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On the possibility of a second kind of mantle plume
Earth and Planetary Science Letters 183 (2000) 61^71 www.elsevier.com/locate/epsl
On the possibility of a second kind of mantle plume L. Cserepes a; *, D.A. Yuen b b
a Department of Geophysics, Eo«tvo«s University, Ludovika te¨r 2, 1083 Budapest, Hungary Department of Geology and Geophysics and Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55415, USA
Received 29 May 2000; accepted 7 September 2000
Abstract Results from recent tomographic imaging of the mantle have revealed plume-like structures under some hotspots and renewed the interest in the theoretically possible forms of ascending jets in mantle convection. It is now a classical view that plumes reaching the lithosphere from below can, in principle, develop from boundary layers either at 660 km or at 2900 km depth. If both types are present in the mantle, the 660 km boundary layer, possibly due to the endothermic spinel^perovskite phase transition, must be partially penetrable. The present study shows that, with a partially penetrable phase boundary at 660 km depth, a further kind of plumes can develop, namely from below the 660 km boundary layer. These `mid-mantle plumes' have no root in the deep lower mantle. If, as recent viscosity inversions suggest, a second low viscosity zone exists under the 660 km discontinuity, then this `second asthenosphere' represents a well-focused source volume for the mid-mantle plumes. These upwellings are the counterparts of avalanche-like downwellings crossing the phase boundary in an intermittent manner. The condition for the development of mid-mantle plumes is that the phase boundary acts as a strong, but not fully impenetrable barrier to vertical flow. In two- and threedimensional numerical simulations using a compressible fluid in a Cartesian box, it has been found that the critical parameters of mantle convection (Rayleigh number, phase transition characteristics) closely meet this condition. Midmantle plumes develop with an eruptive vigor, much faster than the boundary layer plumes and can produce huge plume heads, exceeding 1000 km in radius. They can thus explain very extensive, episodic flood basalt volcanism on the surface. If mid-mantle plumes really exist, they can contribute to the explanation of the diversity of hotspot basalt isotopic signatures since they sample a geochemical reservoir distinct from the classical plume sources. ß 2000 Elsevier Science B.V. All rights reserved. Keywords: mantle; convection; mantle plumes; numerical models
1. Introduction The main upwellings of mantle convection are concentrated in hot columnar features, i.e. the
* Corresponding author. Fax: +36-1-210-1089; E-mail: [email protected]
plumes. Not all kinds of thermal convection must assume this structural form for the upwellings, but a long series of theoretical investigations has by now established the consensus that ascending £ow in the mantle is organized in plume-like structures (e.g. [1^7]). There is however a basic uncertainty in the theory of plumes and this concerns their depth of origin. It is now a classical thesis that thermal plumes rise from a basal or
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internal boundary layer of the convecting £uid. The Earth's mantle may have such boundary layers at the core^mantle boundary (above the depth of 2900 km) and at the base of the upper mantle (above the depth of 660 km). This latter is probably associated with the endothermic spinel^ perovskite phase transition which can constitute an impermeable or partially impermeable internal boundary in the mantle and can, therefore, make mantle convection two-layered [8^10]. No decisive observations are available at present which could settle the question whether mantle plumes originate from the core^mantle boundary (CMB), from the 660 km boundary layer, or from both. Detection of the plume anomaly by seismic tomographic methods is very di¤cult because the plume stems are thin [11]. Nevertheless, the resolution of tomographic inversion is improving at an astonishing speed and will certainly provide more and more useful data on the plume structures in the near future. Intriguing recent results concern e.g. the Iceland hotspot below which hot columnar features have been revealed in the upper mantle [12] or, in an other study, in both the upper and lower mantle [13]. Similar plume-like anomalies have been shown to exist in the lower mantle beneath the hotspots of Hawaii [14] and the Bowie seamount [11], and more and more details come to light about the lower-mantle upwelling beneath Africa [12]. The nature of these plumes is still uncertain as to whether they extend through the whole mantle as a contiguous dynamical feature or consist of di¡erent segments which are only thermally coupled across the 660 km discontinuity [15^17]. Indirect evidence suggests that some of the plumes may have their source in the 660 km boundary layer. There are `weak' plumes with low buoyancy £ux which could not produce the observed volcanism and the necessary high temperatures if they originated in so deep sources as the CMB [18]. Assuming a one-to-one correspondence between hotspots and plumes, hotspot lists which possibly contain more than 100 items [19] might require a much shallower source layer than the whole mantle, for convection calculations show that the average distance between
plumes cannot be less than their depth of origin [20]. Among indirect evidence about plume sources, arguments of mantle geochemistry play an important role. Trace element and isotopic chemistry of oceanic volcanism, especially the di¡erence between mid-ocean ridge basalts and ocean island basalts (OIB) strongly favors a kind of layered convection [21] for which the most plausible explanation is to suppose the presence of an internal boundary at 660 km depth. Moreover, the multicomponent nature of the OIB which are thought to be products of mantle plumes indicates that there must be di¡erent source regions from which the parent plumes originate [22^24]. For these plume basalt sources, schematic models of `chemical geodynamics' [25] include the boundary layers at 660 km and 2900 km depth as well as the bulk upper and lower mantle which may feed the boundary layer plumes by entrainment [21,26]. Based on numerical convection experiments, the present study introduces a new kind of plumes which, in contrast to the `classical' plumes rising from hot boundary layers, develop from beneath a `leaky' internal boundary. It has already been known for some time [9,27^29] that the 660 km discontinuity, due to the endothermic nature of the spinel^perovskite transition, can act as a mostly impermeable boundary with periods when it lets fast £ushing £ows through some spots, upward and downward. We have found that under certain circumstances the upward directed gushes are fed by lower-mantle material right below the 660 km boundary with no deep sources, and in the upper mantle they take the form of narrow cylindrical plumes. Preliminary model examples of this kind of upwellings have already been shown by Yuen et al. [30]. The formal resemblance between these `eruptions' of the middle mantle and the classical boundary layer plumes induces us to call the former ones as `mid-mantle plumes' although their dynamical origins are radically di¡erent. It will be shown that the possible presence of a low viscosity channel under the 660 km phase change boundary promotes the formation of such mid-mantle plumes, and then this low viscosity channel is the source zone of the ascending jets. Fig. 1 illus-
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Fig. 1. Schematic portrayal of plumes possible in a convectively layered mantle. Grey bands denote boundary layers, stippled bands are supposed low viscosity zones.
trates the four kinds of plumes which can coexist in the mantle if the 660 km discontinuity is a partially impenetrable internal boundary. The new `mid-mantle' type of plumes can o¡er, among others, a new possibility to explain the diversity of OIB sources. In the next sections we will describe two- and three-dimensional numerical convection models which develop mid-mantle plumes from below the endothermic spinel^perovskite phase transition boundary. 2. Model description The fundamental features of our convection models are the endothermic phase change at 660 km depth and the depth-dependent viscosity pro¢les (Fig. 2) which contain one or two low viscosity zones. Of the two large phase transitions of the upper mantle, it is su¤cient to retain the endothermic zone at 660 km as the only one which has a strong and spectacular in£uence on the £ow structure. Of the two viscosity pro¢les used here, one has the traditional low viscosity zone (LVZ, asthenosphere) between 100 and 250 km depths; the other pro¢le, in addition, contains a `second asthenosphere' in the top part of the lower mantle, lying between 660 and 1000 km depth. This second LVZ merits some words. A horizontal boundary layer such as the one presumably connected with the spinel^perovskite transition, or the lithosphere itself, represents a steep vertical temperature gradient in a narrow depth interval. In this thin layer the temperature-dependence of viscosity must be predominant in determining the
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viscosity variation, therefore producing a large viscosity drop downwards. Further down the pressure increase causes an increase in the viscosity, thus a viscosity minimum is expected below the boundary layer. This is the explanation for the classical asthenosphere below the lithospheric boundary layer, and an analogous LVZ can be assumed below 660 km. Recent inversion studies of the oceanic geoid based on tomographic images of the mantle show that the assumption of a second asthenosphere is consistent with the observed data [31^33]. In our two- and three-dimensional Cartesian models the convective layer is 2900 km deep, its viscosity is depth-dependent with the pro¢les shown in Fig. 2. The phase change at 660 km depth is treated by e¡ective material constants as in [8,34]. The density contrast due to the phase transition is taken to be 10%, while the Clapeyron slope is 33 MPa/K. The equations to be solved are based on the anelastic-liquid approximation of the convection problem [35]. In their original, primitive-variable forms, they are written as: D j 8 uj 0 2 3 8 gei 3D i p D j R D j ui D i uj 3 D i R D j uj 0 3
8 cp
DT Dp Dh 3K T 8 Tvs D j K D j T x H Dt Dt Dt
Fig. 2. Viscosity pro¢les used in this study. The two pro¢les, (a) with dashed lines and (b) with solid lines, di¡er only between 660 and 1000 km depth where pro¢le (b) has a second low viscosity zone or `second asthenosphere'.
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where 8 is the density, uj are the components of velocity, g is gravity, ei is the unit vector pointing upwards, p is the pressure, R is viscosity, cp is the speci¢c heat, T is the temperature, D/Dt is the substantial derivative with respect to time, K is the thermal expansivity, vs is the entropy change related to the phase transition, h is the fraction of the denser phase (0 9 h 9 1), K is thermal conductivity, x is the viscous dissipation and H is the rate of internal heating. The medium is considered to be compressible, 8 is the function of T, p and h. The coe¤cients K, cp , K and H are constants. In the numerical implementation we have employed a poloidal potential for representing the velocity vector, and transformed all variables onto nondimensional scales. As it is usual in the anelastic-liquid approximation [35], the background density increases exponentially with depth, but in the phase transition zone, where h varies in a thin layer, an additional density increase occurs. Variation of h is con¢ned to a ¢xed thin depth interval around 660 km in the form of a hyperbolic tangent function, according to the e¡ective-variable treatment of the phase transition [8]. By this technique, the latent heat term (the one containing Dh/Dt) can be incorporated into the ¢rst two advective terms of the third equation. Details of the equations can be found in [34]. The Rayleigh number, de¢ned with the surface value of the variable parameters (density, viscosity) and therefore called `surface Rayleigh number', is in the order of 107 (see later). The dissipation number [35] is ¢xed as 0.5, the Gru«neisen parameter is 1 and the nondimensional surface temperature is 0.1. Models with and without internal heating have been computed, in the former case the nondimensional heat generation is 10 which corresponds to a chondritic concentration of radioactive elements. The upper and lower boundaries are stress-free and isothermal; mirror symmetry is assumed on the sides of the rectangular model box. The box size is 4U1 or 4U4U1, in 2D and 3D, respectively. Finite di¡erences and spectral methods are combined in the numerical solution, and the grids use 256U128 points in 2D or 256U256U128 points in 3D.
Some of our results will be presented in terms of the normalized vertical mass £ux: w w x; y; z
1 8 uj ej F
where Z Z Z 1 8 uj 2 dxdydz 1=2 F V is the root-mean-square value of the total mass £ux in the model volume V. We also de¢ne the horizontal average of w as: Z Z 1 w z w w2 dxdy 1=2 A where A is the area of a horizontal plane in the model box. 3. Results It is known that an increase of the Rayleigh number Ra in £uids with an internal endothermic phase change shifts the £ow structure to a greater degree of layering [8,10,29,36]. At low Ra, the £ow is not much a¡ected by the phase transition and occurs in a single-layer style, while at very high Ra the phase change represents an impenetrable obstacle to the £ow which is then organized in two separate layers. The real mantle £ow is likely to occur in an intermediate regime, when the phase transition blocks vertical £ow partially. This can be inferred from the various forms of subducting slabs, many of them distorted, others undeformed at the 660 km discontinuity [37^40]. Therefore the present study focuses on this intermediate regime. Our experiments show that this intermediate, partially layered convection style leads to some, hitherto unexplored, phenomena when Ra is around 107 , a plausible value for the Earth's mantle today. First, we present two 2D models. In the case of Fig. 3, the Rayleigh number is 5U106 , there is no internal heating and the model includes both
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Fig. 3. Two-dimensional model with two low viscosity zones; Ra = 5U106 . (a) Isotherms. (b) Streamlines. Contours in panels (a) and (b) are equispaced between minima and maxima; ticks on the sides show the depth of the phase boundary at 660 km. (c) Vertical mass £ux w at 660 km depth. Positive means upwards.
LVZs of Fig. 2. The result is a time-dependent convection alternating between the completely layered and partially layered regimes as e.g. in [28]. `Completely layered' means that there is no mass £ux across the phase change boundary at 660 km depth, while in a `partially layered' state this boundary leaks at several spots allowing mass transfer between the upper and lower mantle. A snapshot of such a `leaky' period is shown in Fig. 3. There are three places where the £ow breaks through the phase boundary at this moment: see Fig. 3c which shows the vertical mass £ux w at 660 km depth. At the left-hand end of the box (x = 0) there is a major downwelling which penetrates down to the base of the box in an avalanche-like manner [28]. At approximately x = 3, a tilted plume rising from the basal boundary layer is just beginning to pierce the phase boundary and to form a plume head in the upper mantle. At xW1.6 there is another plume with a large asymmetric head in the upper mantle. This plume, already in its dying period, comes from below the 660 km discontinuity, but it has no deep root in
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the lower mantle: its source region can be located in the second asthenosphere below 660 km (cf. the streamlines in Fig. 3b and the vertical mass £ux curve in Fig. 3c). This mid-mantle plume developed with an `eruptive' vigor in an earlier stage, at the same time as the downwelling avalanche at the left side, and its source is the hot material accumulated in the second LVZ by lower-mantle plumes during the earlier layered period of the £ow. Such a lower-mantle plume, which cannot intrude into the upper mantle, can be seen at the right-hand side of the box. To check the role of the second LVZ in forming mid-mantle plumes, we carried out a calculation without the second LVZ (pro¢le (a) in Fig. 2). Since this means an increase of the average viscosity, we increased the surface Rayleigh number to 107 to keep the model comparable with that of Fig. 3. No other changes were made in the parameters. The £ow is again of the intermittent style (just as in all our subsequent models), with completely layered and leaky periods. A typical snapshot with one upwelling and one downwelling which penetrate through the 660 km boundary is shown in Fig. 4. The upwelling plume (at
Fig. 4. Two-dimensional model with no low viscosity zone below 660 km; Ra = 107 . (a) Isotherms. (b) Streamlines. (c) Vertical mass £ux w at 660 km depth. Units and notation as in Fig. 3.
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Fig. 5. Three-dimensional model with no low viscosity zone below 660 km; Ra = 2U107 . `A', `B' and `C' mark up- and downwellings described in the text. (a) Perspective view with two isotherms; for the blue surface T = 0.28, for the red surface T = 0.53. Horizontal lines on the box sides represent the depth of 660 km. (b) Contour map of the vertical mass £ux w at 660 km depth. Positive means upwards. Vertical mass £ux is practically zero almost everywhere in this plane, the exceptions are the indicated circular spots. (c) Map of the temperature in the upper mantle at 435 km depth. (d) Temperature ¢eld in a vertical section across plume `B'; in panel (c) an arrow marks the direction of this cross-section. (e) Horizontally averaged vertical mass £ux w´ as a function of depth. Contours are equispaced in panels (b), (c) and (d). The usual rainbow coloring is applied in (c) and (d), with red for warm and blue for cold.
x = 2.5 in the upper mantle) has a rather broad head and stem, this latter is 400 km wide. This plume again has its root in the lower mantle, but not in the basal boundary layer. The root region of this mid-mantle plume is deeper and much more di¡use in this model than in the previous one which had a second LVZ below the depth of 660 km (cf. the streamlines of Figs. 4b and 3b). This comparison shows clearly that the second asthenosphere, if present, can be a well concentrated source layer for mid-mantle plumes. Next we show two 3D models. In the ¢rst one (Fig. 5), the Rayleigh number is 2U107 , there is no internal heating, and the second asthenosphere is absent. Fig. 5a is a perspective view of the model box showing two isothermal surfaces: a cold (blue) and a hot (red) one. These particular isotherms were chosen with the intention of illustrating the upwelling plumes. This is a moment when the £ow is partially layered. Many plumes rise from the 660 km boundary layer and from the
basal boundary layer: they are upper-mantle plumes and lower-mantle plumes in the strict sense. There are only three spots where the phase boundary is penetrable (Fig. 5b), two of them upwards (marked by `A' and `B') and one downwards (`C'). The large avalanche-like downwelling which sinks from the upper mantle down to the bottom of the model can be seen at the back side of Fig. 5a (`C'). The two penetrating upwellings appear in the forefront of Fig. 5a and are well marked by their very large mushroom heads (`A' and `B'). Plume `A' is located in the corner of the box, thus, because of the symmetry conditions imposed on the sides, only a quarter of it can be seen. These penetrating upwellings are midmantle plumes in the sense that they come from the top part of the lower mantle and not from the basal boundary layer. Fig. 5c is a horizontal map of the temperature ¢eld taken in the upper mantle at 435 km depth and shows the distribution of the plumes: the small `hotspots' are upper-mantle
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Fig. 5 (continued).
Fig. 5 (continued).
plumes and the two broad ones (`A' and `B') are the mid-mantle plumes. Most of the plumes are concentrated in the front half of the box in Fig. 5a, i.e. far from the big downwelling `C'. A vertical cross-section centered on the mid-mantle plume `B' (Fig. 5d) shows well the layering of the £ow and that plume `B' has no root in the
deep lower mantle. Fig. 5e is a graph of the average vertical mass £ux w ´ as a function of depth, showing that layering is partial: there is a nonzero minimum in the mass £ux near the depth of 660 km. In the model of Fig. 6 uniform internal heating is added to the basal heating and the second asthenosphere is included in the viscosity function. To compensate for these factors which increase the vigor of convection, we reduced the surface Rayleigh number with respect to the previous case, now it is Ra = 107 . The rather high value of the internal heating (H = 10) changes the style of convection in the lower mantle: the upwellings are organized in broad, gently sloping `ridges' and there are no well-developed plumes as is characteristic of predominantly internally heated £ows [3,41,42]. However, the plumes are still present in the upper mantle. Fig. 6a shows a close-up of the most interesting corner of the model box with upper-mantle plumes and lower-mantle hot `ridges'. The snapshot is taken again at a partially layered stage of the £ow. Plume `D' of Fig. 6a penetrates through the phase boundary, and, as it is clear from the ¢gure, it has no deep root. Detailed analysis proves that it is fed by a predominantly horizontal £ow in the second asthenosphere which radially converges just below the `leak' of the 660 km discontinuity. The other plumes of Fig. 6a are upper-mantle plumes. This corner of the model box is so densely populated by plumes that their heads coalesce into one big pancake-like hot feature in the asthenosphere. Fig. 6b shows the two spots where there is mass
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Fig. 6. Three-dimensional model with two low viscosity zones and with internal heating; Ra = 107 . `D' marks the upwelling described in the text. (a) Perspective view of a corner of the model box with two isotherms; for the blue surface T = 0.40, for the red surface T = 0.80. (b) Contour map of the vertical mass £ux w at 660 km depth. Vertical mass £ux is practically zero almost everywhere in this plane, the exceptions are the indicated spots. (c) Map of the temperature in the upper mantle at 435 km depth. (d) Temperature ¢eld in a vertical section across plume `D'; in panel (c) an arrow marks the direction of this cross-section. (e) Horizontally averaged vertical mass £ux w ´ as a function of depth. Units, contouring, coloring and other markings as in Fig. 5.
£ow across the phase boundary, and Fig. 6c is a map of the temperature distribution at the depth of 435 km, showing the location of the mid-mantle plume `D' and the thinner upper-mantle plumes. Fig. 6d is a vertical section across plume `D', indicating also an upper-mantle plume. It is obvious that plume `D' makes a hole in the 660 km boundary layer, while the other one rises from the top half of this internal boundary layer. The average vertical mass £ux pro¢le in Fig. 6e shows clearly that there is vigorous £ow in the second asthenosphere below the phase boundary. 4. Discussion and concluding remarks The principal aim of this study is to demonstrate the possibility of a new style of convective plumes in the mantle. The necessary conditions for the existence of these `mid-mantle plumes' is that the spinel^perovskite phase transition at 660
km depth should act as a strong, but incomplete barrier to vertical £ow. If this barrier leaks at relatively small spots, upward directed `eruptions' of the lower-mantle material take, in the upper mantle, the form of the usual mushroom-shaped plumes. These mid-mantle plumes are the upward directed equivalents of the downwelling avalanche events which received great publicity in earlier studies of the dynamic consequences of an endothermic phase change [9,27,28]. In the preceding section we have shown in several examples that simple models of the mantle with the spinel^perovskite transition reproduce the conditions for mid-mantle plumes if the Rayleigh number is around 107 . It is known [8,36] that, with ¢xed properties of the endothermic transition, the increase of the Rayleigh number tends to inhibit mass transfer across the transition zone, while the decrease of Ra leads to extensive £ow across the phase boundary, destroying eventually all signs of £ow strati¢cation. Our models
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Fig. 6 (continued).
Fig. 6 (continued).
show that there must be an interval of Ra where convection is strongly strati¢ed but cylindrical jets pass through the transition zone at several spots. This range of the Rayleigh number is found around 107 which can be a representative value for the real mantle. Then the ascending penetrative jets are thin and plume-like.
The root region of these mid-mantle plumes is a localized volume in the topmost part of the lower mantle, below the phase boundary. If there is a low viscosity layer (`second asthenosphere') below the spinel^perovskite transition zone, this layer focuses a predominantly horizontal £ow towards the spot where the plume breaks through the phase boundary. Then the second asthenosphere constitutes the source volume of mid-mantle plumes. As for example Fig. 3a shows, the possibility of mid-mantle plumes does not exclude that some `classical' CMB plumes cross the 660 km discontinuity at the same time. This means that three kinds of plumes can reach the base of the lithosphere simultaneously (Fig. 1): classical boundary layer plumes rising from either the depth of 660 km or from 2900 km, and the mid-mantle plumes described in this study. A fourth kind, lower-mantle plumes in the strict sense, cannot penetrate into the upper mantle and will not have direct e¡ects on the Earth's surface. It is worthy of note that in models (e.g. in Fig. 6) where internal heating is predominant in the lower mantle and basal heating gives a relatively little contribution, there are no well-developed lower-mantle plumes. In such a case the only way to get upwellings from below a strong endothermic transition is in the form of `mid-mantle plumes'. The mid-mantle plumes of our models are very vigorous and robust convective upwellings. The vertical velocity along their axis can be 5^10 times higher than the velocity in the center of the classical upper-mantle plumes, therefore they can de-
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velop a surface hotspot very rapidly. The stem of the mid-mantle plumes is thicker than that of the upper-mantle plumes, and can reach a diameter of 400^500 km in the models presented above. The plume heads can be as large as 1000^1500 km in radius, with much higher central temperatures than in the upper-mantle plumes. Due to their large dimensions, the tomographic identi¢cation of the mid-mantle plumes, if they exist in the Earth, should be much easier than the detection of the classical boundary layer plumes. The surface manifestation of these eruptions of the topmost lower mantle can be profound, e.g. extensive £ood basalt volcanism can be expected over at least as large areas as in the case of newly initiated CMB plumes [43,44]. The mid-mantle plumes sample a particular volume at the top of the lower mantle, and not only by some vaguely known mechanism of entrainment [23,26], but by transporting bulk lower-mantle material to the surface. This is a completely di¡erent source region than that of the classical plumes which rise from one of the boundary layers of the mantle. In this way, the mid-mantle plumes can sample a distinct geochemical reservoir, o¡ering a new possible agent for the explanation of the enigmatic diversity of isotopic signatures observed in hotspot basalts [21^24].
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Acknowledgements The authors thank discussions with David Brunet, Volker Steinbach and Fabien Dubu¡et on various matters of interactions between plumes and phase transitions. Helpful comments on the manuscript by Arie van den Berg and Ctirad Matyska are gratefully acknowledged. This research has been supported by the Hungarian grant OTKA T026630 and the geophysics programme of the National Science Foundation.[AC] References
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convergent and divergent plate boundaries, Geophys. Res. Lett. 16 (1989) 433^436. A. Galsa, L. Cserepes, The number of hotspots in mantle convection: E¡ect of depth-dependent viscosity and internal heating in two-dimensional models, Acta Geodaet. Geophys. Hung. (2000) in press. A.W. Hofmann, Mantle geochemistry: the message from oceanic volcanism, Nature 385 (1997) 219^229. A. Zindler, S. Hart, Chemical geodynamics, Annu. Rev. Earth Planet. Sci. 14 (1986) 493^571. S.R. Hart, E.H. Hauri, L.A. Oschmann, J.A. Whitehead, Mantle plumes and entrainment: isotopic evidence, Science 256 (1992) 517^520. B.B. Hanan, D.W. Graham, Lead and helium isotope evidence from oceanic basalts for a common deep source of mantle plumes, Science 272 (1996) 991^995. C.J. Alle©gre, Chemical geodynamics, Tectonophysics 81 (1982) 109^132. E.H. Hauri, J.A. Whitehead, S.R. Hart, Fluid dynamic and geochemical aspects of entrainment in mantle plumes, J. Geophys. Res. 99 (1994) 24275^24300. P.J. Tackley, D.J. Stevenson, G.A. Glatzmaier, G. Schubert, E¡ects of an endothermic phase transition at 670 km depth in a spherical model of convection in the Earth's mantle, Nature 361 (1993) 699^704. L.P. Solheim, W.R. Peltier, Avalanche e¡ects in phase transition modulated thermal convection: A model of Earth's mantle, J. Geophys. Res. 99 (1994) 6997^7018. L. Cserepes, D.A. Yuen, Dynamical consequences of midmantle viscosity strati¢cation on mantle £ows with an endothermic transition, Geophys. Res. Lett. 24 (1997) 181^184. D.A. Yuen, L. Cserepes, B.A. Schroeder, Mesoscale structures in the transition zone: Dynamical consequences of boundary layer activities, Earth Planets Space 50 (1998) 1035^1045. í ¨|zkova¨, O. C í adek, D.A. Yuen, H. Zhou, Slope of the H. C geoid spectrum and constraints on mantle viscosity strati¢cation, Geophys. Res. Lett. 23 (1996) 3063^3066. í adek, Inferences of viscosity from the oceM. Kido, O. C anic geoid: Indication of a low viscosity zone below the 660-km discontinuity, Earth Planet. Sci. Lett. 151 (1997) 125^137.
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í adek, T. Nakakuki, Mantle [33] M. Kido, D.A. Yuen, O. C viscosity derived by genetic algorithm using oceanic geoid and seismic tomography for whole-mantle versus blocked£ow situations, Phys. Earth Planet. Inter. 107 (1998) 307^ 326. [34] L. Cserepes, D.A. Yuen, B.A. Schroeder, E¡ect of the mid-mantle viscosity and phase-transition structure on 3D mantle convection, Phys. Earth Planet. Inter. 118 (2000) 135^148. [35] G.T. Jarvis, D.P. McKenzie, Convection in a compressible £uid with in¢nite Prandtl number, J. Fluid Mech. 96 (1980) 515^583. [36] D.A. Yuen, D.M. Reuteler, S. Balachandar, V. Steinbach, A.V. Malevsky, J.J. Smedsmo, Various in£uences on three-dimensional mantle convection with phase transitions, Phys. Earth Planet. Inter. 86 (1994) 185^203. [37] R. van der Hilst, R. Engdahl, W. Spakman, G. Nolet, Tomographic imaging of subducted lithosphere below northwest Paci¢c island arcs, Nature 353 (1991) 37^43. [38] Y. Fukao, M. Obayashi, H. Inoue, M. Nenbai, Subducting slabs stagnant in the mantle transition zone, J. Geophys. Res. 97 (1992) 4809^4822. [39] R. van der Hilst, Complex morphology of subducted lithosphere in the mantle beneath the Tonga trench, Nature 374 (1995) 154^157. [40] S.P. Grand, R.D. van der Hilst, S. Widiyantoro, Global seismic tomography: A snapshot of convection in the Earth, GSA Today 7 (4) (1997) 1^7. [41] G. Houseman, The dependence of convection platform on mode of heating, Nature 332 (1988) 346^349. [42] L. Cserepes, E¡ect of depth-dependent viscosity on the pattern of mantle convection, Geophys. Res. Lett. 20 (1993) 2091^2094. [43] R.A. Duncan, M.A. Richards, Hotspots, mantle plumes, £ood basalts, and true polar wander, Rev. Geophys. Space Phys. 29 (1991) 31^50. [44] A. Marzoli, P.R. Renne, E.M. Piccirillo, M. Ernesto, G. Bellieni, A. De Min, Extensive 200-million-year-old continental £ood basalts of the central Atlantic magmatic province, Science 284 (1999) 616^618.
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On the possibility of a second kind of mantle plume L. Cserepes a; *, D.A. Yuen b b
a Department of Geophysics, Eo«tvo«s University, Ludovika te¨r 2, 1083 Budapest, Hungary Department of Geology and Geophysics and Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55415, USA
Received 29 May 2000; accepted 7 September 2000
Abstract Results from recent tomographic imaging of the mantle have revealed plume-like structures under some hotspots and renewed the interest in the theoretically possible forms of ascending jets in mantle convection. It is now a classical view that plumes reaching the lithosphere from below can, in principle, develop from boundary layers either at 660 km or at 2900 km depth. If both types are present in the mantle, the 660 km boundary layer, possibly due to the endothermic spinel^perovskite phase transition, must be partially penetrable. The present study shows that, with a partially penetrable phase boundary at 660 km depth, a further kind of plumes can develop, namely from below the 660 km boundary layer. These `mid-mantle plumes' have no root in the deep lower mantle. If, as recent viscosity inversions suggest, a second low viscosity zone exists under the 660 km discontinuity, then this `second asthenosphere' represents a well-focused source volume for the mid-mantle plumes. These upwellings are the counterparts of avalanche-like downwellings crossing the phase boundary in an intermittent manner. The condition for the development of mid-mantle plumes is that the phase boundary acts as a strong, but not fully impenetrable barrier to vertical flow. In two- and threedimensional numerical simulations using a compressible fluid in a Cartesian box, it has been found that the critical parameters of mantle convection (Rayleigh number, phase transition characteristics) closely meet this condition. Midmantle plumes develop with an eruptive vigor, much faster than the boundary layer plumes and can produce huge plume heads, exceeding 1000 km in radius. They can thus explain very extensive, episodic flood basalt volcanism on the surface. If mid-mantle plumes really exist, they can contribute to the explanation of the diversity of hotspot basalt isotopic signatures since they sample a geochemical reservoir distinct from the classical plume sources. ß 2000 Elsevier Science B.V. All rights reserved. Keywords: mantle; convection; mantle plumes; numerical models
1. Introduction The main upwellings of mantle convection are concentrated in hot columnar features, i.e. the
* Corresponding author. Fax: +36-1-210-1089; E-mail: [email protected]
plumes. Not all kinds of thermal convection must assume this structural form for the upwellings, but a long series of theoretical investigations has by now established the consensus that ascending £ow in the mantle is organized in plume-like structures (e.g. [1^7]). There is however a basic uncertainty in the theory of plumes and this concerns their depth of origin. It is now a classical thesis that thermal plumes rise from a basal or
0012-821X / 00 / $ ^ see front matter ß 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 1 X ( 0 0 ) 0 0 2 6 5 - X
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internal boundary layer of the convecting £uid. The Earth's mantle may have such boundary layers at the core^mantle boundary (above the depth of 2900 km) and at the base of the upper mantle (above the depth of 660 km). This latter is probably associated with the endothermic spinel^ perovskite phase transition which can constitute an impermeable or partially impermeable internal boundary in the mantle and can, therefore, make mantle convection two-layered [8^10]. No decisive observations are available at present which could settle the question whether mantle plumes originate from the core^mantle boundary (CMB), from the 660 km boundary layer, or from both. Detection of the plume anomaly by seismic tomographic methods is very di¤cult because the plume stems are thin [11]. Nevertheless, the resolution of tomographic inversion is improving at an astonishing speed and will certainly provide more and more useful data on the plume structures in the near future. Intriguing recent results concern e.g. the Iceland hotspot below which hot columnar features have been revealed in the upper mantle [12] or, in an other study, in both the upper and lower mantle [13]. Similar plume-like anomalies have been shown to exist in the lower mantle beneath the hotspots of Hawaii [14] and the Bowie seamount [11], and more and more details come to light about the lower-mantle upwelling beneath Africa [12]. The nature of these plumes is still uncertain as to whether they extend through the whole mantle as a contiguous dynamical feature or consist of di¡erent segments which are only thermally coupled across the 660 km discontinuity [15^17]. Indirect evidence suggests that some of the plumes may have their source in the 660 km boundary layer. There are `weak' plumes with low buoyancy £ux which could not produce the observed volcanism and the necessary high temperatures if they originated in so deep sources as the CMB [18]. Assuming a one-to-one correspondence between hotspots and plumes, hotspot lists which possibly contain more than 100 items [19] might require a much shallower source layer than the whole mantle, for convection calculations show that the average distance between
plumes cannot be less than their depth of origin [20]. Among indirect evidence about plume sources, arguments of mantle geochemistry play an important role. Trace element and isotopic chemistry of oceanic volcanism, especially the di¡erence between mid-ocean ridge basalts and ocean island basalts (OIB) strongly favors a kind of layered convection [21] for which the most plausible explanation is to suppose the presence of an internal boundary at 660 km depth. Moreover, the multicomponent nature of the OIB which are thought to be products of mantle plumes indicates that there must be di¡erent source regions from which the parent plumes originate [22^24]. For these plume basalt sources, schematic models of `chemical geodynamics' [25] include the boundary layers at 660 km and 2900 km depth as well as the bulk upper and lower mantle which may feed the boundary layer plumes by entrainment [21,26]. Based on numerical convection experiments, the present study introduces a new kind of plumes which, in contrast to the `classical' plumes rising from hot boundary layers, develop from beneath a `leaky' internal boundary. It has already been known for some time [9,27^29] that the 660 km discontinuity, due to the endothermic nature of the spinel^perovskite transition, can act as a mostly impermeable boundary with periods when it lets fast £ushing £ows through some spots, upward and downward. We have found that under certain circumstances the upward directed gushes are fed by lower-mantle material right below the 660 km boundary with no deep sources, and in the upper mantle they take the form of narrow cylindrical plumes. Preliminary model examples of this kind of upwellings have already been shown by Yuen et al. [30]. The formal resemblance between these `eruptions' of the middle mantle and the classical boundary layer plumes induces us to call the former ones as `mid-mantle plumes' although their dynamical origins are radically di¡erent. It will be shown that the possible presence of a low viscosity channel under the 660 km phase change boundary promotes the formation of such mid-mantle plumes, and then this low viscosity channel is the source zone of the ascending jets. Fig. 1 illus-
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Fig. 1. Schematic portrayal of plumes possible in a convectively layered mantle. Grey bands denote boundary layers, stippled bands are supposed low viscosity zones.
trates the four kinds of plumes which can coexist in the mantle if the 660 km discontinuity is a partially impenetrable internal boundary. The new `mid-mantle' type of plumes can o¡er, among others, a new possibility to explain the diversity of OIB sources. In the next sections we will describe two- and three-dimensional numerical convection models which develop mid-mantle plumes from below the endothermic spinel^perovskite phase transition boundary. 2. Model description The fundamental features of our convection models are the endothermic phase change at 660 km depth and the depth-dependent viscosity pro¢les (Fig. 2) which contain one or two low viscosity zones. Of the two large phase transitions of the upper mantle, it is su¤cient to retain the endothermic zone at 660 km as the only one which has a strong and spectacular in£uence on the £ow structure. Of the two viscosity pro¢les used here, one has the traditional low viscosity zone (LVZ, asthenosphere) between 100 and 250 km depths; the other pro¢le, in addition, contains a `second asthenosphere' in the top part of the lower mantle, lying between 660 and 1000 km depth. This second LVZ merits some words. A horizontal boundary layer such as the one presumably connected with the spinel^perovskite transition, or the lithosphere itself, represents a steep vertical temperature gradient in a narrow depth interval. In this thin layer the temperature-dependence of viscosity must be predominant in determining the
63
viscosity variation, therefore producing a large viscosity drop downwards. Further down the pressure increase causes an increase in the viscosity, thus a viscosity minimum is expected below the boundary layer. This is the explanation for the classical asthenosphere below the lithospheric boundary layer, and an analogous LVZ can be assumed below 660 km. Recent inversion studies of the oceanic geoid based on tomographic images of the mantle show that the assumption of a second asthenosphere is consistent with the observed data [31^33]. In our two- and three-dimensional Cartesian models the convective layer is 2900 km deep, its viscosity is depth-dependent with the pro¢les shown in Fig. 2. The phase change at 660 km depth is treated by e¡ective material constants as in [8,34]. The density contrast due to the phase transition is taken to be 10%, while the Clapeyron slope is 33 MPa/K. The equations to be solved are based on the anelastic-liquid approximation of the convection problem [35]. In their original, primitive-variable forms, they are written as: D j 8 uj 0 2 3 8 gei 3D i p D j R D j ui D i uj 3 D i R D j uj 0 3
8 cp
DT Dp Dh 3K T 8 Tvs D j K D j T x H Dt Dt Dt
Fig. 2. Viscosity pro¢les used in this study. The two pro¢les, (a) with dashed lines and (b) with solid lines, di¡er only between 660 and 1000 km depth where pro¢le (b) has a second low viscosity zone or `second asthenosphere'.
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where 8 is the density, uj are the components of velocity, g is gravity, ei is the unit vector pointing upwards, p is the pressure, R is viscosity, cp is the speci¢c heat, T is the temperature, D/Dt is the substantial derivative with respect to time, K is the thermal expansivity, vs is the entropy change related to the phase transition, h is the fraction of the denser phase (0 9 h 9 1), K is thermal conductivity, x is the viscous dissipation and H is the rate of internal heating. The medium is considered to be compressible, 8 is the function of T, p and h. The coe¤cients K, cp , K and H are constants. In the numerical implementation we have employed a poloidal potential for representing the velocity vector, and transformed all variables onto nondimensional scales. As it is usual in the anelastic-liquid approximation [35], the background density increases exponentially with depth, but in the phase transition zone, where h varies in a thin layer, an additional density increase occurs. Variation of h is con¢ned to a ¢xed thin depth interval around 660 km in the form of a hyperbolic tangent function, according to the e¡ective-variable treatment of the phase transition [8]. By this technique, the latent heat term (the one containing Dh/Dt) can be incorporated into the ¢rst two advective terms of the third equation. Details of the equations can be found in [34]. The Rayleigh number, de¢ned with the surface value of the variable parameters (density, viscosity) and therefore called `surface Rayleigh number', is in the order of 107 (see later). The dissipation number [35] is ¢xed as 0.5, the Gru«neisen parameter is 1 and the nondimensional surface temperature is 0.1. Models with and without internal heating have been computed, in the former case the nondimensional heat generation is 10 which corresponds to a chondritic concentration of radioactive elements. The upper and lower boundaries are stress-free and isothermal; mirror symmetry is assumed on the sides of the rectangular model box. The box size is 4U1 or 4U4U1, in 2D and 3D, respectively. Finite di¡erences and spectral methods are combined in the numerical solution, and the grids use 256U128 points in 2D or 256U256U128 points in 3D.
Some of our results will be presented in terms of the normalized vertical mass £ux: w w x; y; z
1 8 uj ej F
where Z Z Z 1 8 uj 2 dxdydz 1=2 F V is the root-mean-square value of the total mass £ux in the model volume V. We also de¢ne the horizontal average of w as: Z Z 1 w z w w2 dxdy 1=2 A where A is the area of a horizontal plane in the model box. 3. Results It is known that an increase of the Rayleigh number Ra in £uids with an internal endothermic phase change shifts the £ow structure to a greater degree of layering [8,10,29,36]. At low Ra, the £ow is not much a¡ected by the phase transition and occurs in a single-layer style, while at very high Ra the phase change represents an impenetrable obstacle to the £ow which is then organized in two separate layers. The real mantle £ow is likely to occur in an intermediate regime, when the phase transition blocks vertical £ow partially. This can be inferred from the various forms of subducting slabs, many of them distorted, others undeformed at the 660 km discontinuity [37^40]. Therefore the present study focuses on this intermediate regime. Our experiments show that this intermediate, partially layered convection style leads to some, hitherto unexplored, phenomena when Ra is around 107 , a plausible value for the Earth's mantle today. First, we present two 2D models. In the case of Fig. 3, the Rayleigh number is 5U106 , there is no internal heating and the model includes both
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Fig. 3. Two-dimensional model with two low viscosity zones; Ra = 5U106 . (a) Isotherms. (b) Streamlines. Contours in panels (a) and (b) are equispaced between minima and maxima; ticks on the sides show the depth of the phase boundary at 660 km. (c) Vertical mass £ux w at 660 km depth. Positive means upwards.
LVZs of Fig. 2. The result is a time-dependent convection alternating between the completely layered and partially layered regimes as e.g. in [28]. `Completely layered' means that there is no mass £ux across the phase change boundary at 660 km depth, while in a `partially layered' state this boundary leaks at several spots allowing mass transfer between the upper and lower mantle. A snapshot of such a `leaky' period is shown in Fig. 3. There are three places where the £ow breaks through the phase boundary at this moment: see Fig. 3c which shows the vertical mass £ux w at 660 km depth. At the left-hand end of the box (x = 0) there is a major downwelling which penetrates down to the base of the box in an avalanche-like manner [28]. At approximately x = 3, a tilted plume rising from the basal boundary layer is just beginning to pierce the phase boundary and to form a plume head in the upper mantle. At xW1.6 there is another plume with a large asymmetric head in the upper mantle. This plume, already in its dying period, comes from below the 660 km discontinuity, but it has no deep root in
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the lower mantle: its source region can be located in the second asthenosphere below 660 km (cf. the streamlines in Fig. 3b and the vertical mass £ux curve in Fig. 3c). This mid-mantle plume developed with an `eruptive' vigor in an earlier stage, at the same time as the downwelling avalanche at the left side, and its source is the hot material accumulated in the second LVZ by lower-mantle plumes during the earlier layered period of the £ow. Such a lower-mantle plume, which cannot intrude into the upper mantle, can be seen at the right-hand side of the box. To check the role of the second LVZ in forming mid-mantle plumes, we carried out a calculation without the second LVZ (pro¢le (a) in Fig. 2). Since this means an increase of the average viscosity, we increased the surface Rayleigh number to 107 to keep the model comparable with that of Fig. 3. No other changes were made in the parameters. The £ow is again of the intermittent style (just as in all our subsequent models), with completely layered and leaky periods. A typical snapshot with one upwelling and one downwelling which penetrate through the 660 km boundary is shown in Fig. 4. The upwelling plume (at
Fig. 4. Two-dimensional model with no low viscosity zone below 660 km; Ra = 107 . (a) Isotherms. (b) Streamlines. (c) Vertical mass £ux w at 660 km depth. Units and notation as in Fig. 3.
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Fig. 5. Three-dimensional model with no low viscosity zone below 660 km; Ra = 2U107 . `A', `B' and `C' mark up- and downwellings described in the text. (a) Perspective view with two isotherms; for the blue surface T = 0.28, for the red surface T = 0.53. Horizontal lines on the box sides represent the depth of 660 km. (b) Contour map of the vertical mass £ux w at 660 km depth. Positive means upwards. Vertical mass £ux is practically zero almost everywhere in this plane, the exceptions are the indicated circular spots. (c) Map of the temperature in the upper mantle at 435 km depth. (d) Temperature ¢eld in a vertical section across plume `B'; in panel (c) an arrow marks the direction of this cross-section. (e) Horizontally averaged vertical mass £ux w´ as a function of depth. Contours are equispaced in panels (b), (c) and (d). The usual rainbow coloring is applied in (c) and (d), with red for warm and blue for cold.
x = 2.5 in the upper mantle) has a rather broad head and stem, this latter is 400 km wide. This plume again has its root in the lower mantle, but not in the basal boundary layer. The root region of this mid-mantle plume is deeper and much more di¡use in this model than in the previous one which had a second LVZ below the depth of 660 km (cf. the streamlines of Figs. 4b and 3b). This comparison shows clearly that the second asthenosphere, if present, can be a well concentrated source layer for mid-mantle plumes. Next we show two 3D models. In the ¢rst one (Fig. 5), the Rayleigh number is 2U107 , there is no internal heating, and the second asthenosphere is absent. Fig. 5a is a perspective view of the model box showing two isothermal surfaces: a cold (blue) and a hot (red) one. These particular isotherms were chosen with the intention of illustrating the upwelling plumes. This is a moment when the £ow is partially layered. Many plumes rise from the 660 km boundary layer and from the
basal boundary layer: they are upper-mantle plumes and lower-mantle plumes in the strict sense. There are only three spots where the phase boundary is penetrable (Fig. 5b), two of them upwards (marked by `A' and `B') and one downwards (`C'). The large avalanche-like downwelling which sinks from the upper mantle down to the bottom of the model can be seen at the back side of Fig. 5a (`C'). The two penetrating upwellings appear in the forefront of Fig. 5a and are well marked by their very large mushroom heads (`A' and `B'). Plume `A' is located in the corner of the box, thus, because of the symmetry conditions imposed on the sides, only a quarter of it can be seen. These penetrating upwellings are midmantle plumes in the sense that they come from the top part of the lower mantle and not from the basal boundary layer. Fig. 5c is a horizontal map of the temperature ¢eld taken in the upper mantle at 435 km depth and shows the distribution of the plumes: the small `hotspots' are upper-mantle
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Fig. 5 (continued).
Fig. 5 (continued).
plumes and the two broad ones (`A' and `B') are the mid-mantle plumes. Most of the plumes are concentrated in the front half of the box in Fig. 5a, i.e. far from the big downwelling `C'. A vertical cross-section centered on the mid-mantle plume `B' (Fig. 5d) shows well the layering of the £ow and that plume `B' has no root in the
deep lower mantle. Fig. 5e is a graph of the average vertical mass £ux w ´ as a function of depth, showing that layering is partial: there is a nonzero minimum in the mass £ux near the depth of 660 km. In the model of Fig. 6 uniform internal heating is added to the basal heating and the second asthenosphere is included in the viscosity function. To compensate for these factors which increase the vigor of convection, we reduced the surface Rayleigh number with respect to the previous case, now it is Ra = 107 . The rather high value of the internal heating (H = 10) changes the style of convection in the lower mantle: the upwellings are organized in broad, gently sloping `ridges' and there are no well-developed plumes as is characteristic of predominantly internally heated £ows [3,41,42]. However, the plumes are still present in the upper mantle. Fig. 6a shows a close-up of the most interesting corner of the model box with upper-mantle plumes and lower-mantle hot `ridges'. The snapshot is taken again at a partially layered stage of the £ow. Plume `D' of Fig. 6a penetrates through the phase boundary, and, as it is clear from the ¢gure, it has no deep root. Detailed analysis proves that it is fed by a predominantly horizontal £ow in the second asthenosphere which radially converges just below the `leak' of the 660 km discontinuity. The other plumes of Fig. 6a are upper-mantle plumes. This corner of the model box is so densely populated by plumes that their heads coalesce into one big pancake-like hot feature in the asthenosphere. Fig. 6b shows the two spots where there is mass
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Fig. 6. Three-dimensional model with two low viscosity zones and with internal heating; Ra = 107 . `D' marks the upwelling described in the text. (a) Perspective view of a corner of the model box with two isotherms; for the blue surface T = 0.40, for the red surface T = 0.80. (b) Contour map of the vertical mass £ux w at 660 km depth. Vertical mass £ux is practically zero almost everywhere in this plane, the exceptions are the indicated spots. (c) Map of the temperature in the upper mantle at 435 km depth. (d) Temperature ¢eld in a vertical section across plume `D'; in panel (c) an arrow marks the direction of this cross-section. (e) Horizontally averaged vertical mass £ux w ´ as a function of depth. Units, contouring, coloring and other markings as in Fig. 5.
£ow across the phase boundary, and Fig. 6c is a map of the temperature distribution at the depth of 435 km, showing the location of the mid-mantle plume `D' and the thinner upper-mantle plumes. Fig. 6d is a vertical section across plume `D', indicating also an upper-mantle plume. It is obvious that plume `D' makes a hole in the 660 km boundary layer, while the other one rises from the top half of this internal boundary layer. The average vertical mass £ux pro¢le in Fig. 6e shows clearly that there is vigorous £ow in the second asthenosphere below the phase boundary. 4. Discussion and concluding remarks The principal aim of this study is to demonstrate the possibility of a new style of convective plumes in the mantle. The necessary conditions for the existence of these `mid-mantle plumes' is that the spinel^perovskite phase transition at 660
km depth should act as a strong, but incomplete barrier to vertical £ow. If this barrier leaks at relatively small spots, upward directed `eruptions' of the lower-mantle material take, in the upper mantle, the form of the usual mushroom-shaped plumes. These mid-mantle plumes are the upward directed equivalents of the downwelling avalanche events which received great publicity in earlier studies of the dynamic consequences of an endothermic phase change [9,27,28]. In the preceding section we have shown in several examples that simple models of the mantle with the spinel^perovskite transition reproduce the conditions for mid-mantle plumes if the Rayleigh number is around 107 . It is known [8,36] that, with ¢xed properties of the endothermic transition, the increase of the Rayleigh number tends to inhibit mass transfer across the transition zone, while the decrease of Ra leads to extensive £ow across the phase boundary, destroying eventually all signs of £ow strati¢cation. Our models
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Fig. 6 (continued).
Fig. 6 (continued).
show that there must be an interval of Ra where convection is strongly strati¢ed but cylindrical jets pass through the transition zone at several spots. This range of the Rayleigh number is found around 107 which can be a representative value for the real mantle. Then the ascending penetrative jets are thin and plume-like.
The root region of these mid-mantle plumes is a localized volume in the topmost part of the lower mantle, below the phase boundary. If there is a low viscosity layer (`second asthenosphere') below the spinel^perovskite transition zone, this layer focuses a predominantly horizontal £ow towards the spot where the plume breaks through the phase boundary. Then the second asthenosphere constitutes the source volume of mid-mantle plumes. As for example Fig. 3a shows, the possibility of mid-mantle plumes does not exclude that some `classical' CMB plumes cross the 660 km discontinuity at the same time. This means that three kinds of plumes can reach the base of the lithosphere simultaneously (Fig. 1): classical boundary layer plumes rising from either the depth of 660 km or from 2900 km, and the mid-mantle plumes described in this study. A fourth kind, lower-mantle plumes in the strict sense, cannot penetrate into the upper mantle and will not have direct e¡ects on the Earth's surface. It is worthy of note that in models (e.g. in Fig. 6) where internal heating is predominant in the lower mantle and basal heating gives a relatively little contribution, there are no well-developed lower-mantle plumes. In such a case the only way to get upwellings from below a strong endothermic transition is in the form of `mid-mantle plumes'. The mid-mantle plumes of our models are very vigorous and robust convective upwellings. The vertical velocity along their axis can be 5^10 times higher than the velocity in the center of the classical upper-mantle plumes, therefore they can de-
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velop a surface hotspot very rapidly. The stem of the mid-mantle plumes is thicker than that of the upper-mantle plumes, and can reach a diameter of 400^500 km in the models presented above. The plume heads can be as large as 1000^1500 km in radius, with much higher central temperatures than in the upper-mantle plumes. Due to their large dimensions, the tomographic identi¢cation of the mid-mantle plumes, if they exist in the Earth, should be much easier than the detection of the classical boundary layer plumes. The surface manifestation of these eruptions of the topmost lower mantle can be profound, e.g. extensive £ood basalt volcanism can be expected over at least as large areas as in the case of newly initiated CMB plumes [43,44]. The mid-mantle plumes sample a particular volume at the top of the lower mantle, and not only by some vaguely known mechanism of entrainment [23,26], but by transporting bulk lower-mantle material to the surface. This is a completely di¡erent source region than that of the classical plumes which rise from one of the boundary layers of the mantle. In this way, the mid-mantle plumes can sample a distinct geochemical reservoir, o¡ering a new possible agent for the explanation of the enigmatic diversity of isotopic signatures observed in hotspot basalts [21^24].
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Acknowledgements The authors thank discussions with David Brunet, Volker Steinbach and Fabien Dubu¡et on various matters of interactions between plumes and phase transitions. Helpful comments on the manuscript by Arie van den Berg and Ctirad Matyska are gratefully acknowledged. This research has been supported by the Hungarian grant OTKA T026630 and the geophysics programme of the National Science Foundation.[AC] References
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