Longevity of small-scale (‘baby’) plumes and their role in lithospheric break-up

results of a systematic parametrical analysis of relatively small thermal anomalies seeded at the base of the lithosphere. In particular, we explore the effects of variations in initial plume temperature ( T = 1500–1700 ◦ C) and size (diameter of 80–116 km), characteristics of the overlying lithosphere (e.g. ‘Cratonic’, ‘Variscan’, ‘Mesozoic’ and oceanic) and intraplate tectonic regimes (neutral or far-ﬁeld extension of 2–10 mm yr –1 ). In tectonically neutral regimes, the expected decay time of a seismically detectable ‘baby’-plume varies from ∼ 20 to > 200 Myr and is mainly controlled by its initial size and temperature, whereas the effect of variations in the thermotectonic age of the overlying lithosphere is modest. These small but enduring plumes are able to trigger localized rifting and subsequent continental break-up occurring from ∼ 10 to > 300 Myr after the onset of far-ﬁeld extension. Regardless of the thermomechanical structure of the lithosphere, relatively rapid (tens of Myr) break-up (observed in models with a hot plume and fast extension) favours partial melting of plume material. In contrast, in the case of a long-lasting (a few hundreds of Myr) pre-break-up phase (relatively cold plume, low extension rate), rifting is accompanied by modest decompressional melting of only ‘normal’ sublithospheric mantle. On the basis of the models presented, we distinguish two additional modes of continental rifting and break-up: (1) ‘semi-active’ when syn-break-up magmatism is carrying geochemical signatures of the deep mantle with deformation localized above the plume head not anymore connected by its tail to the original source of hot material and (2) ‘semi-passive’ when the site of ﬁnal lithospheric rupture is controlled by a thermal anomaly of plume origin but without invoking its syn-break-up melting. These intermediate mechanisms are applicable to several segments of the passive continental margins formed during Pangea fragmentation.


I N T RO D U C T I O N
Most studies devoted to the interaction of the Earth's lithosphere with mantle hotspots are traditionally focused on classic Morgantype plumes originating from the lower mantle (Morgan 1971). However, such 'primary' superplumes can stagnate beneath the 660 km phase change boundary and create numerous thermal perturbations in the upper mantle corresponding to so-called 'secondary' plumes (Courtillot et al. 2003). According to predictions by  and , mantle upwelling from the core-mantle boundary should develop plume heads of up to ∼2000 km in width after it flattens into a 'pancake' shape beneath the lithosphere (Stern et al. 2020), whereas the heads of plumes originating within the upper mantle would have a characteristic diameter of ∼600 km. Over the last decades a number of much smaller plumes with horizontal size of only ∼100-200 km ('baby' plumes) have been detected in the upper mantle below Europe (Granet et al. 1995;Ritter et al. 2001;Babuška et al. 2008) and China (Tang et al. 2014;Xia et al. 2016;Kuritani et al. 2017).
Despite the detected presence of these 'baby' plumes in various areas around the globe (Ritter 2007;Xia et al. 2016) and their potential importance for lithosphere break-up (Gac & Geoffroy 2009), a systematic and comprehensive quantitative analysis of their properties and impact on the overlying lithosphere has been lacking so far. The bulk of previous numerical and analogue modelling studies has explored consequences of plume-lithosphere interactions in very different tectonic settings, including rifting/continental breakup Burov & Gerya 2014;Koptev et al. 2015Koptev et al. , 2016Beniest et al. 2017aBeniest et al. , 2017b, subduction initiation (Burov & Cloetingh 2010;Gerya et al. 2015;Baes et al. 2020aBaes et al. , b, 2021Cloetingh et al. 2021) and microcontinental separation (Dubinin et al. 2018;Koptev et al. 2019;Neuharth et al. 2021). However, all these studies have till now focused on relatively large (>>100 km in the resulting horizontal size of the 'pancake'-shaped head) mantle plume anomalies.
Here we provide the first systematic analysis of small thermal anomalies ('baby' plumes). In our experiments 'baby' plumes are initially seeded just below the bottom of the lithosphere. In this respect, it is important to note that the source and emplacement mechanism of these small-scale thermal anomalies remains beyond the scope of our study. We intentionally focus on the consequences of the implementation of the 'baby' plumes rather than on the scenarios for their origin, thus enabling a broad interpretation and application of obtained modelling results. First, we explore the longevity of 'baby' plumes of different temperatures and sizes seeded underneath different types of overlying lithosphere (i.e. lithospheres of different thicknesses and different thermorheological structure). Subsequently, we investigate the impact of 'baby' plumes on location, timing and style (magmatic/amagmatic) of the break-up when the overlying lithosphere is subjected to external tectonic extension. In our study, we pay particular attention to the temporal evolution of the width of the thermal anomaly that permits us to test seismic detectability of the 'baby' plumes over the modelled time period.
Our results are not only relevant for small plume anomalies presently detected in Europe and China, but also important for possible scenarios for Pangea fragmentation complementing existing end-member views on 'active' and 'passive' rifting and break-up. In particular, we resolve apparent contradictions and disputes on non-plume and plume-driven break-up by introducing intermediate ('semi-active' and 'semi-passive') modes which could be viable mechanisms for the formation of several modern continental rifted margins.

B A C KG RO U N D
The origin of stresses in the lithosphere plays a key role in our understanding of geodynamic and geologic processes. Since the acceptance of continental drift (Holmes 1965) and plate tectonics (Wilson 1966) in the 1960s, three main sources have been recognized for plate motions and stresses in the lithosphere, including: (1) horizontal tractions at the base of the lithosphere arising from mantle convective flow ('basal drag'), (2) forces exerted by cold, dense oceanic plates sinking into the mantle at a subduction zone due to its own weight ('slab pull') and (3) lateral variations in the lithosphere's gravitational potential energy (topographic driving forces; e.g. 'ridge push'). These mechanisms have been thoroughly explored by global (Forsyth & Uyeda 1975;Harper 1975;Richardson et al. 1979;Conrad & Lithgow-Bertelloni 2002;Lithgow-Bertelloni & Guynn 2004;Bird et al. 2008;Koptev & Ershov 2010;Naliboff et al. 2012;Yang & Gurnis 2016) and regional (Wortel & Cloetingh 1985;Cloetingh & Wortel 1986;Richardson & Reding 1991;Coblentz & Richardson 1996;Flesch et al. 2001;Liu & Bird 2002;Reynolds et al. 2002;Burbidge 2004;Rajabi et al. 2017;Tunini et al. 2017) numerical modelling. Nevertheless, the driving mechanism of plate tectonics still remains controversial. In particular, the role of upwelling mantle flow in the dynamics of continental rifting and break-up systems (namely, 'active' versus 'passive' rifting) is a long-debated topic (e.g. Fitton 1983;Foulger et al. 2000;Foulger & Hamilton 2014). In the 'active' or plume-assisted scenario (Morgan 1971;Hill 1991), rifting occurs as a result of active mantle diapirs rising through the mantle when extension is imparted by (1) horizontal viscous forces caused by radial flow of the plume head below the lithosphere and (2) buoyancy forces associated with topographic uplift over a plume (Westaway 1993). On the contrary, the 'passive' scenario (McKenzie 1978) calls for the processes originating far away from the rifting zone when tensional far-field forces (e.g. remote pull of the subducting slab) are transmitted through the lithospheric plate causing its extension and thinning within a localized area, while upwelling of underlying mantle and associated decompressional melting are both a passive consequence of rifting-related stretching of the lithosphere.
This controversy between 'active' and 'passive' modes of rifting becomes even more critical when considering mechanisms of supercontinent break-up, a key component of the Earth's tectonic and geodynamic evolution (Wilson 1966;Bradley 2011;Yoshida & Santosh 2011). On the one hand, slab rollback is proven as a viable mechanism to induce extension in the overriding plate (e.g. Schellart & Moresi 2013;Holt et al. 2015;Yoshida 2017), whereby the dragging force from slab retreat in oceanic subduction zones surrounding a supercontinent (Collins 2003;Zhong et al. 2007) has been proposed as the main driving mechanism for its dispersal (Bercovici & Long 2014). On the other hand, extension caused by subduction retreat has been shown to be focused along the marginal zones only while having far less impact on the interior of the supercontinent (Zhang et al. 2018). According to this (Zhang et al. 2018) and other recent numerical models of global mantle convection (Huang et al. 2019;Dang et al. 2020), the main reason for supercontinent break-up resides in the push by the rise of mantle plumes from the subcontinental mantle (Li et al. 1999(Li et al. , 2008. Thick mid-Jurassic oceanic crust in the Atlantic and Indian oceans is also Downloaded from https://academic.oup.com/gji/article/227/1/439/6295312 by guest on 16 July 2021 indicative of hotter upper mantle underneath Pangea before the disintegration of this supercontinent (Lenardic 2017;Van Avendonk et al. 2017). As a step to reconcile these end-member views on the dominant force responsible for supercontinent dispersal it has been demonstrated that deeply subducting slabs might penetrate into the lower mantle and trigger upwelling and return flow that results in mantle superplumes (Zhang et al. 2010;Heron et al. 2015;Dal Zilio et al. 2018).
The timing and volume of rift-related magmatism are traditionally considered as a primary proxy for identification of the 'active' component associated with mantle plume upwelling (Şengör & Burke 1978). As has been noted for almost five decades (Scrutton 1973), continental break-up in different parts of the Pangea supercontinent was shortly preceded by intensive and massive magmatic events leading to the formation of so-called Large Igneous Provinces (LIPs). LIPs are large volumes of predominantly mafic rocks that distinguish themselves from magma generated by processes at plate boundaries (Coffin & Eldholm 1994;Bryan & Ernst 2008;Ernst 2014). Based on an assumption of a genetic link between voluminous magmatism and the upwelling of hot mantle material (e.g. Richards et al. 1989), plume impingement has been postulated as a pre-requisite for continental break-up and subsequent formation of major oceanic basins during Pangea dispersal (Courtillot et al. 1999). However, at the same time it was found that presumably 'active' break-up of Pangea accompanied by LIP emplacement is frequently preceded by long-lasting (up ∼200 Myr in the case of the North Atlantic) phases of almost amagmatic (and, therefore, 'passive') rifting (Ziegler & Cloetingh 2004, and references herein). Therefore, according to the classic interpretation by Şengör & Burke (1978), such a relative timing of rifting and volcanism (major rift formation predates magmatic activity) corresponds to a 'passive' scenario when extension is imparted by the horizontal movement of plates. Moreover, both location and orientation of the Pangea break-up axes frequently follow pre-existing orogenic sutures (Buiter & Torsvik 2014) which are mechanically weaker relative to the cratons surrounding them Ryan & Dewey 1997). These findings are complemented by suggestions on the presence of a sufficiently low (50-100 K) potential temperature anomaly beneath Iceland (Foulger & Anderson 2005), the region where a seismically detected Amaru 2007;Rickers et al. 2013) thermal plume rising from the deep mantle has been almost universally involved (e.g. Campbell & Davies 2006;Campbell 2007) to explain both massive magmatism (Saunders et al. 1997;Storey et al. 2007) and onshore and offshore topographic uplift (Rohrman et al. 1995;Rohrman & van der Beek 1996;Japsen & Chalmers 2000;Koptev et al. 2017) along the adjacent North Atlantic passive margins. The aforementioned contradictions to an idealized plume-impingement model inspire a fundamental reappraisal of the causes for (super)continental breakup and, in particular, their link to LIPs (Peace et al. 2020). This has fueled 'antiplume' conceptions and brought several authors to argue in favour of shallow tectonics (i.e. 'passive') mechanisms during break-up of different Pangea segments including those associated with LIPs and traditionally attributed to 'active' rifting mechanisms: break-up in North, Central and South Atlantic and in East and West Gondwana (Lundin & Doré 2005;Peace et al. 2020, and references herein).
However, all these 'antiplume'/'shallow tectonics' scenarios and views are in general at odds with findings from modern seismic tomography showing evidence for the widespread presence of low velocity anomalies extending down to the core-mantle boundary (Romanowicz & Gung 2002;Montelli et al. 2006;French & Romanowicz 2015;Davaille & Romanowicz 2020). In the proximity of these plumes mid-ocean ridges exhibit a greater overall content of volatiles and excess bathymetry (Gibson & Richards 2018). Moreover, the geochemistry of LIPs has demonstrated a major contribution of undepleted material derived from primitive, undegassed reservoirs located in the lowermost mantle (Jackson et al. 2010(Jackson et al. , 2017. Finally, the fact that LIPs occur close to final break-up (Buiter & Torsvik 2014), and are frequently preceded by long-lasting amagmatic phases of 'passive' rifting (Ziegler & Cloetingh 2004), cannot disprove a plume-triggered scenario when a mantle plume is emplaced below a lithosphere already extended over a wide area (Reemst & Cloetingh 2000) localizing distributed deformation in a narrow zone of break-up. By means of ultra-high resolution 3-D thermomechanical modelling, it has been shown that in the case of a combined 'active-passive' scenario initial impingement of a mantle plume can precede final break-up of the overlying lithosphere by up to 100 Myr under the condition of ultra-slow (halfrate of <3 mm yr -1 ) tectonic extension (Koptev et al. 2018a), thus reconciling documented evidence for syn-break-up magmatism of deep-mantle geochemical signatures and long-lasting prior phases of quasi-amagmatic rifting.
Much of the focus in the current discussion on the impact of mantle plumes and their role in (super)continental break-up and LIPs formation has been restricted to the classical plume concept when a large and continuous plume body rises through the entire mantle from the core-mantle boundary (Morgan 1971;Koppers et al. 2021). As originally discovered by Burke & Torsvik (2004) and subsequently confirmed by statistical analysis by Doubrovine et al. (2016), the sources of LIPs-related plumes are not randomly distributed over the core-mantle boundary but, in contrast, are preferentially localized along the edges of two large low shear wave velocity provinces (LLSVPs) located beneath Africa and the Pacific Oceanic and christened by Kevin Burke as 'TUZO' and 'JASON', respectively (Burke 2011). The plumes arising from LLSVP borders are thought to be triggered by subducted slabs sinking in the lowermost mantle . Alternatively, they could be just a result of the insulating thermal effect of LLSVPs making the conductive core-mantle heat transfer focused at their boundaries (Niu 2018). Regardless of the underlying mechanism, established correlations between reconstructed eruption sites of LIPs and kimberlites with LLSVP margins are in support of long-lived existence and fixed locations of LLSVPs during the last 200 Myr (Torsvik et al. 2006), 300 Myr (Torsvik et al. 2008) and possibly for the entire Phanerozoic (Torsvik et al. 2010 or even since early (>2 Ga) Earth history (Dziewonski et al. 2010;Burke 2011;Torsvik et al. 2016).
However, apart from this 'Burke Earth' end-member model  which is focused on first-order (or 'primary') hotspots originating from the deep mantle (Fig. 1a1), other types of plumes have been proposed (Courtillot et al. 2003). In particular, a 'primary' superplume stagnated at the base of, or within, the upper-lower mantle transition zone (MTZ: 410-660 km; Helffrich & Wood 2001) can create numerous thermal perturbations extending throughout the upper mantle, forming so-called 'secondary' plumes which can further generate or contribute to the shallow 'tertiary' hotspots ( Fig. 1a2). In contrast to the 'primary' and 'secondary' plumes continuously fed from below (whether from LLSVPs at the core-mantle boundary or from bunched plume material at 660 km depth), 'tertiary' hotspots are traditionally thought to have an exclusively superficial origin being linked to tensile stresses and cracking in the lithosphere and decompressional melting (Courtillot et al. 2003;Torsvik et al. 2016). In another end-member scenario (a1) 'Burke Earth' with only 'primary' plumes derived from margins of thermochemical piles (LLSVPs) at core-mantle boundary (Burke 2011); (a2) 'Courtillot Earth' with three types of 'primary', 'secondary' and 'tertiary' plumes (Courtillot et al. 2003); and (a3) 'Andersonian Earth' with only superficial 'tertiary' hotspots (Anderson 2000). Abbreviations: pBn, post-Bridgmentite; PGZ, plume generation zone; ULVZ, ultra-low velocity zone. (b) Upwelling of small-scale mantle plumes ('baby' plumes) below European lithosphere (from Granet et al. 1995). Insets are images from seismic tomography for French Massif Central (from Granet et al. 1995 corresponding to the so-called 'Andersonian Earth' (Anderson 2000) where any communication between the upper and lower mantle is excluded, these 'tertiary' hotspots become the only source of intraplate magmatism (Fig. 1a3). Numerous examples can be given for each category of mantle upwelling and associated thermal perturbations in the mantle (Courtillot et al. 2003). Interaction of 'primary' plumes with oceanic lithosphere is known to generate hotspot tracks characterized by the time progression of magmatism as a result of tectonic plates motion over large-scale columnar upwelling in the mantle (Wilson 1963;Morgan 1972;Steinberger et al. 2004;Doubrovine et al. 2012;Torsvik et al. 2017). Within continents, the sudden onset of continental flood volcanism over a large area of up to 10 6 km 2 attributed to melting of hot material from plume sources ) is usually manifested in tens of Myr after initial plume-related surface uplift (Rainbird & Ernst 2001) of ∼0.5-2 km (Griffiths et al. 1989;Farnetani & Richards 1994;Şengör 2001). This rapid, transient domal uplift above the plume axis is followed by subsidence (Burov & Cloetingh 2009;Friedrich et al. 2018;Gögüş 2020) due to flattening of the plume head below the base of the lithosphere (White & McKenzie 1989). The radial flow away from a plume's axis leads to a mushroom-like shape of the plume: a large disk-shaped head (∼1000 km in diameter) with a narrow long tail (Campbell & Davies 2006;Campbell 2007). Note that a symmetrical configuration might be complicated by preexisting zones of lithospheric thinning acting as sinks for a buoyant mantle plume (Sleep 1996(Sleep , 1997. The resulting long-distance (>1000 km) propagation of hot plume material along the elevated lithosphere-asthenosphere boundary is reflected in alkaline volcanism (Ebinger & Sleep 1998) and regional uplift (Koptev et al. 2017) in the areas remote from the point of initial plume impingement. Given this strong filter of mantle plume activity by thick continental lithosphere, evidence for hotspot chains within continents is seldom. The commonly cited example of the Yellowstone hotspot (Smith et al. 2009) demonstrates a time-progressive track in a direction that is not consistent with North American plate motion (Jordan et al. 2004;Meigs et al. 2009;Wagner et al. 2010). The first confirmed example of a continental hotspot track aligned with plate motion has been recently detected in the eastern United States, where a linear (∼200-250 km wide) seismic anomaly with reduced P-wave velocity in the lower lithosphere (Chu et al. 2013) has been formed as a result of the westward passage of the North American Plate (Cox & Arsdale 2002) over a 'primary', deep-sourced thermal mantle plume presently located beneath the Bermuda-Sargasso Sea region . Based on combined analysis of seismic tomography, uplift, volcanism and heat-flow data, three trajectories of separate hotspots have been also detected Downloaded from https://academic.oup.com/gji/article/227/1/439/6295312 by guest on 16 July 2021 below Arabia and the Horn of Africa (Vicente de Gouveia et al. 2018). In this case, however, these tracks correspond to distinct 'secondary' plumes (Afar, East-Africa and Lake-Victoria) originated from the same deep-sourced (super)plume which raised from LLSVPs but subsequently stagnated below the upper mantle transition zone at 660 km (Vicente de Gouveia et al. 2018). Similar 'secondary' structures have been detected in the upper mantle beneath Europe by seismologists during the last decades (Granet et al. 1995;Ritter et al. 2000Ritter et al. , 2001Plomerova et al. 2007;Babuška et al. 2008;Fig. 1b). Given that they are characterized by extremely small horizontal sizes of ∼100 km, these structures have been dubbed 'baby' plumes (Cloetingh & Ziegler 2009). Apart from their small size, the 'baby' plumes also have a relatively small seismic velocity contrast (< 3 per cent) with respect to the surrounding mantle and, therefore, their detection requires specifically designed seismological experiments on a regional and local scale (Ritter 2005). The origin of these small-scale thermal anomalies characterized by a modest excess of potential temperature of ∼150-200 • C remains controversial. Based on a global tomographic model, a deep magma source in the lower mantle has been proposed (Goes et al. 1999(Goes et al. , 2000. In contrast, the regional studies in the French Massif Central (Granet et al. 1995, Sobolev et al. 1997) and the Eifel volcanic fields of northwestern Germany (Ritter et al. 2000(Ritter et al. , 2001 provide evidence for the tail of a mantle plume extending only to a depth of 300-400 km, thus indicating their shallower origin from the MTZ. It should be noted, however, that the plume tails in the MTZ and deeper may not be visible in seismic tomography data because of their narrow width. The likely presence of plume conduits is indirectly confirmed by volcanic rocks and gases in these regions which often have the geochemical signatures of a deep source in the lower mantle (Hoernle et al. 1995;Buikin et al. 2005;Caracausi et al. 2016), although the interpretation of data is ambiguous (Lustrino & Carminati 2007). For the western Bohemian Massif, a low-velocity anomaly beneath the Tertiary Eger Rift system is confined to a depth of 250 km (Plomerová et al. 2007(Plomerová et al. , 2016Babuška et al. 2008;Koulakov et al. 2009). This anomaly and associated magmatism (Ulrych et al. 2011), therefore, could be attributed to the category of 'tertiary' hotspots which are presumably related to shallow tectonic processes and upwelling of the lithosphere-asthenosphere boundary. However, a possible link to deeper sources (and thus belonging to the category of 'secondary' plumes) is not to be excluded: the isolated bodies of thermal anomalies presently residing at shallow depths might only have lost their initial connection with the deep source of hot material either due to exhaustion of this source or just because of plate movement. In the latter case, the head of such 'secondary' plume has been attached to the bottom of the lithosphere and subjected to lateral shift with respect to the feeding channel in the sublithospheric mantle (i.e. plume tail).
More recently, seismological evidence for 'baby'-plume-like structures has been also obtained in the Western Pacific and adjacent areas of mainland China (Tang et al. 2014;Xia et al. 2016;Kuritani et al. 2017). In particular, a 'primary' plume with an extending columnar tail beneath southernmost China (Hainan Island area) appears to spread laterally within the MTZ, thus ponding at the level of the lower part of the upper mantle. This 'plume head' is seated deeper than 'normal' 'primary' plumes (which are usually flattened below the lithospheric bottom), and is further decomposed into smaller separate patches (Xia et al. 2016), identical to 'secondary' 'baby' plumes proposed by Granet et al. (1995) for the European region (compare Figs 1b and c). Similar finger-like upper mantle structures have been also detected below northeast China near the border between China and North Korea (Tang et al. 2014).
There, the ascent of the mantle plumes has been presumably caused by decompressional melting of nearly water-saturated material (socalled 'hydrous plumes'; Kuritani et al. 2017Kuritani et al. , 2019 in the MTZ (Fei et al. 2017;Fomin & Schiffer 2019;Long et al. 2019) where an excess of fluids is commonly attributed to subduction of oceanic fluid-rich plates and their subsequent accumulation at the 660 km discontinuity boundary (Hetényi et al. 2009;Kovács et al. 2020). Alternatively, widespread intraplate volcanism in northeast China above a stagnated Pacific slab has been explained by a return flow of sublithospheric mantle material entrained beneath the subducting plate and then escaped through a gap in the slab resulting in focused 'baby'-plume-like upwelling in the upper mantle (Tang et al. 2014). It is important to note that European 'baby' plumes are developed in conjunction with the Cenozoic rift system (Bourgeois et al. 2007) formed within a continental foreland on the subducting plate (Ziegler & Dèzes 2007). This indicates, therefore, that emplacement of small-scale mantle anomalies might occur in a broad spectrum of possible geodynamic settings across the subduction zone from foreland (Europe) to hinterland (China).
Another observation that is known since almost two decades, but so far not taken into consideration in the 'baby' plumes context, is that volcanic passive margins are frequently punctuated every 50-150 km by long-lived igneous centers (Geoffroy 2001;Fig. 1d1). These are related to large crustal magma chambers developed over mantle diapirs which have been interpreted as a consequence of small-scale convection cells at the level of the shallowest asthenosphere (Geoffroy 2005). In view of their small (∼100 km) characteristic size and moderate (∼150-200 K) temperature contrast it seem to be reasonable to consider the mantle diapirs described by Geoffroy (2001) as the equivalent of the 'baby' plumes discussed above. It is also noteworthy that despite the relatively shallow depth extent of these mantle diapirs, the question on the origin of such 'baby' plumes of 'tertiary' class remains open and a potential role of a deep mantle source in their establishment is feasible.
Despite their modest dimension and magnitude and regardless of the mechanism of their emplacement, thermal instabilities related to 'baby' plumes are known to have a pronounced expression not only in magmatism (Wilson & Downes 1992) and vertical surface motions (Guillou-Frottier et al. 2007;Fauquette et al. 2020;Kreemer et al. 2020) but also in the rheological structure of the overlying lithosphere (Garcia-Castellanos et al. 2000;Tesauro et al. 2009a, b). This appears to be also the case for asthenospheric diapiric instabilities emplaced in volcanic rifted margin settings (Geoffroy 2001). There, the thermal consequences of mantle diapirs (or 'baby' plumes as we call them here) lead to the development of the rheological soft-points which expectedly concentrate the regional extension around them. As shown by analogue (Callot et al. 2002) and numerical (Gac & Geoffroy 2009) modelling, initially isolated mantle soft points produce not only simultaneous localized extension over them but also, given their narrow spacing, interconnect zones of localized stretching ultimately leading to continental break-up and volcanic passive margin formation (Fig. 1d2).
Below two fundamental aspects are central. The first principal question concerns the preservation in time of the plumes of different scales after their emplacement. Because of long-term stability of LLSVPs (from 200 Myr to >2 Gyr; see Burke 2011;Torsvik et al. 2016), 'primary' large-scale plumes can be preserved and remain seismologically detectable during hundreds of Myr. 'Primary' plumes of intermediate size potentially resulting in 'hidden' hotspot tracks (as, for example, detected in the eastern USA by a few hundred km wide corridor of low seismic velocities in the lithospheric mantle, see Chu et al. 2013) can survive more than 100 Myr according to thermochemical numerical models by Yang & Leng (2014).
In contrast, small-scale mantle anomalies of 'secondary'/'tertiary' category are known to produce no hotspot tracks associated with the volcanism (e.g. Ritter et al. 2000Ritter et al. , 2001 and the life span of these 'baby' plumes is still an open question. Although seismological evidence apparently underpins their existence, it remains unclear whether these tomographic snapshots are related to very recent emplacement or whether these 'baby' plumes have a life span long enough to still allow their detection for tens of million years or even longer after impingement. The second key question concerns the consequences of the small and isolated thermal anomalies for break-up tectonics (Gac & Geoffroy 2009). Important is in this context also their potential link to large-scale tectonic processes related to supercontinental fragmentation.

Code description
The numerical experiments presented here were conducted with a 2-D version of the thermomechanical viscous-plastic code I3ELVIS (Gerya & Yuen 2007;Gerya 2010) that solves Stokes flow and heat conservation equations using finite-differences combined with a marker-in-cell technique. In this numerical scheme, physical properties are transported by Lagrangian markers that move according to the velocity field interpolated from the fixed fully staggered Eulerian grid.
The Stokes flow approximation is given by conservation of momentum: and conservation of mass which is ensured by the incompressible continuity equation: where η is the material viscosity, ν is the velocity field, P is the pressure, ρ is the density and g is the gravity acceleration (9.8 m × s −2 ). The mechanical equations are coupled to the heat conservation equation that takes the following form: where T is the temperature, c p is the heat capacity, k is the thermal conductivity and H r is the radiogenic heat production ( Table 1). The code uses non-Newtonian viscoplastic rheologies (Burov 2011) where the viscosity for dislocation creep (η cr eep ) is defined as follow (Karato & Wu 1993;Ranalli 1995;Ershov & Stephenson 2006): whereε II = 1/2ε i jεi j is the second invariant of the strain rate tensor and A D , E, V , n and R are the pre-exponential constant, the activation energy, the activation volume, the stress exponent, and the gas constant (8.314 J × K −1 × mol −1 ), respectively (see also  Table 1). Different ductile flow law mechanisms such as diffusion (Karato 1986), grain boundary sliding (Précigout et al. 2007) and Peierls (Karato 2008) creep are neglected. In order to combine the ductile rheology with a brittle rheology, the Mohr-Coulomb yield criterion (Ranalli 1995) is implemented  Mantle density and heat capacity are computed as function of pressure and temperature using the Perple X algorithm (Connolly 2005) with the thermodynamic database taken from Holland & Powell (1998, revised 2002) and the LOSIMAG composition by Hart & Zindler (1986). For the crustal rocks, heat capacity c whereas density is calculated from Boussinesq approximation: MPa −1 is adiabatic compressibility, and ρ 0 is reference density (at P 0 = 0.1 MPa and T 0 = 298 K) which is taken as 2700 and 3000 kg × m −3 for upper and lower crust, respectively. Basaltic oceanic crust is modelled with the same material properties as mafic lower continental crust. Downloaded from https://academic.oup.com/gji/article/227/1/439/6295312 by guest on 16 July 2021 by limiting creep viscosity (η creep ) as follows: with the plastic strength (σ yield ) determined as: where C and ϕ are the residual rock strength and the internal frictional angle that decrease with increasing values of total strain due to linear strain softening (Huismans & Beaumont 2002;Brune & Autin 2013): where ε is the second invariant of strain and C 0 , C 1 , b 0 , b 1 , ε 0 and ε 1 are softening parameters (maximal and minimal cohesion, sines of frictional angle and strains, respectively) provided in Table 1.
For a detailed description of the code we refer to Gerya & Yuen (2007) and Gerya (2010).

Model design
The model setup encompasses an area of 1500 km in length and 400 km in depth. The regular rectangular grid contains 430 × 115 nodes, resulting in a spatial resolution of ∼3.5 km in each direction.
This study incorporates two groups of kinematic boundary conditions: (1) a tectonically neutral regime with free slip commonly adopted for all border elements and (2) a regime of tectonic extension when a constant, time-independent extensional tectonic forcing is applied along the entire length of the vertical sides of the model domain with a half-rate (V ext ) varying from 2 mm × yr −1 to 10 mm × yr −1 . In the latter group of experiments, compensating vertical velocities are introduced along the upper and lower model boundaries in order to ensure mass conservation within the model box.
In all simulations, the uppermost part of the model consists of a 30-km-thick layer of low-viscosity (10 18 Pa × s) and low-density (1.0 kg × m −3 ) 'sticky air' (Fig. 2) allowing to approximate the upper surface of the crust as a free surface (Duretz et al. 2011;Crameri et al. 2012).
The internal model structure corresponds to a laterally homogenous crust and mantle lithosphere overlying the sublithospheric (asthenospheric) mantle. We test four types of lithosphere: three continental of different thermotectonic ages ('Cratonic', 'Variscan' and 'Mesozoic') and one oceanic (∼40 Myr old). For this purpose, we vary the thickness and composition of the crustal layers, and the depth of the lithosphere-asthenosphere boundary (LAB). In the 'continental' experiments, the crustal thickness has a constant value of 36 km (equally divided into upper and lower crust), whereas the LAB depth changes from 250 km ('Cratonic' lithosphere; Regardless the type and thickness of the overlying lithosphere, the mantle plume is always seeded by a circular-shaped temperature anomaly within the asthenospheric mantle maintaining 10 km distance between the LAB and the uppermost point of this anomaly . Together with the applied velocity of far-field extension (V ext ) and lithospheric type, the initial diameter (d init : 80, 100 or 116 km) and initial temperature (T init : 1500, 1600 or 1700 • C) of the mantle plume represent the key variable parameters of our study (see Section 3.3 and Table 2). The range of tested initial temperatures is adopted following previous studies indicating that plume excess temperatures in the upper mantle vary between 200 and 350 • C (e.g. Schilling 1991;White & McKenzie 1995;Thompson & Gibson 2000;Herzberg & Gazel 2009). Note that modelled mantle plumes are assumed to be purely thermal, that is without compositional buoyancy component commonly attributed to so-called 'thermal-chemical' plumes (e.g. Dobretsov et al. 2008;Sobolev et al. 2011;Baes et al. 2016).
We use a felsic composition described by a wet quartzite rheology for the upper crust in all 'continental' models  and for the lower crust of 'Variscan' and 'Mesozoic' lithospheres (Figs 2b and c). In contrast, a mafic composition and rheology (plagioclase flow law) is adopted for the lower crust of the 'Cratonic' lithosphere ( Fig. 2a). The basaltic crust of the oceanic lithosphere ( Fig. 2d) is assumed to have the same properties as mafic lower continental crust. Both lithospheric and sublithospheric mantle are approximated by an ultra-mafic composition with the rheology of dry olivine, whereas the mantle plume is supposed to be slightly 'moist' with a wet olivine rheology (Table 1).
The initial temperature distribution within the continental lithosphere is approximated by a nonlinear steady-state geotherm defined by temperatures of 0 and 1300 • C at the top of the upper crust (depth of 0 km) and the bottom of the lithosphere (depth of 125, 150 or 250 km depending on the type of lithosphere-see above) while taking into account heat production in the upper and lower crust and lithospheric mantle (Table 1; Figs 2a-c). For the oceanic lithosphere, the initial temperatures are computed using a semi-infinite half-space cooling model (Turcotte & Schubert 2002) for the adopted age of ∼40 Myr (Fig. 2d). In all experiments, the sublithosphere geotherm is defined by an adiabatic thermal gradient of 0.3 • C km −1 (Sleep 2003). As thermal boundary conditions, we apply a constant temperature at the upper surface of the model domain, a constant conductive heat flux at the model bottom, and thermally insulating (zero conductive heat flux) vertical sides.

Modelling procedure
In total, we performed numerical calculations for a set of 42 models by varying four controlling parameters (Table 2): (1) initial temperature (T init ) and (2) diameter (d init ) of the mantle plume; (3) type of lithosphere and (4) half-rate of applied tectonic extension (V ext ).
The first group of the experiments (models 1-18) is characterized by a tectonically neutral regime (V ext : 0 mm × yr −1 ; see Section 4.1).
Here we start with a series of models where the mantle plume of different initial temperatures (T init : 1500, 1600 or 1700 • C) and sizes (d init : 80, 100 or 116 km) is seeded below 'Variscan' continental lithosphere (models 1-9; Section 4.1.1). Subsequently, we test various types of overlying lithosphere (models 10-18; Section 4.1.2)-'Cratonic' (models 10-12), 'Mesozoic' (models 13-15) and oceanic (models 16-18)-with the plume of different temperatures (T init : 1500, 1600 or 1700 • C) but of constant diameter (d init : 100 km). For the tectonically neutral thermomechanical simulations, we have additionally performed their thermal model analogues that exclude a kinematic component aiming to determine the purely thermal effect of the seeded anomaly. The time span of all models with a tectonically neutral regime is 300 Myr.

Tectonically neutral regime (Models 1-18)
4.1.1 Effect of initial plume temperature and diameter (models 1-9) As mentioned above, we start our modelling with a series of experiments aimed to explore the variations in initial temperature (T init ) and size (d init ) of the circular thermal anomaly (mantle plume) seeded underneath unstressed (V ext : 0 mm × yr −1 ) 'Variscan' continental lithosphere.
In the case of an intermediate plume temperature (model 2; T init : 1600 • C), vertical and horizontal movement of the plume body results in the configuration dubbed an 'inverted pear' (Figs 3a and 4b1). Limited buoyancy contrasts in the experiment with the lowest plume temperature (model 1; T init : 1500 • C) prohibit almost any motion in the compositional field making indistinguishable the modifications in the circular shape of the original mantle plume which keeps its initial configuration throughout the entire modelling time interval (Figs 4a1 and A1a). The plume material of the hottest thermal anomaly (model 3; T init : 1700 • C) first flows upwards and then spreads laterally below the LAB (Figs 4c1 and A2a). As a result, the plume body changes its shape from an original circular (Fig. 2b) into a heart-like configuration ( Fig. A2a; time slice of 15 Myr). Subsequently, the latter evolves into a quasi-elliptical form with an aspect ratio of vertical height (d ver ) to horizontal length (d hor ) of ∼1:2 (Figs 4c1 and A2a; time slices of ≥60 Myr). Note that in both models 2 and 3, the final figure of the plume is established at Downloaded from https://academic.oup.com/gji/article/227/1/439/6295312 by guest on 16 July 2021 ∼50-60 Myr after model onset without subsequent changes (Figs 3a and A2a). The presence of the thermal anomaly seeded just below the lithospheric bottom leads to upward deflection of the 1300 • C isotherm by several tens of km (e.g. model 2; Fig. 3b) This deflection not only remains discernible over the whole time span of all models (including the experiment with the 'cold' mantle plume-see model 1 in Figs 4a2 and A1b) but also appears to be more pronounced (in terms of both width and amplitude; Figs 4c2 and A2b) when the plume is 'hot' (model 3; T init : 1700 • C). In the latter case a stronger thermal impact is accompanied by a mechanical component of the vertical uplift combined with horizontal propagation of the plume material underneath the lithosphere (Figs 4c1 and A2a).
However, regardless the adopted initial temperature T init the mantle plumes themselves become almost invisible in the temperature fields (T ) after several tens to 100 Myr (see Figs 3b, A1b and A2b). In order to illustrate in more detail the evolution of explored plumerelated thermal anomalies, we compute the temperature contrast ( T ) defined as the difference between the current temperature in the corresponding grid node and the temperature from the nearedge column taken at the same vertical level. Distributions of the temperature contrast ( T ) are calculated for each time step (see 2) Maximum horizontal extent or width (w x ) of the area (A x ) characterized by a temperature contrast ( T ) higher than a predefined threshold value (x). We present here w x estimated for A x corresponding to x = 300, 200, 100, 75 and 50 • C (i.e. w 300 , w 200 , w 100 , w 75 and w 50 , respectively). Examples of areas A x defined for various x as well as corresponding w x are illustrated in Fig. 3c; 3) Temperature contrast integral ( T int x ) taken over the area A x (see above) as follow: As mentioned above, the initial maximum temperature contrast ( T max at 0 Myr or T init ) varies from of ∼200 to ∼400 • C depending on the initial plume temperature (T init ). In all experiments, T max decreases quickly during the first ∼50-100 Myr after that cooling slows down (Fig. 5, upper row). Although all curves of T max look at first sight similar, the time points when they descent below the reference temperature values (e.g. 200, 100 or 75 • C) appear to vary over a wide range from one experiment to another. In particular, the difference in the timing of cooling below 100 • C between 'cold' plume model 1 (T init : 1500 • C) and 'hot' plume model 3 (T init : 1700 • C) is exceeding 100 Myr. The temporal evolution of w 100 (horizontal width of the plume segment where T max remains higher than 100 • C) also significantly differs within these models (Fig. 5, middle row). The 'cold' model 1 shows a quick decrease of w 100 in a quasi-parabolic manner from initial 100 km (at 0 Myr) to 0 km at ∼55 Myr. On the contrary, w 100 of the 'warm' experiment (model 2) remains close to the original value of 100 km over the first ∼60 Myr before its parabolic drop to zero during the following ∼65 Myr. As mentioned above, the 'hot' plume anomaly (model 3; T init : 1700 • C) flattens below the LAB thus subjecting the originally circular plume to significant horizontal stretching (Fig. 4c1). As a result, at the early stage of evolution w 100 becomes wider than its initial value of 100 km reaching ∼150 km at ∼20-60 Myr whereas its subsequent quasi-parabolic descent lasts more than a hundred Myr (∼130 Myr, i.e. >2 time longer than in models 1 and 2) ending at ∼190 Myr. Given that a temperature contrast of 100 • C is close to the minimum T value detectable by seismic tomography imaging (e.g. Cammarano et al. 2003), we exploit w 100 to identify quantitatively the moment in time when the plume evolution enters into the terminal phase. For this purpose, we introduce a new parameter t(w 50 100 ) which refers to the time point when w 100 subsides below 50 km (i.e. half of original w 100 ; Fig. 5b2), thus approaching the resolution limit of modern seismic tomography (e.g. Rickers et al. 2013;Plomerová et al. 2016). While t(w 50 100 ) characterizes a 'decay time' of the thermal anomaly, a plume 'lifespan' corresponds to the time period between model onset (0 Myr) and t(w 50 100 ). Despite the extremely small size (d init : 100 km) of the 'baby' plumes explored here, their lifespan appears to cover long time intervals varying from ∼40 Myr (model 1; T init : 1500 • C) through ∼110 Myr (model 2; T init : 1600 • C) to ∼170 Myr (model 3; T init : 1700 • C).
Graphs of integrated temperature contrasts ( T int x ) for the models 1-3 are summarized in the lower row of Fig. 5. The quasiparabolic reduction of each T int x during the first ∼20-30 Myr is faster than their subsequent quasi-linear decrease. Expectedly, the steepness of both non-linear and linear trends of T int x evolution is mainly controlled by the T threshold limit (i.e. x) which defines integrating area A x for each T int x (see above): higher x values result in a steeper decrease of T int x . On the contrary, the initial value of T int x (i.e. T int x at 0 Myr) is independent from x because an original A x coincides with the circular area of the imposed thermal anomaly for all tested T threshold limits (i.e. x) that are lower than T init (i.e. T max at 0 Myr). Thus, the initial T int x in the model 1 (T init : 1500 • C) is ∼1.2 × 10 12 • C × m 2 for all x ≤ 100 • C (see grey star in Fig. 5a3). This initial T int x corresponds to an integrated value of plume buoyancy of ∼1.2 × 10 11 kg × m −1 . In the models 2 (T init : 1600 • C) and 3 (T init : 1700 • C), T int x for x = 100 • C (i.e. T int 100 ) decreases to the same value (∼1.2 × 10 12 • C × m 2 ) at ∼35 and ∼95 Myr, respectively (see grey stars in Figs 5b3 and c3). Note also that the values of w 100 corresponding to these time points (∼35 and ∼95 Myr) in these experiments (models 2 and 3) are close to or even slightly exceed the initial d init of 100 km. Therefore, it appears that the evolution of 'warm' (model 2; T init : 1600 • C) and 'hot' (model 3; T init : 1700 • C) mantle plumes is characterized by time intervals of tens to 100 Myr when the sum temperature excess concentrated within the area of a seismically detectable thermal anomaly ( T >100 • C; w 100 ≥100 km) remains higher or roughly equal to the original (i.e. at 0 Myr) temperature contrast integrated over the surface of a 'cold' mantle plume (model 1; T init : 1500 • C).
In order to investigate the role of initial plume size we performed the models with different d init : 80 km (models 4-6) and 116 km (models 7-9). The values of 80 and 116 km are chosen to ensure that variations in the initial plume area are by a factor of ∼2 between the smallest and largest end-members: given that A = π d 2 4 , A(T init = 116 km) ≈ 2×A(T init = 80 km) because 116 2 ≈ 2 × 80 2 .
For intermediate temperature (T init : 1600 • C), variations in the initial diameter (d init : 80, 100 or 116 km) of the plume anomaly appear to have a similar effect to that of initial temperature changes (T init : 1500, 1600 or 1700 • C) in the 'standard' diameter (d init : 100 km) models (compare Figs 5 and 6). A plume with a reduced initial diameter (d init : 80 km) starts to decay ∼55 Myr earlier (at (2) maximum horizontal width of the area A x (w x ; middle row) and (3) temperature contrast integrated over the area A x ( T int x ; lower row). A x is the area where T is higher than a threshold limit x. The values of x vary from 300 to 50 • C. Grey stars mark the value of T int 100 corresponding to the initial value of T int x in the model 1 (∼1.2 × 10 12 • C × m 2 ). * Other experimental parameters: d init : 100 km; type of lithosphere: 'Variscan'; V ext : 0 mm × yr −1 . lifespan of the plume by ∼50 Myr up to ∼160 Myr (Fig. 6c2). Note, however, that the total range of t(w 50 100 ) resulting from temperature variations (T init : 1500, 1600 or 1700 • C) for a standard diameter (d init : 100 km) is wider than that caused by diameter changes for intermediate temperature (T init : 1600 • C): ∼130 (∼170-40) Myr and ∼105 (∼160-55) Myr, respectively.
The minimum plume lifespan (t(w 50 100 ) of ∼20 Myr) is detected in the model 4 with the minimum initial temperature (T init : 1500 • C) and diameter (d init : 80 km) whereas the maximum plume size (d init : 116 km) combined in the model 9 with the hottest temperature (T init : 1700 • C) leads to >10 times longer (t(w 50 100 ) of ∼245 Myr) life expectancy (see Figs A3 and A4, respectively).
The end-member model 9 (T init : 1700 • C; d init : 116 km) is characterized by the most pronounced 'mechanical' component expressed in vertical and horizontal movements of the plume material leading to significant changes in the configuration of an initially circular plume body (see also model 3 in Fig. 4c1). Fig. 7 illustrates the differences in the evolution of temperature (T ) and temperature contrast ( T ) fields for the thermomechanical model 9 (Fig. 7a) and its purely thermal analogue (Fig. 7b). While the plume anomaly of the thermal model remains symmetrical in both directions, in the thermomechanical case it takes the shape of an ellipse stretched horizontally. As a result, the plume-related upward deflection of the LAB (corresponding to uplift of the 1300 • C isotherm) becomes significantly wider in the thermomechanical model during the first tens to 100 Myr while this difference in 'thermomechanical' and 'thermal' LAB configurations recedes over the final stage (>200 Myr) of system evolution (compare Figs 7a and b).
During the first ∼100-150 Myr the immovable circular plume of the thermal model cools slower than its thermomechanical counterpart: the maximum temperature contrast ( T max ) descends below 300 and 200 • C at ∼45 and ∼95 Myr only (Fig. 8b1), that is ∼25-30 Myr later than in the thermomechanical experiment (Fig. 8a1). At the same time, lateral displacements allowed in the thermomechanical model favour a rapid increase in all examined w x from w 300 to w 50 during the first 15-30 Myr (Fig. 8a2). This is in striking contrast to the thermal model where w 300 and w 200 start to decrease immediately after model onset while growth in w 100 , w 75 and w 50 is of more moderate magnitudes (Fig. 8b2). In particular, w 100 of the thermomechanical model reaches the maximum value of ∼200 km (at ∼25-65 Myr) whereas its thermal counterpart hardly exceeds ∼130 km. Moreover, the value of 'thermomechanical' w 100 remains higher than that of the 'thermal' one over the entire time interval when T max exceeds 100 • C (∼255 Myr in the thermomechanical case; Fig. 8a1). Therefore, the plume lifespan (defined as t(w 50 100 )) is paradoxically shorter (∼235 Myr) in the thermal version of model 9 (Fig. 8b2) than in its thermomechanical analogue (∼245 Myr; Fig. 8a2) which, at first sight, seems to be faster-cooled (compare Figs 8a1 and b1). Note also that in both thermomechanical and thermal versions of the model 9 the value of T int 100 becomes lower than ∼1.2 × 10 12 • C × m 2 (initial T int x in the model 1; Fig. 5a3) after 150 Myr only (see grey stars in Figs 8a3 and b3).
In general, models 1-9 show that plume life expectancy (or lifespan)-time period t(w 50 100 ) when the thermal anomaly is seismically detectable ( T >100 • C; w 100 ≥50 km)-is mainly controlled by initial temperature contrasts (initial T int x ) integrated over the surface of the imposed thermal anomaly (Fig. 9). In most cases, values of t(w 50 100 ) in the thermomechanical model and its purely thermal analogues coincide: only two experiments with a plume of large size (d init : 116 km) and intermediate (T init : 1600 • C) to hot (T init : 1700 • C) temperatures (models 8-9) demonstrate a ∼10 Myr delay of the decay time in the thermomechanical model version (see red stars in Fig. 9). A detailed explanation of this phenomenon is given above based on an examination of the end-member case of the model 9 (see also Figs 7 and 8). Interestingly, t(w 50 100 ) defined in thermal models can be approximated by linear functions of initial T int x for each d init (see blue, green, and red lines in Fig. 9 corresponding to d init of 80, 100 and 116 km, respectively). The vertical shifts by ∼10 Myr between neighboring lines indicate that for the same amount of integrated temperature excess plume bodies of smaller size will have longer lifespans in comparison with their larger counterparts.

Effect of the lithospheric type (models 10-18)
In order to explore the consequences of different types of overlying lithosphere, we present the three following groups of experiments characterized by (1)  In these models, we also vary initial plume temperature (T init : 1500, 1600, or 1700 • C) while keeping its diameter constant (d init : 100 km). Fig. 10. summarizes the results for thermomechanical models (Fig. 10a) and their thermal analogues (Fig. 10b) for an unchanged initial temperature of the plume (T init : 1600 • C) but different types of overlying lithosphere corresponding to the four configurations tested in our study ('Cratonic', 'Variscan', 'Mesozoic' and oceanic: models 11, 2, 14 and 17, respectively). In contrast to parameters characterizing the plume itself (initial temperature and diameter; see Section 4.1.1), the type of lithosphere appears to have a much more limited impact on the evolution of w x (horizontal width of the plume sector with T max > x, where x varies from 200 to 50 • C). In fact, w x variations in the thermal versions of the models are almost visually undistinguishable (Fig. 10b): 'Cratonic' (model 11) and oceanic (model 17) end-members give a relatively small total difference (∼15 Myr) in the plume lifespans (i.e. t(w 50 100 )) expected in these models. On the contrary, thermomechanical experiments with 'Mesozoic' (Fig. 10a2) and oceanic (Fig. 10a1) lithosphere differ by an abrupt (i.e. during the first ∼10-20 Myr) increase of w 100 up to ∼130 and ∼210 km, respectively (resulting from a kinematic effect related to lateral spreading of the plume material below the lithosphere-see above, Section 4.1.1). In the case of oceanic lithosphere (model 17), fast growth in w 100 quickly doubling its initial value of 100 km is followed by an almost equally rapid drop leading to a 'premature death' of the plume: its lifespan t(w 50 100 ) of ∼65 Myr appears to be significantly shorter (by ∼35-50 Myr) than in other thermomechanical and thermal experiments presented in Fig. 10 (∼100 . This shortening of the plume life span in the thermomechanical model is due to faster heat exchange of the moving plume body in comparison to purely diffuse cooling in the thermal model. Note, however, that under specific conditions ('Variscan' lithosphere, d init of 100 km) a 'thermomechanical' plume could be, in contrast, formally 'longer-lived' than its fixed and, therefore, slower-cooled 'thermal' counterpart (see models 8 and 9 in Figs 8 and 9). As mentioned above (Section 4.1.1), this counter-intuitive phenomenon is related to initial mechanical widening of w 100 that increases decay time t(w 50 100 ) thus paradoxically slightly (by ∼10 Myr) extending the apparent life-span of a 'thermomechanical' plume (which remains, however, 'faster-cooled' in terms of initial speed of T max descent below 300 and 200 • C; see Fig. 8). Given that plume anomalies in all experiments shown in Fig. 10 have the same initial temperature and size (and, therefore, similar values for their buoyancies), variations in their mechanical behaviour (i.e. immovable circle under 'Cratonic' lithosphere versus uplift and horizontal stretching below an oceanic lithosphere) should be controlled by the differences in viscosity of the surrounding sublithospheric mantle. In order to characterize quantitatively the relation between buoyancy of the plume and viscosity of the asthenosphere, we use a simplified approximation of the Rayleigh number analogue (d' Acremont et al. 2003;Burov & Guillou-Frottier 2005) for the plume seeded underneath the lithosphere: where g is the gravity acceleration (9.8 m × s −2 ), d is initial plume diameter (d init : 100 km), A ρd A is the density contrast ρ between plume material and its surroundings integrated over the initial plume surface A (both plume and non-plume mantle density are calculated from thermodynamic model Perple X by Connolly 2005), χ is thermal diffusivity of the mantle (10 −6 m 2 × s), and η is viscosity of the sublithospheric mantle defined as a function of pressure and temperature (Section 3.1, eq. 4) and, therefore, characterized by increased values in the models with thicker lithosphere because it gives higher lithostatic pressure within the asthenospheric zone of roughly equal temperatures. Analysis of R a estimated for different initial plume temperatures (T init : 1500, 1600 or 1700 • C; see blue, green, and red curves in the graph of Fig. 11a, respectively) seeded below different types of the lithosphere ('Cratonic', 'Variscan', 'Mesozoic' and oceanic; the horizontal axis of the graph in Fig. 11a) shows that the kinematic behaviour of the system (see compositional fields at the time slice of 15 Myr in Fig. 11b) actually depends on the relation between buoyancy of the plume and viscosity of the mantle under the lithosphere. Low values of R a (< 20; blue dashed ellipse in Fig. 11a) correspond to a minimum (almost negligible) mechanical component in the system evolution resulting in the circular (unchanged; models 1 and 10-13) to inverted pear (slightly deformed; model 2) plume configuration (see plots bounded by blue polygon in Fig. 11b). On the contrary, intermediate buoyancy/viscosity relations (15 < R a < 25; green dashed ellipse in Fig. 11a) lead to a heart-like plume shape (models 3, 14 and 16; green polygon in Fig. 11b) while elevated ones (R a > 25; red dashed ellipse in Fig. 11a) favour its further transformation with establishment of a horizontally stretched ellipse (red polygon in Fig. 11b) characterized by aspect ratios varying from ∼1/3 (model 15) through ∼1/4 (model 17) to ∼1/5-1/6 (model 18). Thus, it appears that a relatively high viscosity of subcratonic asthenosphere (i.e. mantle under 'Cratonic' lithosphere) always prevents any motions of the plume body (Fig. 11b, low row) even in the case of the hottest (and, therefore, the most buoyant) plume anomaly (T init : 1700 • C; model 12). At the same time, regardless the type of overlying plate and, therefore, viscosity of the sublithospheric mantle, a low buoyancy contrast in the models with a cold plume anomaly (T init : 1500 • C) in all cases produces very limited intra-plume deformation as well (Fig. 11b, right-hand column). Only specific parameter combinations corresponding to the highest values of R a -that is warm to hot thermal anomaly (T init : 1600-1700 • C) placed under sufficiently thin overlying lithosphere ('Mesozoic' or oceanic)allow for significant mechanical movements of the mantle plume mass associated with its stretching and spreading below the Figure 9. Models 1-9 (T init : 1500-1700 • C; d init : 80-116 km; type of lithosphere: 'Variscan'; V ext : 0 mm × yr −1 ): plume lifespan t(w 50 100 ) as a function of initial T int x . Blue, green, and red colours correspond to d init of 80, 100 and 116 km, respectively. Values obtained in thermal models are shown by circles whereas these from thermomechanical experiments (when different) are indicated by stars. Star-shaped hole inside the circle means that the value of t(w 50 100 ) for the corresponding thermomechanical experiment is different. LAB (Fig. 11b, top right-hand corner). It is also noteworthy that in all cases the system behavior is controlled by the total thermal thickness of the overlying lithosphere (Artemieva 2006;Koptev & Ershov 2011), whereas its internal rheological stratification (Burov 2011) is irrelevant.
As mentioned above, faster cooling in the thermomechanical model 17 (T init : 1600 • C; oceanic lithosphere) than in its thermal analogue leads to a significant difference (∼50 Myr) in expected plume life spans: 'thermal' t(w 50 100 ) reaches ∼115 Myr whereas t(w 50 100 ) in the thermomechanical version is ∼65 Myr only (see green star in Fig. 12). In two other models characterized by high values of R a (models 15 and 18) 'thermomechanical' t(w 50 100 ) is also reduced by ∼30 and ∼100 Myr, respectively (see red stars in Fig. 12). Apart from these advection-related deviations, in the experiments with the same initial plume temperature (T init ) the life span t(w 50 100 ) varies within a relatively narrow time interval of <30 Myr (Fig. 12). This means that in general (i.e. excluding particular cases of the highest R a ) the type of overlying lithosphere appears to have only limited impact on the system evolution in comparison to variations in initial plume temperature and size (Section 4.1.1).
The temporal evolution of the model 20 (T init : 1600 • C; V ext : 2 mm × yr −1 ) is presented in Fig. 13. In contrast to the corresponding experiment with a neutral tectonic regime (V ext : 0 mm × yr −1 ;  model 2) where the inverted pear shape of the plume does not change after ∼60 Myr (see Fig. 3), slow and constant extension applied in model 20 leads to permanent stretching of the plume body attached to the bottom of the tectonically extending lithosphere. At the final stages of the experiment the plume 'pancake' width reaches values of ∼400-500 km (Fig.13a). Brittle deformation at the crustal level which is equally distributed over the entire model domain at ∼90 Myr becomes more concentrated within the area overlying the mantle plume at ∼165 Myr to be subsequently transformed into a narrow zone of localized lithospheric thinning at ∼195 Myr (Fig.  13c). Continental break-up occurs soon after (i.e. ∼15 Myr later) at ∼210 Myr (Fig. 13a). Note that at the final stage of lithospheric rupture the asthenosphere below the break-up axis is subjected to partial melting whereas plume material attached to the LAB at both sides of the broken lithosphere remains unmelted (Fig. 13a).
The models with the same extension velocity (V ext : 2 mm × yr −1 ) but different initial temperatures of the plume (T init : 1500 and 1700 • C; Figs A8  In contrast to models with a tectonically neutral regime demonstrating an inexorable fading of the thermal anomaly with time, in the models with applied tectonic extension an initial decrease of T max (maximum temperature contrast with respect to 'standard' near-edge column; see Section 4.1.1) is followed by its accelerating growth (Figs A10-A12) due to localized uplift of plume material and/or underlying asthenosphere through the lithospheric mantle in the central part of the modelling area (Figs 13a, b and 14b). This raise in T max lasts until break-up during the time period varying from ∼100 to 170 Myr in the experiments with V ext of 2 mm × yr −1 (models 19-21) to ∼20-70 Myr when V ext is 3 mm × yr −1 (models 22-24). Higher values of V ext (4, 5 and 10 mm × yr −1 ) result in shorter pre-break-up phases (∼10-40 Myr) sometimes initiated immediately after onset of the experiments (i.e. without initial cooling stage when T max decreases). Note also that the 'pre-break-up phase' of growing T max is also characterized by a quick increase of w x and T int x (Figs A10-A12). Importantly, in the case of the coldest plume (T init : 1500 • C) and slowest extension (V ext : 2 mm × yr −1 ) the initial cooling stage is characterized by a w 100 that is less than 50 km during the time interval of ∼60-110 Myr (model 19; Fig.  A10b2). This indicates that a thermal anomaly controlling the location of the future break-up center could remain invisible in seismic tomography data for time periods on the order of tens of Myr.
The timing of lithospheric break-up (Fig. 14) appears to be mainly a function of boundary half-rate (V ext ): under the slowest extension (V ext : 2 mm × yr −1 ) break-up times always exceed 150 Myr reaching ∼175-275 Myr while they shorten by a factor of >10 (up to ∼10-15 Myr) when the rate of extension approaches the fastest value (V ext : 10 mm × yr −1 ). The predicted impact of the initial plume temperature (T init ) also decreases with the grow of V ext (see relative positions of blue, green and red lines in Fig. 14a): when the value of V ext is low (2 mm × yr −1 ) the lithospheric rupture is postponed by ∼100 Myr in the 'cold' plume model (T init : 1500 • C; model 19) with respect to its 'hot' plume counterpart (T init : 1700 • C; model 21) whereas for V ext of 10 mm × yr −1 this difference between 'hot' and 'cold' experiments (models 31 and 33) becomes almost negligible (∼5 Myr). In the models 19-22 (break-up time is >100 Myr) mantle plume material remains unmelted whereas decompressional melting occurs within 'normal' (i.e. non-plume) sublithospheric mantle being usually confined to a depth of ∼50-75 km (Fig. 14b, upper row). On the contrary, for models 23-33 (break-up time is <100 Myr) partial melting resides exclusively within the body of the mantle plume penetrating through ruptured lithospheric mantle up to the bottom of extended and thinned crust (snapshots shown in Fig. 14b correspond to the moments in time just preceding rupture at crustal levels and establishment of oceanic spreading). Note that the volume of the plume material involved in decompressional melting is sufficiently larger in the models with higher V ext (compare models 23 and 33 in Fig. 14b). A break-up time of ∼100 Myr appears to be a 'characteristic threshold' separating the models involving and without partial melting of mantle plume material at the syn-break-up stage (Fig. 14a). We should note, however, that given some level of uncertainty in the initial thermal profile (Section 5.3) the modelled timing and extent of the melting are to be considered as estimates.

Different types of lithosphere (Models 34-42)
In the final set of models, we analyse various lithospheric types-'Cratonic' (models 34-36), 'Mesozoic' (models 37-39) and oceanic (models 40-42)-in the context of moderate values of V ext (2, 3 or 4 mm × yr −1 ) and invariable T init (1600 • C). As shown in Fig. 15 summarizing the models with slow extension (V ext : 2 mm × yr −1 ), onset of 'pre-rift stage' (reflected in simultaneous growth in the parameters derived from temperature contrast A similar tendency (longer break-up time for thicker and stronger lithosphere) persists for V ext of 3 and 4 mm × yr −1 as well (Fig. 16). Note that the most pronounced contrast in break-up time occurs for the transition from 'Cratonic' (250 km thick) to non-cratonic ('Variscan'; 150-km-thick) lithosphere whereas the difference in break-up times between the models with 'Variscan' and 'Mesozoic' lithosphere is much more limited, thus reflecting a moderate difference (by 25 km only) in their LAB depths (see model configurations for different lithospheric types in Fig. 2).
Similarly to the effect of initial plume temperatures (T init ) explored in previous model series for a 'Variscan' type of lithosphere (Section 4.2.1 and Fig. 14), the role of the lithospheric structure in the break-up timing becomes less pronounced when values of V ext increase. Note also that a 'characteristic threshold' value for the break-up time defining the transition between melted and unmelted plumes remains to be close to ∼100 Myr (black dashed line in Figs 14a and 16).

Summary of numerical results
The presented numerical results show that predicted variations in the decay time of a 'baby' plume (defined by the parameter t(w 50 100 ) characterizing the time span for which the plume thermal anomaly remains seismically detectable: T >100 • C; w 100 ≥50 km) mostly depend on plume buoyancy which is controlled in our models by its initial temperature (T init ) and size (d init ). In particular, expected plume life spans t(w 50 100 ) vary from ∼20 Myr when both temperature and diameter are minimum (model 4 with T init of 1500 • C and d init of 80 km) to ∼245 Myr when they are of maximum magnitudes (model 9 with T init of 1700 • C and d init of 116 km). It is also noteworthy that the sum of temperature excess defined within the seismically detectable part of the thermal anomaly ( T >100 • C; T int 100 ) for initially 'warm' (T init : 1600 • C) and 'hot' (T init : 1700 • C) plumes remains higher than that associated with a 'cold' (T init : 1500 • C) plume at the moment of model initiation (t = 0 Myr) for more than tens or even 100 Myr (Figs 5 and 8).
In the experiments with extension, plumes usually persist over the entire model duration being a controlling factor in the location of lithosphere break-up (Fig. 13). We, therefore, selected as the main analysed parameter for this group of models the time span from model initiation to lithospheric break-up (Figs 14-16). Our modelling results demonstrate that the rate of applied extension appears to be the main controlling parameter of the break-up time. For slow extension (V ext : 2 mm × yr −1 ) it can exceed the maximum model span of 300 Myr (see 'Cratonic' lithosphere case in model 34) whereas lithosphere rupture can be induced in only 10 Myr when V ext is 10 mm × yr −1 (model 33). The amount of plume material involved into partial melting as well as the presence of this melting at all are controlled by break-up time. For all experiments performed, a 'characteristic threshold' break-up time of roughly 100 Myr defines a transition between the models with melted and unmelted plumes. Therefore, it appears that even an initially 'cold' (T init : 1500 • C) plume can produce melting under condition of sufficiently fast extension (V ext : 4-10 mm × yr −1 ) and, therefore, rapid break-up (break-up time of <100 Myr). On the contrary, a long duration of the rifting (break-up time is >100 Myr) typical for slow extension (V ext : 2 mm × yr −1 ) prevents melting in the plume even when the original anomaly was 'hot' (T init : 1700 • C) restricting the melt formation only to 'normal' (depleted) asthenospheric mantle (Fig. 14b).
In summary, three striking features become apparent from our models: 1. Small-scale 'baby' plumes, despite their limited size and moderate value of initial temperature contrast, not only control the location of the break-up axis but also, when combined with sufficiently fast extension and rapid break-up, could be involved into decompressional melting during their ascent through the ruptured lithosphere in the syn-break-up phase. This could, therefore, contribute to the formation of volcanic passive margins bearing deep mantle plume geochemical signatures (Jackson et al. 2010(Jackson et al. , 2017. As mentioned above, initially 'warm' (T init : 1600 • C) and 'hot' (T init : 1700 • C) plumes can conserve the integrated temperature contrast ( T int 100 ) which is higher or equivalent to the initial T int 100 for a 'cold' (T init : 1500 • C) plume during time periods from ∼35 to ∼95 Myr (Fig. 5). This means that if a 'hot' (T init : 1700 • C) plume after about one hundred Myr of cooling would suddenly be subjected to fast tectonic extension, the evolution of this system could be quite similar to that of the model 31: the plume is 'cold' (T init : 1500 • C) but extension is switched on immediately after its emplacement. Therefore, magmatic material at volcanic passive margins can be supplied from plume anomalies emplaced at different stages during pre-break-up history even if (i) the size of these plumes is limited and (ii) the time of their impingement is well in advance of not only the time of final break-up but even of the onset of prior tectonic extension and rifting.
2. Even for the cases when the mantle plume is not melted (under the condition of slow extension V ext of 2 mm yr -1 with resulting break-up time in excess of 100 Myr) its initial location remains a controlling factor for positioning the break-up axis (rupture of the lithosphere always occurs directly above or close to the initial site of the plume-see Fig. 14b). Thus, it appears that an amagmatic passive margin could be formed due to this hidden effect of the mantle plume which was faded before break-up, not leading to plume-related magmatism usually observed at volcanic rifted margins. In this context, it should be noted that frequently in 'passive' rifting/break-up models a small temperature heterogeneity is applied at the bottom of the lithosphere at the site of the prospective rift (e.g. Gerya 2013b; Brune 2014). This could actually correspond to our fading 'baby' plume below the location of future break-up. Therefore, the question is raising on the actual 'passivity' of these classic 'passive' rifting models and, in particular, how rifting can be considered 'passive' when its location (being one of its key characteristics) is controlled by a thermal anomaly that could be of deep origin.
3. In a tectonically neutral regime in the overlying plate, the decay time of a 'baby' plume defined as t(w 50 100 ) can vary from 20 Myr to more than 200 Myr. Such a large temporal variability in the life span of small-scale plumes could explain why sometimes (e.g. Bohemian Massif) low-velocity anomalies reside at relatively shallow depths (200 km) without evidence for a plume tail below (Plomerová et al. 2007(Plomerová et al. , 2016. In this case, the plume head attached to the bottom of the lithosphere could be shifted with respect to its original feeding channel (plume tail) due to lateral movements of the tectonic plates over geological time. This also implies that small-scale mantle diapirs below crustal magma chambers punctuated every 50-150 km along volcanic rifted margins are not a mandatory result of shallow convection within the uppermost asthenosphere as hitherto supposed (Geoffroy 2001(Geoffroy , 2005 but could be potentially linked with deeper laterally displaced sources. This also points to a younger age for 'finger-like' 'baby' plumes such as detected under the Eifel volcanic fields and associated with present-day seismicity (Hinzen et al. 2007), active topographic uplift (Kreemer et al. 2020), Quaternary magmatic activity (Buikin et al. 2005) and mantle degassing (Berberich et al. 2019).

Implications for modes of rifting and break-up
Our findings lead us to propose a new classification for the modes of continental rifting (Table 3). In doing so we complement the old classification separating 'passive' rifting (amagmatic, non-plume) from 'active' rifting (magmatic, plume-activated). Previously, several studies attempted to reconcile these end-member views. In particular, it was demonstrated that initially 'passive' extension and thinning of the lithosphere triggers convective upwelling of the asthenosphere during which thermal buoyancy may dominate the far-field intraplate stresses thus causing a change of the rifting mode to 'active' (Huismans et al. 2001). On the other hand, studies by Burov & Gerya (2014) and Koptev et al. (2015Koptev et al. ( , 2016 have shown that in the scenario of ('active') mantle plume upwelling from the lower mantle the simultaneous presence of external ('passive') tectonic extension is a necessary prerequisite for localizing rifting deformation. Both these attempts to reconcile 'active' and 'passive' conceptions end up with the recognition of the importance of a so-called 'active/passive' mode when far-field forcing and mantle upwelling are acting together. Here we complement the concepts of 'active' and 'passive' with two principally new modes of rifting and break-up: 'semi-active' and 'semi-passive'. These new modes explain observed deviations from predictions of the endmember models (Fig. 17). In the following, we describe the key characteristics of these four different modes of 'active', 'passive' and 'semi-active' and 'semi-passive' rifting/break-up and provide natural examples for each of them (Table 3).
In the 'active' scenario ( Fig. 17a), ascent of a large-scale hot/buoyant plume from the deep mantle initially results in symmetrical domal topographic uplift of the order of a few km (Şengör 2001). This is followed by a phase of widespread magmatism related to decompressional melting of the hot plume material spreading below the lithosphere ). Subsequently, the gravity effect of dynamic topography in combination with a horizontal drag at the base of the lithosphere imparted by radial flow of the plume head induces an 'active' extension of the overlying lithosphere (Westaway 1993). Therefore, the main criterion of the 'active' (plume-induced) mechanism is the presence of plumerelated (i.e. bearing corresponding geochemical signatures) magmatic events preceding the onset of the deformation associated with rifting (Şengör & Burke 1978). Some recent studies have pointed out that during fragmentation of Pangea, the most recent of Earth's supercontinents, extensional deformation in the areas of future continental break-up has been initiated before emplacement of corresponding LIPs, thus excluding 'active' mechanisms throughout Pangea dispersal (Peace et al. 2020 and references herein). However, it was also shown that in many cases pre-magmatic rift basins have orientations which are oblique to future passive margins, thus indicating that pre-LIP rifting and LIP-related continental break-up might be tectonically independent (Guan et al. 2021). For example, on the one hand, the Colorado Basin, Salado Basin and Punta del Este Basin in South America/South Africa are formed since the Early Jurassic (Max et al. 1999;Franke et al. 2006) indeed preceding the Parana-Etendeka LIP event which is roughly coeval with the Early Cretaceous break-up in South Atlantic (Franke 2013). On the other hand, these pre-LIP rift basins are oriented transversal with respect to the present passive margins thus advocating in favour of an 'active' scenario when mantle plume impingement not only results in a voluminous magmatic event (Parana-Etendeka LIP) but also generates extensional stresses which are (1) characterized by principally different orientation with respect to that most prevalent  before plume arrival and thus independent from the previous geodynamic regime controlling 'passive' extension and rifting and (2) sufficient to trigger continental break-up and subsequent opening of the ocean in the South Atlantic (Guan et al. 2021). Similar spatial and temporal relationships between pre-magmatic rifting, LIPs, and syn-or post-magmatic break-up can be also found in the areas of separation between India and the Seychelles (Deccan LIP; ∼65 Ma) and Arabian Peninsula and Africa (Afar LIP; ∼30-25 Ma), which are proven to be induced in an 'active' mode by sublithospheric mantle upwelling (Guan et al. 2021). The split between India and Madagascar at ∼84 Ma (Coffin & Rabinowitz 1988;Müller et al. 1997) which is, according to all evidence, linked to the Madagascar LIP emplaced during 91-83 Ma interval (Torsvik et al. 1998(Torsvik et al. , 2000Cucciniello et al. 2010Cucciniello et al. , 2021 could be another example of 'active' break-up contributing to fragmentation of Pangea. An additional argument in favour of a 'primary' plume origin for the Parana-Etendeka, Madagascar and Deccan LIPs is that they mark the spatial and temporal beginning of well-known oceanic hotspot tracks: Tristan (Gassmöller et al. 2016), Marion (Georgen et al. 2001) and Réunion (Bredow et al. 2017), respectively. The hotspot track created by the Afar plume on the continental part of the African plate has been also recently restored by means of global models of mantle convection (Hassan et al. 2020).
During fragmentation of Pangea, several break-up regions show a mixture of characteristics between 'active' and 'passive' endmembers described above. The most prominent example of such 'intermediate' behaviour is the opening of Central Atlantic Ocean corresponding to the earliest break-up episode in Pangea. Seafloor spreading started in the Central Atlantic at around 195-175 Ma (Klitgord & Schouten 1986;Sahabi et al. 2004;Labails et al. 2010), almost contemporaneously with a significant magmatic event, namely the Central Atlantic Magmatic Province (CAMP; Marzoli et al. 1999) at ∼200 Ma (Leleu et al. 2016). Similar to many other areas of Pangea dispersal, continental rifting around the Central Atlantic was initiated before the emplacement of CAMP: formation of Triassic basins within the Appalachian orogenic suture (Swanson 1986) started earlier than 230 Ma (Olsen 1997). However, in contrast to, for example, the South Atlantic rifting-to-break-up system (see above), these Triassic pre-magmatic basins are oriented parallel to future volcanic passive margins formed by syn-LIP magmatic break-up in Early Cretaceous (Guan et al. 2021) at odds with a scenario advocated for 'active' segments of Pangea break-up where plume-induced forces leading to lithosphere rupture are tectonically independent (and thus oriented differently) with respect to those governing a prior phase of 'passive' extension. Combined with the lack of evidence for pre-LIP uplift, these observations currently fuel 'antiplume' conceptions and views on the mechanisms of the continental break-up in the Central Atlantic (Peace et al. 2020). However, geochemical investigations of CAMP dolerite dikes (Cebria et al. 2003) and of the oldest basalts sampled from the Central Atlantic oceanic crust (Janney & Castillo 2001) display clear isotopic and chemical signals of plume contamination.
In order to reconcile these apparent contradictions, we introduce here a new, 'semi-active' mode of continental rifting and break-up (Fig. 17b). This mode assumes extension and rupture of the plate produced by far-field tectonic stresses but in the presence of mantle plume(s) of modest size and temperature seeded below passively stretched lithosphere. In this scenario, thermal anomalies are initially of deep origin as equivalent to the 'secondary' plumes in the 'Courtillot Earth' (Fig. 1a). Given their relatively small size and moderate temperature contrast, 'secondary' plumes are not able to produce by their impingement either high domal topography or intensive widespread magmatism. However, as shown by our modelling, even extremely small end-members of these thermal anomalies corresponding to so-called 'baby' plumes with a characteristic diameter of the order of only 100 km might be preserved below the lithosphere during very long time spans varying from tens to hundreds Myr (Section 4.1). During such long time intervals the heads of these plumes which remain attached to the lithosphere after their emplacement could be significantly shifted with respect to their original sources in the lower mantle or MTZ due to plate movements. As demonstrated by our experiments, in the case of (re-)activation of a tectonic extensional regime by far-field tectonics, small and isolated thermal anomalies can be sufficient to localize deformation in the overlying lithosphere (Section 4.2). In the case of narrow spacing between these anomalies, they are able to interconnect the areas of localized stretching along-strike to form a continuous zone of continental break-up (Gac & Geoffroy 2009). Moreover, under condition of sufficiently high temperature excess and sufficiently fast transition to lithospheric rupture, the syn-break-up phase is accompanied by partial melting of plume material (Section 4.2; Fig. 14) leading to intensive volcanism concentrated at the ocean-continent boundary accompanied by formation of SDRs, the main indicator of volcanic passive margins. In case of thermal anomalies of slightly larger sizes than adopted in our models and in the study by Gac & Geoffroy (2009), pre-break-up thinning of the lithosphere would be also accompanied by plume-related magmatism, potentially even more voluminous and widespread, corresponding to LIPs erupted directly before the start of SDRs emplacement as observed in the Central Atlantic (Davis et al. 2018). Therefore, the 'semi-active' mechanism permits reconciliation of two (and apparently contradictory) lines of thinking which include: (1) prolonged tectonic activity which started in the Central Atlantic >30 Myr before CAMP magmatism and subsequently evolved to break-up without a change in extension direction after LIP emplacement and (2) the presence of magmatic rocks with depleted mantle plume geochemical signatures. Extremely voluminous and widely spread magmatism associated with CAMP (McHone 2003;Marzoli et al. 2018) can be thus explained by an ensemble of numerous 'secondary' plumes originally emerging from the deep-sourced 'primary' plume stagnated below the upper mantle transitional zone (Courtillot et al. 2003).
Interestingly, present-day hotspots in the adjacent oceanic area-Azores, Canaries, and Cape Verde )-have been interpreted as 'secondary' plumes extending from a large thermal anomaly ponding beneath the endothermic 660 km phase transformation (Saki et al. 2015). Note, however, that these volcanic islands and seamounts are much younger than the Central Atlantic break-up (Geldmacher et al. 2005;Silveira et al. 2006;Long et al. 2020) and, therefore, no volcanic plume track from Downloaded from https://academic.oup.com/gji/article/227/1/439/6295312 by guest on 16 July 2021 CAMP is evident, in contrast to the LIPs associated with an 'active' break-up mechanism (see above). This might be explained by ancient emplacement of CAMP-related 'secondary' plumes (prior to break-up and, probably, even prior to onset of the rifting). As mentioned above, during the time interval between impingement of the mantle plumes at the lithosphere-asthenosphere boundary and their surface manifestation (LIP eruption), the feeding source in the lower mantle could be either exhausted or considerably shifted laterally due to horizontal motion of the lithosphere, thus precluding generation of a time-progressive hotspot track over newly-forming oceanic lithosphere.
Continental rupture between South Africa and Antarctica (Veevers 2012) and opening of the North Atlantic (Lundin & Doré 2005) could be other natural examples of the 'semi-active' rifting mode (Table 3). There, thin-skinned plate tectonics accomplished by exploitation of inherited suture zones provides the main control on the location and timing for both rifting and break-up processes, which are, nevertheless, accompanied by voluminous magmatism with plume-related geochemical signatures: Karoo LIP (Ellam et al. 1992;Duncan et al. 1997;Riley et al. 2005) and North Atlantic Igneous Province (NAIP; Saunders et al. 1997;Storey et al. 2007), respectively.
Finally, as shown by our modelling, the rupture of the lithosphere is not always accompanied by decompressional melts of mantle plume material. Under the condition of a relatively cold initial plume and slow tectonic extension, continental break-up is preceded by a long-lasting rift phase and thus occurs when the initial thermal anomaly becomes too cool to be subjected to partial melting even at the stage of lithospheric rupture when the plume material was uplifted and reached the shallowest depth levels (Fig. 14). In this case, the system evolves with only a small-volume of melting in deeper, non-plume, sublithospheric depleted mantle and likely resulted in minor to no syn-break-up volcanism. We call this regime a 'semi-passive' mode of rifting and break-up (Fig. 17c) as the location of the break-up axis is still controlled by a thermal anomaly of potentially deep origin ('secondary' mantle plume) but rupture of the lithosphere occurs without extrusion of large volumes of volcanic rocks. As a result, break-up in a 'semi-passive' regime evolves into non-volcanic (SDRs-free) passive margins, similarly to the 'passive' mode and in contrast to 'active' and 'semi-active' scenarios characterized by development of volcanic (SDRs bearing) passive margins (see above).
At first sight, the 'semi-passive' mode seems to be difficult to distinguish from a purely 'passive' mechanism based on available data for structural characteristics of passive margins. As mentioned above, aerial flood basalt eruptions leading to formation of SDRs are usually assisted by magmatic intrusions/underplating reflected in the high velocity bodies residing at the level of the lower crust along the volcanic passive margins. However, similar high velocity lower crust anomalies are also detected along non-volcanic (i.e. deprived of SDRs) passive margins: for example, in the northern part of the South Atlantic to the north of the Florianopolis (also referred to as Rio Grande) fracture zone (see e.g. Beniest et al. 2017a). According to Dupré et al. (2011), the underplated high density lower crust layer beneath the Gabon margin might be related to magmatism caused by the impact of a 'high thermal anomaly', which resides in the mantle part of the lithosphere since the early stage of rifting (Dupré et al. 2007). We attribute this 'high thermal anomaly' to 'secondary' mantle plume(s) potentially linked to the same source as the adjacent Parana-Etendeka LIP. Derived from partial melting of plume rocks during the rifting, the mafic magmas were intruded through a system of sills and dykes into the lower crust thus forming zones of anomalous seismic velocity. The following continental break-up, however, operated in a non-volcanic mode because plume material was cooled down before it reached the surface, in accordance with the 'semi-passive' scenario described above. Therefore, a possible criterion to identify a 'semi-passive' break-up regime could be the presence of anomalously high velocity/high density bodies located in the lower crust of non-volcanic margins, in contrast to totally amagmatic (or quasi-amagmatic) passive margins corresponding to a purely 'passive' mode.
Another example of 'semi-passive' break-up could be the separation between East Antarctica and Australia. Although East Antarctica and Australia have been connected since the Proterozoic in the Mawson-Gawler Craton (Flinn et al. 2006;Boger 2011), they were rifted obliquely to all Gondwana's orogenic structures and split at 99-84 Ma (Seton et al. 2012;Williams et al. 2013), at first sight, without evident plume influence (see review by Buiter & Torsvik 2014 and references herein). However, given the presence of a small amount of syn-rift magma intruded in the crust (Ball et al. 2013), the sublithospheric component of mantle activity, presumably associated with the Kerguelen plume (e.g. Coffin et al. 2002;Bredow & Steinberger 2018), can be suspected to be involved. The 'semipassive' mechanism is, therefore, extremely important for understanding break-up in the areas where it does not follow pre-existing weak sutures. In particular, the role of 'hidden' plumes, which control the localization of deformation in the lithosphere and, therefore, define the position of rifting and break-up center but do not leave any volcanic evidences of its presence and participation, deserves to be explored in more detail in future research.

Model limitations and future perspectives
The 2-D approach adopted in this study lacks consideration of 3-D phenomena such as: (1) the alignment of the plume 'pancake' head with the rift axis (Burov & Gerya 2014) sometimes associated with irregular along-strike structure of the fault zone (Koptev et al. 2018b, c); (2) fast and distal propagation of hot plume material toward the areas remote from its initial emplacement (Ebinger & Sleep 1998;Faccenna et al. 2013;Koptev et al. 2017;François et al. 2018) and (3) oblique (Brune et al. 2012;Brune & Autin 2013) and/or multidirectional (Georgen 2011;Dordevic & Georgen 2016) tectonic extension which can act as selector between successful ocean basin formation and failed rifts (Heine & Brune 2014) and/or as a potential mechanism for (plume-triggered) initiation of a divergent triple junction Koptev et al. 2018d). Although the relative importance of the aforementioned phenomena could be limited in the case of small-scale plumes with respect to their large-scale counterparts, the role of 'baby' plumes in lithospheric break-up warrants thorough further examination in forthcoming 3-D studies.
More detailed modelling procedures are also needed to evaluate the impact of uncertainties in the initial thermal profile of the lithosphere and sublithopsheric mantle. In particular, radiogenic heat generation in the continental crust is known to vary greatly across different tectonic units (Artemieva & Mooney 2001), thus requiring a systematic analysis of such parameters as near-surface heat production and characteristic depth of heat source distribution (Koptev et al. 2021). Moreover, variations in estimates of the adiabatic gradient for the asthenospheric (convecting) mantle from 0.3 • C km −1 (Turcotte & Schubert 2002;Sleep 2003) to 0.5 • C km −1 (Stixrude & Lithgow-Bertelloni 2005;Katsura et al. 2010) are also to be taken into account in future modelling studies. Finally, the temperature at the lithospheric base could have been adjusted to include the adiabatic gradient across the whole model depth (including the conductive lithosphere). This would ensure similar values of the potential mantle temperature in the experiment with different LAB levels.
Future studies of 'baby' plumes and their role in plate tectonics and geodynamics are not limited to the consequences of their impingement at the base of the lithosphere. Various scenarios and mechanisms for the origin of such small-scale plume anomalies should be explored in different tectonic and geodynamical settings. Particular attention needs to be paid to the upwelling rates of 'secondary' plumes in the upper sublithospheric mantle as it might be the key factor controlling excess temperatures at the moment of their emplacement at the lithosphere-asthenosphere boundary (probably, the most uncertain parameter in the study presented here). In addition, buoyancy of a small-scale thermal anomaly and, therefore, mode of its interaction with the overlying lithosphere could be affected by the presence of plume conduit(s) in the upper and, potentially, lower mantle. Therefore, thermomechanical modelling of mantle plumes which are relatively small in terms of their horizontal extent but which are continuously 'fed' from below represents an extremely important and promising topic in geodynamics for further investigation.

C O N C L U S I O N S
We present the results from the first systematic parametric analysis focused on the life-cycle of small-scale thermal upper mantle anomalies (so-called 'baby' plumes) and their impact on the style of lithosphere rifting and continental break-up. In this study, we have tested four controlling parameters including: (1) temperature and (2) diameter of the plume, (3) rheological structure of the overlying lithospheric plate and (4) style of intraplate tectonics. From this, we draw the following conclusions: 1. Under a tectonically neutral regime, the life span of 'baby' plumes is mainly conditioned by their buoyancy (which, in turn, depends on initial size and temperature), varying over a wide range of time intervals (from ∼20 to >200 Myr). Seismically detectable thermal anomalies can thus be sustained over geologically long timescales (>100 Myr).
2. In the case of extensional tectonic settings, even relatively small (100 km diameter) and moderately hot (temperature contrast of 150-200 • C) thermal anomalies ('baby' plumes) are shown to be sufficient to localize deformation in the lithosphere directly above them, triggering rifting and subsequent break-up.
3. The duration of the pre-break-up stage (time interval between onset of extension and lithosphere break-up) is a function of the level of external stresses, initial temperature of the plume and the integrated strength of the overlying lithosphere, varying from 10 to >300 Myr.
4. Lithospheric rupture in the experiments with a long-lasting phase (a few hundreds of Myr) of pre-break-up rifting is accompanied by modest amounts of melts within depleted asthenospheric upper mantle whereas a relatively fast (tens of Myr) transition to break-up promotes decompressional melting of enriched plume material.
5. Our findings have important implications for the styles of rifting induced by small thermal anomalies, leading to the recognition of two novel intermediate modes of rifting and break-up: 'semi-active' and 'semi-passive', complementing classical 'passive' versus 'active' concepts. Several segments of the passive margins formed during Pangea fragmentation have been developed under these intermediate regimes, which could, therefore, be potentially quite common in geological history.

A C K N O W L E D G E M E N T S
This study is cofunded by an Alexander von Humboldt Foundation fellowship (A. Koptev), ERC Consolidator grant 615703 EX-TREME (T. A. Ehlers, A. Koptev), the Distinguished Guest Scientist Fellowship Program of the Hungarian Academy of Sciences (S. Cloetingh), an Alexander von Humboldt Research Award (S. Cloetingh), and a German Science Foundation grant DFG-EH329/19-1 (T. A. Ehlers). The numerical simulations were performed on the University of Tübingen cluster. We thank Taras Gerya for providing the numerical code I3ELVIS. Discussions with Istvan Kovács and Christoph Glotzbach are appreciated. We thank Antonio Cordoba and Marzieh Baes for very insightful and constructive reviews.
Author contributions: A. Koptev and S. Cloetingh elaborated the conceptual idea and model. A. Koptev and T. A. Ehlers developed methods and modelling strategy. A. Koptev designed and conducted experiments and took the lead in writing the manuscript. All authors discussed the results and implications and commented on the manuscript at all stages.

DATA AVA I L A B I L I T Y
The figures in the supporting information contain the numerical simulation data. The computer code I3ELVIS used to generate our thermomechanical numerical models is provided in Gerya (2010).

S U P P O RT I N G I N F O R M AT I O N
Supplementary data are available at GJ I online. Figure A1. Temporal evolution of model 1 (T init : 1500 • C; d init : 100 km; type of lithosphere: 'Variscan'; V ext : 0 mm × yr −1 ): (a) material phase field. Given its limited buoyancy, the mantle plume keeps its original circular configuration over the entire modelling time; (b) distribution of the temperatures (T); (c) temperature contrasts ( T). Black line in the panels 'b' and 'c' corresponds to an isotherm of 1300 • C which is, by definition, an equivalent of the LAB (see Methods). Figure A2. Temporal evolution of model 3 (T init : 1700 • C; d init : 100 km; type of lithosphere: 'Variscan'; V ext : 0 mm × yr −1 ): (a) material phase field. A heart-like shape of the plume body at 15 Myr is further transformed into a quasi-elliptical configuration that remains unchanged since 60 Myr; (b) distribution of the temperatures (T); (c) temperature contrasts ( T).   Figure A8. Temporal evolution of model 19 (T init : 1500 • C; type of lithosphere: 'Variscan'; V ext : 2 mm × yr −1 ; d init : 100 km): (a) material phase field; (b) temperature contrasts ( T); (c) strain rate (ε). Figure A9. Temporal evolution of model 21 (T init : 1700 • C; type of lithosphere: 'Variscan'; V ext : 2 mm × yr −1 ; d init : 100 km): (a) material phase field; (b) temperature contrasts ( T); (c) strain rate (ε). Please note: Oxford University Press is not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the paper.