Statement of the problem
Understanding convection in the Earth’s mantle is a primary prerequisite for understanding planetary evolution. It has long been debated whether the whole mantle convects whether separate lower- and upper-mantle convection occurs, or both [1, 2]. In 1971 Morgan proposed the so-called, plume mode of convection . Plumes, hypothetical hot buoyant structures, were postulated to represent uprising convective flow penetrating the whole mantle. Originally they were considered to rise subvertically from the lower mantle, break through the rigid lithospheric plates, and move subhorizontally providing the driving force for plate tectonics. Numerous computer simulations utilising dimensionless numbers, and analogue laboratory experiments on materials such as paraffin, have shown the primary characteristics of plume mode convection – a large head and a thin conduit (see  for a general review, and Figure 1a for a typical representation of a plume ).
Figure. 1. Comparison of (a) mantle plume convection, (b) the observed structure of the mantle (from Ritsema et al., 1999) and (c) penetrative convection. Drawings are slightly modified from ,  and  respectively. Bluish, yellow and brownish colors represent high-, normal- and low-velocity anomalies, respectively.
The clear postulates of the convection plume model, and logical explanation in the framwork of plate tectonics for the unidirectional migration of volcanism in some oceanic chains (e.g. Hawaii) and continental volcanic fields (e.g. Yellowstone) persuaded the majority of researchers, the author being no exception, to believe that plumes do exist. Consequently, the number of volcanic fields explained by plumes as the primary source of magma grew from about 20  to up to 5,200 in the extreme .
However, as the number of “plume-related” volcanic fields increased, the controversies and circular reasoning involved became obvious [6, 7]. One example is deep seismic tomography models, such as those presented by Ritsema and co-authors [8, 9] (Figure 1b). The large low-velocity anomalies in these models do not resemble envisaged plume structures, but are more similar to the high-velocity anomalies which are interpreted as subducted slabs by almost all researchers. Care must be taken, however, because the resolution of deep seismic tomography models is currently low  and there is a tendency for tomographic methods to widen artificially vertical anomalies in the lower mantle .
What if the shapes of large low-velocity anomalies in the mantle are real? Certainly they cannot then be explained in terms of classical plume model, because 1) they are too deflected from the vertical compared with what is expected  and 2) they are not circular in cross section, but instead they are sheet-like. Having noted these features, S.O. Balyshev and I postulated that such anomalies might be ancient heated lithospheric plates (slabs) buried in the mantle as a result of subduction . The concept that a velocity inversion could develop in a subducted slab as it warms up and partially melts, encouraged by the presence of volatiles, was originally suggested by T. Gasparik in 1997, who viewed this process as occurring in the upper mantle . To change dense, cold slabs to low-density, and thus low-velocity structures, we explored radioactivity as a source of heating.
We used the following initial assumptions for the calculations:
With these assumptions, heating of the subducted slab is easily possible .
In Figure 1c the penetrative convection model is shown, taken from the original publication of Silver et al. . In this model cooling and subduction of oceanic plates is the driving force for mantle convection. In reality, the subducting slabs are themselves the downwelling convective flows. Silver et al.  assumed that buried mantle slabs warm to reach the ambient temperature of the mantle and at that time become buoyant because of the difference in chemical composition between the slab and the mantle. When buoyant, slabs start to rise from the lower mantle towards upper mantle. In this way, the reheated slabs comprise the upwelling convective flows. To my knowledge, the conversion of dense slabs to low-density structures at ambient mantle temperatures had not been tested. However, radiogenic heating of the slabs strengthens the model of penetrative convection. If it is correct, plate tectonics acquires a primary role in convection on the scale of the whole mantle.
When re-examining seismic tomography images of the mantle (Figure 1b) in the light of the penetrative convection concept, a candidate explanation for at least two of the most prominent low-velocity structures becomes immediately obvious – the anomalies are sheet-like because they are ancient, reheated subducted slabs.
Detailed discussion of the radiogenic isotope geochemistry of oceanic basalts that is commonly used to support the plume hypothesis is beyond the scope of this brief article. Nevertheless, a few comments are worthwhile. In our paper  S.O. Balyshev and I repeated the common mistake of geochemists that high 3He/4He ratios can be used as reliable tracer of a lower mantle contribution. Indeed, this is not the case [15, 16]. Other isotopes, for instance Sr-Nd-Pb isotopes, can say nothing about a lower mantle contribution either. According to conventional geochemical interpretations, three of the four so-called mantle tetrahedron end-members EM1, EM2 and HIMU, are considered to be related to the subduction of continental lithosphere, pelagic sediments and oceanic lithosphere, respectively ( and references therein). In many standard plume models these components are thought to be stored at either the core-mantle- or lower-upper-mantle boundaries for prolonged intervals of time (1-2 billion years) where they attain their highly evolved radiogenic-to-stable isotope ratios (e.g. low 143Nd/144Nd for EM1, high 87Sr/86Sr for EM2 and high 207Pb/204Pb and 206Pb/204Pb for HIMU). They are then sampled at these depths by mantle plumes. Again, if we re-examine the data from the point of view of penetrative convection, there is no need for plumes at all to transport these components to the surface, and we do not need to change the geochemical interpretations. Heated, uprising slabs can deliver these components to the surface instead of plumes.
attributes the conversion of seismic anomalies in subducted slabs to the
development of small amounts of melt within them. Anderson 
suggests that melts can develop within slabs as a consequence of conductive
heating of the slab by ambient mantle and that the time scale for this
process is of the order of 20 Myr or less. Indeed this is plausible explanation.
However, some older, slab-like low-velocity anomalies are
Experimental data suggest that water-bearing minerals (e.g., superhydrous phase B) may survive within a slab up to the depths below upper-lower mantle transition zone and hence can provide significant flux of water into the lower mantle. Under greater depths these minerals provide water for Mg- and Ca-perovskite and magnesiowustite, the major water concentrators in the lower mantle ( and references therein). These minerals will dehydrate at different P-T conditions. Thus, slabs probably convert to low- and high-velocity anomalies several times during their storage in the mantle while degassing and melting because of conductive and further radiogenic heating.
When discussing the two largest low-velocity anomalies in the present day mantle, the African and South Pacific anomalies, we should also keep in mind that ancient ages are expected for them from enriched isotopic features of “hot spot” volcanic rocks. These anomalies cannot be related to recent subduction zones and hence if they result from velocity conversions, a radiogenic source of heating is still required.
The concept of penetrative convection in my view is logical and requires fewer ad hoc assumptions than the mantle plume model does at present. However, the model is not yet fully developed or understood. We nevertheless re-introduce it to highlight that it has to be thoroughly considered from different points of view, including physical modeling, 3D seismological probing and geological testing.
 Davies G.F., Richards M.A. Mantle convection.
J. Geology, 100, 151-206, 1992.