Constraints on the composition and temperature of LLSVPs from seismic properties of lower mantle minerals
Kenny Vilella, Thomas Bodin, Charles-Edouard Boukaré, Frédéric Deschamps, James Badro, Maxim Ballmer, Yang Li
CConstraints on the composition and temperature of LLSVPsfrom seismic properties of lower mantle minerals
Kenny Vilella a,b, ∗ , Thomas Bodin c , Charles-Edouard Boukar´e d , Fr´ed´eric Deschamps b ,James Badro e , Maxim Ballmer f , Yang Li g a JSPS International Research Fellow, Hokkaido University, Japan b Institute of Earth Sciences, Academia Sinica, Taipei, Taiwan c Laboratoire de G´eologie de Lyon, UMR 5276, Universit´e de Lyon, Villeurbanne, France d Earth and Planetary Science Laboratory, ´Ecole Polytechnique F´ed´erale de Lausanne, Lausanne,Switzerland e Institut de Physique du Globe, Univ. Paris Diderot, Sorbonne Paris Cit´e, CNRS, Paris, France f Institute of Geophysics, Department of Earth Sciences, ETH Zurich, Zurich, Switzerland g Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy ofScience, Beijing, China
Abstract
Seismic observations have suggested the presence of two Large Low Shear VelocityProvinces (LLSVPs) in the lowermost mantle. These regions are likely to be chemi-cally distinct from the bulk mantle while influencing the thermal evolution of the wholeEarth. Despite their importance, the nature and origin of LLSVPs are still debated.Several studies have tried to infer their potential composition using seismic observa-tions with the hope to identify their formation mechanism. In particular, compositionsenriched in iron ( ∼
12 – 14 wt%) and bridgmanite ( ∼
90 vol%) are believed to begood candidates. Interestingly, these characteristics are somewhat consistent with thereservoirs produced by the solidification of a primitive magma ocean, except that theiron enrichment should be much larger ( >
20 wt%). Here, we provide a reappraisal ofpotential LLSVPs compositions based on an improved mineralogical model including,for instance, the e ff ects of alumina. We also systematically investigate the e ff ects of sixparameters: FeO and Al O content, proportion of CaSiO and bridgmanite (so that theproportion of ferropericlase is implicitly investigated), Fe + / (cid:80) Fe and temperature con- ∗ Corresponding author
Email address: [email protected] (Kenny Vilella)
Preprint submitted to Elsevier April 24, 2020 a r X i v : . [ phy s i c s . g e o - ph ] A p r rast between far-field mantle and LLSVPs. From the 81 millions cases studied, only79000 cases explain the seismic observations. Nevertheless, these successful cases in-volve a large range of parameters with, for instance, FeO content between 12–25 wt%and Al O content between 3–17 wt%. We then apply a principal component analysis(PCA) to these cases and find two robust results: (i) the proportion of ferropericlaseshould be low ( < + -bearing bridgmanite is much morefavored than other iron-bearing phases. Following these results, we identify two end-member compositions: a Bm-rich and a CaPv-rich. For each end-member composition,a large range of parameter is possible. We note, however, that a low temperature con-trast ( <
500 K) is more favored, and that a certain proportion between FeO content,Al O and oxidation state should be maintained. Finally, we discuss di ff erent scenar-ios for the formation of LLSVPs and propose that investigating the mineral proportionproduced by each scenario is the best way to evaluate their relevance. For instance, thesolidification of a primitive magma ocean may produce FeO and Al O content similarto those suggested by our analysis. However, the mineral proportion of such reservoirsis not well-constrained and may contain a larger proportion of ferropericlase than whatis allowed by our results.
1. Introduction
The emergence of tomographic models has led to an increased knowledge of thestructure and composition of the Earth’s mantle. A key result provided by these modelsis the existence of two large anomalous volumes located at the bottom of the mantle be-neath Africa and the Pacific (first reported by Su et al., 1994). These two nearly antipo-dal reservoirs, usually referred to as Large Low Shear Velocity Provinces (LLSVPs),cover up to 30% of the core-mantle boundary (CMB) and may reach a height up to1000 km (see review by Garnero et al., 2016, for more details). LLSVPs are charac-terized by a reduction of the shear velocity V S ( > V P ( > V φ . This causes an anti-correlation between V S - and V φ -anomalies (Masters et al., 2000), also observed in nor-mal mode data (Trampert et al., 2004). Early studies have noted that, while a tempera-ture excess may explain the reductions in V S and V P , it should also induce a reductionof V φ that is not observed. The anti-correlation between the behavior of V S and V φ wastherefore interpreted to as evidence of the thermo-chemical nature of LLSVPs (Ishiiand Tromp, 1999), i.e., these structures di ff er in temperature and composition from thefar-field mantle.Since their discovery, important e ff orts have been made to determine the natureand origin of LLSVPs. In particular, several geodynamical studies have explored vari-ous possible scenarios that may lead to the formation of structures mimicking LLVSP(Tackley, 1998; McNamara and Zhong, 2005; Nakagawa et al., 2010; Li et al., 2014). Acommon conclusion of these studies is that a reservoir of material denser than the bulkmantle can explain the shape of LLSVPs. However, it is di ffi cult to estimate preciselythe required density excess because other parameters (e.g., rheology) also influence thethermo-chemical structure (Deschamps and Tackley, 2008). In these works, the authorsmainly used the shape of the LLSVPs to assess the relevance of their models neglect-ing the constraints given by the seismic wave speeds anomalies. Alternatively, somestudies have used available data from mineral physics to constrain the potential com-position of LLSVPs (Samuel et al., 2005; Deschamps et al., 2012). More specifically,they calculated the density and seismic wave speeds for a large range of compositionsand compared them to seismological and geodynamical constraints. They found that areservoir enriched in bridgmanite ( ∼
90 vol%) and iron ( ∼
12 – 14 wt%), with respectto a pyrolitic composition, provides a good fit to observations.Previous studies, however, have left behind several important parameters such asthe e ff ects of alumina, ferric-ferrous iron ratios, and spin state transition. Here, we usea model including these e ff ects, together with an updated database for the properties3f minerals, to investigate the ability of about 81 millions thermo-chemical models toexplain the seismic signature of LLSVPs. Our mineralogical model is characterizedby six free parameters that are allowed to vary in large ranges: phase proportions inthe mineralogical assemblage (bridgmanite, Ca-silicate perovskite, and ferropericlase,which is dependent on the previous two as their sum must be 100%), iron and alu-minium content in that assemblage, ferric / ferrous iron ratio in bridgmanite (the onlyphase hosting iron in those two valence states), and temperature. For each set ofparameters, the density and seismic wave speed anomalies are calculated using theMie-Gr¨uneisen-Debye equation of state. The incorporation of alumina in bridgmanitechanges its bulk modulus, density and the Fe-Mg exchange coe ffi cient between bridg-manite and ferropericlase (Catalli et al., 2011; Piet et al., 2016; Shukla et al., 2016),while spin state transition a ff ects mainly the density and bulk modulus of ferropericlase(Fei et al., 2007; Catalli et al., 2010). As a consequence, these new features induce im-portant modifications on the calculated properties. For instance, a much higher contentof FeO can be incorporated (up to 25wt%) without leading to excessively high density.The identification of plausible thermo-chemical models requires to compare our re-sults with observations. Generally, available seismic observations provide robust con-straints on the seismic wave speed anomalies of LLSVPs. We therefore calculate theseanomalies by comparing the seismic wave speeds obtained for the di ff erent thermo-chemical models considered, with the ones obtained for a typical composition andpressure-temperature conditions of the bulk lower mantle. The calculated anomaliesare then compared to the observed ones. Due to uncertainties, we consider as success-ful all the cases with: (i) V S -anomalies between -2% and -7%; (ii) V P -anomalies lowerthan -0.5%, both being based on seismic tomography observations (e.g., Houser et al.,2008; Koelemeijer et al., 2016); (iii) positive V φ anomalies, for example observed innormal mode data (Trampert et al., 2004); (iv) compositional density ( ρ ) increase be-tween 2% and 2.8%, based on the values required by geodynamical studies to produce4eservoirs with the shape of LLSVPs (Li et al., 2014). From all the models we tested,a collection of 79000 cases, involving a large range of properties, satisfies these con-straints. We then describe and discuss in details these successful compositions.
2. Mineralogical model of the lower mantle
In order to calculate the density and seismic wave speed anomalies of LLSVPs, itis first necessary to know the properties of the bulk (far-field) mantle. In this section,we provide its general characteristics and the method used to calculate its density andseismic wave speeds. This process is based on an approach similar to that of Vilellaet al. (2015).
Our (reference) pyrolitic composition is composed of 18 vol% ferropericlase (Mg,Fe)O(hereafter called Fp), 75 vol% Bridgmanite (Mg,Fe)(Al,Si)O (hereafter called Bm),and 7 vol% Ca-silicate perovskite CaSiO (hereafter called CaPv). The assemblagecontains 8 wt% FeO and 3.6 wt% Al O to stick to a primitive mantle composition(e.g. McDonough and Sun, 1995). We further assume that iron in bridgmanite is 50%ferric and 50% ferrous, with an oxidation state Fe + / (cid:80) Fe equal to 0.5. The Fe-Mgexchange coe ffi cient between Bm and Fp, K Bm − Fp = (cid:18) FeMg (cid:19) Bm (cid:18) FeMg (cid:19) Fp , (1)is assumed to be constant and equal to 0.5 (Piet et al., 2016). Using this value, com-bined with the assumed FeO content, we can obtain the proportion x f p of FeO inferropericlase, (1 − x f p )MgO-( x f p )FeO, and the proportion x Bm of iron in Bm (Sup-plementary Material). To determine the proportion of the di ff erent phases in Bm, weassume that ferrous iron enters into Bm as FeSiO , while ferric iron enters into Bm as5eAlO . If there is an excess of Fe + , Fe O enters into Bm, whereas if there is anexcess of Al, Al O enters into Bm. Finally, we include the e ff ect of the Fe + spin statetransition in ferropericlase following Vilella et al. (2015). A more detailed descriptionof the model is available in Supplementary Material. We first estimate the isothermal bulk modulus at ambient conditions K T of pureend-members assuming a Voigt-Reuss-Hill average and using measurements of poly-crystal (Supplementary Table 1). Using these derived values combined to the pro-portion of the di ff erent mineral phases (described in section 2.1 and SupplementaryMaterial), we calculate the K T of the three minerals assuming again a Voigt-Reuss-Hill average. We then use the Mie-Gr¨uneisen-Debye equation of state (Jackson andRigden, 1996) to calculate the ratio V / V (or equivalently ρ/ρ ) of each mineral, P = K T (cid:20)(cid:18) V V (cid:19) / − (cid:18) V V (cid:19) / (cid:21)(cid:26) −
34 (4 − K (cid:48) T ) (cid:20)(cid:18) V V (cid:19) / − (cid:21)(cid:27) + ∆ P th , (2)where ∆ P th is the thermal pressure and the subscript zero indicates ambient conditionsfor volume V , temperature T , isothermal bulk modulus K T and its pressure derivative K (cid:48) T . Values used for mineral properties are reported in Supplementary Table 1 and 2.To obtain the density ( ρ ) of each mineral we now only need to calculate their densityat ambient conditions ( ρ ). For this, we estimate V for each mineral following aprocedure similar to that for K T , except that we use a simple arithmetic mean insteadof a Voigt-Reuss-Hill average. Finally, the density of the rock assemblage is obtainedby calculating the arithmetic mean of the density for the three minerals considered.6 .3. Seismic wave speed of the rock assemblage The calculation of the bulk sound speed, V φ = (cid:115) K s ρ , (3)requires only the determination of the isentropic bulk modulus K s that can be obtainedfrom the isothermal bulk modulus K T , K s = K T (1 + αγ T ) , (4)where α is the thermal expansion coe ffi cient and γ the Gr¨uneisen parameter. All theparameters in the eq. 4 can be calculated using the formalism of the Mie-Gr¨uneisen-Debye equation of state, so that the calculation of V φ is straightforward.The determination of V S and V P is however more complicated because they furtherdepend on the shear modulus ( G ), V S = (cid:115) G ρ , V P = (cid:115) K s + (4 / G ρ . (5)We calculate G in two steps. First, we use an available equation of state to account forthe pressure dependence (e.g., Bina and Hel ff rich, 1992), G ( T = K , P ) = (cid:18) V V (cid:19) / (cid:20) G + . (cid:20) − (cid:18) V V (cid:19) / (cid:21) (cid:18) G − G (cid:48) K T (cid:19)(cid:21) , (6)with G and G (cid:48) being the shear modulus and its pressure derivative at ambient condi-tions. Second, the temperature dependence is calculated following, G ( T , P ) = G ( T = K , P ) + dG / dT ( T − , (7)where G / dT is the temperature derivative of the shear modulus. Values of dG / dT G and G (cid:48) are estimated usingmeasurements of polycrystal following a similar procedure that for the isothermal bulkmodulus (Table 1).It is important to note that the determination of the shear modulus is subject to muchlarger uncertainties than the determination of the density and bulk modulus. First, theexperimental measurements are more challenging. Less data are available, and mea-surements are less robust. As such, we also consider results from ab-initio calculationsfor the shear modulus of Al-bearing bridgmanite (Shukla et al., 2015, 2016). Second,eqs. 6 and 7 used to extrapolate measurements are also less accurate. In particular,we use the temperature derivative of the shear modulus to estimate its temperature de-pendence (eq. 7), while it is likely to induce large uncertainties, since this temperaturederivative is probably not constant with pressure (Shukla et al., 2016).The procedure developed here allows to calculate the density, S-wave velocity, P-wave velocity and bulk sound speed as a function of pressure and temperature. Forthis, we assumed a typical pyrolitic composition that is appropriate for the lower man-tle. However, the same procedure can be applied to a large diversity of compositions,especially to compositions that may be relevant for LLSVPs. In the following section,we describe all the potential compositions investigated, with a particular emphasis onthose explaining the seismic signature of LLSVPs.
3. Potential compositions of LLSVPs
The purpose of this work is not to test specific LLSVPs compositions or natures,but to follow an approach with no preconception on their compositions. However, it isin practice impossible to consider all the minerals that potentially exist at the bottomof the mantle. The compromise proposed here is to focus only on rock assemblagesconsisting of the three minerals expressed in a pyrolitic composition (Bm, CaPv, Fp),8hile varying all compositional parameters within this assemblage. By varying theproportions of SiO , MgO, CaO, Al O , and FeO, we can vary the phase proportions ofBm, CaPv, and Fp, as well as the iron and aluminium content in these phases along withthe oxidation state. For the sake of simplicity, we chose to describe these compositionalparameters as the volumetric phase proportions of Bm and CaPv (Fp is bound to theothers as the sum Fp + Bm + CaPv has to be 100%), Al O content which is incorporatedin Bm, FeO content which partitions between Bm and Fp according to the partitioncoe ffi cient (Eq. 1), and the oxidation state (Fe + / (cid:80) Fe in Bm). Each of these parametersis varied in a systematic way within the lower and upper bounds listed in Table 2.Finally, we to prescribed the pressure and temperature conditions relevant for boththe far-field mantle and LLSVPs. We consider a far-field mantle with a pressure of P =
130 GPa, corresponding to the lowermost mantle, and a temperature of T = P is considered for LLSVPs, while, be-cause LLSVPs temperature is unknown (and likely to vary laterally), we allow theirtemperature T + ∆ T to vary. The temperature contrast ( ∆ T ) between far-field mantleand LLSVPs stands as the sixth parameters of our model (Table 2). In the follow-ing, this six-dimensional space is sampled uniformly giving an ensemble composed bymore than 81 millions models to investigate. Before identifying and discussing potential compositions of LLSVPs, it is im-portant to characterize the e ff ects of the six parameters on density and seismic wavespeeds. Because of the relatively large number of models and input parameters, wemainly present results using 2D histograms showing the distribution of all models asa function of one input parameter and one output ( V P , V S , V φ , ρ ). The main inter-est of these histograms is to reveal the trends between input parameters and outputs.Narrow distributions and large variations indicate that the input parameter is likely thedominant parameter a ff ecting the output. By contrast, wide distributions without clear9ariations suggest that the input parameter does not substantially a ff ect the output. Weplotted the 2D histograms for each output as a function of all 6 parameters. Figure 1shows the histograms corresponding to the dominant parameters (other histograms areshown in Supplementary Material).The V S anomaly is dominantly a ff ected by the temperature contrast, with decreas-ing V S as the temperature contrast increases. Note that the V S anomaly decreases byabout 1% for only a 200 K increase, which stands as a very strong e ff ect. The Al O content also plays a role, with a ∼
2% decrease of V S for a 10wt% increase of theAl O content. However, large change in Al O content is required to impact V S , sothat temperature variations appear to be a more straightforward mechanism to produce V S anomalies in the lower mantle. The V P anomaly exhibits a similar behavior as the V S anomaly, except that the Al O content has now a slightly larger impact than tem-perature. The V φ anomaly is mainly a ff ected by the Al O content, with V φ decreasingas Al O content increases, and to a lesser extent by the oxidation state, V φ increasingwith Fe + / (cid:80) Fe. Finally, density is, as expected, mainly a ff ected by the FeO content,with increasing ρ as FeO content increases.From a more general perspective, one may note that the three seismic wave speedsexhibit similar behaviors with variations of input parameters (Supplementary Figure2–4). In particular, seismic wave speeds are decreasing with increasing FeO content.The e ff ects of the temperature contrast and FeO content are therefore in agreement withthe findings of previous studies (Samuel et al., 2005; Deschamps et al., 2012). Perhapsmore surprising is the nonlinear e ff ect of the Al O content (figure 1). For Al O con-tent up to 4 wt%, seismic anomalies slightly increases and decreases for larger contents.This nonlinear e ff ect shows that it may not be fully appropriate to consider a constantseismic sensitivity throughout the explored parameter range as it has been done forsimpler mineralogical compositions (Deschamps et al., 2012). Finally, we note that theFeO contents investigated here (up to 28wt%) are much higher than in previous stud-10es (up to 14wt%). Our results suggest that adding Al O in the composition changesimportantly the properties of the rock assemblage and allows to incorporate a muchlarger proportion of iron while maintaining a reasonable density. The incorporation ofalumina is therefore crucial to investigate realistic mantle compositions and to obtainmore robust results. It is di ffi cult to determine unambiguously the precise characteristics of LLSVPs.First, these properties are likely to vary laterally, because of lateral variations of tem-perature and composition (Ballmer et al., 2016). Second, di ff erent tomographic modelssuggest di ff erent properties depending on the dataset and methods used. Third, tomo-graphic models are generally obtained through a linearized and regularized inversionthat includes damping and smoothing, so that the actual seismic signature of LLSVPsmay be underestimated.As a consequence, we choose here to select compositions satisfying rather conser-vative conditions: • V S anomaly compared to the far-field mantle between -7% and -2%. • V P anomaly compared to the far-field mantle lower than -0.5%. • Positive V φ anomaly compared to the far-field mantle.Note that constraining the V φ anomaly is challenging because it relies on the deter-mination of V S and V P that are usually imaged with separate tomographic inversionsat di ff erent resolution and with di ff erent levels of uncertainties. Nevertheless, seismictomography (Masters et al., 2000; Houser et al., 2008) and normal mode data suggesta positive anomaly (Ishii and Tromp, 1999; Trampert et al., 2004). We thus follow aconservative approach by applying this condition without setting an amplitude for theanomaly. In addition to these seismic constraints, we also use geodynamical constraintsand restrict our study to models with a compositional density di ff erence between 2%11nd 2.8% compared to the far-field mantle. This condition is suggested by the densitydi ff erence required to produce chemically distinct reservoirs with the shape of LLSVPsin geodynamic models (e.g., Li et al., 2014). For lower compositional density di ff er-ences, the material is entrained and mixed by mantle convection so that reservoirs arenot stable. For larger compositional density di ff erences, gravity segregation occurs andreservoirs tend to form layers without large topography. Among the ∼
81 millions mod-els studied, only about 79000 satisfy these conditions. Figure 1 suggests that most ofcases are compatible with the V P and V S anomalies deduced from seismic observa-tions. Hence, constraining potential compositions of LLSVPs requires constraints on V φ and ρ . Interestingly, as discussed in section 3, our calculation of V φ and ρ is muchmore robust than of V P and V S . Therefore, uncertainties on the determination of theshear modulus, and thus on V P and V S , do not a ff ect significantly our results. Note thatfrom a seismological point of view, it is the opposite, since V P and V S are much betterconstrained than bulk velocity and density. In the remainder of this study, we focus onthe 79000 successful models. The 1D and 2D-histograms showing the distribution of the successful models arereported in figure 2 for the six parameters. It is important to note that these distributionsare not indicative of the probability of a composition to explain LLSVPs, as changingthe sampling of the input parameters (i.e., lower and upper bounds) may change sub-stantially the observed distributions. Moreover, the sampling of the parameter space isintrinsically uneven because of the overall decreasing number of possible compositionwith increasing proportion of Bm. A simple way to explain this is that in the extremecase of 100% of Bm, CaPv is of course absent, whereas for a proportion of Bm equalto 60%, the proportion of CaPv + Fp is equal to 40%, so that the proportion of CaPvcan take any values between 0 and 40%. This uneven sampling tends to increase thefrequency of occurrence for low proportion of Bm or CaPv. It is therefore important12o focus only on the trends between the di ff erent parameters and on the conditions forwhich no successful composition have been found, which are both robust features.A thorough analysis of the results is however di ffi cult because of the large numberof parameters and successful models. To overcome this issue, we can try to reduce thenumber of parameters by identifying existing trade-o ff s. For instance, there is a stronganti-correlation between the proportion of Bm and CaPv (figure 2), i.e., an increase inthe proportion of Bm have to be balanced by a decrease in CaPv (and vice versa). Morespecifically, figure 2 shows that the proportion of Fp should remain almost constant andis typically < V φ of Fp compared to other minerals. Furthermore, this anti-correlation also suggeststhe existence of a linear relationship between the proportion of Bm and CaPv, i.e., thesetwo parameters are not independent and one of them can be chosen as a representativefor the two. In order to identify and quantify all the existing trade-o ff s, we apply aprincipal component analysis (PCA) to our dataset. The PCA provides a projection of a dataset in a new orthogonal coordinate systemwhere the vectors, called components, are linear combinations of the input parameters.In this approach, the new vectors are successively built such that they best explain thevariability of the dataset. The relative importance of each component is given by theircorresponding eigenvalue. If one or several eigenvalues are much lower than others,then all the variability can be explained by a lower number of parameters, indicating theexistence of one or several trade-o ff s between the input parameters. The componentswith a high eigenvalue can be analyzed to highlight the underlying trade-o ff s, and inturn reduces the number of independent parameters. The six components of our datasetwith their eigenvalues are reported in Table 3. Because the eigenvalues 1-3 are muchhigher than the eigenvalues 4-6, the components 4-6 can be viewed as negligible andthe components 1-3 are the principal components. The dimension of our parameter13pace can therefore be reduced from 6 to 3 independent parameters. To verify this, weplotted our dataset in the orthogonal system formed by the eigenvectors 1-3 (figure 3).In this coordinate system, the distributions do not exhibit any trade-o ff s confirmingthat all the information have been extracted by the PCA. We now conduct a detailedanalysis of the principal components in order to identify these trade-o ff s.The first component is dominated by the opposite contribution from the proportionof Bm (0.600) and CaPv (-0.591). Note that, although weaker, a similar behavior canbe observed in the components 2 and 3. This corresponds to the anti-correlation be-tween CaPv and Bm discussed in section 3.4. The second component is dominated bythe contribution of the Al O content and oxidation state, while the temperature contri-bution is also significant. By comparing the three principal components, one may seethat the FeO content, Al O content and oxidation state are always correlated. Thesecorrelations can also be seen from the 2D-histograms displayed in figure 2 and fromthe end-members identified in figure 3. Interestingly, these three elements are requiredto form the FeAlO phase in Bm. We therefore postulate that the FeAlO phase hasa better ability to explain observations than other iron-bearing phases, which causesa robust correlation between the FeO content, Al O content and oxidation state. Tosupport this point, we have verified the low proportion of Al O and Fe O phasesin all the successful cases (see Supplementary Figure 5). Furthermore, increasing theproportion of the FeAlO phase has the direct e ff ect of increasing density. This com-ponent may thus be interpreted as a density shift vector. The third component a ff ectsalmost exclusively the temperature and can be viewed as a temperature shift vector. Itseems that the compositional (components 1 and 2) and temperature (components 3)contributions are separated and independent from each other. This can also be seenwith the end-member 3 (figure 3), since it is the only end-member that constrain onlyone parameter (temperature).From the analysis of the end-members in figure 3 and the principal components,14e postulate that all the successful cases can be separated in two end-member com-positions: one CaPv-rich and one Bm-rich. For both composition, we applied a PCAand found the same trade-o ff s as for the full set of successful models, i.e., we can in-dependently vary the temperature (component 3) provided that we respect a certainproportion for the FeO content, Al O and Fe + / (cid:80) Fe. We now study in more detailthese two end-member compositions beginning by the Bm-rich case.
Building on the results of the PCA, we apply an additional condition to our success-ful models, that is the Bm proportion should be larger than 90vol%. The purpose of thiscondition is to extract the Bm-rich end-member composition from the tally of success-ful models. We have selected this specific proportion because it is high enough to berestrictive, while providing a number of cases ( ∼ ffi cient for the data analysis.In the following, the results are displayed using histograms of the successful models asa function of two input parameters. As suggested by the PCA, we focus on the e ff ectof ∆ T and the FeO content, which can be viewed as a representative parameter for theAl O content and oxidation state.Figure 4a shows the distribution of the Bm-rich models as a function of ∆ T andFeO content. For these models, a large range of temperature is possible, while largertemperatures seem slightly more likely for FeO content ∼ > O content (typically > O content and oxidation state while involvingslightly lower temperature contrasts. 15 .4.3. End-member composition: CaPv-rich We follow a similar procedure for the CaPv-rich end-member composition by se-lecting only the successful cases with a proportion of CaPv larger than 30vol%. A totalof 32000 cases was obtained from the 79000 initial successful cases. The main resultsare displayed in figure 4b. As for the Bm-rich case, a wide range of temperature is pos-sible, but observations seem easier to explain with a temperature contrast lower than500 K. Note that the distribution is now slightly more scattered than in the Bm-rich caseand does not exhibit any specific trend with increasing proportion of CaPv, this resultbeing valid for all the parameters. The FeO content is typically between 10wt% and21wt%, the Al O content between 3wt% and 13wt%, and the oxidation state largerthan 0.3.
4. Discussion
We investigated a large range of models for LLSVPs with varying FeO content,Al O content, proportion of CaPv, proportion of bridgmanite, oxidation state Fe + / (cid:80) Fe,and temperature contrast with respect to the far-field mantle ∆ T . We found that con-straints on density and bulk sound speed of LLSVPs are by far the most useful ob-servations to identify the potential composition of these structures. By contrast, thelow V S and V P observed are easily achieved as long as LLSVPs are a few hundredsKelvin hotter than the far-field mantle. Two robust results are that the proportion of Fpshould be low ( < + -bearing bridgmanite is muchmore favorable than other iron-bearing phases. As a consequence, we observed a cleartrade-o ff between FeO content, Al O content and Fe + / (cid:80) Fe. To describe the largenumber of models, we identified two end-member compositions: one Bm-rich and oneCaPv-rich. For each end-member, a large range of temperature is possible, although itseems easier to explain seismic observations with low temperature contrasts ( <
500 K).16urthermore, we found fairly high FeO and Al O content, up to 25wt% and 19wt%,respectively. It is important to note that a full range of compositions is possible betweenthese two end-members, so that, from a more general perspective, a very large rangeof parameters is possible for LLSVPs. Interestingly, temperature excess deduced fromnormal modes data (Trampert et al., 2004) and attenuation (Deschamps et al., 2019) arein good agreement with our findings, while the high Al O content is consistent withthe super-chondritic Ca / Al ratio measured for the accessible Earth (e.g., Walter et al.,2004). ff ects of post-perovskite Our results rely on the selected lower mantle mineralogy and on the thermo-elasticproperties of these minerals. More specifically, other minerals that the three used in ourmodel may be present in the lowermost mantle. In particular, we did not account forthe possible presence of post-perovskite (PPv, see Shim, 2008, for a review), a high-pressure phase of bridgmanite. PPv is characterized by a slightly higher density, lowerbulk sound speed, and higher shear-wave speed than Bm (see Cobden et al., 2015, for acompilation), such that its presence outside LLVSPs has been advocated as an explana-tion for the anti-correlation between V φ and V S -anomalies (e.g., Davies et al., 2012). Adi ffi culty, however, is to precisely determine the stability field of PPv, which dependson temperature and pressure (e.g., Catalli et al., 2009), but also on the amount of ironand alumina (e.g., Sun et al., 2018). In particular, the transition pressure increases withincreasing temperature and decreasing alumina and iron content. Because of these de-pendencies, and following the assumed conditions and composition, PPv may or maynot be present in the lowermost mantle. In our case, the assumed far-field mantle islikely composed of a mixture of Bm and PPv. If only the thermal e ff ect is accountedfor, the transition pressure of PPv should be too large to occur within LLSVPs. How-ever, if LLSVPs are strongly enriched in alumina and iron, the transition pressure of17Pv may be smaller than the CMB pressure (Sun et al., 2018), i.e., PPV may be stablewithin LLSVPs. In that case, PPv may be present both outside and within LLSVPs,such that its seismic signature would be reduced. Unfortunately, available constraintsconcerning the e ff ects of alumina and iron content on the properties of PPv are tooscarce to allow a careful estimate of its e ff ects. One way to reduce the range of plausible thermo-chemical models for LLSVPs is touse tighter constraints. For instance, improvement in tomographic models, leading to aprecise estimate of the V φ anomaly, would reduce the range of possible compositions.Additional constraints may also be useful. For instance, tidal tomography (Lau et al.,2017) provides a constraint on the e ff ective density di ff erence ( ∆ ρ tot ), i.e., including thethermal and compositional e ff ects, between LLSVPs and the far-field mantle. Using asimple model of the lower mantle composed of three 340 km thick layers, Lau et al.(2017) found that LLSVPs should be ∼ ∆ ρ tot of our successful cases is ∼ ∆ ρ tot in tidal tomography models due to a dilution e ff ect, or may be indicative ofa lower density di ff erence between LLSVPs and far-field mantle than the one assumedin this work. In both cases, constraining the e ff ective density di ff erence stands as avery robust way to infer the nature and composition of LLSVPs. Supplementary con-straints may further include seismic attenuation. Assuming that seismic attenuation ismainly a ff ected by temperature, it can be used to constrain the temperature conditionsof LLSVPs (Deschamps et al., 2019). Although it may be a ff ected by several sources ofuncertainties, it is interesting to note that in the western tip of the Pacific LLVSP, mod-eling of attenuation predicts a temperature excess of 350 +/ - 200 K (Deschamps et al.,2019), a value consistent with the temperature excess suggested by our calculations.A better knowledge of mineral properties may refine the modeling of attenuation, al-lowing sharper constraints on the potential composition of LLSVPs, and therefore the18xploration of more complex and detailed mineralogical models. Alternatively, and asillustrated in the next section, the range of potential compositions may be reduced byconsidering the potential process that created these LLSVPs, and whether the producedcompositions are reasonable. Some authors have postulated that the final stages of the solidification of a primi-tive magma ocean could be the source of LLSVPs (e.g., Labrosse et al., 2007; Ballmeret al., 2017). However, the potential composition produced by such a scenario remainslargely uncertain, mainly because the solidifying process itself is uncertain (see Solo-matov, 2015, for more details). First, di ff erent modes of crystallization are possiblethat may or may not produce chemically distinct reservoirs. Second, the sequence ofcrystallization is highly debated and depends, in particular, on the relative behavior ofthe adiabatic temperature gradient and the liquidus profile (e.g., Boukar´e and Ricard,2017), which, again, is uncertain at lower mantle conditions (Andrault et al., 2011;Nomura et al., 2011). Moreover, depending on the value of the iron partitioning coef-ficient between solid and melt, the crystals could be denser than melt or not (Nomuraet al., 2011; Andrault et al., 2012; Tateno and Hirose, 2014). Considering all theseuncertainties, the magma ocean could solidify from the bottom and propagate to thesurface (bottom-up scenario), from the surface to the CMB (top to bottom scenario), orfrom the middle and propagate to both the surface and the CMB (middle-out scenario).In the two latter cases, a basal magma ocean (BMO) is produced that may give birth toLLSVPs. In the bottom-up scenario, the dense reservoir is located near the surface andshould overturn to produce a stable density gradient (Elkins-Tanton et al., 2003).Independently of the solidification scenario, the residual liquid should be enrichedin iron and alumina (Tateno and Hirose, 2014; Boujibar et al., 2016). A first orderestimate of such an enrichment can be obtained using the simplified model proposed19y Boukar´e et al. (2015, 2018). In this model, the Nerst partition coe ffi cient D betweenmelt and solid is assumed to be constant so that, C s = C s , (cid:18) R min − R max R min − R (cid:19) − D , (8)where C s is the proportion of the element in the solid phase, C s , the initial proportion, R max the Earth’s radius, R min the CMB radius, R the radius considered. Consideringthat LLSVPs originate from a layer 300 km thick, we obtained a FeO content of about28wt% for D = . D = .
4. A reasonable FeO content cantherefore only be obtained for D > .
5, which may require a low degree of melting(Boujibar et al., 2016). For such low degrees of melting, alumina may be partitionedequally between melt and solid (Boujibar et al., 2016). This stands in contradictionto the alumina enrichment suggested by our results. Alternatively, in the bottom-upscenario, the dense reservoir (highly enriched in FeO) could undergo partial meltingduring its overturn (Ballmer et al., 2017). The subsequent rock-melt interactions mayalter the composition of the dense reservoir, decreasing its FeO content while increas-ing its Al O and SiO content. Overall, because element partitioning are challengingto measure, it is di ffi cult to estimate precisely the composition of the produced reser-voirs.Another way to evaluate the relevance of the magma ocean origin is by looking atmineral proportion. It has been suggested that Bm is the first mineral to crystallize,followed by Fp and CaPv (Tronnes and Frost, 2002). In that case, the residual liquidof magma ocean should be enriched in CaPv and, to a lesser extent, in Fp. However,our results suggest that a low proportion of Fp ( ∼ to prevent the formation of Fp. If oneassumes that LLSVPs are related to magma ocean solidification, then an additional20rocess, such as the one proposed by Ballmer et al. (2017), is required to explain thedepletion in Fp. As a consequence, we propose that the low proportion of Fp may be amore robust constraint than the FeO content to confirm or not the magma ocean originfor LLSVPs. Another possible origin for LLSVPs is the accumulation of MORB materials. Atlower mantle conditions, MORB is believed to be composed of ∼ ∼ ∼ contents,our results are not able to evaluate this hypothesis. Furthermore, before addressingthe seismic signatures of these materials, the first step would be to better resolve theirdensities under deep mantle conditions. Indeed, the ability of MORB materials to ac-cumulate near the CMB is depending on their density contrast with the far-field mantle,so on their assumed composition (Nakagawa et al., 2010). Based on geochemical evidences, Tolstikhin and Hofmann (2005) suggested thatthe subduction of a primitive crust produced just after the magma ocean solidifica-tion could be at the origin of LLSVPs. This primitive crust should be a mixture ofkomatiitic crust and chondritic regolith, whose proportion and individual compositionare uncertain. Nevertheless, we can attempt to verify whether such a mixture couldbe compatible with our results. Based on lunar regolith composition (e.g., McKayet al., 1991), one may postulate that terrestrial regolith should be enriched in FeO,CaO and Al O compared to a pyrolitic composition. Regoliths with a moderate FeO-21nrichment (16wt%) are characterized with a reasonable Al O content ( ∼ O ( ∼ O . Using appropriate compositions, we verify that a mix-ture of regolith and komatiite is compatible with our results. It is however necessary toconsider a large proportion of regolith (typically larger than 70%) with moderate FeO-enrichment, otherwise the mixture has a lower FeO content than the ones suggested byour results.
5. Concluding remarks
Using a massive sampling of the parameter space and a principal component anal-ysis, we find that the seismic signature of LLSVPs could be explained as long as theproportion of Fp is low, and that a certain ratio between FeO content, Al O contentand Fe + / (cid:80) Fe is maintained. As a result, the seismic signature of LLSVPs can beexplained with a large range of compositions. We thus tried to restrict the range ofpotential compositions by considering di ff erent possible sources for LLSVPs, e.g., so-lidification of the magma ocean or subduction of a primitive crust. Di ff erent scenariosgenerate reservoirs with a compatible concentration of major elements. However, ow-ing to the lack of constraints available, the mineral proportions of these reservoirs areuncertain. It is therefore di ffi cult to evaluate the relevance of these scenarios.22 able 1: Shear modulus ( G ) along with its pressure ( G (cid:48) ) and temperature ( dG / dT ) derivative at ambientconditions for several compounds. Compounds G (GPa) G (cid:48) dG / dT (GPa K − )Ferropericlase - - -0.02 a MgO 131 b b -0.92MgO-0.08FeO (HS) 113 a a -0.92MgO-0.08FeO (LS) 130 a a -Bridgmanite - - -0.02 a MgSiO c c -0.875MgSiO -0.125FeSiO c c -0.875MgSiO -0.125Fe O d d -0.875MgSiO -0.125FeAlO d d -0.875MgSiO -0.125Al O d d -CaSiO e e -0.002 ea Murakami et al. (2012). b Murakami et al. (2009). c Shukla et al. (2015). d Shukla et al. (2016). e Values obtained by fitting the experimental data in Table 8 of Li et al. (2006).23 able 2: Range of values investigated for each compositional parameter considered in our LLSVPs model.The step value indicates the step between 2 adjacent values.
Parameter min value step value max valueFeO content (wt%) 8 1 28Al O content (wt%) 1 0.5 19Proportion of CaPv (vol%) 0 1 40Proportion of Bm (vol%) 60 1 100Fe + / (cid:80) Fe 0 0.1 1 ∆ T (K) 0 100 100024 able 3: Results of the principal component analysis (PCA) applied to our set of successful models. Notethat the data have been centered and normalized before analysis, so that the results are here shown in adimensionless form. Components1 2 3 4 5 6Eigenvalues 0.681 0.296 0.262 0.023 0.003 0.001Proportion CaPv -0.591 0.314 -0.187 -0.267 -0.147 0.651Proportion Bm 0.600 -0.307 0.200 -0.083 -0.255 0.658 ∆ T O content 0.339 0.395 -0.301 -0.528 -0.518 -0.302Fe + / (cid:80) Fe 0.283 0.516 -0.377 0.692 -0.012 0.18025 igure 1: 2D histograms showing the distribution of all the models as a function of one input parameter(x-axis) and one output (y-axis). The e ff ect of only two parameters, corresponding to the dominant ones, arereported for each seismic wave speed. Other histograms are shown in Supplementary Material. igure 2: Histograms and 2D-histograms showing the distribution of the successful models for all the inputparameters (see text for more details). F r e qu e n c y o f o cc u rr e n ce ( % ) − − C o m pon e n t − C o m pon e n t F r e qu e n c y o f o cc u rr e n ce ( % ) − − C o m pon e n t − − Component 1 − Component 2 F r e qu e n c y o f o cc u rr e n ce ( % ) − − Component 3
High CaPv proportion/Low FeO contentHigh CaPv proportion/High FeO content/High Δ THigh CaPv proportion/High FeO content/Low Δ T High Bm proportion/High FeO contentHigh Bm proportion/Low FeO content/Low Δ THigh Bm proportion/High FeO content/High Δ THigh Δ T Figure 3: Histograms and 2D-histograms showing the distribution of the successful models in the principalcomponents space (see text for more details). The di ff erent end-members cases shown by the 2D-histogramsare identified and characterized. 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