Abstract

The spatial clustering of vents in basaltic volcanic fields within a stretched continental crust is here used as a proxy for crustal thickness. Basaltic monogenetic vents show self-similar clustering with a power-law distribution defined by the correlation exponent (D) computed in a range with lower and upper cutoffs. The upper cutoff for the fractal clustering of vents yields the thickness of the crust. The spatial distribution of vents is analyzed in the Afar Depression (the northern termination of the East African Rift system in Africa), where the continental crust has thinned considerably. More than 1700 vents were identified and mapped in the Afar region through the use of Landsat ETM+ (enhanced thematic mapper) satellite image mosaics. Vents cluster in seven main groups corresponding to the principal structural features of the Afar Depression. The mapped vents are generally younger than 2 Ma, and most are Holocene age. The Afar vents show self-similar clustering (D = 1.39 ± 0.02) in the ∼2–23 km range. The upper cutoff of ∼23 km matches well the thickness of the crust in the Afar region as derived from seismic and gravity data (∼25 km). The distribution of vents in the Afar Depression is compared with that of vents in the northern Main Ethiopian Rift.

INTRODUCTION

Volcanic eruption requires hydraulically open pathways that allow magmas to move upward from crustal or subcrustal reservoirs to the surface. The bulk permeability of the crust may be enhanced through fracturing; rock-fracturing processes allow the ascent of magma at rates that are akin to the time scale characterizing volcanic activity (Rubin, 1993; Petford et al., 2000; Canon-Tapia and Walker, 2004). It has been proposed that fractures filled by magma (i.e., dikes) tend to coalesce during their ascent to the surface, thereby controlling the final level of magma emplacement and the distribution of volcanic vents at the surface (Takada, 1994a, 1994b; Ito and Martel, 2002). Evidence for hydrofracturing has also been observed in mantle rocks from mid-ocean ridges (Cannat, 1996) and in ophiolites (Nicolas et al., 1994).

The link between volcanism and tectonics has long been recognized (e.g., Nakamura, 1977; Takada, 1994a; van Vyk de Vries and Merle, 1996), and essentially depends on two main parameters: (1) brittle deformation of the crust (fracture network formation), and (2) magma availability (magma supply rate and eruptive style). The link between fractures and volcanic vents has been established, especially for monogenetic volcanoes (Tibaldi, 1995). Monogenetic volcanoes are volcanic vents formed during single episodes of volcanic activity, and occur in volcanic fields composed of tens to hundreds of monogenetic vents (Connor and Conway, 2000). Volcanic fields are common in continental rifts and in backarc extensional areas; they often comprise both monogenetic and polygenetic volcanoes that are essentially basaltic in composition (Connor and Conway, 2000; Mazzarini and D'Orazio, 2003; Mazzarini, 2004; Mazzarini et al., 2004). The basaltic composition of cones in volcanic fields testifies to the presence of deep crustal or subcrustal magma reservoirs requiring a connected fracture network throughout the crust to feed cones.

The correlation between vent distribution and fracture network properties is such that the spatial distribution of vents may be studied in terms of self-similar (fractal) clustering (Pelletier, 1999; Mazzarini, 2004), as in the case of fracture networks (Bour and Davy, 1999; Bonnet et al., 2001). Findings based on this approach suggest that, for basaltic volcanic fields in a stretched continental crust, the distribution of monogenetic vents is linked to the mechanical layering of the crust (Mazzarini, 2004). Vents tend to cluster according to a power-law distribution defined over a range of lengths approximating the thickness of the fractured medium (crust). This correlation has been studied in volcanic fields within extensional continental settings in backarcs, such as in southernmost Patagonia (Mazzarini and D'Orazio, 2003), and in continental rifts, such as the Ethiopian Rift system (Mazzarini, 2004).

The hypothesized link between vent clustering and crustal thickness is investigated in the Afar Depression, the most stretched portion of the East African Rift system connecting the Red Sea and Gulf of Aden oceanic spreading axes with the Main Ethiopian Rift (e.g., Bonini et al., 2005). The East African Rift system is a classic seismically and volcanically active continental rift extending several thousands of kilometers in a N-S direction (e.g., Rosendahl, 1987; Braile et al., 1995; Chorowicz, 2005); it accommodates extension between the Nubian (Africa) and Somalian plates (e.g., Chu and Gordon, 1999). The bulging and extension of the crust and the consequent widespread volcanism have been ascribed to the impinging of one or two plumes on the base of the East Africa crust (Ebinger and Sleep, 1998; Rogers et al., 2000) or, more recently, to a broader mantle upwelling (the African superplume); the Afar hotspot is a surface manifestation of this (Benoit et al., 2006). Several volcanic fields occur in the Afar Depression, where volcanic rocks are widespread; this region is thus a natural laboratory to test the hypothesized correlation between crustal thickness and the upper limit (upper cutoff) of the power law describing the distribution of vents. This correlation has been described for the northern part of the Main Ethiopian Rift (Mazzarini, 2004) and is here investigated for the Afar Depression, where the locations of several monogenetic vents have been identified and their spatial clustering has been analyzed in terms of self-similar clustering. Results will be compared with crustal thicknesses derived from existing geophysical data on the selected study sites.

GEOLOGICAL SETTING OF THE AFAR DEPRESSION

The Afar Valley is located at the confluence of the Main Ethiopian Rift, the western Gulf of Aden, and the southern Red Sea (Fig. 1). The low-lying part of the Afar triple junction covers an area of ∼200,000 km2 called the Afar Depression. It is flanked to the west and the southeast by the Ethiopian and Somali Plateaus and to the east by the Danakil and Aysha'a blocks (Fig. 1). Elevations in the adjacent plateaus reach 3000 m, and in the Danakil Alps exceed 2100 m. These elevations are in marked contrast with those of the depression, which range from about +800 m to −100 m. This low-lying region is dotted with a number of topographically high shield volcanoes (CNR–CNRS-Afar team, 1973; Barberi and Varet, 1977; Mohr, 1983).

The geology of the Afar Depression has been investigated since the early 1970s (Gass, 1970; CNR–CNRS-Afar team, 1973; Barberi and Varet, 1977; Zanettin et al., 1978; Merla et al., 1979; Zanettin, 1993; Tefera et al., 1996; Manighetti et al., 1998; Lahitte et al., 2003a, 2003b; Kidane et al., 2003; Bosworth et al., 2005; Beyene and Abdelsalam, 2005). The depression is mainly floored by Pliocene and younger volcanic rocks. Based on the above studies, the following divisions can be made: (1) a pre-rift sequence consisting of Neoproterozoic basement rocks, Mesozoic sedimentary rocks, and pre-Miocene volcanic and igneous rocks; (2) lava flows of the Afar Stradoid series; (3) lava flows of the late Stradoid basaltic series; (4) deposits of Pliocene–Pleistocene silicic centers; (5) basalts of the rift segments; and (6) Quaternary sediments (Fig. 2).

Interaction between the southern Red Sea and Aden oceanic ridges and the Afar stretched continental crust led to the formation of rifts and associated volcanism (Manighetti et al., 1998; Lahitte et al., 2003a, 2003b, and references therein). Five main physiographic units thus define the Afar Depression: the rift plateaus (Ethiopia and Somalia Plateaus), the Danakil-Aysha'a blocks, the Danakil depression (North Afar), the Central Afar, and the South Afar (Fig. 2).

The rift plateau unit comprises the highest areas flanking the Afar Depression. It consists of pre-Miocene and Miocene basaltic and rhyolitic lava flows (Trap series); a series of fault escarpments mark the transition between this unit and the rift depression (e.g., Lahitte et al., 2003a; Beyene and Abdelsalam, 2005).

The Danakil and the Aysha'a blocks flanking the eastern border of the Afar Depression consist of basement rocks, old Miocene volcanic rocks, recent lava flows, and volcanoes (Fig. 2; e.g., Beyene and Abdelsalam, 2005).

The Danakil depression, or North Afar, is between the Danakil-Aysha'a blocks and the western rift plateau, and represents an area of highly thinned crust (e.g., Redfield et al., 2003) affected by active volcanism and crustal extension (Wright et al., 2006). This area is characterized by the occurrence of NNW-SSE–trending axial volcanoes that mark the inland propagation of the Red Sea ridge (Manighetti et al., 1998, and references therein). Basaltic volcanism is Quaternary to Holocene (Lahitte et al., 2993a, 2003b, and references therein) and has produced several scoria cones and eruptive fissures (Fig. 3). Faults and fractures strike NW-SE and NNW-SSE, following the rift trends.

In Central Afar, the Aden Ridge spurred the development of minor rift systems (Manighetti et al., 1998, and references therein). The area is characterized by the intersection of the NS faults marking the western escarpment, the NE-SW faults of the Main Ethiopian Rift, and the NW-SE and E-W faults of the propagating rifts (Manda Hararo–Goba'ad and Manda Inakir–Asal-Ghoubbet rifts). The Manda Hararo–Goba'ad system consists of NNW-SSE, NW-SE, and E-W rifts as long as 80 km and several kilometers wide. Rifts are characterized by active deformation and axial volcanic ranges. Both silicic and basaltic magmas have erupted (Lahitte et al., 2003a, 2003b, and references therein); the oldest silicic lavas are ca. 1.3 Ma, and 30 ka basalts are widespread (Lahitte et al., 2003a). Deformation in the Manda Hararo rift segments becomes younger southeastward (Manighetti et al., 1998), and basaltic volcanism (spatter cones and eruptive fissures) postdates the formation of large silicic volcanoes (Lahitte et al., 2003a, 2003b). Three main fault systems interact in the Manda Hararo–Goba'ad area: the NW-SE Red Sea, the E-W Aden Ridge, and the NE-SW South Afar systems. On the basis of structural and geomorphic considerations, Tesfaye et al. (2003) located the present position of the Afar triple junction in this area. The Manda Inakir–Asal-Ghoubbet system is composed of several rifts resulting from the encroachment on land in the Afar region by the Aden Ridge (e.g., Manighetti et al., 1998). All these structures mark the southeast to northwest propagation of seismically (e.g., Hofstetter and Beyth, 2003) and volcanically (e.g., Lahitte et al., 2003a) active rifts. The southeastern segments (Asal-Ghoubbet rifts), ∼40 km long and 10 km wide, strike NW-SE. The northwestern propagation of deformation is associated with volcanism leading to the formation of spatter cones and eruptive fissures. The northwestern Manda Inakir rift is a NW-SE structure with a NNW-trending, right-stepping array of three main segments (Manighetti et al., 1998). The Manda Inakir rift is ∼10 km long and 3 km wide. Recent volcanism in the Manda Inakir–Asal-Ghoubbet rifts has produced basaltic lavas, shield volcanoes, and numerous spatter cones; these volcanic centers have Pleistocene and Holocene ages (Manighetti et al., 1998; Lahitte et al., 2003a, 2003b), and formed above volcanic surfaces dated as 3 Ma (Lahitte et al., 2003a, 2003b).

The South Afar is dominated by N- to NE-trending horst and graben structures; it connects the NE-SW– and NNE-SSW–trending fault systems of the northern Main Ethiopian Rift with the NW-SE– and E-W–trending rifts of Central Afar (Tesfaye et al., 2003; Fig. 2).

The Afar region is characterized by strong crustal attenuation: Bouguer gravity data indicate crustal thinning (Makris and Ginzburg, 1987; Woldetinsae and Gotze, 2005) with an average thickness of ∼25 km. Inverse modeling of gravity data shows a crustal thickness of 23 km in the Afar Depression and 24 km in South Afar (Tiberi et al., 2005). Differences in the elastic thickness of the lithosphere derived by gravity data inversion (Ebinger and Hayward, 1996; Hayward and Ebinger, 1996) indicate that the Main Ethiopian Rift and Afar have undergone different degrees of stretching. Seismic refraction data imaged a crustal thickness of 28–30 km in the northern Main Ethiopian Rift, 23–25 km in the southern Afar region, and only 15 km in the Danakil depression to the north (Berckhemer et al., 1975; Prodehl and Mechie, 1991; Prodehl, et al., 1997). Analysis of receiver functions from broadband seismic data (Dugda et al., 2005) reveals that the crust is 27–30 km thick in the Main Ethiopian Rift, and 25 km thick in the Afar Depression. Both gravity and seismic data reveal a crustal thickness of 35–40 km in the shoulders of the rifts.

SPATIAL DISTRIBUTION OF VOLCANOES

The spacing of volcanoes in relationship to crustal thickness, fracture patterns, and lithospheric thickness at convergent and divergent plate boundaries has been debated since the early 1970s (e.g., Vogt, 1974); in extending oceanic and continental plates, it has been linked to the response of the lithosphere to the load of the volcanic pile (e.g., ten Brink, 1991). In particular, the spacing of central volcanoes within continental rift settings has been linked to the elastic thickness of the lithosphere (Mohr and Wood, 1976). Vent alignment has often been used (1) to infer the direction of the minimum horizontal principal stress (Lutz, 1986; Wadge and Cross, 1988), (2) as evidence for structural control on vent location (Connor, 1990; Connor et al., 1992), and (3) to outline the importance of strain rate in the style of volcanism (Takada, 1994a; Alaniz-Alvarez et al., 1998; Mazzarini et al., 2004). A strong correlation between fractures and vent alignments has been identified in active Holocene volcanic fields (e.g., Iceland, Kamchatka); these geometric relationships have been ascribed to the exploitation of favorably oriented preexisting structures by the ascending magma (Connor and Conway, 2000, and references therein). The feeder system of monogenetic apparatuses (see Connor and Conway, 2000) consists of dikes, and the flow of magma may be represented as a channeled flow through a rock volume enhanced by secondary permeability (i.e., permeability due to fractures in the rock volume). Each feeder may be used only one time, as the cooled magma seals the hydraulic pathway. This condition is met in cinder and spatter cones within volcanic fields. Several types of eruptive vents may be assumed to be monogenetic apparatuses: cones, small vents along fractures, and eruptive fractures. I (Mazzarini, 2004) developed a simple model for visualizing the relationship between vents and the geometric properties of fractures. This model assumes that the aperture of a fracture is greatest at its barycenter and that volcanic vents erupt at the point of maximum fracture aperture (Fig. 4); the resulting vent distribution is thus closely linked to the hydraulic properties of both the crust and fractures.

HYDRAULIC PROPERTIES OF FRACTURES AND VENT DISTRIBUTION

The connectivity of fractures defines the portion of the existing fracture network that hydraulically connects the system boundaries, allowing fluids to flow (Margolin et al., 1998; Darcel et al., 2003). In a rock volume the connected network is a subset of the existing fracture network (e.g., Roberts et al., 1998, 1999), defined as the backbone in percolation theory (Stauffer and Aharony, 1992).

Hydraulic features of fractures such as fracture connectivity and aperture are scale invariant (Bonnet et al., 2001). In particular, the spatial clustering of a fracture network, represented as the fracture barycenter, has been directly linked to the hydraulic properties of the fracture network (Renshaw, 1999; Bour and Davy, 1999; Darcel et al., 2003). Assuming a direct genetic and spatial link between fracture and vent (Connor and Conway, 2000; Mazzarini, 2004), scale invariance in vent distribution reflects the fractal properties of the connected part of a fracture network (i.e., the backbone).

The main geometric features of a fracture network are generally measured and mapped (fracture attitude, aperture, spacing, intersections, length, and density) at different scales of observation, from satellite images to field mapping, showing scale invariance spanning several orders of magnitude (Bonnet et al., 2001; Marrett et al., 1999). The way in which fractures fill space (i.e., the spatial distribution of fractures) depends strictly on the spacing of fractures. The latter geometric feature is correlated with the thickness of the fractured medium calculated on the basis of the stress saturation model (Wu and Pollard, 1995; Gross et al., 1995; Ackermann and Schlische, 1997).

A robust way to define how fractures fill space is to analyze their self-similar clustering (Bonnet et al., 2001). The definition of self-similar clustering for the analyzed spatial correlation of fractures (i.e., computation of the fractal exponent; see Bonnet et al., 2001, and references therein) is performed for a range of lengths (the size range) between a lower and an upper cutoff.

The upper cutoff is here considered to be directly linked to the mechanical layering of the medium. Mandelbrot (1982) suggested that there are upper and lower cutoffs for the scale-invariant characteristics of fractures (e.g., spacing, length, density), and that these are functions of mechanical layers and rock properties. Experimental studies on normal fault populations suggest the presence of upper and lower cutoffs in the power law describing the distribution of the geometric properties of fractures (Ackermann et al., 2001). Moreover, the thickness of both sedimentary beds and the crust controls the scaling law of fractures and earthquakes (Pacheco et al., 1992; Davy, 1993; Ouillon et al., 1996).

The dependence of the fracture network spatial distribution on the rheologic layering of the medium (i.e., the crust) can also be inferred from the connected part of the network. The connected fracture network allows 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 vents can thus reveal the mechanical layering of the crust.

DATA ACQUISITION

Landsat 7 ETM+ (enhanced thematic mapper) images were used to identify and map volcanic vents (Goward et al., 2001; http://land-sathandbook.gsfc.nasa.gov/handbook.html). A mosaic of 29 ETM images was used to map a large portion of East African Rift system (courtesy of the Maryland University Global Land Cover Facility; http://glfc.umiacs.umd.edu/index.shtml). The images are georeferenced to the Universal Transverse Mercator projection (zone 37 N –WGS84) and displayed as RGB (red, green, blue) false color composites (with ETM+ band 7 in the red channel, ETM+ band 4 in the green channel, and ETM+ band 2 in the blue channel). The original spatial resolution of Landsat ETM+ images is 30 × 30 m. The 15 × 15 m spatial resolution of the Landsat ETM+ mosaic was obtained through a color transform using the 15 × 15 m geometric resolution of the Landsat ETM+ panchromatic band (Janza et al., 1975; Vrabel, 1996). One Landsat 7 ETM+ scene was also processed to investigate the spectral behavior of basaltic scoria cones (path 167 row 051, acquisition date 28 November 2000, courtesy of the Maryland University Global Land Cover Facility; http://glfc.umiacs.umd.edu/index.shtml).

Images clearly show volcanic features as well as fractures and faults (Fig. 3), and vent positions were identified in a geographic information system environment (ArcView 3.3). The locations of vents were identified on the satellite images with an accuracy of one pixel (i.e., 15 × 15 m). This error in vent location is lower than that arising through the use of 1:50,000 scale topographic maps (Mazzarini, 2004). Moreover, relationships between vents and fractures are well imaged by the synoptic view of satellite images. As many as 1725 vents were identified, and their coordinates were stored in a file. The vents are located in structurally controlled areas, where they are unevenly distributed.

Afar Vents

In order to identify the occurrence of vent clusters in the Afar Depression, the spatial distribution of vents was investigated through multivariate analysis by applying a clustering approach based on an agglomerative hierarchical method (using the MINITAB statistical software package). This approach is used when clusters are initially unknown. The optimal number of clusters is derived by analyzing the dendrogram (Fig. 5) that depicts the amalgamation of observations into one cluster. The similarity at any step is defined as the percent of the minimum distance at that step relative to the maximum interobservation distance (i.e., the maximum distance between the vents in this case). The step where values change abruptly may mark the point for cutting the dendrogram. Eight clusters were identified for the analyzed vents (Fig. 5). They are characterized by the number of vents, the location of the cluster center (centroid), and by the average distance of all the vents within the cluster from the centroid of their respective cluster. Three clusters are in the Northern Afar unit, two are in the Danakil block, two are in the Central Afar unit, and one is in the South Afar unit (Fig. 6; 01Table 1).

The identified clusters were subsequently grouped into data sets according to the following criteria: (1) each data set had to include more than 100 vents to ensure statistical significance (see Mazzarini, 2004); and (2) the data set had to spatially relate to major structural features of the Afar region.

On this basis, six new data sets were generated. They are localized in the following structures of the Afar Depression: two data sets are in the Danakil block: data set DB-na (north of Assab) and data set DB-a (Assab area); one data set is in the North Afar depression: data set NA (zone with Erta Ale, Alayuto, and Tat Ale volcanoes); two sets are in the Central Afar depression: data set CA-1 (Manda Hararo and Goba'ad rifts) and data set CA (Manda Inakir, Asal, Ghoubbet rifts and the western border of the Danakil block); and the last data set is in the South Afar depression: data set SA (junction between Afar and the Main Ethiopian Rift).

A data set (Afar) of all the detected vents in the Afar Depression was also created (Fig. 6).

The identified vents (mainly scoria cones) are generally of Pleistocene and Holocene age (younger than 1.8 Ma) and are mainly basaltic in composition (Lahitte, et al., 2003a, 2003b; Kidane et al., 2003). The detected vents (1725) may be roughly divided into the recent basaltic lavas of the Erta Ale area (data set NA) and Central Afar (data sets CA-1 and CA) and the relatively older basaltic volcanism. Young basaltic cones generally have dark blue hues, well-preserved flanks, and a defined crater rim (Fig. 3A), with an average basal diameter of 370 m. Old cones have red hues, show disrupted cones and gullies on their flanks, and erosion often highlights cone breaching; their average basal diameter is 439 m (Fig. 3B). Old vents share similar morphologic features both in areas with basaltic rocks and in those with silicic rocks. They are all assumed to be basaltic. For example, the vents of data set CA and those of data set SA are all assumed to be basaltic, although the cones are located in areas where silicic volcanic centers also occur (Fig. 2). Using the pixel values in satellite images, a rough spectral comparison between the vents of data set CA (in an area with silicic volcanic rocks) and those of data set DB-na (in an area with recent basaltic rocks) was performed to validate the assumption that all the detected vents have a basaltic composition. The sampled pixels belonging to the CA and DB-na vents show similar pixel values that clearly differ from those of pixels sampled on silicic volcanic centers (Fig. 7).

DATA ANALYSIS

Methods

The Afar vents were analyzed in terms of self-similar clustering and mean vent separation (Mazzarini, 2004); cone density was also investigated. The spatial distribution of vents was analyzed by calculating the correlation exponent D (Bonnet et al., 2001). A two-point correlation function method was used to measure the fractal dimension of the vent population. For a population of N points (vent centers), the correlation integral C(r) is defined as the correlation sum that accounts for all the points at a distance of less than a given length r (Bonnet et al., 2001, and references therein). In this approach, the term C(r) is computed as:  
formula
where N(r) is the number of pairs of points whose distance is <r. If scaling holds, equation 1 is valid, and the slope of the curve in a log(C[r]) versus log(r) diagram yields the D value.

Following equation 1, the computed D value is valid for a defined range of distances (r). The distance interval over which equation 1 is valid is defined by the size range. For each analysis, the size range of samples is in turn defined by a plateau in the local slope versus log(r) diagram: the wider the range the better the computation of the power-law distribution (Walsh and Watterson, 1993).

Truncation and censoring affect the computation of the fractal distribution for fractures (Bonnet et al., 2001) and cones (Mazzarini, 2004). In order to fit the data for a scale range probably not affected by these effects, at least 150–200 objects (cones in this case) must be analyzed (Bonnet et al., 2001; Bour et al., 2002).

The distribution of vents in the Afar Depression was also analyzed in terms of vent separation. Vent separation (or spacing) is analyzed by computing the average minimum distance between vents. The coefficient of variation CV (Gillespie et al., 1999, and references therein) for the distribution of vent separation describes the degree of vent clustering. CV > 1 indicates clustering of vents, CV = 1 indicates a random or Poisson distribution of vents, and CV < 1 indicates anticlustering (a homogeneous distribution) of vents. CV is defined as:  
formula
where S is the standard deviation and m is the mean.

In order to analyze the density of vents taking into account their spatial distribution, the vent closeness (VC) method was introduced. This method computes the number of vents within a radius r centered on each vent of the data set; three different search radii were used. The resulting vent density for each data set is the average of the measures relative to all the vents in the data set.

RESULTS

As a whole, the vents in the Afar Depression have a very similar separation (spacing), with an average of 1.24 km in the 0.91–1.30 km range 02(Table 2). Vents in the Danakil block (set DB-a) show the widest spacing (∼1.30 km). Data set DB-na in the Danakil block has the closest vent spacing (1.14 km). The vent spacing distribution can be described by the coefficient of variation, CV. Data sets DB-na (CV = 0.88) and DB-a (CV = 0.77) have an anticlustered (homogeneous) distribution of vent spacing, whereas the remaining data sets show CV values >1, indicating a clustered distribution of vent spacing 02(Table 2). The higher the CV value, the more clustered the distribution.

Self-similar clustering of vents is described by the correlation exponent D (the higher the correlation exponent D the more homogeneous the distribution i.e., anti-clustered; e.g., Bonnet et al., 2001).

Data sets show different degrees of clustering 03(Table 3), with D = 1.42 ± 0.02 for the Afar vents as a whole. Data sets NA (D = 1.34 ± 0.02) and SA (D = 1.19 ± 0.04) show the highest self-similar clustering of cones. Data sets DB-a (D = 1.69 ± 0.02), CA-1 (D = 1.52 ± 0.02), and DB-na (D = 1.50 ± 0.01) show low self-similar clustering. The D exponent for the CA data set is very similar to that for the Afar vents as a whole (1.43 ± 0.02).

Overall, the vents in the Afar Depression show a well-established fractal behavior over more than one order of magnitude (1.2–23 km); the computed upper cutoff is 23.4 ± 2.0 km. Three data sets (CA, DB-na, and SA) have an upper cutoff of ∼23 km 03(Table 3). Data sets DB-a and CA-1 have upper cutoff values of 12.5 ± 1.6 km and 11.5 ± 0.8, respectively. The NA data set has an upper cutoff of 14.2 ± 2.3 km.

The vents closeness (VC) density was computed using 5 km, 2.5 km, and 1.4 km search radii. The smallest radius (1.4 km) was used because it is close to the maximum computed spacing of vents (1.30 km) (Fig. 6; 02Table 2). As a whole, VC ranges from 0.1 to 0.3 vents km−204(Table 4). Density does not show large variations; the highest values (0.3) derive from the Afar, CA, and NA data sets using a search radius of 1.4 km, whereas the lowest values (0.1) were computed using a search radius of 5 km 04(Table 4).

DISCUSSION AND CONCLUSIONS

The vents in the Afar Depression clearly show self-similar clustering (D = 1.42 ± 0.02) in the 1.2–23.4 km range, with an upper cutoff (Uco) of ∼23 km (23.4 ± 2.0). The computed correlation exponent for the Afar vents is similar to that of vents along the northern Main Ethiopian Rift (Fig. 8). The Main Ethiopian Rift vents show self-similar clustering (D = 1.41 ± 0.02) and Uco of ∼27 km; the Uco value matches well the crustal thickness of the northern Main Ethiopian Rift (Mazzarini, 2004). The difference (∼5 km) in the Ucos of the Afar Depression and the northern Main Ethiopian Rift may thus reflect different degrees of crustal stretching (e.g., Hayward and Ebinger, 1996). Moreover, the observed Uco value for the Afar Depression fits well with the crustal thickness of ∼25 km derived from geophysical data from the region.

Most of the analyzed data sets show similar Uco values (DB-na, CA, and SA); the average of 23.2 ± 0.5 km clearly matches the Uco value computed for the Afar vents (23.4 ± 2.0 km). The NA data set, from northern Afar where large volcanoes occur, has a Uco value of 14.2 ± 2.3 km that closely matches the crustal thickness of the area based on seismic refraction data (e.g., Prodehl et al., 1997). Data set DB-a also has a low Uco value (12.5 ± 1.6 km) along an EW volcanic range close to Assab in the Danakil block (Fig. 6). The CA-1 data set in the Manda Hararao–Goba'ad rifts shows the lowest Uco value (11.5 ± 0.8 km). The low Uco value for the Manda Hararo–Goba'ad rifts (CA-1) is consistent with data (seismic, synthetic aperture radar interferograms, and field surveys) collected in September–October 2005 in the northwestern termination of the Manda Hararo rift during the formation of eruptive fissures and vents, and during the emplacement of a dike extending from 2 to ∼9 km in depth (Wright et al., 2006), suggesting a brittle crust thickness of ∼10 km.

The inferred Uco values for the Afar Depression can be considered proxy measures of different degrees of stretching in an extending continental crust; extension is mainly localized in areas where the propagation of the spreading ridge (the Red Sea for the NA data set and the Gulf of Aden for the CA-1 data set) (Manighetti et al., 1998) leads to strain localization.

Global plate reconstruction based on geodetic, geophysical, and geological data (Chu and Gordon, 1999; Sella et al., 2002; Kreemer et al., 2003; Fernandes et al., 2004) yields an average spreading rate of 1.6–7 mm yr−1 for the East African Rift system. Strain rates in the East African Rift system vary from south to north, and an average strain rate of 5–7 mm yr−1 can be assumed in the Afar. Using these values as proxy for the strain rate in the Afar Depression, and assuming pure shear deformation, a crustal necking of ∼5 km is accomplished in ∼1–3 m.y. The basaltic vents used to determine the thickness of the crust in the Afar region are younger than 2 Ma, and most are Holocene age (Manighetti et al., 1998; Lahitte et al., 2003a, 2003b; Kidane et al., 2003); the vents thus formed just after or during the late stages of crustal extension. The basaltic magma thus rose from deep crustal or subcrustal reservoirs through a thinned crust to the surface, giving rise to monogenetic vents and forming volcanic fields. In the Afar Depression, the spatial distribution of vents imaged the heterogeneous thickness of the crust (see the analyzed data sets, 03Table 3), thereby confirming that crustal extension in the Afar region is ongoing and not uniform. The local-scale distribution of vents can thus provide insight into localized crustal extension.

The exposure and tectonic setting of the Afar Depression make it an ideal location for investigating the link between vent distribution (self-similar clustering) and crustal thickness. In general, several factors (e.g., changes in strain rate) may change the style and chemistry of volcanism. In the Afar region, for example, basaltic activity marks periods of high extensional strain (e.g., Lahitte et al., 2003a). The occurrence of monogenetic basaltic volcanism requires a channeling of magma from deep reservoirs to the surface without formation of intracrustal magma chambers, regardless of the brittle layer thickness. The style of volcanism may change through time, generating more evolved magma and fissure magmatism and determining the formation of central volcanoes (e.g., Lahitte et al., 2003a). In this case the distribution of volcanic vents may be controlled by strain rate and brittle and/or ductile layering of the crust.

More data sets on the distribution of vents in basaltic volcanic fields within extensional or contractional continental tectonic settings are required to better define the link between crustal thickness and the upper vent distribution cutoff value. Once this hypothesis is confirmed by robust statistics, the distribution of basaltic vents can be used as a proxy measure of crustal and/or lithospheric thickness in large and remote areas of the Earth or on planets with evidence of volcanic activity.

I thank G. Corti and two anonymous reviewers for comments and suggestions that improved the manuscript.