Monogenetic vent self-similar clustering in extending continental crust: Examples from the East African Rift System

Francesco Mazzarini* and Ilaria Isola Istituto Nazionale di Geofi sica e Vulcanologia, Sezione di Pisa, Via della Faggiola, 32, 56126, Pisa, Italy

ABSTRACT 2004). It is widely accepted that the transport and are formed if basaltic magmas stop at inter- of magma from lower crustal-upper mantle mediate to shallow crustal magma chambers, The spatial clustering of fracture networks source/reservoir regions to its fi nal level of whereas monogenetic volcanoes erupt only once and vents in basaltic volcanic fi elds has been emplacement mainly occurs through dykes and (e.g., MacDonald, 1972) and are constructed analyzed in three sectors of the East Afri- sills (Lister and Kerr, 1991; Petford et al., 1993; when magma directly erupts from feeders. can Rift System, the classical example of an Rubin, 1995; Petford et al., 2000). These fl uid- According to Connor and Conway (2000) vol- active continental rift. Fracture trace maps driven fractures or hydro-fractures are generally canic fi elds are dominantly basaltic in composi- and monogenetic basaltic vents have been opening-mode fractures (e.g., Gudmundsson, tion and are formed by monogenetic vents each thus collected in the Afar Depression, in the 2002; Gudmundsson and Brenner, 2004). The produced by a single episode of volcanic activ- Main Ethiopian Rift, and in the Virunga Belt magma ascent rate depends on magma prop- ity and associated to feeder dykes. The occur- (Western Rift). The mapped vents are gen- erties (including viscosity, density, tempera- rence and spatial distribution of monogenetic erally younger than 2 Ma, and most are of ture, and heat content), country rock properties eruptive structures within volcanic areas are Holocene age. (including temperature, density, thermal con- linked to fracture systems and associated stress All the analyzed fracture networks have ductivity, and permeability), and the stress fi eld. fi elds (Takada, 1994a). Moreover, morphomet- self-similar clustering with fractal exponents Several lines of evidence, e.g., high-density ric parameters of monogenetic cones, such as − (Df) varying in the 1.54 1.85 range. Also, xenolith settling in basalt magmas (Basu, 1977; cone elongation, breaching direction, and cone vents show a self-similar clustering with frac- Spera, 1980; Petford et al., 2000), numerical alignment, indicate the direction of fractures − tal exponents (Dv) in the 1.17 1.50 range. For analysis (Dahm, 2000a, 2000b), and magma acting as magma feeders (Tibaldi, 1995).

all the studied sectors, the relationship Df > cooling rates (Maaloe, 1973), indicate veloci- It has been proposed that fractures fi lled by −2 −1 −1 Dv has been observed. The fractal exponents ties of magma ascent of 10 ms up to 1 ms , magma (i.e., dikes) tend to coalesce during

for vents (Dv) of power-law distributions which imply high bulk permeability of the crust. their ascent to the surface, thereby controlling are computed in a range of lengths with a Rock-fracturing processes enhance the bulk per- the fi nal level of magma emplacement. The lower and an upper cutoff. The upper cutoff meability of the crust and allow the ascent of actual distribution of volcanic vents at the sur- (Uco) for the fractal clustering of vents in the magma at rates that are akin to the time-scale face, i.e., the formation of monogenetic and/or studied sectors of the East African Rift Sys- characterizing magmatic activity (Rubin, 1993; polygenetic volcanoes, is mainly controlled by tem are compared with the respective crust Petford et al., 1993; Petford et al., 2000; Canon- the magma input rate and the crustal strain rate thickness derived by independent geophysi- Tapia and Walker, 2004). Fluid-driven fracturing (e.g., Fedotov, 1981; Takada, 1994a, 1994b). cal data. The computed Ucos for the studied (fractures fi lled by magma, i.e., dyke formation) High-strain rate or small magma input rate pro- sectors well match the crust thickness in the is thus the viable mechanism for emplacing mote the formation of monogenetic volcanoes volcanic fi elds. A preliminary conceptual magma within the crust (e.g., Turcotte, 1982; whereas low-strain rate and high magma input model to explain the relationships between Hutton, 1996; Petford et al., 2000). Depending rate mainly generate polygenetic volcanoes. the upper cutoffs of the fractal distribution on magma buoyancy relative magnitude, crust’s It is important to emphasize that basaltic of vents and the thickness of the crust in the fracture toughness, crustal mechanical disconti- monogenetic vents testify to the presence of volcanic fi elds is thus proposed in the light of nuities, and magma availability, dykes may stop deep crustal or subcrustal magma reservoirs the percolation theory. at some levels in the crust or, eventually, they directly connected via fracture network to may also construct magmatic chambers or reach the surface, involving a hydraulic connection INTRODUCTION directly the surface generating eruptions (e.g., through the whole crust or a large portion of Ida, 1999; Dahm, 2000a; Gudmundsson, 2002; it between source and surface. Moreover, the Fluids commonly migrate through the Taisne and Tait, 2009). correlation between vent distribution and frac- Earth’s crust in hydro-fractures such as min- In particular, eruptions of basaltic magmas ture network properties is such that the spatial eral veins or dykes, stopping at various depths imply the transfer of magmas from deep res- distribution of vents may be studied in terms in the crust (e.g., Watanabe et al., 1999; Dahm, ervoirs up to intermediate magma chambers of self-similar (fractal) clustering (Mazzarini 2000a, 2000b; Gudmundsson and Brenner, in middle upper crust or directly to the Earth’s and D’Orazio, 2003; Mazzarini, 2004, 2007; surface. Polygenetic volcanoes repeatedly erupt Mazzarini et al., 2008), as in the case of frac- from the same general vent (summit or crater) ture networks (Bonnet et al., 2001). Findings *E-mail: [email protected]

Geosphere; October 2010; v. 6; no. 5; p. 567–582; doi: 10.1130/GES00569.1; 7 fi gures; 5 tables.

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based on this approach suggest that, for basal- and in the Springerville Volcanic Field in Ari- The connectivity of fractures defi nes the por- tic volcanic fi elds in a deformed continental zona (Connor et al., 1992; Condit and Connor, tion of the existing fracture network that hydrau- crust, the distribution of monogenetic vents is 1996). Vent alignment has often been used to lically connects the system boundaries, allowing linked to the mechanical layering of the crust. infer the direction of the minimum horizontal fl uids to fl ow (Margolin et al., 1998; Darcel et Vents tend to cluster according to a power-law principal stress (Nakamura, 1977; Lutz, 1986; al., 2003). Connectivity mainly depends on distribution defi ned over a range of lengths Wadge and Cross, 1988), and vent distribution fracture size (length), density, orientation, and bounded between a lower limit (Lower cutoff, has been used as evidence for structural con- on the spatial correlation among fractures (e.g., Lco) and an upper limit (Upper cutoff, Uco); the trol on vent location (Connor, 1990; Connor Renshaw, 1999; Berkowitz et al., 2000; Darcel upper cutoff approximates the thickness of the et al., 1992) and to outline the importance of et al., 2003). fractured medium (crust). This correlation has strain rate in the style of volcanism (Takada, Fracture lengths in nature often display a been studied in volcanic fi elds within exten- 1994a; Alaniz-Alvarez et al., 1998; Mazzarini power-law distribution in the form sional continental settings in back-arcs, such et al., 2004). as in southernmost Patagonia (Mazzarini and Volcanoes tend to form clusters, showing sta- N(l) ∝ l – a, (1)

D’Orazio, 2003) and in continental rifts such as tistical self-similarity in both space and time as the Main Ethiopian Rift (Mazzarini, 2004) and documented in hot spots on oceanic crust (Shaw where N(l) is the number of fractures whose Afar (Mazzarini, 2007), as well as in contrac- and Chouet, 1991) and in continental magmatic length is longer than l and a is the fractal expo- tional continental settings as the Andean fore- arcs (Pelletier, 1999). Vent clustering in basaltic nent (e.g., Bonnet et al., 2001, and references land (Mazzarini et al., 2008). volcanic fi elds has been also described in the therein). In this work we present a qualitative model to Newer Volcanic Province, southeast Australia A robust way to defi ne how fractures fi ll explain the observed relationships between the (Lesti et al., 2008) and in Afar, east Africa (Maz- space is to analyze their self-similar cluster- upper limit of the fractal distributions of basal- zarini, 2007). ing (Bonnet et al., 2001). This is accomplished tic monogenetic vents and the crust’s thickness As previously discussed, the occurrence by computation of the correlation sum that on the base of the percolation theory (Stauffer of basaltic monogenetic volcanism implies accounts for all the points at a distance of less and Aharony, 1992). In this model the mono- the existence of a portion of the fracture net- than a given length l (Bonnet et al., 2001, and genetic vents represent the intersection of the work allowing a direct connection between references therein) following the equation connected part of the actual fracture network, the magma reservoir at depth and the surface which effectively ties the source of magma to (vents). Clearly this feature points to the geo- C(l) ∝ l – D, (2) the surface (i.e., the backbone in the percolation metric and hydraulic characteristics of the theory, see below), with the surface and their actual fracture network. On this basis, Maz- where C(l) is the correlation sum and D is the self-similar clustering linked to the fracture zarini (2004) developed a simple model for fractal exponent. self-similar clustering. visualizing the relationship between vents and These two parameters strongly control the Successively, the model will be tested in three the geometric properties of fractures. This connectivity of the fracture network, high val- different sectors of the East African Rift System model assumes that the aperture of a fracture ues of the a exponent in Equation (1) imply (EARS) in a context of continental extension is greatest at its barycenter and that volcanic high frequency of short fractures, whereas low and new data on vent and fracture distributions vents erupt at the point of maximum fracture values of the a exponent mean that the system is will be discussed in the light of the proposed aperture; the resulting vent distribution is thus mainly controlled by long fractures (Fig. 1A). model and critically compared with available closely linked to the hydraulic properties of the Moreover, the higher the values of the D expo- independent geophysical data. actual fracture network. nent in Equation (2), the more the fractures are The main geometric features of a fracture homogenously distributed, on the other hand VENT DISTRIBUTION, FRACTURE network (fracture attitude, aperture, spacing, the lower the D exponent, the higher the frac- NETWORK, AND PERCOLATION intersections, length, and density) are gener- ture clustering (Fig. 1A). THEORY ally measured and mapped at different scales of Generally fracture networks exhibit fractal observation, showing scale invariance spanning length distributions with exponent a < 3 (Ren- The spatial distribution of volcanism in several orders of magnitude (e.g., Marrett et al., shaw, 1999) or a < 4 (Bonnet et al., 2001). The terms of volcano spacing and its relationship 1999; Bonnet et al., 2001; Bour et al., 2002). case where exponent a < 1 is very infrequent with fracture patterns and lithospheric struc- The way in which fractures fi ll space (i.e., the implying that system connectivity is controlled ture has been studied since the early 1970s in spatial distribution of fractures) strictly depends by very long fractures spanning through the oceanic and continental settings (e.g., Vogt, on the spacing of fractures, that in turn is corre- whole system. For a > 3 the network connectiv- 1974; ten Brink, 1991). In particular, the spac- lated with the thickness of the fractured medium ity is ruled by faults smaller than the system size ing of central volcanoes within continental rift calculated on the basis of the stress saturation and classical laws for percolation theory apply settings has been linked to the elastic thickness model (Wu and Pollard, 1995; Gross et al., (Bour and Davy, 1997). of the lithosphere (Mohr and Wood, 1976). 1995; Ackermann and Schlische, 1997). Fracture density in terms of fracture length Several authors have investigated the spatial Hydraulic features of fractures such as frac- distribution and fracture spatial distribution and temporal distribution of volcanoes and ture connectivity and aperture are scale invariant mainly control the overall permeability of the monogenetic cones, focusing on the close rela- (Bonnet et al., 2001). In particular, the spatial system. A critical fracture density for which tionship between tectonics and volcanism, for clustering of a fracture network, represented as the network is connected allowing a direct example in the Michoacan-Guanajuato Volca- the fracture barycenter, has been directly linked connection between the network’s boundaries nic Field (Hasenaka and Carmichael, 1985; to the hydraulic properties of the fracture net- must exist. The percolation theory quantifi es Connor, 1987, 1990), in the Camargo Volcanic work (Renshaw, 1999; Bour and Davy, 1999; the existence of the critical fracture density for Field in Mexico (Aranda-Gomez et al., 2003), Darcel et al., 2003). which the network is connected and defi nes

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some important parameters that describe the behavior of a network as it becomes a percolat- D1 D2 ing network (Orbach, 1986; Stauffer and Aha- rony, 1992; Song et al., 2005). If the density of fractures in a network (ρ) is greater or equal ρ to a critical density ( c), the network becomes connected and a cluster of connected fractures spanning the whole sample will form (the infi - a ρ 2 nite cluster; Stauffer and Aharony, 1992); c is defi ned as the percolation threshold, and for a two-dimensional (2D) system it is 0.59 (Stauffer and Aharony, 1992). The connected portion of the network is a subset of the existing fracture D1 < D2 network (e.g., Roberts et al., 1998, 1999). a < a A simple example of a percolating network 1 2 is a grid; the link between nodes of the grid is defi ned as a bond. The grid on the left side of Figure 1B has a bond density of ~44% and there is no connection between the lower and the a1 upper side of the square. The grid on the right side of Figure 1B has a bond density of ~60% and it is at the percolation threshold, in this case a cluster of connected fractures (the infi nite cluster) connects the lower and the upper side of A the square (blue portion of the grid). During the transfer of magma within the crust, as simplifi ed in Figure 1B, the pressure gradient is essentially vertical and the connected network spans the whole path between source and the fi nal location of the magma. No assump- tion is done about the isotropy of the medium. Anyway, in layered sequences lateral connec- tivity of fractures is a function of the fracture spacing that in turn is a function of the layer thickness (e.g., Wu and Pollard, 1995). The portion of the infi nite clusters that actually allows the connection, for example, the portion of the fracture network in which fl uid actually fl ows, is named backbone. Above the percola- ρ ≥ ρ tion threshold (i.e., c) the network and the backbone are statistically self-similar (Orbach, 1986; Stauffer and Aharony, 1992). A perco- lating network is self-similar in a well-defi ned ρ=44% ρ=60% B range of lengths comprised between a lower and an upper cutoff, that is the percolating network is Figure 1. Control of fracture length distribution and fracture self-similar clustering in fractal for length scales r between α ≤r ≤ ξ; the the fi nal network connectivity. (A) Conceptual models of fracture networks with differ- lower cutoff α could be seen as the elementary

ent self-similar clustering (fractal exponent D1 and D2) and power-law distribution for grid, that is there are no bonds connecting pairs

fracture length (fractal exponent a1 and a2). Left portion of the panel has self- similar of nodes shorter than the elementary grid. The clustering higher than self-similar clustering of the right portion of the panel (i.e., upper cutoff is often referred to as the percola- ξ D1

number of small fractures than the lower portion of the panel, the higher value of a2 than connectedness length for percolation or, in other

a1 implies higher frequency of short fractures. (B) Simple grid where each side (bond) words, the maximum dimension of voids in the of the grid cell represents a possible fracture; ρ is the fracture density defi ned as the infi nite clusters, in the case of r ≥ ξ the perco- percentage of active bond in the grid. In the left the thick gray paths represent the active lating network appears homogeneous (Orbach, fractures with ρ = 44%. On the right the ρ for active fractures is 60%, that is above the 1986; Stauffer and Aharony, 1992). The defi ni- percolation threshold. In this case an infi nite cluster of fracture (thick blue paths) forms tion of self-similar clustering for the analyzed connecting the system boundaries. spatial correlation of fractures (i.e., computation of the fractal exponent, see Bonnet et al., 2001,

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and references therein) is thus performed for a Johnson et al., 2007, and references therein). of crust stretching, crust thickness, and intensity range of lengths (the size range) between lower Anyway, a strong consistency exists between of volcanism (Table 1 and Fig. 2). and upper cutoffs. According to the defi nitions geologic and geodetic data, suggesting that the described above for a percolating fracture net- ESE-WNW Nubia–Somalia relative motion Afar Depression work, the backbone in the infi nite clusters is the may have remained steady over the past 3 Myr actual fl uid pathway thus ξ represents the dis- (Corti, 2009, and references therein). The Afar Depression is located at the con- tance between the system’s boundaries (i.e., the Bulging of the lithosphere, crustal extension, fl uence of the Main Ethiopian Rift, the west- source and the surface for vents). and consequent widespread volcanism have ern Gulf of Aden, and the southern Red Sea The upper cutoff is here considered to be been ascribed to the impinging of one or two (Fig. 2). The Afar Depression is mainly fl oored directly linked to the mechanical layering of plumes on the base of the East African litho- by Pliocene and younger silicic volcanic rocks the medium. Mandelbrot (1982) suggested sphere in late Eocene–early Oligocene (e.g., and basalts and by Quaternary sediments (Bey- that there are upper and lower cutoffs for the Ebinger and Sleep, 1998; Rogers et al., 2000) ene and Abdelsalam, 2005; Mazzarini, 2007, scale-invariant characteristics of fractures (e.g., or, more recently, to multiple plume branches and references therein). Interaction between spacing, length, and density) and that these are rising from a deep-seated mantle upwelling (the the southern Red Sea and Aden oceanic ridges a function of mechanical layers and rock prop- African superplume, e.g., Furman et al., 2006). and the Afar stretched continental crust led to erties. Experimental studies on normal fault Crustal stretching (fi nal width/initial width; the formation of rifts and associated volcanism populations suggest the presence of upper and β), crustal thickness, and intensity of volca- (Manighetti et al., 1998; Lahitte et al., 2003a, lower cutoffs in the power law describing the nism greatly vary along the EARS moving from 2003b, and references therein). Basaltic volca- distribution of the geometric properties of frac- south, western branch Virunga area, to the north, nism is Pleistocene to Holocene and has pro- tures (Ackermann et al., 2001). Moreover, the Afar Depression (Ebinger, 1989a, 1989b; Braile duced several scoria cones and eruptive fi ssures thickness of both sedimentary beds and the crust et al., 1995; Ebinger and Furman, 2002; Bey- (Lahitte et al., 2003a, 2003b, and references controls the scaling law of fractures and earth- ene and Abdelsalam, 2005; Dugda et al., 2005, therein). The AD is characterized by strong quakes (Pacheco et al., 1992; Davy, 1993; Ouil- 2007; Corti, 2009). crustal attenuation: Bouguer gravity data indi- lon et al., 1996). Three sectors of the EARS are here investi- cate crustal thinning (Makris and Ginzburg, The dependence of the fracture network spa- gated in terms of their fracture and vent spatial 1987; Woldetinsae and Gotze, 2005) with an tial distribution on the rheologic layering of the clustering: the Afar Depression (AD), the Main average thickness of ~25 km. Inverse model- medium (i.e., the crust) can thus be inferred Ethiopian Rift (MER), and the Virunga Belt ing of gravity data shows a crustal thickness of from the backbone of the network (i.e., the (VB; in the EARS’s western branch). These 23–24 km in the AD (Tiberi et al., 2005). Seis- vents). The connected fracture network allows sectors are characterized by a different degree mic refraction data imaged a crustal thickness basaltic magma to rise to the surface from deep crustal or subcrustal reservoirs, passing through most or the whole of the crust. Analysis of the fractal character of the spatial distribution of RSRS vents can thus reveal the mechanical layering of the crust. Assuming a direct genetic and spatial link between fracture and vent (e.g., Connor and Conway, 2000; Mazzarini, 2004), scale invari- AADD GAGA ance in vent distribution refl ects the fractal prop- 10 erties of the backbone. The backbone of the per- NubianNubian N SomalianSomalian colating network should be more clustered than plateplate R the network (Stauffer and Aharony, 1992), i.e., E plateplate t MERM f the fractal D values estimated through Equation i T R (2) for the backbone (D ) should be lower than t b if t the value for the network (D ). R s n a t s EastE Rift 0 e VBVB CASE STUDY WestW Rift KRKR The proposed correlation between the dis- tributions of vent and fractures and the crustal thickness is here explored in the East African Rift System (EARS). The EARS is a classical seismically and volcanically active continental rift extending several thousands of kilometers 25 35 45 in a N-S direction accommodating the exten- sion between the Nubian (Africa) and Somalian Figure 2. Location map of the Horn of Africa (DEM from GEO- plates (Fig. 2; e.g., Rosendahl, 1987; Braile et TOPO30 data set; http://edc.usgs.gov/products/ elevation/gtopo30/ al., 1995; Morley et al., 1999; Chorowicz, 2005). gtopo30.html). AD—Afar Depression; MER—Main Ethiopian The boundary between the Nubia and Somalia Rift; VB—Virunga Belt; KR—Kenya Rift; T—Turkana Depres- plates is complex and the position of the pole of sion; N—Nazret. Latitude (left axis) and longitude (bottom axis) rotation is still a matter of debate (e.g., Horner- are in degrees.

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TABLE 1. SUMMARY OF CRUST STRETCHING, THICKNESS, AND INTENSITY AND AGE OF MER, and Afar, volcanism in the Western Rift is VOLCANISM FOR THE STUDIED AREAS ALONG EARS spatially and volumetrically small, leaving the Site AD MER VB vast majority of the Western Rift devoid of mag- Crust stretching (β) 1.7– ≥ 2 1.1–1.7 < 1.2 matism (Braile et al., 1995; Ebinger and Furman, Crust thickness (km) 25–23 27–38 20–30 2002). The volcanic activity started since 11 Ma Intensity of volcanism very high high low Age of sampled vents < 3 Ma < 2 Ma < 2 Ma has produced basaltic lava fl ows ~500 m thick Note: AD—Afar Depression; MER—Main Ethiopian Rift; VB—Virunga Belt. fl ooring the rift, successive activity focused in near E-W corridors, with a period of tholei- itic and alkalic volcanism beginning at 2 Ma and continuing to historic time. Erupted mag- of 23–25 km in the southern Afar Depression, The crustal structure of MER has been mas are characterized by silica-undersaturated and only 15 km in the northern part of the Afar imaged during gravity and seismic surveys. mafi c products and the local development of Depression (Berckhemer et al., 1975; Prodehl The crustal thickness estimated by analysis of evolved products from central volcanoes (Ebin- and Mechie, 1991; Prodehl et al., 1997). Analy- seismic data and by gravity data inversion is 28 ger 1989a, 1989b; Ebinger and Furman, 2002). sis of receiver functions from broadband seis- ± 2 km (Makris and Ginzburg, 1987). Gravity Analysis of broadband seismic data reveals that mic data (Dugda et al., 2005, 2007) reveals that data inversion imaged a crustal section in the rift the crust is 30–35 km thick in the Westrn rift the crust is 25 km thick in the Afar Depression. valley composed by 3–5 km of sedimentary infi ll and the Virunga belt area (Dugda et al., 2005). Both gravity and seismic data reveal a crustal and by upper crust ~20 km thick (Mahatsente Locally, crust thickness is supposed to be less thickness of 35–40 km in the shoulders of the et al., 1999). Seismic refraction data imaged a than 30 km in basins located in transfer zones rifts. Crustal stretching in AD varies from β = crustal thickness of 28–33 km in the northern as the VB area (see Ebinger 1989a, 1989b; Corti 1.7 in its southern part to β > 2 (Berckhemer et Main Ethiopian Rift fl oor and ~40 km at the rift et al., 2002). Analysis of earthquake catalog al., 1975; Eagles et al., 2002; Tiberi et al., 2005; margins (Berckhemer et al., 1975; Prodehl and and focal depth distribution in the Virunga area Beyene and Abdelsalam, 2005). Mechie, 1991; Prodehl et al., 1997). Further- (Albaric et al., 2009) shows that the number of more, analysis of receiver functions and joint crustal earthquakes is maximum at 10–15 km Main Ethiopian Rift inversion of Rayleigh wave group velocities and of depth and then decreases down to a depth of receiver functions from broadband seismic data ~32 km. Recently, teleseismic P-wave receiver The Main Ethiopian Rift (MER) connects the reveal that the crust is 30–35 km thick in the function analysis (Tuluka, 2009) imaged a crust Afar depression, at the Red Sea–Gulf of Aden Main Ethiopian Rift (Dugda et al., 2005, 2007). mantle transition at a depth varying from 30 to junction, with the Turkana depression and Kenya A new seismic experiment has been conducted 42 km, and a low velocity zone at depth varying Rift to the south (Fig. 2). It is commonly divided in MER in 2003 (EAGLE project; Maguire et from 18 to 30 km in the area of the large active into three sectors: north, central, and south al., 2003, 2006). EAGLE data show crust thick- Nyamuragira and Nyiragongo volcanoes. In the (Hayward and Ebinger, 1996; Corti, 2009). The ness along MER varying from 30 to 35 km in Virunga area we thus assume a crust thickness MER contains a large quantity of volcanic prod- the north segment of the rift to ~35–40 km in the in the range 20–30 km (Table 1). Crustal stretch- ucts characterized by a bimodal distribution of central segment (Keranen et al., 2004; Maguire ing is low, β < 1.2 (Ebinger, 1989a, 1989b). basic and acidic magma types (e.g., Trua et al., et al., 2006; Keranen et al., 2009; Corti, 2009). 1999). The MER is a late Miocene NE-SW– (in At the junction of the north and central segments DATA AND METHODS the north) to N-S– (in the south) trending fault of MER (at the latitude of Nazret; Figs. 2 and bounded basin, fi lled by late Miocene to Holo- 3D), the new seismic data highlights 30–35 km Data Collection cene volcanic rocks and continental sedimen- of crust thickness (Keranen et al., 2009). New tary deposits (e.g., Corti, 2009, and references seismic data by the EAGLE project (Keranen The analyzed data sets consisted of the loca- therein). The rift valley is intersected by nar- et al., 2004) also support that basaltic volcanic tions of mongenetic vents and the fracture trace row NNE–trending structures (the Wonji Fault fi elds in the rift fl oor (e.g., Debre Zeyt; Mazza- maps produced for the Afar Depression, Main Belt; Mohr, 1987) consisting of fault bounded rini et al., 1999) are localized on right-stepping Etiophian Rift, and Virunga Belt. In these areas, lava units aged less than 0.5–0.3 Ma (Morton en echelon N-S–trending zones (e.g., Ebinger exposed volcanic products consist of lava fl ows, et al., 1979; Chernet et al., 1998; Abebe et al., and Casey, 2001), where uppermost brittle crust pyroclastic deposits, and ignimbrites associated 2005). Exposed volcanic products consist of is only 10–11 km thick lying above a lower crust with central volcanoes, spatter and scoria cones, basalts, rhyolites, ignimbrites, and pyroclas- that has been strongly modifi ed by magmatic maars, and lava domes. The mapped vents cor- tic deposits. Monogenetic activity, consisting intrusions. Crustal stretching along MER varies respond to different types of monogentic vol- of spatter cones, scoria cones, maars, and lava from β = 1.1 in its south and central segments to canoes such as cinder or lava cone, domes, and domes (e.g., Mazzarini et al., 1999; Abebe et al., β = 1.7 in its northern segment (Ebinger et al., maar. The ages of mapped vents range from 2005; Rooney et al., 2007; Corti, 2009), is wide- 1993; Ebinger and Furman, 2002; Wolfenden et ca. 3 Ma to Holocene (Table 1). More evolved spread on the rift fl oor as well as along the rift al., 2004; Tiberi et al., 2005). lavas (mainly rhyolites) are generally associated margins (e.g., Rooney et al., 2007). These vents with domes, tuff rings, and central volcanoes, are formed by evolved lavas (mainly rhyolites) Virunga Belt whereas cones and maars are generally basal- in the case of domes, and by basalts in the case tic (Mazzarini et al., 1999; Corti et al., 2003; of cones. Vent ages range from ca. 5 Ma (mainly The Virunga Belt (VB) is a volcanic prov- Lahitte et al., 2003a, 2003b; Mazzarini, 2004; domes) to Holocene, with prevalent basaltic ince that lies near the northern end of the west- Mazzarini et al., 2004; Abebe et al., 2005; Maz- activity since late Pliocene–early Pleistocene ern branch of the East African Rift System: the zarini, 2007). (Morton et al., 1979; Chernet et al., 1998; Maz- Western rift (Fig. 2). In contrast to the wide- Vent locations have been acquired by care- zarini et al., 1999; Abebe et al., 2005). spread volcanism observed in the Eastern Rift, ful inspection of Landsat ETM+ images (e.g.,

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1 1

2

2 km 8 km

D

C

6 km

E F

n = 680 n = 4140

Figure 3. (A) Cones (1) and fault escarpment (2) are well visible in volcanic fi elds south of Gedemsa caldera in the Main Ethiopian Rift. (B) Fault escarpments (1) in the northern Afar Depression. (C) Example of rectangular drainage pattern in the rift fl oor in the Main Ethiopian Rift. (D) DEM of the northern Main Ethiopian Rift (SRTM data; http://srtm.csi .cgiar.org) with the locations of fi eld survey (yellow dots). (E) Rose diagrams of the measured fractures (joints and faults) in the Main Ethiopian Rift (see Fig. 3D), arrows indicate the main trends. (F) Rose diagrams of detected lineaments in the MER, arrows indicate the main trends.

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Goward et al., 2001; http://landsathandbook ture patterns (e.g., Wise et al., 1985; Abebe et ments, and linear scarp faces have been mapped, .gsfc.nasa. gov/handbook.html). Mosaics of al., 1998; Zakir et al., 1999). We assume that lin- identifi cation of fracture traces in images is also ETM images were thus used to map a large por- eaments are the intersection of the fracture net- based on color and tonal differences between tion of EARS (courtesy of the Maryland Univer- work with the Earth’s surface; we thus consider different surface units (Figs. 3A–3C). sity Global Land Cover Facility). The images lineaments as traces of fractures and will here- Clearly, in active volcanic fi elds magmatic are geo-referenced to the UTM projection (zone after refer to lineaments as fractures. Accord- products tend to cover previous volcanic con- 37 N –WGS84 for AD and MER data sets, and ing to Pollard and Aydin (1988), we defi ne as structs and topography (i.e., fault escarpment) zone 35 S –WGS84 for VB data set) and dis- fracture any brittle rupture of rocks defi ned by and competition between magmatic and tectonic played as RGB false color composites (with two nearly planar parallel surfaces that meet at activity control the overall morphology of rift ETM+ band 7 in the red channel, ETM+ band 4 in the fracture front and with the relative displace- zones. The relationship between dikes, topog- the green channel, and ETM+ band 2 in the blue ment small compared to the fracture length. In raphy, and deformation in rifts zones has been channel). The original spatial resolution of Land- this scheme, joint and fault differs for the differ- a matter of debate. Dike intrusion focused sub- sat ETM+ images (pixel size) is 30 m. The 15 m ent type of the relative displacement of the two sidence and faulting (Rubin and Pollard, 1988), spatial resolution of the Landsat ETM+ mosaic blocks (Mode I, II, or III). accommodated crust stretching, and prevented was obtained through a color transform using the Fracture trace maps of the studied sectors of slip on faults (Parsons and Thompson, 1991), 15 m geometric resolution of the Landsat ETM+ the EARS have been derived by the analysis of and the blade-like dike focuses deformation at panchromatic band (Janza et al., 1975; Vrabel, shaded relief images derived from the digital the rift axis, leading to the formation of an axial 1996). Vent locations for the Afar Depression elevation model and satellite images. For each rift valley (Behn et al., 2006). Examples of fault- have been acquired by Mazzarini (2007). The studied area, images with different sun azimuth ing and vents in Afar and MER are reported in vent locations for the Main Ethiopian Rift and are derived from the SRTM digital elevation Figure 3; it is apparent that cones as well as fault in the Virunga Belt have been newly acquired model with a cell size of 90 m (Farr and Kobrick, traces are well expressed. through methods described in Mazzarini (2007) 2000; http://www2.jpl.nasa.gov/srtm/); in order We compared the azimuth distribution of using Landsat ETM+ images in order to obtain to emphasize features a vertical exaggeration detected lineaments with fi eld data collected accuracy in vent locations comparable to that for (3×) was used. The images have been rotated in the MER (Fig. 3D). Azimuth distribution of the Afar data set. The new data set for vents in at random angles (in Microstation Bentley soft- fi eld data (joints and faults) has a main peak at the Main Ethiopian Rift contains basaltic vents ware environment), making fractures identifi ca- N-S, N10°E and a secondary peak at N45°E- that are located inside the rift valley in order to tion independent from image orientation and a N50°E (Fig. 3E). Lineaments show a main smooth out any infl uence of crustal structure 1:250,000 scale has been utilized. peak at N20°E-N30°E and a secondary peak beneath the rift margins, thus differing from the Satellite images are analyzed using Google at N45°E-N50°E (Fig. 3F). There are ~10° data set used by Mazzarini (2004). Earth software (http://earth.google.com/) between the main peaks of fi eld and lineament Detection of vents by satellite image anal- where panchromatic SPOT images (http:// data sets, while secondary peaks are similar. ysis provides thus a sample of the true vent www.spotimage.com) with pixel resolution This difference could be easily explained tack- population in the volcanic fi eld. This sample ranging from 2.5 to 20 m are available. Surfi ng ing into account the different scale of observa- clearly does not contain vents with a diameter in Google Earth allows a complete rotation of tion, in fact: (i) the average length of detected smaller than a few pixels (i.e., less than 60 m), images and the continuous variation of points lineaments is ~6 km (Table 2); and (ii) the most and vents that have been covered by younger of view thus providing a very useful tool for recent deformation (N-S fractures) is the most volcanic products and continental deposits. To lineament mapping. expressed at the outcrop scale. obtain a meaningful sample of the true vent Geomorphologic features such as aligned Satellite and DEM derived images clearly population a few hundreds of vents should be ridges and valleys, straight drainage channel seg- show volcanic features as well as fractures detected (see below). In order to check how good the sampling was, a random sample of 20% of the vents has been TABLE 2. LENGTH AND SPACING STATISTICS FOR FRACTURES AND removed from the MER data set. The fractal VENTS IN THE STUDIED AREAS ALONG EARS dimension of this new data set remains practi- AD MER VB cally constant (less than 0.01% of variation) Number 5580 4140 4098 max (km) 28.3 38.3 29.0 and the error on the estimation of the upper Fracture spacing min (km) 0.05 0.05 0.2 and lower bounds of the distribution is 1%–2%. mean (km) 2.3 2.6 1.5 As discussed later, the sampling of hundreds σ (km) 2.0 2.4 1.3 of vents for the self-similar clustering gives a Number 5580 4140 4098 robust estimation of fractal exponent and cutoffs max (km) 37.2 41.8 22.6 of the vent distribution. Fracture length min (km) 0.1 0.2 0.4 Structural analysis of DEM and satellite mean (km) 4.4 5.7 4.3 images is based on the detection of rectilinear σ (km) 3.1 4.0 2.2 features (lineaments) of regional to continental Number 1725 391 287 scale. Lineaments consist of sharp tonal differ- max (km) 18.4 21.2 9.6 min (km) 0.09 0.2 0.1 ences and alignments of morphological features Vent spacing mean (km) 1.2 1.3 0.9 (e.g., volcanic cones, triangular facets, portions σ (km) 1.3 1.9 1.0 of streams, aligned ridges, and crests). Within CV 1.1 1.5 1.2 tectonically active areas, lineaments usually Note: AD—Afar Depression; MER—Main Ethiopian Rift; VB—Virunga match the fracture network and the main frac- Belt.

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and faults (Fig. 3), and vent positions were of the lower and upper cutoffs (Lco and Uco, of the vent distribution is lower than the upper identifi ed in a GIS environment (ArcView respectively) are done according to Mazzarini cutoff of the fracture distribution. 3.3). The location of vents was identifi ed on (2004) by selecting the wider length range for In the VB fracture spacing is in the ~0.2 to the satellite images with an accuracy of one which the correlation between log(l) and local ~29 km range with an average of 1.5 km; frac- pixel (i.e., 15 m). slope is greatest. ture length ranges between ~0.4 and ~23 km and A substantial database is considered to averages 4.3 km (Table 2). Vents are clustered Methods exceed the threshold of sampling lines (or vents) (CV = 1.2, Figure 6, Table 2) and show spacing that is required in order to obtain stable statis- values varying between ~0.1 and ~10 km with The detected vents were analyzed in terms of tical results; in fact truncation and censoring an average of 0.9 km. Also for VB, self-similar their spacing and self-similar clustering. Vent affect the computation of the fractal distribution clustering of fractures and vents is well defi ned; spacing (or separation) is analyzed by com- (e.g., Bonnet et al., 2001). Indeed, this thresh- fracture has D = 1.85, Lco = 1.4 km, and puting the average minimum distance between old has varied considerably among different Uco = 22.1 km. Vents in VB have distribution vents. The coeffi cient of variation (CV) (Gil- authors (see André-Mayer and Sausse, 2007). with fractal exponent D = 1.50, Lco = 1.0 km, lespie et al., 1999, and references therein) for About 200 values were recommended by Priest and Uco = 21.6 km. In VB the upper cutoffs of the distribution of vent spacing describes the and Hudson (1976) and Bonnet et al. (2001). In fracture and vent distributions are similar and degree of vent clustering. CV > 1 indicates clus- this study, the used data sets ranging from ~350 the fractal exponent of the fracture distribu- tering of vents, CV = 1 indicates a random or to more than 5500 values are considered to be tion is higher than that of the vent distribution Poisson distribution of vents, and CV < 1 indi- robust enough for statistical analyses. (Table 3). cates anticlustering (a regular distribution) of Summarizing, in the analyzed sectors of the vents. CV is defi ned as RESULTS East African Rift System both fracture net- works and vents show well-defi ned self-similar S CV = , (3) The spacing of analyzed fracture networks clustering with the fractal exponent of fracture m and vents is listed in Table 2. In all the studied distribution higher than that of vent distribution sites the average length and spacing of fractures (Table 3). The higher clustering of vents than the where s is the standard deviation and m is are in the ~4 to ~6 km and ~1 to ~3 km ranges, clustering of fractures is well defi ned consider- the mean. respectively. Vent spacing for the analyzed data ing some parameters, namely: the ratio (Sr) of

The spatial distribution (self-similar cluster- sets is very similar (~1 km) and it varies in the spacing of fractures (Sf) to the spacing of vents

ing) of fractures and vents was analyzed by cal- ~0.9 to ~1.3 km range; all the analyzed data sets (Sv), the ratio (Dr) of fractal exponent (Df) of

culating the correlation exponent D applying the show values of the coeffi cient of variation >1 fracture distribution to the fractal exponent (Dv) two-point correlation function method (Bonnet (Table 2). of vent distribution and the value of the fractal

et al., 2001; Mazzarini 2004, 2007). For a popu- The spacing of fractures in AD varies in exponent (Dv) of the vent distribution. lation of N points (fracture barycenters or vent the <0.1 to ~28 km range with an average of The values of the Dr ratio are >1 for all the centers), the correlation integral C(l) is defi ned 2.3 km; the fracture lengths have an average of analyzed data sets (Table 4), consistently with as the correlation sum that accounts for all the 4.4 km in the 0.1 to ~37 km range (Table 2). the higher degree of vents’ clustering than frac- points at a distance of less than a given length l Vents are clustered (CV = 1.1, Figure 4, Table 2) tures’ clustering. The Sr ratio shows values (Bonnet et al., 2001, and references therein). In and show spacing values varying between 0.1 between 2 and 1.7 (Table 4) pointing to a higher this approach, the term C(l) is computed as and ~18 km with an average of 1.2 km (see closeness for vents than for fractures. Finally, also Mazzarini, 2007). Both fractures and vents we observe that, for the analyzed data sets, 2× N(l) C(l) = , (4) show self-similar clustering defi ned over an the higher the Sr ratio the lower the D value N × (N −1) v order of magnitude (Table 3). Fractures have (Table 4). D = 1.54, Lco = 2.5 km, and Uco = 23.6 km; where N(l) is the number of pairs of points vents have D = 1.42, Lco = 1.2 km, and Uco = DISCUSSION whose distance is less than l. If scaling holds, 23.4 km. The upper cutoffs of distributions of Equation (2) is valid, and the slope of the curve both fractures and vents are very similar and the Before we go further into the results, a in a log(C(l)) versus log(l) diagram yields the fractal exponent for the fractures is higher than few points have to be discussed. (1) Is a bi- D value. that for vents. dimensional fractal analysis valid to charac- Following Equation (2), the computed D In the MER site, spacing of fractures ranges terize a network that actually operates in three value is valid for a defi ned range of distances between <0.1 and ~38 km with an average of dimensions? (2) Is the isotropy of the crust a (l). The distance interval over which Equation 2.9 km; fracture length is in the ~0.2 to ~42 km prerequisite for the model to work? (3) How (2) is valid is defi ned by the size range. For range with an average of 5.7 km (Table 2). Vents does evolution of volcanic fi eld account for each analysis, the size range of samples is in are clustered (CV = 1.5, Figure 5, Table 2) and crust thickness changes? turn defi ned by a plateau in Δlog(C(l))/Δlog(l) show spacing values varying between ~0.2 and Most of the observations of fracture distri- (i.e., the local slope) versus log(l) diagram: the ~21 km with an average of 1.3 km. Self-similar bution (length, density, self-similar clustering) wider the range the better the computation of clustering of fractures is defi ned between Lco = derive from the analysis of fracture trace maps, the power-law distribution (Walsh and Watter- 2.1 km and Uco = 41.7 km with a fractal expo- that is from analysis of 2D data. If size distribu- son, 1993). The derivation of the cutoffs is a cru- nent D = 1.61. Self-similar clustering of vents tion of the fractures follows a power law, trace cial point and is generally not trivial, especially has exponent D = 1.17, Lco = 2.8 km, and Uco lengths in an intersecting plane are also power

when the local slope does not show a regular = 10.1 km; also in this case the fractal exponent law with an exponent, a2D, equal to a3D − 1 (e.g., and wide plateau. The choice of the zones where of the fracture distribution is higher than that of Marrett, 1996; Piggott, 1997; Berkowitz and the plateau is well defi ned and the determination the vent (Table 3). In this case the upper cutoff Adler, 1998; Bonnet et al., 2001). Similarly, the

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Figure 4. Fracture and vent distribu- tions in the Afar Depression. Black A solid lines are the outline of the stud- ied area. (A) Red lines— fracture traces; blue dots—vent locations. size range DEM derived from SRTM data (http://srtm.csi.cgiar.org). (B) Plot 0 4.0

km of log(l) versus log(C(l)) for the frac- -1 D=1.54±0.01 3.5 tures, the dashed line is used for the

.5±0.4 computation of the fractal exponent D 3.0 -2 for data between the lower (Lco) and

local slope Lco=2 2.5 Upper (Uco) cutoffs. (C) Plot of log(l) -3 versus log(C(l)) for the vents, the 2.0 dashed line is used for the computa- -4 tion of the fractal exponent D for data

log(C(l))

km 1.5 between the lower (Lco) and Upper -5 1.0 (Uco) cutoffs.

3.6±2.5 fractures -6 n: 5580 0.5

B Uco=2 -7 0.0 22.533.544.555.5log(l)

0 5.0 size range D=1.42±0.02 4.5

km -1 4.0

.2±0.5 3.5

-2 local slope

±2.0 km 3.0 Lco=1 2.5 -3 vents o=23.4 n: 1725 2.0

log(C(l))

Uc 1.5 -4 1.0 -5 0.5 C 0.0 -6 -0.5 22.533.544.555.5 log(l)

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TABLE 3. SELF-SIMILAR CLUSTERING STATISTICS FOR FRACTURES AND VENTS IN THE STUDIED AREAS ALONG EARS Fractures Vents Lco ± σ Uco ± σ Lco ± σ Uco ± σ CD ± σ R 2 CD ± σ R 2 (km) (km) (km) (km) AD 5.3 x 10-9 1.54 ~± 0.01 0.99 2.5 ± 0.4 23.6 ± 2.5 7 x 10-7 1.42 ± 0.02 0.99 1.2 ± 0.5 23.4 ± 2.0 ~ MER 3 x 10-9 1.61 ± 0.01 0.99 2.1 ± 0.5 41.7 ± 3.7 3 x 10-6 1.17 ± 0.02 0.99 2.8 ± 0.3 10.1 ± 1.4 VB 9 x 10-10 1.85 ~~±0 .01 0.99 1.4 ± 0.3 22.1 ± 2.7 3 x 10-7 1.50 ± 0.01 0.99 1.0 ± 0.1 21.6 ± 3.1 Note: AD—Afar depression; MER—Main Ethiopian Rift; VB—Virunga Belt.

intersection of a 3D fractal by a plane results in structures) favor the extrapolation of 2D analy- question now rises, how does the vents self-

a fractal with D2D equal to D3D − 1, according to sis to a 3D system. This is markedly different similar clustering account for the continuous fractal theory (Mandelbrot, 1982). Moreover, it than the model of Takada (1994a, 1994b), where crustal stretching in a deforming crustal setting has been observed that joints in thinly layered intruding magma creates the fractures (hydro- such as an active continental rift? sedimentary rock typically span the mechanical fracturing) in an isotropic crust. In order to answer this question as a fi rst- thickness of the layer and the general linear rela- Volcanic fi elds evolve in time in terms of vent order approximation, a pure shear deformation tionship between spacing S and layer thickness distribution, density, and age as, for example, in for the crustal thinning along the EARS is here H has been observed (e.g., Gross, 1993; Narr the Springerville (Arizona; Condit and Connor, assumed and an average Poisson’s ratio ν~0.3 and Suppe, 1991; Renshaw, 1997). The general 1996) and Michoacan-Guanajuato (Mexico; for the crust in east Africa (Zandt and Ammon, relationship S = f(H) results thus in fracture sys- Hasenaka and Carmichael, 1985; Connor, 1987; 1995) is used; the extensional rate times the tems that can be idealized as two-dimensional Connor, 1990) volcanic fi elds. duration of volcanism in the studied sectors of with the fracture length defi ned along the layer When is a fully infi nite cluster formed in a the EARS (i.e., 2 Myr) is considered the hori- ε (i.e., bedding plane, mechanical layer). fracture network? Infi nite cluster forms as the zontal strain ( x). During the last 2 Myr exten- Self-similar clustering of fractures is per- fracture network density is greater than the per- sional rate is ~20 mm/yr for the Afar Depres- formed by applying Equation (4) to points colation threshold (see above). At the early stage sion (AD; Eagles et al., 2002), and ~6 mm/yr selected along the fracture traces, namely the there are only a few vents that clearly are con- and ~2 mm/yr for the Main Ethiopian Rift fracture barycenters. As stated in Bour et al. nected to the magma reservoir at depth. System (MER) and the Virunga Belt (VB), respectively (2002) the result of this analysis is valid what- boundaries could be connected by an infi nite (Stamps et al., 2008). The horizontal strain ε ε ever the point used to defi ne fracture location cluster or by a unique bond that spans all of the ( x) is related to the vertical strain ( y) by the ε νε ν (barycenter, fracture tips, or any point taken at system. The few vents formed in Afar during simple relationship x =− y, where is the random in the fracture). This is because the deri- the volcano-tectonic crisis in September 2005 crustal Poisson’s ratio. Accordingly, since late vation of two-point correlation dimension is sta- (Wright et al., 2006) are an example of a dike Pliocene–early Pleistocene (ca. 2 Ma ago) tistically dominated by the numerous small frac- ~10 km in height that spanned the whole crust crust stretching reduced the crust thickness by tures, for which the error in the determination of between the magma reservoir and the surface. In ~10 km in AD, ~4 km in MER, and ~1 km in the precise spatial location is relatively insignifi - the proposed model the fully self-similarity and VB. With the exception of Afar Depression, cant. For the same reason the censoring effects the strict relationships between the Uco and the these values are of the same order of the errors (fractures that intersect the system boundaries; distance between the source and the surface are in the computation of the Ucos (Table 3). An Pickering et al., 1995) did not affect the deri- achieved after some time, the time the network error of 15% for both upper cutoff and crust’s ρ vation of the fractal dimension. Therefore vents necessitates to reach the threshold density ( c). thickness is thus assumed, accounting for the could be assumed as points along the fracture We tentatively assume that the density at the per- measurements’ precision (Tables 1 and 3) and traces and they are samples of the intersection colation threshold is achieved after the crust in of the role of the crustal stretching that acted in of the backbone with the surface. Providing a the volcanic fi eld reached its fracture saturation. the EARS since 2 Myr. large number of points (>200, see Bonnet et al., Indeed, after a certain amount of strain in layered As expected for a percolating cluster (i.e., the 2001), the sampling of the backbone is thus sta- sequences the ratio between fracture spacing and backbone) the clustering of the vents is higher tistically robust. layer thickness becomes constant and does not than the clustering of the fracture network

Self-similar clustering does not require isot- change as strain increases (e.g., Wu and Pollard, (Df > Dv; Tables 3 and 4). In the Afar Depression ropy of the crust, magma exploits already formed 1995). In order to model works properly, a com- both fractures and vents have Uco values that fi t fractures and creates by itself new ones to reach mon depth for the magma reservoir is assumed in very well with the crust thickness (Table 3) the surface. In the Lizard Ophiolite Complex, for the analyzed vents. Clearly, the style of vol- as also reported for the vent distribution in the Cornwall (Jolly and Sanderson, 1997) and in canism may change through time, generating northern portion of the depression (n-AD; see the Mull swarm in Scotland (Jolly and Sander- more evolved magma and fi ssural magmatism Mazzarini, 2007). son, 1995) dikes exploited favorably oriented and determining the formation of central volca- In the Virunga Belt area (Table 3) the Uco preexisting fractures and created new ones. The noes (e.g., Lahitte et al., 2003b; Mazzarini et al., value is less than 30 km as suggested by geo- actual fracture network will thus consist of all 2004). In this case the distribution of volcanic physical and geologic observations (Ebinger, the structures that allow a hydraulic connec- vents may be controlled by strain rate and brittle/ 1989a, 1989b; Corti et al., 2002; Albaric et al., tion to operate in order to transfer magma from ductile layering of the crust. 2009). Anyway, also for the Virunga Belt area depth to surface (an overall vertical movement). The analyzed vents along the EARS show both fractures and vents have very similar Uco Therefore, as a preliminary consideration, the ages varying between 0 and 2 Ma (see above values (Table 3). anisotropies due to crust mechanical layering and Table 1), whereas available geophysical The analyzed vents in the Main Ethiopian and occurrence of weakness planes (inherited data image the current crustal structures. A Rift have a self-similar clustering bounded by a

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Figure 5. Fracture and vent distri- butions in the Main Ethiopian Rift. A Black solid lines are the outline of the studied area. (A) Red lines— fracture traces; blue dots—vent loca- size range tions. DEM derived from SRTM data 0 4.5 (http://srtm.csi.cgiar.org). (B) Plot 4 of log(l) versus log(C(l)) for the frac- -1 tures, the dashed line is used for the 3.5 computation of the fractal exponent D -2 D=1.61±0.01 3 for data between the lower (Lco) and

local slope Upper (Uco) cutoffs. (C) Plot of log(l) 2.5 -3 versus log(C(l)) for the vents, the 2 dashed line is used for the computa- -4 1.5 tion of the fractal exponent D for data

log(C(l))

km between the lower (Lco) and Upper -5 1 (Uco) cutoffs.

1.7±3.7 fractures 0.5 -6 n: 4140 0

Lco=2.1±0.5 km B Uco=4 -7 -0.5 22.533.544.555.5log(l)

size range

km

m

1 6

0.1±1.4

.8±0.3 k 0 5

Uco=1

Lco=2

-1 4 local slope vents -2 D=1.17±0.02 n: 391 3

log(C(l)) -3 2 -4 C 1 -5 0 22.533.544.555.5 log(l)

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NANA NINI

Figure 6. Fracture and vent distri- butions in the Virunga Belt, Ni— Nyiragongo volcano; Na—Nyamura- gira volcano. Black solid lines are the A outline of the studied area. (A) Red lines—fracture traces; blue dots— vent locations. DEM derived from 0 size range 3.0 SRTM data (http://srtm.csi.cgiar. org). (B) Plot of log(l) versus log(C(l)) -1 2.5 for the fractures, the dashed line is used for the computation of the frac- -2 tal exponent D for data between the 2.0 local slope lower (Lco) and Upper (Uco) cutoffs. -3 (C) Plot of log(l) versus log(C(l)) for 1.5 D=1.85±0.01 the vents, the dashed line is used for log(C(l)) -4

.7 km the computation of the fractal expo- fractures 1.0 nent D for data between the lower -5 ±0.3 km n: 4098 (Lco) and Upper (Uco) cutoffs.

=22.1±2 -6 0.5

Lco=1.4 B Uco -7 0.0 22.533.544.555.5 log(l)

6 2.5 size range 5 D=1.50±0.01 2.0

local slope 4 1.5 3

log(C(l)) vents 1.0 2 km n: 287

0.5

1 21.6±3.1

Lco=1.0±0.1 km

C Uco= 0 0.0 22.533.544.555.5log(l)

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TABLE 4. RATIOS OF FRACTAL EXPONENTS Volcanism clearly clusters along magmatic data from the Pali Aike volcanic fi eld in south- (DR = D /D ) AND SPACING (SR = S /S ) FOR F V F V segments in the rift refl ecting the localized ernmost Patagonia (Mazzarini and D’Orazio, FRACTURES AND VENTS, AND FRACTAL strong modifi cation of the crustal structure by 2003), the Payen volcanic fi eld in the Andean EXPONENT OF VENTS (DV) FOR THE STUDIED AREAS ALONG EARS magma intrusion. To defi ne whether magmatic foreland (Mazzarini et al., 2008), and in the Parameters AD MER VB segmentation is controlled by magmatism or northern sector of the Afar Depression (Mazza- rift obliquity and crustal inherited structures is rini, 2007). Despite the differences in the geody- Df /Dv (Dr) 1.1 1.4 1.2

Sf /Sv (Sr) 1.9 2.0 1.7 beyond the aim of this contribution. Anyway, namic settings of the analyzed volcanic fi elds, a 2 Dv 1.42 1.17 1.50 in the Main Ethiopian Rift, since Pleistocene, linear correlation (Uco = 1.0481CT − 1.8367, R Note: AD—Afar Depression; MER—Main deformation and volcanism focused in the rift = 0.9856 where CT is the crust thickness in kilo- Ethiopian Rift; VB—Virunga Belt. fl oor (see Ebinger and Casey 2001; Corti, 2009 meters) is clearly defi ned, indicating a strong and references therein) and vent self-similar correlation between the upper cutoff of the frac- clustering appears to record such as tectono- tal distribution of vents and the crust thickness Uco value (~10 km, Table 3) that is lower than magmatic setting (Table 3). in the volcanic fi elds. the upper cutoff (~27 km) derived in the same In the Main Ethiopian Rift the fracture net- area by Mazzarini (2004). This difference is due work shows Uco (41.7 km) well matching the CONCLUSION to the difference between the two analyzed data derived regional crust thickness of ~40 km (e.g., sets. Vents in Mazzarini (2004) included also Keranen et al., 2004; Maguire et al., 2006), Fracture networks and monogenetic vents cones in the western border area outside the rift while Uco for vents is 10.1 km. The apparent have been analyzed in volcanic fi elds in three valley and with ages older than 2 Ma (Mazzarini discrepancy between fractures and vents Ucos sectors along the East African Rift System: the et al., 1999), whereas the data set used in this in MER could be explained by differences in Afar Depression, the Main Ethiopian Rift, and analysis is composed only by very young vents the extent of the two data sets: (1) fractures span the Virunga Belt, respectively (Fig. 2). Despite in the rift valley. the whole rift architecture from the border to the differences between the three investigated sec- The EAGLE data show that the crust in MER fl oor and encompasses a long history in the rift tors in crust’s stretching, crust’s thickness, and is in the range 30–40 km (e.g., Keranen et al., evolution, that is from ca. 10 Ma to the pres- in the intensity of the volcanism, both fractures 2004; Maguire et al., 2006; Keranen et al., 2009; ent (Corti, 2009, and references therein) thus and vents show a clear self-similar clustering. Corti, 2009), well above the 10–11 km derived accounting for an initial stage of broad mechani- In particular, vents in all three analyzed sectors by the self-similar clustering of vents collected cal crustal extension; and (2) vents are localized in the EASR as well as in other volcanic fi elds in the rift-fl oor. Moreover, EAGLE data also in the rift fl oor and account for the Pleistocene in Afar and southern South America (Maz- show that crust beneath magmatic segments to Holocene evolution of the rift with focused zarini and D’Orazio, 2003; Mazzarini, 2007; in the MER (see Ebinger and Casey 2001) is magma intrusion in lower crust. The occur- strongly modifi ed by huge magma injection rence of weak and partially molten lower crust generating strong rheological layering (Corti, beneath the MER (Keranen et al., 2009) could 60 2009 and references therein). We infer that thus result from recent rift evolution and is well when the crust is strongly modifi ed by localized recorded by volcanism distribution. 50 magmatic processes, as in the case of northern The classical segmentation of the MER in 40 MER, vent self-similar clustering record local northern, central, and southern segments, based crust layering induced by magma emplacement on different geophysical, geological, and defor- 30 within the crust (i.e., ~10 km is the thickness of mation characters (Bonini et al., 2005; Keranen

the upper competent layer). and Kemplerer, 2008; Corti, 2009), is not here Uco (km) 20 Geophysical and geochemical data (Keir et considered being the vents mainly located in al., 2006; 2009; Rooney et al., 2007; Bastow the central and northern MER segments. Future 10 y = 1.0481x - 1.8347 et al., 2005) suggest that MER represents the analysis will focus on the characterization of the R2 = 0.9856 transition from a broad mechanical crustal MER segmentation. 0 01020 30 40 50 60 extension (faulting and stretching) toward In the Afar Depression although the average CT (km) narrow zones of magma intrusion prior to the crust thickness is ~23 km, as calculated from onset of sea-fl oor spreading (e.g., Ebinger and vent self-similar clustering, local variations Figure 7. Plot of crust thickness derived by Casey, 2001; Buck, 2006). On the other hand, exist (see Mazzarini, 2007). Differently, in the geophysical data (CT) and the computed velocity structure of the uppermost mantle MER vent self-similar clustering records very upper cutoff (Uco) for the self-similar clus- beneath MER shows no correlation with crustal localized crust structure, and only vents outside tering of the analyzed volcanic fi elds and magmatic segmentation (Bastow et al., 2005; the rift fl oor record the average crust thickness from volcanic fi elds from literature. P— 2008), suggesting that the different distribution (e.g., Mazzarini, 2004). In fact, the rifting pro- Payen volcanic fi eld (Mazzarini et al., 2008); of crustal deformation and magmatism are not cess in Afar is more evolved than MER and the PA—Pali Aike volcanic fi eld (Mazzarini related to mantle features. Corti (2008), on the magmatic modifi cation of the lithosphere is and D’Orazio, 2003); AD—Afar Depres- base of analogue modeling, concluded that rift widespread whereas magmatic modifi cation of sion; VB—Virunga Belt; n-AD—northern evolution and segmentation are controlled by the crust is only localized in narrow zones in the sector of the Afar Depression (Mazzarini, rift obliquity independently by magmatic pro- MER (e.g., Ebinger and Casey, 2001). 2007); MER—Main Ethiopian Rift. The cesses. Moroever, Agostini et al. (2009) sug- The crust thickness derived from geophysi- errors bars are 15% for both Uco and CT gested that oblique reactivation of pre-existing cal data is plot against the Uco values (Fig. 7) (see text). Solid black line—best fi t line crustal weakness plays a major role in the rift defi ned for the self-similar clustering of the (Uco = 1.0481CT−1.8367; R2 = 0.9856); evolution and architecture. vents in the sectors of the EARS together with dashed black line—line Uco = CT.

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Bonnet, E., Bour, O., Odling, N.E., Davy, P., Main, I., TABLE 5. FRACTAL EXPONENTS FOR FRACTURES (D ) AND VENTS (D ) FOR F V Cowie, P., and Berkowitz, B., 2001, Scaling of fracture OTHER VOLCANIC FIELDS FROM LITERATURE systems in geological media: Reviews of Geophysics, v. 39, p. 347–383, doi: 10.1029/ 1999RG000074. Volcanic fi elds Df Dv References Bour, O., and Davy, P., 1997, Connectivity of random fault Pali Aike (PA) 1.74 1.45 Mazzarini and D’Orazio (2003) networks following a power law fault length distribu- Payen (P) 1.62 1.33 Mazzarini et al. (2008) tion: Water Resources Research, v. 33, p. 1567–1583, north Afar (n-AD) 1.83 1.34 Mazzarini (2007, this work) doi: 10.1029/96WR00433. Bour, O., and Davy, P., 1999, Clustering and size distribu- tion of fault patterns: Theory and measurements: Geo- physical Research Letters, v. 26, p. 2001–2004, doi: mechanical layer thickness on scaling laws: Journal of 10.1029/1999GL900419. 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