RESEARCH ARTICLE Seismic Moments of Intermediate‐Depth Earthquakes 10.1029/2018TC005336 Beneath the Hindu Kush: Active Stretching of a Blob Special Section: of Sinking Thickened Mantle Lithosphere? Fifty Years of Plate Tectonics: then, now and beyond Peter Molnar1 and Rebecca Bendick2

1Department of Geological Sciences and Cooperative Institute for Research in Environmental Sciences, University of Key Points: Colorado Boulder, Boulder, Colorado, USA, 2Department of Geosciences, University of Montana, Missoula, Montana, • Intermediate‐depth seismicity beneath the Hindu Kush suggests USA rapid stretching and sinking of mantle lithosphere • This region shows removal of Abstract Intermediate‐depth seismicity beneath the Hindu Kush may reveal the Earth's best example of mantle lithosphere in action, better a stretching blob of mantle lithosphere sinking through the asthenosphere. Seismically, this region is the than anywhere Earth's most active at intermediate depths (70–300 km). Fault plane solutions show nearly vertical stretching of the region in which the earthquakes occur, and a summation of seismic moment tensors implies that on average material at a depth of 300 km moves downward at ~40 mm/year relative to the Correspondence to: overlying crust. As shown by Kufner et al. (2017, https://doi.org/10.1016/j.epsl.2016.12.043) and Zhan and P. Molnar, [email protected] Kanamori (2016, https://doi.org/10.1002/2016GL069603), the central part of the zone stretches so rapidly that this rate there is ~100 mm/year, much faster than the present‐day convergence rate of ~15 mm/year at the surface and across the Hindu Kush. The pattern of stretching, with maximum strain rates in the Citation: Molnar, P., & Bendick, R. (2019). middle depths of the intermediate‐depth range, resembles that beneath the southeastern Carpathians, where Seismic moments of Lorinczi and Houseman (2009, https://doi.org/10.1016/j.tecto.2008.05.024) have shown that seismicity is ‐ intermediate depth earthquakes consistent with a blob of mantle lithosphere stretching rapidly and sinking into the asthenosphere, though beneath the Hindu Kush: Active stretching of a blob of sinking more slowly than occurs beneath the Hindu Kush. thickened mantle lithosphere? Tectonics, 38, 1651–1665. https://doi. org/10.1029/2018TC005336 1. Introduction Received 20 SEP 2018 Although many have come to believe that mantle lithosphere beneath some continental regions has been Accepted 9 APR 2019 removed, controversy continues to surround the mechanisms by which this occurs, with some doubting that Accepted article online 17 APR 2019 Published online 15 MAY 2019 the process occurs at all (e.g., McKenzie & Priestley, 2008). Bird (1979) proposed that mantle lithosphere could delaminate from the overlying crust by peeling away from it, and as a result, the overlying crust would rapidly become exposed to the hotter underlying asthenosphere. Houseman et al. (1981) suggested alternatively that the enhanced gravitational instability of the mantle lithosphere, when thickened along with the overlying crust during horizontal shortening, could grow rapidly so that much if not most of the mantle lithosphere would des- cend into the underlying asthenosphere and be removed. Numerous studies exploited these possibilities to explain surface uplift supplemental to isostatic compensation of thickened crust (e.g., Bird, 1979; England & Houseman, 1989), compositions of major elements of volcanic rock in convergent belts like the Andes (e.g., Jull & Kelemen, 2001; Kay & Kay, 1993; Kay & Mahlburg‐Kay, 1991), and trace elements and isotopic ratios of volcanic rock in Tibet and elsewhere (e.g., Turner et al., 1993; Turner, Arnaud, et al., 1996; Turner, Kelley, et al., 1996; Turner et al., 1999). Some of these cases may have involved removal of lower crust along with mantle lithosphere. Although a few tomographic images suggest that mantle lithosphere is descending into the asthenosphere—for instance beneath the Sierra Nevada of California (e.g., Jones et al., 2014), the Alpine belts of Europe (e.g., Lippitsch et al., 2003; Ren et al., 2012), and perhaps Tibet (e.g., Chen et al., 2017; Ren & Shen, 2008)—demonstrations of ongoing removal of continental mantle lithosphere are few. Among the evidence of oceanic lithosphere sinking into the asthenosphere, inclined zones of earthquakes beneath island arc structures are perhaps the most convincing (e.g., Isacks et al., 1968), and the case for negative buoyancy of old oceanic lithosphere is well established (e.g., Isacks & Molnar, 1969, 1971). Lorinczi and Houseman (2009) extended that logic by exploiting the nearly vertical zone of earthquakes beneath the southeastern Carpathians to estimate the rate at which a blob mantle lithosphere stretches as it sinks into the asthenosphere. We exploit similar analyses by Kufner et al. (2017), Lister et al. (2008),

©2019. American Geophysical Union. and Zhan and Kanamori (2016) to the Hindu Kush region to address how a blob of mantle lithosphere All Rights Reserved. may be sinking beneath that region.

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When plate tectonics was first recognized, Isacks et al. (1968) deduced that intermediate‐ and deep‐focus earthquakes occurred in descending slabs of stiff, cold, negatively buoyant oceanic lithosphere. In general, these descending slabs could be linked through the shallow part of subduction zones to lithosphere at the surface, either with a continuous zone of earthquakes or through mechanical arguments related to stress transfer in strong material (e.g., Elsasser, 1969). Then, in a synthesis of fault plane solutions for intermedi- ate and deep earthquakes around the globe, Isacks and Molnar (1969, 1971) showed that for deep earth- quakes, P axes, orientations of maximum compressional strain, consistently plunge down the dips of seismic zones at depths >300 km; for intermediate‐depth earthquakes, however, T axes, orientations of maximum extensional strain, plunge downdip, in many, though not all, regions. Thus, slabs seem to be stretching as gravity acting on excess mass in the slabs pulls them down, like dangling springs hanging from and attached to lithosphere above. The intermediate and deep zones of seismicity are also spatially asso- ciated with low attenuation of seismic waves (e.g., Oliver & Isacks, 1967; Utsu, 1966) and high seismic wave speeds (e.g., Mitronovas & Isacks, 1971; Utsu, 1971), both of which are signatures of cold lithospheric mate- rial at depth. When plate tectonics was recognized, also obvious was a difference between continental and oceanic litho- sphere: thick continental crust makes continental lithosphere buoyant (e.g., McKenzie, 1969). With such buoyancy, subduction of continental lithosphere should be either rare or different from that of oceanic litho- sphere. Among 29 zones of intermediate and/or deep earthquakes that Isacks and Molnar (1971) considered, four lie within continental regions, and three of them cannot yet be reconciled with subducting slabs of ocea- nic lithosphere that can be traced to the surface. The dipping zone of the intermediate‐depth earthquakes beneath the Indo‐Burman Ranges, just east of India, clearly does reflect subduction of lithosphere beneath the Ranges (e.g., Chen & Molnar, 1990; Hurukawa et al., 2012; Le Dain et al., 1984; Ni et al., 1989). The rela- tionship of the 1954 deep Spanish earthquake to subduction remains obscure. The remaining two, the Vrancea zone beneath the southeastern Carpathians and the Pamir‐Hindu Kush in central Asia, lie in regions of recent if not active convergence, but each is complicated in its own way. Lorinczi and Houseman (2009) suggested that the intermediate‐depth earthquakes of the Vrancea zone occur not in a subducted slab of lithosphere, but rather in a sinking blob of mantle lithosphere drawn into it from the surrounding regions, as would occur as a convective instability grew. Convective instabilities should lead to high internal strain rates in the sinking material, higher than where nearly rigid, plate‐like lithosphere sinks at subduction zones. Indeed, Lorinczi and Houseman (2009) reported unusually high strain rates at intermediate depths. We extend Lorinczi and Houseman's logic and similar analyses taken by Kufner et al. (2017), Lister et al. (2008), and Zhan and Kanamori (2016) to the Hindu Kush region, the Earth's most active region of intermediate‐depth seismicity, to explore whether a blob of mantle lithosphere might similarly be sinking beneath that region.

2. Carpathians The Carpathian mountain belt wraps around the Pannonian Basin (Figure 1), which underwent stretching and thinning of its lithosphere in Miocene time (e.g., Horváth, 1993; Horváth et al., 2006; Royden, Horvath, Nagymarosy, et al., 1983; Royden, Horvath, & Rumpler, 1983) and is underlain by thinned continental crust (e.g., Środa et al., 2006). Seismic tomography reveals low P and S wave speeds in the uppermost mantle beneath the basin and hence corroborates the inference of lithospheric thinning (Dando et al., 2011; Mitterbauer et al., 2011; Ren et al., 2012). Starting before and continuing during the stretching and thinning of the Pannonian crust, the Carpathian mountain belt developed by crustal shortening and thickening (e.g., Behrmann et al., 2000; Burchfiel & Nakov, 2015; Castelluccio et al., 2016; Faccenna et al., 2014; Knapp et al., 2005). Although some argue that subduction of oceanic lithosphere occurred beneath the Carpathians, Knapp et al. (2005) inferred that subduction of oceanic lithosphere cannot account for the extent of lithosphere required by the zone of intermediate‐depth earthquakes. High seismic wave speeds characterize the mantle underlying the Pannonian Basin between depths of ~400 and ~650 km, and have been interpreted as foundered mantle lithosphere (e.g., Dando et al., 2011; Mitterbauer et al., 2011; Ren et al., 2012). The deep high‐speed zone lies above the 660‐km discontinuity, which is deflected downward ~40 km, consistent with temperatures lower than normal in that region (Hetényi et al., 2009).

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Figure 1. Topographic map of the Carpathian and Pannonian Basin region, with cross sections showing results of P wave tomography of Ren et al. (2012) on three profiles. Dark blue and dark red show wave speed anomalies that are 2% higher and lower, respectively, than average. Red dots show hypocenters of earthquakes in the Vrancea zone in the southeast corner of the Carpathians. Note the absence of high speeds beneath most of the Carpathians.

Gemmer and Houseman (2007) (Houseman & Gemmer, 2007) suggested that the present‐day structure is the result of removal of lithosphere beneath the Pannonian Basin in sheets, drips, or blobs that sank beneath the surrounding mountain belts. Only beneath the southeastern Carpathians, where the intermediate‐depth earthquakes occur, does that removal continue today. Tomograms of the Carpathian region show low speeds beneath the mountain belt except in the southeast corner where the intermediate‐depth earthquakes occur (Figure 1; Ren et al., 2012; Sperner et al., 2001). To quantify rates of deformation within the seismically active high‐speed zone, Lorinczi and Houseman

(2009) used seismic moments of earthquakes within the zone. Seismic moment is a scalar: Mo = μAΔu, where μ is the shear modulus in the region of the earthquake, A is the area that ruptured during the earth- quake, and Δu is the average slip on the fault surface (Aki, 1966; Aki & Richards, 1980). Brune (1968) showed how the sum of seismic moments of earthquakes on a fault can be used to estimate the slip rate on it. Gilbert (1970) generalized the seismic moment to take into account different orientations of faulting and slip by

proposing the seismic moment tensor, Moij, a symmetric tensor, whose scalar magnitude is Mo. Later, Kostrov (1974) showed how the sum of N moment tensors, Moij,k(k =1toN), within a volume, V, can be used to estimate strain within that volume associated with earthquakes in it:

1 N ε ¼ ∑ M ; (1) ij 2μV k¼1 oij k

Dividing strains given by equation (1) by the duration covered by the earthquake catalogue, yields strain rates.

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Lorinczi and Houseman (2009) summed the seismic moments of earthquakes within four 50‐km depth ranges of the seismic zone beneath the Carpathian zone. Not surprisingly, they found the highest strain rates in the 50–100‐km depth range where the largest earthquakes have occurred. Although no consistent orien- tations of nodal planes characterize the majority of earthquakes in the region, nearly all show approximately vertical T axes. Thus, the material in which the earthquakes occur is stretching vertically. For the lateral dimensions of the zone they took 30 × 80 km2, but noted that Oncescu and Bonjer (1997) obtained strain rates nearly an order of magnitude larger, because they used a smaller areal extent of the seismically deform- ing zone. Lorinczi and Houseman (2009) concluded that the region between depths of 50 and 100 km stretches at a rate of 35%/Myr. Thus, the material at 100‐km depth moves downward at 17.5 mm/year, or 17.5 km/Myr, with respect to material at a depth of 50 km. Strain rates in the depth ranges of 0–50, 100–150, and 150–200 km are notably lower. The integrated strain rates have the region at a depth of 200 km moving downward 23 mm/year relative to the surface. GPS measurements show that horizontal convergence across the southeastern Carpathians has stopped, and in fact, the region to the southeast now seems to diverge slowly from that to the northwest (van der Hoeven et al., 2005). Nowhere within Europe, except in the Aegean region, do regions move horizontally as fast as 15 mm/year with respect to one another. Therefore, the cold mantle lithosphere containing these intermediate‐depth earthquakes is stretching faster than most of Europe deforms today. We note that others interpret the Vrancea seismic zone beneath the southeastern Carpathians differently from that described above. Fillerup et al. (2010), Gîrbacea and Frisch (1998), and Göğüş et al. (2016) suggested that the earthquakes occur in lithosphere that has peeled back and delaminated from beneath the Pannonian Basin. Fillerup et al. (2010), in fact, suggested that the earthquakes occur in what had been the lower crust of the basin.

3. Hindu Kush The east‐west trending Hindu Kush stretches across northeastern Afghanistan into northwestern Pakistan to form a broad zone of high elevation that merges with the Karakorum and Himalaya toward the southeast and with the Pamir to the northeast (Figure 2). In most mountain ranges where crustal shortening is rapid (e.g., Himalaya or Pamir), crustal shortening occurs by slip on a single major thrust fault. By contrast, as in the Carpathians, deformation across the Hindu Kush is not associated with such a fault, or if it is, that fault has not yet been identified. Instead, crustal seismicity in the Hindu Kush region appears to occur on several relatively indistinct thrust faults that follow the margin of the Tajik Depression (e.g., Abers et al., 1988; Kufner et al., 2018; Perry et al., 2019; Yeats & Madden, 2003). The spatial distribution of intermediate‐depth earthquakes beneath the Pamir‐Hindu Kush region also is more complex than that beneath the Carpathians, and allows at least two different interpretations. Seismicity, at least for earthquakes deeper than ~100 km, defines two separate zones: one dipping southward beneath the Pamir and a second dipping steeply northward beneath the Hindu Kush (Figures 2 and 3; Billington et al., 1977; Chatelain et al., 1980; Roecker et al., 1980; Sippl et al., 2013). Improved resolution of the seismicity beneath the Pamir (Pegler & Das, 1998; Sippl et al., 2013) shows that the zone dips southward along the northern edge of the Pamir (Figure 3c) and varies smoothly to dip southeastward and eastward beneath the western edge of the Pamir. The surface projection of the inclined seismic zone wraps around the western margin of the Pamir, where surface deformation occurs by a combination of left‐lateral strike slip (e.g., Kuchai & Trifonov, 1977; Kufner et al., 2018; Mohadjer et al., 2010; Trifonov, 1978) and northwest‐southeast crustal shortening (e.g., Abers et al., 1988; Ischuk et al., 2013; Perry et al., 2019). The apparently continuous zone of earthquakes with depths between 60 and ~100 km beneath the Pamir and Hindu Kush has led some to favor the view that the zone marks a single, warped slab of lithosphere that is continuous from the eastern end of the northern edge of the Pamir to the western end of the Hindu Kush seismic zone (e.g., Billington et al., 1977; Koulakov & Sobolev, 2006; Nowroozi, 1971; Pegler & Das, 1998). Although Pavlis and Das (2000) and Koulakov and Sobolev (2006) suggested that the intermediate‐depth earthquakes beneath the Pamir are part of lithosphere attached to the Indian Plate but overridden by that plate as it penetrated northward into the rest of Eurasia, evidence of southward underthrusting of Eurasian lithosphere beneath the Pamir seems overwhelming. Analogous to oceanic subduction zones, a belt of shallow‐focus earthquakes showing thrust faulting marks the northern margin of the Pamir (e.g., Burtman & Molnar, 1993; Hamburger et al., 1992; Kufner et al., 2018; Sippl et al., 2013). Quaternary faulting

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Figure 2. Seismicity of the Hindu Kush and Pamir region, with color coding showing depths. Note the discontinuity in earthquakes deeper than ~60 km, with seismicity deepening to southeast beneath the southwestern Pamir and to the north beneath Hindu Kush. Boxes show regions used to draw profiles in Figure 3. The earthquake hypocenters were determined by Kufner et al. (2017, 2018) and Sippl et al. (2013).

(e.g., Arrowsmith & Strecker, 1999; Nikonov et al., 1983) and GPS velocities (Figure 4) show concentrated deformation along that belt (e.g., Ischuk et al., 2013; Perry et al., 2019; Reigber et al., 2001; Zubovich et al., 2010). East‐west trending belts of sedimentary rock in the Tajik Depression are truncated at the western edge of the Pamir, but all such rock can be found in tightly folded strata along the northern edge of the Pamir (Burtman & Molnar, 1993; Suvorov, 1968). The displaced rock units call for a minimum 300 km of northward displacement of the northern edge of the Pamir past the Tajik Depression to the west. Particularly impressive is a study by Schneider et al. (2013), who used receiver functions to map southward dipping interfaces under the Pamir. The interfaces define a dipping zone in which wave speeds decrease from bottom to top at the lower interface and then increase at the upper interface. Schneider et al. (2013) recognized the two interfaces as marking the top and bottom of Asian crust, 10–15 km in thickness, that has been thrust beneath the Pamir. They interpreted this as lower crust that has been thrust beneath the Pamir, with upper crust scraped off and contributing to crustal thickening. Crustal thicknesses beneath the Tajik Depression decrease from west to east and are only ~20 km at the eastern edge of the basin (Burtman & Molnar, 1993; Kulagina et al., 1974). Extrapolated eastward, crust as thin as

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Figure 3. Profiles of seismicity in the Hindu Kush and Pamir regions in cross sections shown in Figure 2. Note the steep northward dip of the Hindu‐Kush zone in profiles (a) and (b), and the gentler southward dip beneath the Pamir in (c). Note too, in (d), the separation of events in the eastern Hindu Kush west of 71.6°E and the thin line of hypocenters to the east which occurred in the Pamir zone. The hypocenters in Figure 2 are used here.

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Figure 4. Topographic map of the Hindu Kush region and GPS velocities. Arrows show GPS velocities relative to Eurasia (Perry et al., 2019). The blue line shows the profile in Figure 5, along which we plotted velocities, with red and blue showing those from control points southwest of the line and northeast of or near it.

10–15 km seems plausible, if not a logical inference. Moreover, from the sediment deposited in the Tajik Depression, Leith (1985) inferred a subsidence history that included thinning of the crust in Jurassic time, followed by a slow cooling of thinned mantle lithosphere. Thus, the thin low‐speed layer that Schneider et al. (2013) inferred to be lower crust could be continental crust that was thinned in Jurassic time and overlies mantle lithosphere that subsequently cooled and thickened before being subducted beneath the Pamir (Burtman & Molnar, 1993). The seismic imaging and hypocenters delineate a continuous slab of lithosphere extending from the deep seismic zone to the Moho, which when extrapolated to the surface reaches the belt of active thrust faulting and seismicity in the upper crust (Figure 3c). We treat Pamir seismicity as distinct from Hindu Kush seismicity and do not address it further, for intermediate‐depth earthquakes beneath the Pamir appear to occur in cold Asian lithosphere that is capped by thin crust. Although this lithosphere does not seem to be oceanic in origin, the logic that intermediate‐ depth earthquakes occur in cold oceanic lithosphere subducted at island arcs (e.g., Isacks et al., 1968; Isacks & Molnar, 1969, 1971) applies to the Pamir zone, where continental mantle lithosphere has cooled since Jurassic time and crust is thin.

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Figure 5. Profiles of topography and velocities of GPS control points in the Hindu Kush region relative to Eurasia along the profile shown by the blue line in Figure 4, from Perry et al. (2019). The top profile shows components parallel to the profile, and bottom—components perpendicular to it. Red arrows correspond to control points southwest of the line in Figure 4, and blue arrows to points northeast of it or close to it. Note that velocities shown by red points indicate that roughly half of the convergence between India and Eurasia occurs in each side of the Hindu Kush. Control points northeast of the profile, blue points, and near 400 km give a deceptive image, because they include the large right‐lateral component of slip on northerly striking left‐lateral strike‐slip faults (e.g., Kuchai & Trifonov, 1977; Kufner et al., 2018; Mohadjer et al., 2010; Trifonov, 1978).

In contrast, the evidence that relates the Hindu Kush seismicity to subduction of intact lithosphere is less convincing than that for the Pamir. Of course, before India collided with southern Asia at ~45–55 Ma (e.g., Bouilhol et al., 2013; Garzanti & Van Haver, 1988; Rowley, 1998), oceanic lithosphere plunged beneath the southern margin of Asia. Ophiolites that presumably are remnants of ocean floor that lay between India and Eurasia can be found south of the Hindu Kush, although many are Cretaceous or older (e.g., Boulin, 1981, 1990, 1991; Tapponnier et al., 1981). Moreover, in discussing the difficulties relating any of these ophiolites to the Hindu Kush seismic zone, Tapponnier et al. (1981) pointed out that suturing had occurred before 40 Ma, at the latest. We cannot rule out the possibility that oceanic lithosphere, or blocks of continen- tal lithosphere with thinned crust like that beneath the eastern Tajik Depression, remained trapped in the region, but we are aware of no geologic evidence, or even hints of it, suggesting either the existence of such lithosphere or a convincing connection of it to a suture south of the Hindu Kush. Tapponnier et al. (1981) pointed out that Cenozoic tectonic development of Afghanistan resembles that of Tibet, where no such seismic zone is present. Thus, it seems likely that the Hindu Kush earthquakes do not occur in a slab of oceanic lithosphere connected to the Indian plate. Indian lithosphere slides beneath the Himalaya east of ~75°E at ~20 mm/year (e.g., Bettinelli et al., 2006; Feldl & Bilham, 2006; Lavé & Avouac, 2000), but convergence across the Himalaya in Pakistan, between

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~68°E and ~74°E, is <10 mm/year (Perry et al., 2019). In fact, new GPS data from Afghanistan (Perry et al., 2019) suggest that the con- vergence of India and Eurasia across the Hindu Kush is equally parti- tioned between shortening on the south‐southeast and north‐ northwest sides (Figures 4 and 5). Although earthquakes in the Hindu Kush have commonly been asso- ciated with subduction of Indian lithosphere (e.g., Billington et al., 1977; Chatelain et al., 1980; Koulakov & Sobolev, 2006; Kufner et al., 2016, 2017; Lister et al., 2008; Mellors et al., 1995; Negredo et al., 2007; Pavlis & Das, 2000; Priestley et al., 2008; Roecker, 1982; Roecker et al., 1980; Zhan & Kanamori, 2016), we exploit the low strain rates and absence of a major thrust fault to develop the view that, like Lorinczi and Houseman's (2009) for the intermediate‐depth earthquakes in the Vrancea zone beneath the Carpathians, earthquakes in the Hindu Kush zone occur in Asian continental mantle lithosphere that has been thickened and now is sinking and ε_ Figure 6. Vertical extensional strain rates, zz , as a function of depth. Average stretching beneath the mountain belt, rather than sinking as a stiff strain rates for the entire region are expressed in units of Myr. subducting lithospheric slab.

4. Seismic Moments of Earthquakes in the Hindu Kush Seismic Zone Fault plane solutions of earthquakes in the Hindu Kush region show nearly vertical T axes (e.g., Chatelain et al., 1980; Isacks & Molnar, 1971; Kufner et al., 2017; Lister et al., 2008; Roecker et al., 1980; Zhan & Kanamori, 2016), as for the Vrancea zone. Earthquakes in the Vrancea seismic zone occur in a cylindrical zone with an ellipsoidal cross section, but Hindu Kush earthquakes occur in a more planar, east‐west trend- ing zone (Figures 2 and 3). Most P axes for Hindu Kush earthquakes trend roughly perpendicular to the seis- mic zone, suggesting that the material in which the earthquakes occur is shortened perpendicular to the roughly planar zone. Following the approach taken by Lorinczi and Houseman (2009) and described above, we exploit the work of Kufner et al. (2017), Lister et al. (2008), and Zhan and Kanamori (2016), who also used seismic moments of earthquakes in the Hindu Kush seismic zone. Whereas these authors ascribed rapid stretching to tearing of a slab of Indian lithosphere that had plunged beneath the Hindu Kush, we suggest that the stretching occurs instead within a blob of thickened mantle lithosphere beneath the mountain belt. The main difference between these end‐member views is that tearing lithosphere should have had continuity with lithosphere at the surface through a shallow localized subduction zone, even if it is currently failing. A convectively unstable mantle lithosphere, however, need not be mechanically linked to the surface and could develop through thickening and negative buoyancy in mantle rock decoupled or partially coupled to the crust above. As described above for the Carpathian region, we use (1) to assess seismic strain rates. For μ, we used values given by Dziewonski and Anderson (1981). Like Kufner et al. (2017) and Lister et al. (2008), we rely on the CMT catalogue of moment tensors of earthquakes (Ekström et al., 2012), and which occurred between 1 January 1976 and 30 June 2018, a duration of 42.5 years, to estimate strain rates. To allow for ruptures that extend outside the width of the hypocenters, we assume a thickness of the seismic zone of 20 km, larger than the 15 km used by Kufner et al. (2017), and an east‐west length of 170 km (2.3° of longitude at a latitude of 36°N; Figure 3d). To estimate strain rates, we binned earthquakes in 10‐km depth ranges, so that for each bin 3 _ V = 34,000 km . We are concerned with rates of vertical extension, εzz (Figure 6), but the orientation of maximum compressive strain is essentially perpendicular to the seismic zone, and therefore oriented north‐south. As Kufner et al. (2017) and Zhan and Kanamori (2016) found, the highest strain rates are in the depth range of ~180–230 km, but seismicity occurs throughout the depth range of 60 to ~300 km with rare deeper earth- quakes (Figure 3). Therefore, strain accumulates throughout the 60–300‐km depth range (Figure 6). _ To estimate the rate that material at different levels move downward, we simply integrated εzz over depth: ðÞ¼ ∫z ε_ V z z surface zzdz (2)

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The strain rates in Figure 6 yield values of Vz(z) shown in Figure 7. Consistent with the strain accumulation, maximum increases in downward components of velocity also occur in the depth range of 180–230 km, with a more minor increase near 100‐km depth. With the dimensions that we use, material at a depth of 300 km is calculated to descend at an average rate of 40 mm/year. Kufner et al. (2017) estimated uncertainties of 25–30% in strain rates associated with seismic moments, the duration of the seismic record, and assumptions of μ, but they recognized that the largest uncertainty comes from the assumed thick- ness of the seismic zone. For example, if we used a width of 15 km instead of 20 km, the 40‐mm/year rate would become 52 mm/year. By comparison, in the longitude range that includes the Pamir and Hindu Kush, the total convergence rate between India and Eurasia is only 28 ± 4 mm/year (DeMets et al., 2010). Although more than half, 20 ± 2 mm/year, is accommodated on the Pamir thrust system, nowhere in the longitude band of the Hindu Kush is as much as 10 mm/year

Figure 7. Downward speeds, Vz from equation (2), as a function of depth absorbed in a narrow zone (Figures 4 and 5). As in the Carpathians, are shown as the average for the whole region (black), and for three subre- the rate of stretching inferred from intermediate‐depth earthquakes is — – — – gions: western 69.7°E 70.5°E (blue), central 70.5°E 71.0°E (red), and much larger than the horizontal convergence rate, requiring large eastern—71.0°E–71.6°E (green) segments. amounts of strain within the sinking lithospheric material. Moreover, the straining of the Hindu Kush zones is much faster than that shown by intermediate‐depth seismicity where subduction of oceanic lithosphere occurs (Bevis, 1988; Holt, 1995). The seismicity in the approximately planar zone between ~69.5°E and 71.6°E and that dips steeply northward is far from uniform, both in numbers of earthquakes and in the distribution of the largest ones. The average descent rate of ~40 mm/year calculated above applies to the region between ~69.5°E and 71.6°E. As Kufner et al. (2017) and Zhan and Kanamori (2016) showed, however, seismicity is much more intense between ~70.5°E and 71.0°E, than farther west or east. If we consider earthquakes only within this short segment of the intermediate‐depth zone, ~45 km wide, 20 km thick, but extending from 60‐ to ~300‐km depth (Figure 3), the calculated rate of descent of material at a depth of ~300 km relative to that at the base of the crust near 50 km is ~100 mm/year (Figure 7; Kufner et al., 2017; Zhan & Kanamori, 2016). Thus, although the intermediate‐depth seismic zone seems to define a nearly vertical, east‐west trending sheet‐like region, deformation within that zone is far from uniform both vertically and laterally. The descent rates calculated from seismic moments of earthquakes in the subregions west and east of this region of especially intense seismicity are ~18 mm/year for the region between 69.7°E and 70.5°E and ~12 mm/year between 71.0°E and 71.6°E (Figure 7). We cannot rule out the possibility that the short time span of the seismicity biases results so that in a longer period, the eastern and western regions will show

higher rates as the catalog grows, but the recurrence of many large earthquakes, with Mw > 7, in the cen- tral segment (e.g., Zhan & Kanamori, 2016) demonstrates that the seismic strain rates are not dominated by a single large earthquake. Thus, at face value, the seismic moments suggest that the central part of the Hindu Kush zone is stretching much faster than the regions east and west of it. Instead of a sheet of mate- rial descending as a slab, the central part of the sinking blob seems to be drawing material from its edges into it.

G. A. Houseman (personal communication, 2018) pointed out that the seismicity of the Hindu Kush differs from that of the Carpathians in that (at least) two depth ranges of high strain characterize the former, but only one the latter. In laboratory experiments of drops passing across a boundary separating a more viscous fluid from a less viscous one, Manga and Stone (1995) observed that the drop could break into more than one smaller drop. The stretching near 100 km beneath the Hindu Kush (Figures 6 and 7) might reflect this process at a depth range where surrounding viscosity decreases with depth from the base of the lithosphere into the asthenosphere. Alternatively, the thickness of the stretching material might be less than that between 130 and 180 km. In any case, the higher strain rates of the Hindu Kush than Carpathians might also allow for higher‐resolution depth variations in strain in the former region.

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The Carpathians and Hindu Kush also differ in that the high‐speed region beneath the Carpathians does not seem to reach deeper than ~400 km (Figure 1; Ren et al., 2012), but that beneath the Hindu Kush seems to reach 600 km (e.g., Kufner et al., 2016; Mellors et al., 1995). If the interpretation that we offer is correct, then obviously more mantle lithosphere must have sunk beneath the Hindu Kush than the Carpathians. Given the much greater convergence between India and Eurasia at the longitude of the Hindu Kush (perhaps thousands of kilometers) than across the Carpathians (tens to maybe 100 km), more mantle lithosphere descending beneath the Hindu Kush than Carpathians ought not surprise many. More problematic is the question: From where was that lithosphere drawn? We presume from the surrounding regions. Accordingly, demonstrations either that crust has not been shortened much in the Hindu Kush region or that mantle lithosphere beneath the region is thick would cast doubt on the interpretation that we offer.

5. Discussion The gospel according to plate tectonics holds that intermediate‐depth earthquakes occur within downgoing slabs of intact lithosphere, presumably oceanic lithosphere. Thus, dipping zones of intermediate‐depth earthquakes mark subduction zones where one plate has plunged beneath another into the asthenosphere as a consequence of the negative buoyancy of the plate overcoming its mechanical stiffness (e.g., Isacks et al., 1968; Isacks & Molnar, 1969, 1971; Mahadevan et al., 2010). At most such zones, oceanic lithosphere plunges beneath an island arc, but subduction of cold continental lithosphere with thin crust also seems to occur beneath the Pamir (e.g., Burtman & Molnar, 1993; Schneider et al., 2013), and may account for the intermediate‐depth seismic zone beneath the Indo‐Burman ranges (e.g., Le Dain et al., 1984). Two regions with steeply dipping zones of intermediate‐depth earthquakes, however, the Hindu Kush in central Asia and the Vrancea zone beneath the Carpathians, differ from the others in a couple of ways. First, both occur within continental settings, whereas most other such zones are associated with a suite of features including deep‐sea trenches, shallow‐focus earthquakes showing thrust faulting, and belts of andesitic volcanoes above intermediate‐depth earthquakes with depths of ~80–120 km that typify subduction zones (e.g., Gutenberg & Richter, 1954). Moreover, although convergence has occurred across both the Hindu Kush (e.g., Boulin, 1981, 1988, 1990, 1991; Hildebrand et al., 2001; Tapponnier et al., 1981; Zaman & Torii, 1999) and Carpathians (e.g., Faccenna et al., 2014) in Cenozoic time, neither zone can be associated with an obvious suture where two continents collided after oceanic lithosphere plunged beneath what is now a mountain belt. Although convergence does occur today across the Hindu Kush (Figures 4 and 5), the rate of ~15 mm/year is hardly high (e.g., Perry et al., 2019), and negligible straining, if not divergence, charac- terizes ongoing deformation in the southeastern Carpathians (van der Hoeven et al., 2005). The Hindu Kush and the Vrancea seismic zones also differ from those at subduction zones where one plate of oceanic lithosphere plunges beneath an overriding plate. Although most shallow focus earthquakes at subduction zones occur on the thrust fault that marks the plate boundary, and the intermediate‐depth earth- quakes occur within the downgoing slab of lithosphere, the shallow and intermediate‐depth earthquakes form a nearly continuous zone. The near absence of shallow focus earthquakes in the Hindu Kush and Vrancea zones, let alone showing thrust faulting on gently dipping planes, deny these regions one clear link between subducted lithosphere and the subduction zone, at least insofar as the Hindu Kush seismicity occurs within subducted lithosphere that is part of a plate still at the surface. Strain rates within the most active parts of the Hindu Kush, like those of the Vrancea zone beneath the − − − Carpathian, exceed 10 14 s 1, or 0.3 Myr 1 (Figure 6; Kufner et al., 2017 ; Zhan & Kanamori, 2016). These strain rates are an order of magnitude greater than those within downgoing slabs of lithosphere, which − − are typically ~10 15 s 1, or less (Bevis, 1988; Holt, 1995). As the stresses within intermediate‐depth seismic zones surely result from gravity acting on cold lithospheric material that is more dense than surrounding asthenosphere, two logical explanations can be offered for the high strain rates: (1) the stretching litho- spheric material beneath Hindu Kush and Carpathians is more dense than that of typical subducted oceanic lithosphere or (2) that material hosting the earthquakes is weaker than subducted oceanic lithosphere. Two aspects of lithosphere beneath the Hindu Kush argue against its being atypically dense, but are consis- tent with its being weak. First, tomographic evidence suggests that crust has been subducted with mantle lithosphere beneath the Hindu Kush, to a depth of at least 150 km and possibly deeper (Kufner et al., 2016, 2017; Roecker, 1982). Crust, obviously, would reduce, not enhance, the mean density of the subducted

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lithosphere. Moreover, when at the same temperature, crustal minerals are weaker than olivine, the main mineral of the mantle (e.g., Brace & Kohlstedt, 1980; Bürgmann & Dresen, 2008). Second, mantle lithosphere that had underlain continental crust would have been warmer than, and hence both less dense and weaker than, subducted oceanic lithosphere. It follows that weak material in the Hindu Kush zone, and by analogy in the Vrancea zone, may facilitate rapid stretching. In estimating strain rates, we assume that the thickness of the straining material that hosts the earthquakes does not vary with depth. A couple of possible explanations can be offered for the apparent weakness at ~200‐km depth. First, the material throughout the straining region might be weak, for example, because the effective viscosity depends inversely with strain rate as with dislocation creep. A second explanation, however, is simply that straining is localized in a region that has thinned as it stretched. We refrain from speculating on what led to marked thinning at the depths where earthquakes occur most commonly, but a thinning of the region hosting the earthquakes seems to be an inevitable consequence of the stretching that is occurring. We differ from Kufner et al. (2017) and Zhan and Kanamori (2016) who exploited seismic moments of earth- quakes in the Hindu Kush to show rapid straining at depths near 200 km, results with which we do not quib- ble. They, like Lister et al. (2008), inferred that the rapid straining implies that a slab of subducted lithosphere is necking so rapidly that the lower part is breaking off from the upper part. We do not question the possible detachment of deeper parts of lithospheric slabs from their upper parts. The distribution of inter- mediate and deep focus earthquakes suggests that in some regions, slabs have detached from their upper parts and sunk into the asthenosphere (e.g., Isacks & Molnar, 1969, 1971). Moreover, the absence of high seismic wave speeds where intermediate‐depth seismicity is also absent has been used to infer slab break‐off (e.g., Chatelain et al., 1992). Thus, we do not assert that any of Kufner et al. (2017), Lister et al. (2008), and Zhan and Kanamori (2016) are wrong in their inference of ongoing slab break‐off. For the reasons given above, however, we contend that the bulk of evidence is more consistent with the sinking and stretching of a blob of lithosphere that thickened beneath the Hindu Kush, as Lorinczi and Houseman (2009) inferred from similar data from the Carpathians.

6. Conclusions The abundant seismicity showing, on average, vertical T axes in the nearly vertically dipping zone of intermediate‐depth earthquakes beneath the Hindu Kush implies that the material containing those earth- quakes is stretching vertically (e.g., Kufner et al., 2017; Lister et al., 2008; Zhan & Kanamori, 2016). A sum- mation of the seismic moment tensors of these earthquakes shows that straining is most rapid near the depth of ~200 km, but also occurs throughout the zone (Figure 6; Kufner et al., 2017; Zhan & Kanamori, 2016). Stretching occurs so fast, that on average deep levels descend at ~40 mm/year, faster than the Indian and Eurasian plates converge in this region. Within the central part of the seismic zone, rates of downward movement could exceed 100 mm/year (Kufner et al., 2017; Zhan & Kanamori, 2016). This rapid stretching resembles that studied by Lorinczi and Houseman (2009) for the Vrancea seismic zone beneath the south- eastern Carpathians, and differs in many ways from classical subduction of oceanic lithosphere. Acknowledgments We thank M. Perry for the help with Moreover, unlike regions of continental collision, no obvious suture lies north or south of most of the Figures 1, 2, 4, and 5; S.‐K. Kufner for Hindu Kush and nearby that region. As Gemmer and Houseman (2007), Houseman and Gemmer (2007), helpful discussions, the catalogue of and Lorinczi and Houseman (2009) inferred for the Vrancea zone, we interpret this rapid stretching of the earthquake locations shown in Figures 2 and 3, and insightful material containing the Hindu Kush earthquakes to show the sinking and stretching of thickened mantle comments; X. LePichon for the lithosphere beneath the Hindu Kush, rather than subduction of a slab of intact lithosphere. Although many encouragement; and H. Gilbert, G. A. have inferred that mantle lithosphere has been removed from beneath continents, the seismic moments of Houseman, Kufner, and Zhongwen fi Zhan for unusually helpful reviews of earthquakes beneath these regions may provide the most de nitive evidence of such removal in action. the paper. A version of this material was presented at a conference at the Collège de France in June 2018 celebrating the References 50th anniversary of plate tectonics. Abers, G., Bryan, C., Roecker, S., & McCaffrey, R. (1988). Thrusting of the Hindu Kush over the southeastern Tadjik Basin, Afghanistan; Figures 1, 2, and 4 were made using Evidence from two large earthquakes. Tectonics, 7,41–56. GMT (Wessel & Smith, 2013). Support Aki, K. (1966). Generation and propagation of G waves from the Niigata earthquake of June 16, 1964, 2, Estimation of the earthquake was provided by the University of moment, released energy, and stress‐strain drop from G wave spectrum. Bulletin of the Earthquake Research Institute Tokyo, 44,73–88. Montana and the Crafoord Foundation. Aki, K., & Richards, P. G. (1980). Quantitative Seismology: Theory and Methods, (p. 932). San Francisco: W. H. Freeman and Co. All data were taken from papers cited in Arrowsmith, J. R., & Strecker, M. R. (1999). Seismotectonic range‐front segmentation and mountain‐belt growth in the Pamir‐Alai region, the text. Kyrgyzstan (India‐Eurasia collision zone). Geological Society of America Bulletin, 111, 1,665–1,683.

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