## Abstract

The statistical correlation between the locations of hot spots at the surface of Earth and the distribution of ultra-low-velocity zones at the base of the mantle has about a 1 percent chance of arising randomly. This correlation is more significant than that between hot spots and negative velocity anomalies in tomographic models of deep mantle compressional and shear velocity. This correlation is consistent with the notion that many hot spots originate in a low-velocity, probably partially molten layer at the core-mantle boundary and undergo little lateral deflection on ascent.

The underlying control on the geographic distribution of hot spots, linear chains of volcanic edifices whose source appears to be fixed relative to surface plate motions, is uncertain. Hot spots tend to be distributed near long-wavelength geoid highs (1) and mid-ocean ridges (2), each of which may in turn be associated with slow seismic velocities in the lower mantle (3, 4). The upwellings that give rise to hot spots are widely thought to originate as instabilities near the core-mantle boundary (CMB) (5, 6), as this region likely represents a major thermal boundary layer. Geophysical observations that support hot spots originating near the CMB have, however, been notably lacking (7), although possible geochemical evidence for such a provenance exists (8). Here we examine whether hot spots are correlated with the presence of recently discovered 5- to 40-km-thick features at the base of Earth's mantle with compressional wave velocities depressed by as much as 10% from the overlying mantle (9–13). These ultra-low-velocity zones (ULVZs) are likely generated by the presence of partial melt at depth (10, 11); it is unclear whether this partial melt differs chemically from the overlying mantle through (for example) either iron enrichment or volatile enrichment (10).

Thus far, the Fresnel zones of seismic waves sample 44% of the CMB for the presence or absence of ULVZs and ULVZs have been observed to be present over 12% of the CMB (12, 13). The locations of the ULVZs are derived from diffracted compressional wave segments traveling along the mantle side of the CMB (9, 12, 14) and from reflected compressional waves that sample the upper boundary of this basal layer (11, 13) (Fig. 1). Where ULVZs have been detected, their thicknesses are >5 km; thinner zones may be present elsewhere, but an ∼5-km thickness is required for detection. The thicknesses of the ULVZs vary by up to 40 km over distances of ∼100 km (and possibly less) (9, 10); as such, the nonobservance of this feature does not preclude the presence of undetected patches of isolated ULVZs with lateral dimensions on the order of tens of kilometers.

ULVZs are present in six distinct regions: beneath the northern and central Atlantic Ocean, beneath Africa, south of Australia, and beneath the southwestern and northern Pacific Ocean (Fig. 1). They do not appear to be present beneath the Americas or beneath southern and central Asia, each of which are regions with relatively few hot spots. For comparison, we used the modified hot spot catalog of Sleep (6, 15), comprising 47 hot spots and estimates of their buoyancy flux.

We calculated the significance of the correlation between the hot spot and ULVZ distribution of Fig. 1 using two separate but complementary statistical approaches. The first approach calculated the numbers (and fluxes) of hot spots lying above ULVZs compared with those expected on the basis of an areally uniform distribution of independent hot spots (16). This algorithm simply determines the probability that a given number (or flux) of hot spots lying above the ULVZs could arise through random processes (17). Our second approach calculated the probability that random rotations of the hot spot distribution can produce improved correlations with the structure of the lowermost mantle; this method is designed to remove biasing of our statistics by either spatial clustering (mutual dependence) of hot spots or by our spatial sampling of the ULVZs.

To determine how many hot spots lie above ULVZs, we indexed the presence or absence of this feature (Fig. 1) on a 1° by 1° grid. On the 60-km length scale of this sampling, a number of hot spots (such as Tahiti) lie above ULVZs. For hot spots near the boundary between ULVZs and zones that have not been seismically investigated (such as Hawaii and Pitcairn Island), we imposed that at least 10% of the area of underlying latitude-longitude grid cells within 2° of the hot spot must lie in the ULVZs (18). In regions where no ULVZ has been observed and known ULVZs are juxtaposed (such as the Tasman hot spot), the number of latitude-longitude grid cells within 2° of the hot spot within the ULVZs must exceed those in which no ULVZ has been detected by at least 10%.

To further assess the robustness of our correlations, we examined the correlation of hot spots and hot spot flux with tomographically derived compressional (P) (19) and shear (S) wave velocity (4) models of the lowermost ∼300 km of the mantle. The spatial coverage of these P - and S -wave models is global, whereas our constraints on where the ULVZ is present or absent are not. We therefore sampled the tomographic models for the same 44% of the planet as was sampled for the ULVZ in Fig. 1 and conducted 10,000 Monte Carlo samplings of the global models at the 44% level.

As shown in Fig. 2, 13 of 47 hot spots lie over the 12% of the CMB containing ULVZs, and 12 lie over the 32% of the CMB in which no ULVZs have been resolved (20) (the rest are over areas of the mantle that have not been sampled). For comparison with the P - and S -wave tomographic models, we selected the velocity contours that have the highest correlation with the hot spot distribution. For similar areas, the ULVZs produced a better correlation with both hot spot distribution and flux than either of the best correlated contours of the tomographic models (Fig. 2; 11 of 47 hot spots lie beneath this contour in the S -wave model). The correlation of the shear-velocity tomographic model with the hot spot distribution decreases for progressively shallower depths in the lower mantle.

The 0.0% velocity anomaly line, the boundary between slower than average and faster than average regions, provides the best tomographically derived prediction of hot spot location (Fig. 2). We attribute this correlation to the well-known avoidance between hot spots and cold downwelling regions of the mantle (1, 21,22). The best match between the hot spot distribution and the tomographic models thus likely reflects a broad length-scale anticorrelation rather than a genetic correlation. In contrast, the correlation between the ultra-low-velocity (and thus probably hot) zones and hot spots is consistent with a genetic association between these features.

A random areal sampling of the tomographic models (at the 44% level) produced correlations with the hot spot distribution that are similar to those derived from a sampling of the same 44% of the planet with ULVZ characterization (Fig. 2C). Again, these samplings produced an inferior correlation with both hot spot flux and hot spot location relative to the ULVZ [<7% of the random samplings of the S -wave model (and <0.03% of the P -wave model) lie beneath more than 13 hot spots and are better correlated with hot spot flux].

To minimize possible spatial biases, we also randomly rotated the hot spot distribution 10,000 times. We used the 44% areal sampling of the CMB of Fig. 1 and determined how many random rotations produced distributions of hot spot number or flux that improved on the match of the real hot spot distribution with the ULVZs (or with the tomographic models). Because there is some spatial clustering of hot spots, the marginal distribution of numbers and fluxes derived from random rotations exceeds that derived from a binomial distribution (Fig. 3, A and B); that is, anomalously large numbers of rotations produce an enhanced number (or flux) of hot spots relative to those expected from a random distribution. In this analysis, larger numbers of hot spots may be rotated into a region by random rotations, but most such clustered hot spots have smaller fluxes. Large hot spots tend to have fewer near neighbors, whereas smaller hot spots are more likely to cluster (6), with such clusters possibly being derived from the same basal source (23). Therefore, the combination of high numbers and high fluxes associated with the ULVZs again renders the correlation of this feature with the hot spot distribution more significant than the correlation with either of the tomographic models (Fig. 2C). The results in Fig. 2 and 3 thus show that of the known velocity variations in the deep mantle, ULVZs (Fig. 1) are most closely correlated with the surficial hot spot distribution. The correlation of this feature with flux-weighted hot spots has an ∼1% probability of arising randomly, whereas the most closely correlated tomographic P - and S -wave velocity anomalies (4,19) have about a 15 and 4% chance of being randomly produced, respectively.

The flux-weighted distribution of plumes is strongly peaked at spherical harmonic degrees 1 and 2 (15); this distribution is compatible with a 40-km-thick layer if the viscosity ratio between the overlying material and the boundary layer is greater than about 5 × 10^{6}. If the basal boundary layer of the mantle is 5 to 30% partially molten (10, 11), the viscosity of this layer could be depressed by substantially more than a factor of 5 × 10^{6}, in accord with the constraints of the power spectrum of hot spot distribution.

The general fixity of hot spots over time relative to plate motions indicates that the plumes tapping this anomalous basal layer, once established, have a relatively long life-span. Our correlation implies either that hot spots require a moderately thick (on the order of 10 km) basal layer to persist or that the local fluid flow associated with the hot spot upwelling provides an efficient means for advecting heat from the surface of the core, resulting in a local upwarping of isotherms and the elevation of a partially molten horizon into the mantle. The correlation of the ULVZs with surface hot spot position further indicates that mantle convection may not notably deflect plumes (24). Our results also support the existence of feedback between plate tectonics and the CMB. Continental breakup has been proposed to be correlated with hot spots (25); if ULVZs control the hot spot distribution, then the lowermost mantle may control the location of divergent plate boundaries at Earth's surface (26). For comparison, subduction may modulate the distribution of hot spots (22); therefore, the location of the ULVZs could in turn be determined by past plate convergence.

↵* Present address: Seismological Laboratory, University of California, Berkeley, CA 94720, USA.