Revisiting the scale of mantle plume–induced hot spot swells

Abstract

Hotspot swells have typically been associated with mantle plume upwelling, yet the origins of much broader but lower superswells remain unclear. This study first reveals that swell width increases while height decreases at younger seafloor ages; it is possible for a single hot spot swell size to approach that of a superswell. Compressible numerical models replicate the observed trend. Modeling results suggest that both hot spot swells and superswells can form from interactions between mantle plumes and oceanic plates. Beneath young seafloors, the lateral redistribution of restitic, hence buoyant and relatively low-viscosity, lower lithospheric mantle due to plume impingement explains the formation of superswell-like morphology. These models effectively demonstrate lithospheric lid effects on mantle melting and support a reassessment of conventional methods for estimating core heat flux.

Superswell origin is linked to plume-lithosphere interaction, and greater plume heat transport from the mantle base is implied.

INTRODUCTION

Hotspot swells are ~1000-km-wide, ~1- to 2-km-high bathymetric features on the seafloor (Fig. 1, A to C) (1). Where found, these features are associated with hot spot volcanism (2), leading to the proposal of various mantle plume–related origins (3–6), although alternative mechanisms have also been proposed (7–12). Hotspot swells are not the only type of mid-oceanic plate topographic high. Later studies recognized a different kind of swell on young South Pacific seafloor, termed a “superswell,” which is two to three times broader yet less than half as high as a typical hot spot swell (Fig. 1, D to F) (13). Existing literature has generally proposed a shallow upper mantle origin for superswells, attributed to the presence of hot materials beneath (14), while the potential contribution of a deep–mantle plume–related process remains ambiguous (6, 15–17). Here, we explore whether mantle plumes can directly generate both types of swells, contingent upon the age/strength of the overriding plate; i.e., that beneath young oceanic plates that already contain a viscous, restitic, ~60- to 70-km-thick “compositional lithosphere” created during mid-ocean ridge melt extraction, which extends beneath their much stronger ~30-km-thick thermal lithosphere, the horizontal squashing of this restitic, buoyant lower lithosphere (BLL) mantle as additional “swell-root” restites to plume melting are added can explain the formation of broader, lower-amplitude superswells.

Fig. 1. Typical examples of a hot spot swell and superswell.

Seafloor depths of Hawaii (A) and southeast Pacific swells (D) (based on “earth_relief_03m.grd” from www.earthbyte.org/). MTS, Mountains. Age-corrected seafloor depths of Hawaii (B) and southeast Pacific swells (E) following the approach used in Morgan et al. (6). Gray contours mark the seafloor age (in Myr). We calculate the age-corrected seafloor depth by subtracting the seafloor depth with an assumed half-space cooling model depth: $d\left(\mathrm{m}\right)=-2650-300\sqrt{\text{age}\left(\text{Myr}\right)}$ (6). Isl, Islands. (C) Seafloor depth of the Hawaii swell, with the transect locations marked in (A) and (B). (F) Seafloor depth of the southeast Pacific swell, with the transect locations marked in (D) and (E).

Relationship between hot spot swell morphology and seafloor age

To summarize hot spot swells in mid-oceanic plate regions characterized by a prominent dome-like swell morphology, we used the hot spot list recompiled by S. D. King and C. Adam (2014) to assess their width and average height (figs. S1 to S24 and table S1) (we did not seek more precise measurements of each swell’s scale compared to previous studies; instead, here, we aim to further clarify general relationships between swell morphology and seafloor age.). On the basis of this summary, (i) swells situated on a >50-Myr seafloor tend to exhibit a narrow and tall shape (except for the Arago swell); (ii) those located on a <20-Myr seafloor primarily develop a broad/low-amplitude morphology (except for the Iceland and Galapagos swells also associated with the much thicker crust produced by hot spot melting directly beneath a spreading center; figs. S1 and S9); and (iii) in cases where swells are near mid-oceanic ridges, there is an elongation of the swell in the direction parallel to the ridge, resulting in a height-to-width ratio along this long axis that can be ~1.4 times smaller than that measured along the short axis (e.g., the Ascension and Marion swells in figs. S3 and S14, respectively; table S1). Therefore, it appears that “classic” hot spot swells and broader superswells tend to develop upon old and young seafloor, respectively.

It is well accepted that the oceanic plate gradually becomes cooler and stronger as it ages and migrates away from the mid-oceanic ridge (18–20). It was later proposed that, due to the extraction of water-rich melts at the mid-oceanic ridge, the oceanic plate contains a “dry” compositional lithosphere to a depth of ~70 km (21–23). The compositional lithosphere extending deeper than the thermal lithosphere created by plate cooling is both more buoyant due to its restitic melt extraction–induced depletion and ~10- to 500-fold more viscous than the underlying, less-melted, and still-damp background asthenosphere (21–23). Here, we will call this relatively viscous, buoyant, lower lithospheric region the BLL. From this perspective, when an oceanic plate is old enough (i.e., >80 Myr), its much higher–viscosity thermal lithosphere will have grown to the base of the BLL, so that the entire “plate” will be composed of very–high-viscosity thermal lithosphere. In contrast, the BLL below younger oceanic plates is still susceptible to deformation under imposed basal stresses or bottom-side additions of similarly buoyant and viscous restitic hot spot swell-root material (6, 21). Consequently, a young oceanic plate will exert fewer restrictions on the upwelling and melting of an underlying plume, leading, for the same upwelling plume flux, to the formation of a broader, lower-amplitude superswell than the hot spot swell formed by the restitic plume materials beneath older lithosphere (6, 16). [In the case of Iceland (and Galapagos) swell, due to the much greater-than-normal crustal thicknesses produced by hot decompression melting beneath the ridge axis and the higher-degree melting of the mantle within the plume-ridge–interaction region, e.g., compared to Jan-Mayen in fig. S10 (24), the young oceanic plate can develop greater crustal-thickness–supported relief than that seen at typical off-axis superswells.]

Numerical modeling of hot spot swell and superswell formation

To explore the above hypothesis, we designed two-dimensional (2D) compressible numerical models to investigate the formation of a hot spot swell beneath oceanic plates (fig. S25 and tables S2 and S3). We considered two sets of initial conditions regarding the thermal structure of the mantle: (i) The mantle beneath the lithosphere has a potential temperature (1350°C) of the mid-ocean ridge basalt (MORB) mantle source, or (ii) the background mantle below the ~300-km depth of the base of the asthenosphere is 200°C lower than 1350°C, as has been proposed in some previous studies (25, 26), while shallower lithospheric depths still follow a half-space cooling model (18) to a MORB-source asthenospheric temperature. In the 607 experiments explored here (table S2), the main variables include (i) the seafloor age of the oceanic plate, which controls the thickness of the initial thermal lithosphere, hence also the thickness of its underlying BLL; (ii) the initial excess temperature of the plume relative to the MORB source; (iii) the scale of the lower-mantle thermal anomaly involved in plume-like mantle upwelling (Fig. 2A and fig. S25); (iv) the density of the plume’s restitic melted residues (21, 26–28); and (v) the thickness, viscous strength, and compositional density of the BLL (29, 30). Details of the model setup and the modeling method are described in the Materials and Methods and Supplementary Materials. Parameters for different materials are given in table S2.

Fig. 2. The styles of hot spot swells formed upon old (80 Myr) and young (10 Myr) oceanic plates.

(A) Temperature snapshot of Run 526 (table S2). Material (B), viscosity (C), and density (D) snapshots at the same time. (E) Temperature snapshot of Run 530 (table S3). Material (F), viscosity (G), and density (H) snapshots at the same time. BLL created by melt extraction at the mid-ocean ridge. Run 530 is the same as Run 526, except for the seafloor age. In the two models, the initial excess temperature of the plume relative to the MORB source (1350°C) is 125°C, and the background mantle below 300 km deep is 200°C lower than 1350°C. The parameters for the outer and inner plume materials are the same (table S1), but the initial temperature of the outer gradually decreases from the inner to the background value (fig. S25). A detailed summary of both models’ evolution is in fig. S26 (temperature) and figs. S30 to S33 (density and viscosity). LAB, the boundary between the BLL and asthenosphere/plume materials. BLL, buoyant lower lithosphere.

Below ~300 km, most numerical models evolve in a similar pattern (fig. S26). Because we focus here on plume-lithosphere interactions, we chose the proposed parameters for mantle phase transformations to facilitate the smooth penetration of the plume through the mantle transition zone (MTZ) (figs. S26 to S28) (31). For these parameters, a thermally induced (2D) plume will have a ~110- to 170-km-wide head and a 20- to 30-km-wide tail (fig. S26). Upon reaching the upper mantle, the plume undergoes initial melting at ~270- to 160-km depths, depending on its excess temperature (fig. S29).

The model evolution patterns begin to diverge, as the plume approaches the overriding plate. In the scenario of an 80-Myr-old oceanic plate (Fig. 2, A to D), the lithosphere maintains a high strength/viscosity to the base of the BLL (~70 km deep), which does not yield to strain-rate weakening (Fig. 2C). Consequently, plume materials stop upwelling at ~70 km deep before expanding horizontally to achieve a ~800-km width (Fig. 2 and fig. S26). Because of the compositional and thermal buoyancy of the melted residues/restites (Fig. 2D), a ~1000-km-wide swell with a ~1000-m average height will form at the surface (Fig. 2A versus Fig. 1C).

In contrast, because of the hotter geotherm of the ~10-Myr oceanic plate, the more fluid BLL (Fig. 2I) permits plume materials to push upward to ~40 km deep (Fig. 2, H and J). The buoyant BLL adjacent to the plume is horizontally squashed from its initial 70-km thickness to become locally thicker than 80 km. This induces surface uplift, with the uplifted region extending to >1000 km from the plume center (Fig. 2K). Consequently, a much broader region of lower uplift will form for the same underlying plume supply—a superswell (Fig. 2E). In addition, the vertical motions associated with additional decompression melting of upwelling plume materials also lead to the generation of ~5 to 20% greater supply of restitic plume materials for the same temperature plume upwelling (figs. S43 and S44). After the ~4-Myr rise time of the initial plume material, restitic plume materials are dominantly distributed shallower than 175 km deep beneath the seafloor (fig. S43 versus fig. S44).

Further sensitivity tests indicate that the width of the modeled hot spot swells tends to increase, while their average height generally decreases with decreasing seafloor age, consistent with observations (Fig. 1 and fig. S1 versus Fig. 3B and figs. S34 to S41). This trend is enhanced by reducing the compositional density of the plume’s melting residue (figs. S34 and S35) or by increasing the BLL thickness (figs. S36 and S37). It is also slightly influenced by the excess temperature of the mantle plume (figs. S34 and S35). A relatively low viscosity of the BLL helps to increase the monotonicity of the trend (figs. S38 and S39). When the BLL is strong (the viscosity of diffusion and dislocation creep is no less than the reference value), the swell formed on a 10-Myr young seafloor is ≤1600 km wide (fig. S38), less than the observed width of superswells (fig. S1). Should the BLL become particularly weak (e.g., if the viscosity of diffusion and dislocation creep is 10⁵ and ~27 times weaker than the reference value, respectively) (figs. S38 and S39) or if the volume of the plume materials is too small (e.g., less than half of the reference value) (figs. S40 and S41), then the trend becomes less monotonic, and a notable swell often does not form. The general relationship between swell morphology and seafloor age remains consistent in models with both “standard-adiabat” and “sub-asthenosphere-cooler-adiabat” mantle geotherms (fig. S42).

Fig. 3. Summary of various sensitivity tests.

(A) Topography snapshots of Runs 526 to 530 at 14 Myr (table S3). Ages next to the line keys denote the corresponding initial seafloor age. (B) Swell morphology in Runs 526 to 535 (table S3). Runs 531 to 535 are the same as Run 526 to 530, respectively, except that the viscosity of the diffusion and dislocation creep of the sublithospheric depleted mantle is 10 and 1.93 times weaker. Visc. A is the preexponential factor in equations for viscosity (eq. S6). (C) Effects of the plume temperature on swell morphology (table S3). Ages in Myr denote the seafloor age, and the temperature marks the initial excess temperature of the plume relative to the mantle source of mid-oceanic ridge basalts (1350°C). (D) Effects of the plume temperature on swell morphology. Aver., Average.

Comparison of numerical experiments with natural examples

In models for young oceanic plates, both the buoyant plume materials and shortened/thickened BLL contribute to the superswell formation. The actual horizontal spreading of new swell-root material can be even more laterally confined than that in models representing an old oceanic plate (Fig. 2B versus Fig. 2F). On the basis of these results, clusters of similar-size swells on young seafloor can merge to form an even broader superswell (Fig. 1E) (17), e.g., due to the thickening of the buoyant yet deformable BLL that surrounds the region of plume-lithosphere interaction (Fig. 2, E and F). Likewise, if the anomalously thick BLL associated with a superswell passes over another hot spot, as has happened in the South Pacific for Arago, Rarotonga, and Macdonald plumes, then there will be greater “superswell-like” spreading of the hot spot swell root (fig. S1) as long as the thermal lithosphere has not yet extended beneath the BLL. Similar lateral redistribution of the BLL could have been more universal in the Archean, where the degree of sublithospheric mantle depletion and related compositional buoyancy may have been even higher than the modern interaction regions of a mantle plume and young oceanic plate (32, 33). Furthermore, in models where the plume exhibits a high excess temperature, although the plume materials below a thick cold lithosphere can spread broadly to a ~1500-km-wide range, the height-to-width ratio of the resulting swell remains >0.8 (Fig. 3C), differing from the characteristic morphology of superswells (Fig. 1F and fig. S1). Thus, the supply of plume materials beneath oceanic lithosphere does not fully constrain the morphology of the induced hot spot swell; instead, the strength and thickness of the BLL, closely linked to seafloor age, will also play a key role.

In nature, seafloor age, lithospheric properties, and mantle potential temperature are unlikely to be as homogeneous as assumed in these simplified models. In regions adjacent to mid-oceanic ridges (especially slowly spreading ones), variations in seafloor age and lithosphere strength occur rapidly in the direction perpendicular to the ridge. Fracture zones with lithospheric age offsets also frequently happen and can shape the lateral spreading of swell-root material (34). In addition, lateral variations in mantle potential temperature may control the presence and the absence of the buoyant and deformable BLL under young oceanic plates (32), which can be more variable than assumed in the simplified models (e.g., fig. S25).

Distribution of plume materials and seismic discontinuities in the upper mantle

Figure 4 illustrates the distribution of plume materials and their melting behaviors in models where the mantle below 300 km is initially 200°C lower than its overlying plume-fed asthenosphere that forms the source for ridge melting (25, 26). At the later stage of these models, melting is concentrated at ~160- to 140-km depths (Fig. 4A and fig. S29) (35). The presence of the plume’s melting residue inhibits further melting below it [i.e., a compositional form of the “lid effect” (36)], while later melting often occurs in regions far from the swell center (fig. S29), consistent with observations at Hawaii (37). The lid effect on mantle melting is further revealed by the volume proportion of the melted plume materials relative to the total. Compared to the model where the seafloor is 80 Myr old, this proportion increases by 5 to 20% in models with a 10-Myr oceanic plate (Fig. 4B and figs. S43 and S44), and the lid effect becomes increasingly evident for high plume temperatures (figs. S43 and S44).

Fig. 4. Distribution of instantaneous melting and plume materials in representative models.

(A) Evolution of melting depths (table S3). +xxx°C demonstrates the initial excess temperature of the plume relative to the mantle source of mid-oceanic ridge basalts. (B) Evolution of the melted plume’s proportion relative to the total plume materials in the upper mantle. Melted plume materials are those with a partial melting degree > 5% and shallower than 175 km deep (21, 30). (C) Migration trajectory of plume materials. (D) Temperature of plume materials at different depths. (E) Cartoon figure summarizing the distribution of melting and plume materials in the upper mantle. Key variables for each run are in table S3. PVG: positive seismic-velocity gradient (37, 38). Another version of this figure with a different colormap is in fig. S45.

In addition to spreading beneath the base of the lithosphere, plume materials can also spread laterally within the MTZ and, for “cool plumes”, possibly even at ~240- to 290-km depths (Fig. 4C) beneath a warmer/more buoyant overlying asthenosphere. Plume materials residing within the MTZ were initially located at the edge of the lower-mantle thermal anomaly with a lower temperature than at the center (fig. S25). During their ascent, they gradually cooled and so had a reduced buoyancy, which impeded their further penetration through the MTZ. Subsequently, this plume material entered small-scale convection within the MTZ (Fig. 4C). Furthermore, certain portions of the “colder” plume materials eventually ascended to a <300-km depth; however, the gradual cooling and associated increase in density prevented their continued upwelling, leading to their descent below ~200-km depths. If the deeper mantle is colder than shallower plume-fed mantle (Fig. 4D and fig. S25B), then the cooled but not sufficiently cold plume materials (denoted by the blue arrow in Fig. 4D) will temporarily remain buoyant above ~300 km deep (Fig. 4C). The accumulation of plume materials within the MTZ could potentially displace portions of more water-enriched materials into the shallower mantle, which could then undergo partial melting (38), potentially contributing to the low seismic-velocity zones (LVZ) above the MTZ in proximity to hot spots (Fig. 4E) (39).

Conversely, in scenarios where the mantle has the same potential temperature as the MORB source, both hotter and cooler plume materials will ascend into the upper mantle without the possibility of becoming trapped within the MTZ (fig. S26); although their cooler portions can sink from the lithosphere base back into the MTZ (fig. S26), thereby preventing plume material accumulation at >200-km depths (fig. S42). This feature of plume dynamics would need additional observations and 3D numerical experimentation to determine whether it could be used to differentiate whether the noncratonic asthenosphere is warmer or at the same potential temperature as its underlying MTZ (fig. S25B).

These experiments are only applicable for a relatively fast-moving plate where the “plume material”, possibly not very hot (40), corresponds to the plume flux associated with the swell root beneath a particular 2D stripe of seafloor. For plumes beneath slowly moving lithosphere or lithosphere with fracture zones, changes in seafloor age, or lateral changes in initial BLL thickness related to ridge melting, similar 3D numerical experiments would be necessary [cf., Yamamoto and Morgan (34)].

Implications for the Earth’s heat budget

On the basis of previous studies, the summed area flux of subducted oceanic plates is ~2.7 to ~4 km²/year (41). Suppose the heat flux from the core is carried by active mantle upwellings, and this total upwelling flux is now contained beneath all magmatic and amagmatic swells, then this upwelling heat flux has been recently reestimated to be ~6.3 terawatts (42). [For comparison, the contribution from radioactive heat production in the mantle was recently reestimated as ~16 terawatts (43) and ~13 terawatts (44).]

The swell area or volume is fundamental to the approach that Hoggard and previous workers have taken to estimate the heat flux from the core-mantle boundary (42, 45–47), and the assumption that the volume of plumes (or mantle upwelling) is fully revealed from swell morphology can contribute to an apparent heat flux gap. According to our above numerical experiments, the swell volume produced for the same plume conditions would vary with seafloor age (Fig. 3, A and B). In the reference model, the volume of the plume materials supporting the swell constitutes only ~¹/₂ to ²/₃ of the total plume materials in the upper mantle (Fig. 4B); the inferred total heat flux of plume/mantle upwelling would be increased by 30 to 50%. However, in 2D Cartesian experiments similar to these, the ratio of (cooler) outer flux of upwelling plume material to hotter central material would be many times smaller than it is for 3D (i.e., axisymmetric) plume upwelling. For example, for uniform-viscosity Poiseuille flow, the velocity profile for a vertical 2D Cartesian channel between x = 0 and x = h is given by $u\left(x\right)=\frac{\mathrm{\Delta \rho }g}{2\mathrm{\mu }}\left[x(h-x)\right]$ , [cf., Turcotte and Schubert (18)], where $\mathrm{\Delta \rho }g$ is the buoyancy and μ is the viscosity of material in the upwelling slot. For this geometry, the central half of the upwelling slot $(\frac{h}{4}<x<\frac{3h}{4})$ has three times the upwelling flux than the outer half of the channel. For axisymmetric 3D upwelling in a pipe of radius R, the velocity profile is given by $u\left(r\right)=\frac{\mathrm{\Delta \rho }g}{4\mathrm{\mu }}(R^2-r^2)$ . In this case, the central upwelling region from $0-\frac{R}{2}$ has only ⁷/₉ the upwelling flux of the region between $\frac{R}{2}-R$ . For this idealized plume conduit, the central upwelling region is ⁷/₂₇ or ~4 times weaker for an axisymmetric 3D plume relative to the plume’s cooler rim flux than in the 2D experiments shown here (see the Supplementary Materials for more details). However, beneath a moving plate, the 2D Cartesian approximation used here does much more accurately capture the 2D-like lateral spreading of swell-root material [see Yamamoto and Morgan (34)]. In some numerical experiments described in the Supplementary Materials, we crudely model this 3D effect by increasing the solidus temperature of plume-rim material (fig. S46). When done, the upwelling plume flux is even larger than the swell-root buoyancy associated with hot spot melting, with the additional plume-fed material spreading beyond the confines of the hot spot swell. This effect, in addition to the inherent subjectivity in measuring swell morphology (42, 48) and the possibility that mantle plumes may not always reach the lithosphere base to cause swell-like uplift (49, 50), all imply that using hot spot swell volumes to infer Earth’s core heat flux is likely to provide only a relatively low-quality constraint on the minimum heat flux crossing the core-mantle boundary.

MATERIALS AND METHODS

We used the MATLAB-based program LaCoDe (51), based on a previous M2TRI code (52–55), to model plume-lithosphere interactions. LaCoDe incorporates a solver for the Stokes equations that treats a compressible nonlinear rheology (51). The model features a free surface at the top (56) (e.g., a top surface with no shear or normal stress), thereby making the topography sensitive to mantle convection. During plume upwelling, both potential decompression and heat-induced melting for a pure peridotite source are calculated at each time step. We also accounted for the effects of melting depletion and source mineral assemblages (asthenospheric versus lithospheric mantle) on the solidus (fig. S25C). Key governing equations are described in the Supplementary Materials.

Because of the motion of its overlying oceanic plate, a mantle plume cannot continuously interact with the lithosphere at a restricted location for long. However, because of the varying plume fluxes and horizontal speeds of oceanic plates, in addition to potential uncertainties involved in plate reconstructions, there is no universally applicable plate velocity or plume flux. For simplicity, we fixed the initial volume of plume materials in each model (fig. S25), so that upwelling beneath a 80-Myr seafloor could induce Hawaii-like surface uplift (e.g., Fig. 2A and fig. S26F). For this implied swell cross-sectional estimate for a plume volume flux of ~320,000 km³/Myr/(80 km/Myr) = 40,000 km² beneath a plate moving with an absolute speed of 80 km/Myr [e.g., absolute Pacific plate speed with respect to Hawaii (57)], our focus is on exploring the factors that cause the observed relationship between hot spot swell morphology and seafloor age (fig. S1). These simplified models cannot be applied to more specific scenarios, where corresponding plume flux versus plate motion parameters should be considered in greater detail, e.g., the overriding plate speed, crustal structure, BLL thickness, mantle potential temperature, mantle plume properties, etc.

In all models, we assumed that the compositional density of unmelted plume materials is equivalent to that of the background mantle (3390 kg/m³) (58, 59). However, for plumes that contain recycled oceanic crust (60), 1% melting can result in >0.1% density reduction (26). For simplicity, in almost all of the presented models, we tested a compositional density of 3310 to 3350 kg/m³ for the melted plume materials (59), consistent with the densities of restitic “pyrolite” peridotite mantle. As we are focused here on the potential lateral spreading of a warm, dry-peridotite hot spot swell root and its interaction with a similar dry-peridotite BLL, this simplification seems appropriate.

To better address the topic of the ratio of hot spot swell-root material to the total upwelling plume flux, a more complex bilithologic peridotite + pyroxenite mantle would need to be investigated, as would calculations that included a much larger relative fraction of cooler plume-rim material to warmer plume-center material consistent with the relative fraction of plume-rim to plume-center material in an axisymmetric 3D plume. As the focus of this study was on hot spot swell evolution beneath old and young oceanic lithosphere, we chose to use these simpler model conditions.

Supplementary Materials

This PDF file includes:

Supplementary Methods

Figs. S1 to S46

Tables S1 to S3

References