d6 (Figures 10g–10i). This agrees well with volume fractions of 57% and 80% deduced from results of inversion of InSAR data for d1–d11 and d2–d12, respectively [Grandin et al., 2010b]. Similarly, the volume of dike d6 represents nearly 120 % of the volume of d2. Resemblance between dikes d6 and d12 is also backed up by the observation that axial eruptions, associated with lava fountains, were emitted from nearly the same fissure system in the late phases of injection of these two dikes (red stars in Figure 1), with intrusion:extrusion volume ratios of 10:1 for d6, and 5:1 for d12 [Ferguson et al., 2010; Grandin et al., 2010b]. Similarity between d2 and d6 (and hence d12) is also suspected from the high coefficient of correlation between their phase vectors (Figure 10). Therefore, in spite of a lack of near-field seismological observation for dikes d6 and d12, one can extrapolate that the low migration velocity observed coeval with dike d2 is also a feature of dikes d6 and d12, and more generally, of small dike intrusions occurring in the vicinity of, or above the midsegment magma reservoir.
Implications of the occurrence of such multiples are potentially important. As these dikes are emplaced in exactly the same sector of the plate boundary, to first order, the main difference between the first and second dike intrusion is the magnitude of tension on the plate boundary at the onset of the intrusion, which may have been significantly decreased due to previous dike intrusions in the sequence, as discussed earlier. However, one may wonder why the volumes of dikes d6 and d12 were the same, whereas the occurrence of an eruption coeval to dike d6 would have suggested that differential tensile stress had been completely relieved in its surroundings by the end of intrusion of d6 [Arnott and Foulger, 1994; Buck et al., 2006]. If this were to be the case, dike d12 should have been entirely extrusive, as no more extensional tectonic stress would have been available to drive dike opening.
The answer may lie in the hypothesis of Grandin et al. [2010b], who calculated that, in the region of emplacement of dikes d6-d12 (2 km south of source reservoir, 2 km depth), the drop in tension associated with d12 on one hand, and the increase in tension by static stress transfer associated with the d7-d8-d9-d10-d11 sequence on the other hand, had competing contributions (−4 MPa versus + 3 MPa). This is due to the spatial configuration of successive dike intrusions d7 (November 2007) to d11 (February 2009), which have surrounded d6 (Figure 1c). Intrusion of a new dike there (d12) would have been required to return to lithostatic conditions in this area, and lead to a second eruption coeval to d12, suggesting a “memory” of the system across several dike intrusions.
Returning to the case of d1 and d11, the fact that increase of tension as a result of intrusions d2 to d10 has not produced the same effect as for the pair d6-d12, may be interpreted as indicating a significant magnitude of differential stress in the d1-d11 area, hence a lower sensitivity to perturbations by other dikes than the d6-d12 area. Since no eruption has been reported in this area prior to d13, we estimate that differential tensile stress in the d1-d11 area must have been at least twice the amount of tension drop coeval with dikes d1 and d11 (−3 MPa in each case) to be capable of preventing the occurrence of an eruption. Taking into account the fact that initial megadike d0 had already induced a tension drop nearly equal to the sum of the tension drops induced by d1 and d11, and that dike d0 has also contributed to releasing tensile stress in the area, this first estimate may be doubled, yielding a minimum value of 12 MPa for σ1 − σ3 in the d1-d11 area. Similarly, interpreting dikes d0a and d10 as multiple dikes [Grandin et al., 2010b], and taking into account that they are the most voluminous dikes in the sequence (0.78 km3 and 0.20 km3, respectively), may imply that differential stress was even more tensile in the d0-d10 area (perhaps as much as 20 MPa or more) prior to onset of diking in September 2005. However, the occurrence of a new eruption near 12.34°N in May 2010 may indicate that this initial amount of differential tensile stress has now been nearly consumed, possibly suggesting that the maximum magnitude of the differential tensile stress in 2005 was near to 20 MPa at 8 km depth. Assuming that the maximum magnitude of differential tensile stress increases with depth at a rate of 10–15 MPa/km (Byerlee's law [e.g., Brace and Kohlstedt, 1980]), this is only 16–25 % of the limit imposed by brittle Mode II rupture of rocks. This suggests that dike intrusions reduce the level of tensile stress in a region of extension much more efficiently than normal faulting.
The lateral dike injections in the Manda Hararo–Dabbahu Rift (MHR), studied from the perspective of the seismicity they induce, provide insights into the magmatic and tectonic processes responsible for crustal accretion in an environment similar to mid-ocean ridges (MOR). The five dikes discussed in this paper were fed from a single midsegment reservoir, located near 12.29°N, i.e., 7 km to the SSE from the topographic summit of the axial depression. Therefore, in the plate boundary setting of the MHR, the hypothesis of a topographic control on the directivity of lateral dike migrations [e.g., Fialko and Rubin, 1998] appears to be contradicted by evidence for lateral dike intrusions directed both up rift and down rift. Velocities of lateral migration of the dikes are in the same range as those deduced in the Krafla rift (Iceland) or slow spreading MOR (∼1–2 km/h). The dikes that migrated up rift, toward the NNW, were generally more voluminous and emplaced at a faster velocity than the dikes that migrated toward the SSE. This suggests that differential tensile stress has a greater magnitude to the NNW than to the SSE of the central magma source. Variations in elastic thickness, or the history of past rifting episodes, may explain this difference, although this issue cannot be resolved currently.
We found that dike-induced seismicity appears to be roughly concentrated near 5 km depth for the best-constrained dike of July 2008, which could suggest that seismicity occurs either at the depth of the dike or below the dike (depending on the confidence on estimated dike depth obtained by inversion of InSAR). Nevertheless, despite considerable uncertainty on hypocentral estimates due to the unfavorable network geometry, the time-space distribution of seismic energy release coeval with the dike intrusion is more compatible with seismicity being primarily released at the depth of the intrusion as a result of stress perturbation in the host rock near the propagating front of the magma-filled crack. After inception of the migration, little seismicity is detected behind the migrating front (1) off to the sides of the dike, (2) at its bottom, (3) in the subsurface above the dike, and (4) near the crack tail. Deformation during dike inflation/growth in these regions is likely to be aseismic, respectively due (1) to tensile stress being relieved, so that stress conditions are brought further from the limit imposed by criteria for brittle rupture, (2) to the ductile rheology of rocks at great depth, which prevents large preintrusion tensile stress accumulation, hence making the intrusion less likely to trigger seismicity, (3) to low confining pressure and slow forcing of subsurface faults, whose large cumulative slip is reached progressively as the dike inflates, possibly by aseismic creep with a substantial component of tensile opening, and (4) to nearly lithostatic stress conditions near the source reservoir, at the entrance point of magma in the brittle-elastic layer.
In view of the volume of magma involved in the intrusions (0.05–0.2 km3), seismic moment release during dike injections is very small (0.03–6.0 % of the geodetic moment release), probably due to the low differential tensile stress in the MHR. This feature may be typical of a mature MOR, where magmatism efficiently prevents accumulation of strong differential tensile stress. Seismic moment release is weakly correlated with dike volume and migration velocity, highlighting the additional influence of the rate of stress change in modulating the level of seismic energy released by dike injections.
Nevertheless, dike-induced seismicity seems to be primarily sensitive to the magnitude of differential tensile stress in the region of dike emplacement, as suggested by the decrease of seismic energy released by successive dikes as the end of the current rifting episode is approaching. Based on a crude analysis of static stress changes associated with the 13 dike injections that occurred from 2005 to 2009 in the MHR, we estimate that the maximum differential tensile stress stored at the onset of the rifting episode in 2005 was ∼20 MPa north of the source reservoir, at a depth of 8 km. This low magnitude of the differential stress suggests that dike intrusions operate at a lower level of tensile stress than is required for normal faulting, so that diking is more efficient than faulting to accommodate plate extension.
This work would not have been possible without the constant support of the Institute of Geophysics, Space Science and Astronomy (IGSSA) of Addis Ababa University (AAU). In particular, Laike Asfaw, Tesfaye Kidane, and Elias Lewi are thanked for their support. We are grateful to Abebe Albie (IGSSA) and Yves Bertrand for their contribution to fieldwork. We thank Michael Asrat (IGSSA) for logistic assistance. François-Xavier Fauvelle and Éloi Fiquet are warmly thanked for the logistic support for fieldwork they provided through Centre Français des Études Éthiopiennes (CFEE), in Addis Ababa. Special thanks are addressed to our drivers from CFEE: Semenh Bacha, Amare Setotaw, and Temechach Yifru. Support from the authorities of the Afar regional government in Semera, particularly Idriss Mohamad, Mohammed Tahiro, and Mohammed Yayo, as well as Assefa Beyene and Adem Bori from Semera University, is acknowledged. Fruitful discussions with Mathilde Cannat, Benoît Taisne, and Steve Tait contributed to improve the paper. Exchanges of ideas and data with Manahloh Belachew, Laura Bennati, Roger Buck, Eric Calais, Cynthia Ebinger, Ian Hamling, Tim Wright, and Gezahegn Yirgu were also greatly appreciated. We thank two anonymous reviewers for their constructive comments on the paper. The acquisition of the seismic stations was possible thanks to support from Bonus Qualité Recherche (BQR) of Institut de Physique du Globe de Paris (IPGP) and support from the Volcanological Observatories of IPGP. Part of the resources for this work also originates from the funding of project Dynamics of Rifting in Afar (DoRA) by French's National Research Agency (ANR). DK was funded by NERC fellowship NE/E013945/1. We thank the European Space Agency (ESA) for programming the Envisat satellite and providing data used in this work (AOE-272, AOE-720). The Repeat Orbit Interferometry Package (ROI_PAC) software was provided by Caltech/Jet Propulsion Laboratory (JPL). The numerical implementation of the method of Tarantola and Valette  was performed by Virginie Penquer'ch. Figures 1, 3, 5–10, and S1 were prepared with the Generic Mapping Tool (GMT) software [Wessel and Smith, 1991]. This is IPGP contribution 3142.