Main

The accretion history of terrestrial planets is punctuated by a global magma ocean stage, which leads to planetary differentiation and the establishment of important reservoirs, such as core, mantle and crust. The subsequent evolution and modification of these reservoirs can substantially affect the thermal and geodynamic regimes of planets. On the basis of mineralogy, rheology and seismic velocity, it has been established that the structure of Earth’s mantle is layered with a principal seismic discontinuity at about 660 km separating the upper and lower mantle domains1,2. However, the extent to which mass transfer occurs within the mantle throughout geologic history remains highly debated. Seismic tomography data suggest that subducted slabs can penetrate into the lower mantle and, at the current rate of mass exchange, Earth’s primordial mantle is not predicted to survive after prolonged whole mantle-scale convection8,9,10. Meanwhile, studies based on noble gases11,12,13,14,15, as well as tungsten16 and neodymium17 isotopes, have suggested instead the existence of primordial mantle domains in the modern deep Earth. Although the preservation of a primordial lower-mantle reservoir over long geological timescales is debated18,19, some geodynamic models show that preservation of primordial mantle domains can occur in a modern-style, whole-mantle convection regime characterized by deep subduction20. Also, both numerical modelling and geological observations21,22,23,24,25 suggest that Earth’s convection regime and, hence, the style of slab subduction may have also evolved considerably through time as a consequence of change in the heat flux and heat transfer25,26. As such, a potential solution to the conundrum is that the high mass transfer between the upper and lower mantle inferred from seismic tomography is a relatively recent feature of Earth’s geologic history such that the primordial, less degassed lower-mantle reservoir has been undergoing disruption but is not yet fully destroyed27. This hypothesis has not been fully evaluated given the lack of an unambiguous geochemical tool that can faithfully trace mass exchange between mantle and crustal reservoirs in deep time.

The stable isotope geochemistry of the refractory lithophile element Ti is a new tracer that can potentially provide a historical record of mass-exchange processes between mantle and crustal reservoirs. The continental crust of Earth can be formed through partial melting of subducting slabs28 and/or thickened mafic crust29,30, which produces felsic melts. Such magmatic processes can result in notable Ti isotopic fractionation between the felsic silicate melts and the residue from this melt extraction, that is, melting residues3,4,5,6,7. By contrast, partial melting of mantle peridotites seemingly does not fractionate Ti isotopes3,4. In detail, the δ49Ti values (that is, the per mil deviation of the 49Ti/47Ti ratio relative to the OL-Ti standard) of Archaean tonalite–trondhjemite–granodiorite (TTG) rocks and Phanerozoic granites5,7, as well as those of evolved volcanic rocks3,6,7,31,32, can be up to +2.0‰ higher than that of oxide-undersaturated mafic/ultramafic rocks3,4. Thus, recycling of melting residues from extraction of continental crust through either delamination or subduction is predicted to generate mantle reservoirs with heterogeneous δ49Ti (ref. 4). Furthermore, the largely immobile nature of Ti allows for a thorough investigation of Ti-stable isotope composition of Archaean mantle-derived rocks despite alteration and metamorphism. However, the application of stable Ti isotopes to understand mantle–crust differentiation and crustal recycling processes is hampered by the scatter in the δ49Ti values of chondrite meteorites used to define the BSE reference value33,34,35, which is probably because of a combination of factors, such as sample heterogeneity, analytical biases and uncertainties, as well as imperfect correction for mass-independent nucleosynthetic effects on 46Ti (Methods).

The δ49Ti value of BSE

We developed new analytical methods for ultrahigh-precision Ti isotope measurements using the next generation of multicollector inductively coupled plasma source mass spectrometers (the Neoma Multicollector ICP-MS). Our protocol allows for the concomitant determination of the mass-independent (±0.15 epsilon on the mass-bias-corrected 50Ti/47Ti ratio) and mass-dependent Ti-stable isotope composition (±0.010‰ for δ49Ti) of individual samples to ultrahigh precision (see details in Methods). Using this approach, we analysed 24 chondrite meteorites covering all of the main chondrite classes. Despite substantial variability in ε50Ti values (that is, the per ten thousand deviation of the mass-bias-corrected 50Ti/47Ti ratio relative to the OL-Ti standard) between the analysed chondrites, they return a restricted range of δ49Ti values that define a weighted mean of +0.053 ± 0.005‰ (2 s.e., n = 22), excluding one CV3 (NWA 2364) and one LL3 (Talbachat n’aït Isfoul) that are probably subject to sample heterogeneity (Methods), which represents a threefold improvement in precision relative to previous estimates33,34,35. The first important observation emerging from the new BSE estimate is that it is distinct from the composition of the modern depleted mantle as sampled by N-MORBs3,4 (δ49Ti = +0.001 ± 0.004‰, 2 s.e., n = 12) that are thought to represent the ‘depleted MORB mantle’.

Earth’s mantle δ49Ti value in deep time

To better understand the importance of the lighter, non-chondritic Ti isotope composition of Earth’s modern depleted MORB mantle reservoirs, we analysed a set of terrestrial samples including 31 well-characterized Archaean to Proterozoic samples (one tonalitic and 30 mafic to ultramafic) with crystallization ages ranging from approximately 3.8 to approximately 2.0 Ga and 21 modern OIBs that have not experienced Fe–Ti oxide fractionation. The Archaean to Proterozoic samples include amphibolites (approximately 3.8 Ga), one Amitsoq gneiss (3.8–3.7 Ga), Ameralik dykes (approximately 3.4 Ga) and Kangâmiut dykes (approximately 2.0 Ga) from Southwest Greenland, as well as peridotitic to basaltic komatiites and tholeiitic basalts from the Kaapvaal Craton (approximately 3.48 Ga Komati Formation and approximately 3.33 Ga Kromberg Formation) and Munro Township from the Abitibi greenstone belt (approximately 2.7 Ga). The modern OIBs are from the Iceland, Caroline and Samoa hotspots, which have Sr and Nd isotope compositions spanning the curve defined by the depleted MORB mantle (DMM), the prevalent mantle (PREMA) and the enriched mantle type II (EM-II) (Extended Data Fig. 1a). As shown in Fig. 1, the early Archaean mantle-derived rocks have δ49Ti values indistinguishable from bulk chondrites, whereas the middle to late Archaean samples have progressively lighter compositions that extend towards the δ49Ti values of modern N-MORBs. By contrast, the approximately 2.0 Ga Kangâmiut dykes and modern OIB samples have highly variable δ49Ti values that range from the chondritic composition to values well below that of modern N-MORBs (Fig. 1). One approximately 3.8 Ga tonalitic sample (SD-2) from Isua records a high δ49Ti value of +0.205 ± 0.003‰, which is indistinguishable from previously reported δ49Ti values for TTG rocks from the Kaapvaal Craton and Acasta Gneiss Complex (δ49Ti = +0.173 ± 0.030‰ to +0.570 ± 0.030‰)5,7 (Fig. 1).

Fig. 1: Mass-dependent Ti isotopic variations in bulk chondrites and Archaean, Proterozoic and modern terrestrial mantle-derived rocks from this study and the literature3,4,6,7,31,32.
figure 1

See the full dataset in the Extended Data Tables 1–5. Note that all the plotted terrestrial mantle-derived rocks are identified to be devoid of Fe–Ti oxide fractionation. The Archaean mantle-derived rocks from this study and ref. 4 have been arranged into three groups based on the formation ages (approximately 3.8–3.5 Ga, approximately 3.4–3.3 Ga and approximately 2.8–2.7 Ga), which show a progressive enrichment in the light Ti isotopes with age. The approximately 2.0 Ga data are from the Kangâmiut dykes samples (Southwest Greenland) in this study. Also shown are the data of approximately 3.6–2.9 Ga TTG rocks from this study and refs. 5,7 and that of modern N-MORBs from refs. 3,4. The box on each group of data defines the 25th–75th percentiles, with the medium value marked in the box and the whiskers standing for 0th to 100th percentiles, excluding outliers.

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Our high-precision δ49Ti data for early Archaean komatiitic to basaltic rocks allows us to evaluate an earlier inference that partial melting of mantle peridotites on Earth produces only minor mass-dependent Ti isotopic fractionation3,4. Komatiitic magmas formed by about 25–40% partial melting of their mantle source36,37 and, as such, are expected to have extracted >90% Ti from their sources. By contrast, basaltic magmas that form from lower degrees of mantle partial melting (about 5–10%, for example, the approximately 3.8 Ga Isua pillow-textured metabasalts or approximately 3.48 Ga Barberton basaltic komatiites) extract approximately half of the Ti from their sources. Thus, a resolvable difference in δ49Ti is expected between the two types of magma if there is notable Ti isotopic fractionation between silicate melts and melting residues during partial melting of mantle peridotites. However, the comparable δ49Ti values between the approximately 3.8 Ga Isua metabasalts (+0.048 ± 0.005‰, 2 s.e., n = 5), the approximately 3.48 Ga Barberton komatiites (+0.044 ± 0.009‰, 2 s.e., n = 4) to basaltic komatiites (+0.048 ± 0.008‰, 2 s.e., n = 4) and chondrite meteorites (+0.053 ± 0.005‰, 2 s.e., n = 22) suggests that, in agreement with previous inferences based on various lines of evidence3,4,38,39, Ti isotopic fractionation between melts and residues from mantle partial melting is negligible. Thus, the near-zero Δ49Timelt-residue values inferred here suggest that metal-saturated melting with presence of Ti3+ is not relevant to the generation of terrestrial mafic/ultramafic magmas40. Moreover, the limited fractionation of Ti from mantle partial melting on Earth implied by our results supports the hypothesis that the studied mantle-derived rocks faithfully record the δ49Ti composition of their mantle sources. As such, our data suggest that sources of the studied mantle-derived rocks were characterized by chondritic δ49Ti values (δ49Ti = +0.053 ± 0.005‰) around approximately 3.8–3.5 Ga and evolved towards a modern depleted MORB mantle composition (δ49Ti = +0.001 ± 0.005‰) by approximately 2.7 Ga. This secular evolution is observed in both Southwest Greenland and the Kaapvaal Craton and is in line with the lower δ49Ti values observed in the late Archaean mantle-derived rocks from Belingwe, Yilgarn and Abitibi. By comparison, the approximately 2.0 Ga Kangâmiut dykes and modern OIBs were derived from the mantle sources different from the modern depleted MORB mantle reservoir.

A long-lived primordial lower mantle

As indicated by the heavy Ti isotopic composition of Archaean TTGs, Phanerozoic granites and differentiated volcanic rocks3,5,6,7,31,32, the formation of a felsic continental crust results in the production of an isotopically light crustal melting residue. Thus, we interpret the observed secular change in the Ti isotopic composition of the Archaean mantle as evidence for the progressive recycling of melting residues through delamination or subduction to Earth’s mantle following continental crust extraction41,42, requiring full isotopic equilibration between the mantle reservoir and the admixed melting residues. Notably, the observed shift towards lower δ49Ti values in the source of Archaean mantle-derived rocks between approximately 3.5 and 2.7 Ga coincides with the main epoch of continental crust extraction proposed in previous studies43,44 (Fig. 2). Adopting the current mass of continental crust (that is, about 0.55% of the BSE), neither whole-mantle convection nor layered-mantle convection with limited mass transfer between the upper and lower mantle can reproduce the approximately 0.052‰ fractionation in the mantle by recycling of melting residues from continental crust formation (Fig. 2). However, it is possible to generate the δ49Ti effect of about 0.052‰ through layered-mantle convection with limited mass transfer between the upper and lower mantle only if the mass of continental crust produced over geological time is greater than the current mass, namely, about 1.43% of the BSE. Such a high production of continental crust throughout Earth’s history has also been inferred in the recent continental crust growth models45, based on the integration of various proxies, such as neodymium and hafnium isotopes. This consistency between studies using distinct geochemical tracers suggests that the mass of continental crust produced in Earth’s history probably exceeded its present-day value, and a large portion of this crust has been destroyed and recycled into the mantle, meaning that a high mass of ancient continental crust has been stored in the deep mantle. An important finding of this work is that only a small fraction of Earth’s mantle (about 20%) has equilibrated with melting residues from continental crust extraction, implying limited mass transfer between the upper and lower mantle in the Archaean. Irrespective of an apparent separation of the lower and upper mantle, after the Archaean, some upwelling of primordial material from the lower mantle has probably occurred since 2 Ga, as evidenced by the elevated δ49Ti values in some of the studied approximately 2.0 Ga Kangâmiut dykes and modern OIBs (Fig. 2).

Fig. 2: Continental crust extraction and the evolution of Ti isotopic composition in mantle-derived rocks.
figure 2

Chondrites and terrestrial mantle-derived rocks are shown in groups as defined in Fig. 1, with individual data points plotted as grey dots. The continental crust growth models from Taylor and McLennan43 and Dhuime et al.44 are shown on the upper plot. Crustal recycling models were made to quantify the potential Ti isotopic effects in the mantle from continental crust formation, in which f represents the fraction of Earth’s mantle to equilibrate with recycling crustal melting residues and k stands for the total mass of continental crust ever produced throughout geologic history after normalization onto its present mass (that is, about 0.55% of the BSE). See equations (13) and (14) and the related descriptions in Methods for details of the models. The box on each group of data defines the 25th–75th percentiles, with the medium value marked in the box and the whiskers standing for 0th to 100th percentiles, excluding outliers.

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Modern OIBs, which are thought to sample a deeper mantle reservoir than MORBs46, provide an opportunity to explore the possible survival of a primordial material in the lower mantle. Although the sources of modern OIBs and enriched-MORBs (E-MORBs) record large δ49Ti variability, most have δ49Ti values that are 0.030–0.045‰ heavier than the composition of the modern depleted MORB mantle sampled by N-MORBs (Fig. 3). Given that marine sediments since the Archaean constantly record high δ49Ti values (+0.20‰ on average5,6), it is possible that the elevated δ49Ti signature of the OIB sources is a result of admixing of subducted marine sediments or, alternatively, upper continental crust material into a modern depleted MORB mantle reservoir. However, increasing the δ49Ti value of a hybrid mantle source by 0.030–0.045‰ using this process should also lead to highly radiogenic Sr isotopic signatures from sediments or upper continental crust47 in the OIB lavas, which is not observed here, except for some lavas from the Samoan hotspot showing 87Sr/86Sr ratios extending towards EM-II (Extended Data Fig. 1a). Thus, the predominantly heavy δ49Ti values of modern OIBs requires sampling of a mantle source that did not equilibrate with recycled crustal melting residues, which we infer to represent a primordial lower-mantle reservoir underlying the modern depleted MORB mantle (Fig. 3). Nonetheless, δ49Ti heterogeneity exists within the mantle sources of OIBs. The lower δ49Ti values relative to the chondritic composition seem to provide evidence for injection of not only recycled sediments or upper continental crust but also melting residues into the lower primordial mantle reservoir. We note that recycling of ancient restites from protocrust extraction in the sources of some OIBs has been suggested on the basis of tungsten isotopes42. This introduction of recycled material to the lower mantle traced by Ti isotopes is consistent with seismic tomography of the Earth that suggests a high rate of mass exchange between the upper and lower mantle in modern times8,9 and other geochemical evidence that indicates the presence of ancient subducted oceanic lithosphere in the sources of OIBs47,48,49,50. It has also been proposed that the anomalous noble gas and tungsten isotope signals in modern OIBs may reflect interaction with core material as opposed to sampling of a primordial mantle reservoir51,52,53. The refractory and lithophile nature of Ti makes its stable isotope composition impervious to the interaction with core material. Thus, the Ti isotope data reported here coupled with the noble gas and tungsten isotope signals identified in modern OIBs11,12,13,14,15,16,54,55 are most consistent with the survival of a primordial, less degassed mantle reservoir in the modern deep Earth.

Fig. 3: Sampling of a primordial mantle reservoir by mantle plume as evidenced by Ti and Sr isotopic records of the modern OIBs from the Iceland, Samoa and Caroline hotspots.
figure 3

Data of the OIB samples from Cape Verde and Azores in ref. 3 are shown as white circles. The N-MORB and E-MORB samples from refs. 3,4 are shown, for which the N-MORB samples without available Sr isotope data have been assumed to have 87Sr/86Sr = 0.7025. The dotted pink trajectories describe the effects from mixing in increments of 0.2% the ancient marine sediments or continental crust material with δ49Ti = +0.200‰ (refs. 5,6) and 87Sr/86Sr = 0.740 (ref. 47) into a modern depleted MORB mantle source with 87Sr/86Sr = 0.7025 (ref. 63) and δ49Ti = +0.001‰ (refs. 3,4) or into a mantle source with 87Sr/86Sr = 0.7035 and a primordial mantle δ49Ti of +0.052‰. Addition of recycled melting residues would lead to lower δ49Ti values in N-MORBs and some of the OIBs.

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The evolving geodynamic regime of Earth

Our new Ti isotope data, which require limited mass exchange between the upper and lower mantle over a substantial part of Earth’s geologic history, provide new insights into Earth’s geodynamic evolution. The chondritic or primordial mantle-like δ49Ti value of the approximately 3.8–3.5 Ga upper mantle indicates limited production of felsic continental crust and recycling of melting residues during the early Archaean, pointing to a long residence of the primordial crust on Earth’s surface. By contrast, progressive enrichment of light Ti isotopes in mantle-derived rocks between approximately 3.5 and 2.7 Ga requires an acceleration in the growth of felsic continental crust and the recycling of melting residues into the mantle. The increased rate of crustal production and recycling suggest Earth’s transition into a geodynamic regime that allowed for progressive recycling of crustal materials back into the mantle. This is in line with the progressive homogenization of 142Nd variations preserved in rocks from the same time period56,57. Felsic continental crust can be generated without plate tectonics through partial melting of hydrated basalts at the base of a thickened crust29,30,41,58,59 or, alternatively, associated with a tectonic regime that includes active subduction of surface materials28,60,61. Regardless, the secular evolution of δ49Ti recorded by the Archaean mantle-derived lavas is best understood to reflect a transition in Earth geodynamic regime promoting accelerated crustal recycling around 3.5 Ga.

The mass of the mantle inferred to have equilibrated with the recycled melting residues (<30%) to explain the shift in Ti isotope composition in mantle-derived rocks is broadly consistent with that of the mantle located above the seismic discontinuity at about 660 km, suggesting that the phase transition associated with this discontinuity may have impeded mass exchange. Such a mantle separation is distinct from modern-style plate tectonics that are characterized by deep plate subduction and penetration of subducted slabs into the lower mantle. This may indicate that, unlike the modern-style regime, the subducted slab may have different fates in deep time, which may experience frequent slab breakoff under the temperature, composition and H2O conditions of the Archaean upper mantle25,26 or, alternatively, accumulate at the transition zone, at which density contrast between subducted slab and surrounding mantle reverses notably62. Thus, before 2.7 Ga, recycling and admixing of subducted slabs into the ambient mantle was limited to the highly convective upper-mantle region instead of penetrating through the mantle transition zone. The coexistence of primordial and evolved δ49Ti signals in modern OIBs and MORBs, respectively, requires that the transition between a layered and whole-mantle convective regime occurred late in Earth’s history. Thus, these results give credence to theoretical models suggesting that modern plate tectonics with deep slab penetration represents a transient phase in the evolution of planets23,27.

Finally, whereas the fundamental causes for the acceleration in continental crust growth and crustal recycling between 3.5 and 2.7 Ga remain unclear, our new δ49Ti data require a regime of mantle convection with limited mass transfer between the upper and lower mantle for a substantial part of Earth’s history. A possibility is that this epoch represents the onset of a tectonic regime allowing the subduction of plates or, alternatively, frequent crustal thickening, which—in both cases—will result in partial melting and extraction of felsic continental crust. Regardless, our data require that efficient recycling and homogenization of the melting residues from felsic continental crust generation was limited to the upper mantle, which implies the long-term preservation of a primordial lower-mantle reservoir. However, the highly variable Ti isotope compositions recorded by modern OIBs suggest that the primordial lower-mantle reservoir is undergoing disruption. Thus, modern-style plate tectonics with whole-mantle-scale convection and deep penetration of subducted slabs may only represent a transient and recent feature of Earth’s history.

Methods

Samples

The chondrite samples analysed in this study include one CI (Orgueil), two CV (NWA 2364 and Allende CAI-free matrix), six CM (Cold Bokkeveld, Murray, Murchison, Bells, Maribo and NWA 4428), two CO (NWA 1232 and NWA 763), one CH (SaU 290), two CK (NWA 1559 and NWA 1563), four CR (NWA 530, NWA 1180, NWA 6043 and NWA 801), one EH (SaH 97159), three L (NWA 5697, Bovedy and Hedjaz) and two LL (Ragland and Talbachat n’aït Isfoul).

The Archaean to Proterozoic samples from three locations were also studied, comprising: (1) five approximately 3.8 Ga pillow-textured metabasalt/metagabbro samples (PB-1, PB-2, PB-3, GB-1 and MG-1), one approximately 3.8 Ga Amitsoq gneiss (SD-2), eight approximately 3.4 Ga doleritic samples of the Ameralik dyke swarm (AM-1, AM-2, AM-8, AM-9, AM-10, AM-12, AM-14 and AM-16) and six approximately 2.0 Ga Kangâmiut dyke samples (430931, 430970, 430981, 430988, 432108 and 432122) from Southwest Greenland, (2) two approximately 3.48 Ga komatiite (1973-543 and 1973-547) and four approximately 3.48 Ga basaltic komatiite samples (1973-544, 1973-545, 1973-546 and 1973-730) of the Komati Formation, as well as three approximately 3.33 Ga tholeiitic basalt samples (1973-549, 1973-555 and 1973-733) of the Kromberg Formation from the Kaapvaal Craton in South Africa, and (3) three approximately 2.7 Ga Pyke Hill komatiite samples (1990-63, 1990-65 and 1990-67) in Munro Township from the Abitibi greenstone belt in Canada. The approximately 3.8 Ga Isua metabasalts and the approximately 3.45 Ga Ameralik dyke samples have been shown to have positive 142Nd excesses of +10.5 ± 0.7 and +4.9 ± 0.5, respectively57. The reduced 142Nd excesses in the Ameralik dyke samples relative to the older metabasalts have been attributed to a recycling of Earth’s primordial crust into the upper mantle57.

As well as the chondrite and Archaean/Proterozoic samples, we selected 21 modern OIBs for study, comprising: (1) ICE-14-16, ICE-14-18, ICE-12-27, ICE-14-29, ICE-14-32A and 408616 from the Iceland hotspot54, (2) KOS-13-4 and KOS-13-19 from the Caroline hotspot64 and (3) OFU-04-05, OFU-05-01 and OFU-05-18 of Ofu Island65, T16, T30, T33, T44 and T45 of Ta‘ū Island65 and AVON3-63-2, AVON3-70-9, AVON3-71-22, AVON3-73-1 and AVON3-77-1 of Vailulu‘u Island66 from the Samoa hotspot. Most of the analysed modern OIB samples have been characterized for both chemical (major and trace elements) and radiogenic isotope (Sr–Nd–Pb–He–W) compositions in the literature54,55,64,65,66. Most of the analysed OIB samples have higher 3He/4He ratios (up to 38.7 Ra, in which Ra represents a normalization onto the 3He/4He ratio of atmosphere) compared with that of N-MORBs (about 8 Ra)54,64,65,66. These OIB samples also have resolvable negative u182W values down to −13.8 ± 3.3 ppm (refs. 16,55).

Although fractional crystallization of Fe–Ti oxides can quickly lead to increasing δ49Ti values for evolved mafic lavas3,6,7,31,32, we argue that the mantle-derived rocks in this study are devoid of Fe–Ti oxide fractionation based on two observations: (1) although at fayalite–magnetite–quartz buffer Fe–Ti oxides normally start crystallizing at late stage of magma differentiation67 (MgO < 5 wt%), the measured samples have high MgO contents of >5.80 wt%, except for sample ICE-14-16 with MgO = 5.02 wt%, and (2) the lavas from the same age groups or the same oceanic islands did not show resolvable increase in δ49Ti with decreasing MgO contents (Extended Data Fig. 1b). We also note that some OIB samples contain the earlier crystallized olivine phenocrysts that would lead to much higher MgO contents, which—however—should have negligible effects on the Ti isotopic compositions of the studied samples in a whole-rock-scale owing to the low TiO2 contents in olivine.

Sample dissolution and chromatographic purification of Ti

Powders of samples were weighed into precleaned Savillex beakers and dissolved with mixtures of 22 M HF and 14 M HNO3 acids in a 2:1 volume ratio. The modern OIBs and four reference materials (that is, BHVO-2, BCR-2, AGV-2 and BIR-1) were digested on a hot plate at 120 °C for four days. Note that all chondrite and Archaean ultramafic/mafic rock samples were digested in Parr bomb vessels at 220 °C for three days to ensure full dissolution of refractory phases. Dissolution of the dried samples in 5–10 ml 6 M HCl at 120 °C and evaporation was carried out several times to decompose the fluorides formed from HF digestion until clear solutions were obtained. An aliquot of each sample was taken and spiked with a prepared 47Ti–49Ti double spike to determine in advance the Ti concentration using an iCAP RQ inductively coupled plasma mass spectrometer at the Centre for Star and Planet Formation (StarPlan) at the University of Copenhagen. Afterwards, aliquots containing 6 µg Ti were taken and mixed with a 47Ti–49Ti double spike as described previously in ref. 34. The dried mixtures were dissolved with 6 M HCl at 120 °C overnight to ensure sample–spike equilibration.

Titanium was separated from matrix elements following a three-step purification protocol using AG1x8 (200–400 meshes) and DGA resins34,68, that is, first to separate Fe with 6 M HCl elution on AG1x8 columns, second to remove most of the major and trace elements through 12 M HNO3 elution and to collect Ti with Milli-Q H2O on DGA columns and third to purify Ti from the remaining matrix elements with 4 M HF cleaning on AG1x8 columns. An extra DGA pass can be carried out to remove trace amounts of Ca and Cr in the final Ti cuts. To destroy the resin particles and organics from column chemistry, the Ti cuts were treated with 14 M HNO3 at 120 °C before storage in 0.5 M HNO3 + 0.01 M HF acids.

Neoma Multicollector ICP-MS

Titanium isotopic compositions of the purified samples were measured using the ThermoFisher Scientific Neoma Multicollector ICP-MS. Sample solutions with 500–800 ppb Ti dissolved in 0.5 M HNO3 + 0.01 M HF were introduced into the multicollector inductively coupled plasma source mass spectrometer by means of an APEX HF desolvating nebulizer from Elemental Scientific and a sapphire injector was used instead of the quartz-made injector to reduce the production of silicon fluorides from the use of HF solvent. An actively cooled membrane desolvation component was attached after the APEX to suppress oxide formation and to stabilize the signals, and N2 gas at a flow rate of a few ml min−1 was added to improve the sensitivity. Such a setting typically provides an intensity of around 15 V on 48Ti+ at an uptake rate of about 50 μl min−1 for a 600-ppb Ti solution under a medium mass-resolution mode.

The increased mass dispersion of the Neoma relative to earlier-generation instruments allows for a simultaneous monitoring of 43Ca+ (L5), 44Ca+ (L4), 46Ti+ (L3), 47Ti+ (L1), 48Ti+ (C), 49Ti+ (H1), 50Ti+ (H2), 51V+ (H3), 52Cr+ (H4) and 53Cr+ (H5) species in a single collector configuration. The medium mass-resolution mode on the Neoma (that is, M/ΔM ≈ 7,000) can resolve the main molecular isobaric interferences on the measured masses (for example, 28Si16O+ on 44Ca+, 28Si19F+ on 47Ti+ and 36Ar14N+ on 50Ti+). Measuring intensities on 44Ca+, 51V+ and 53Cr+ with those of Ti allows for a high-precision correction of the related isobaric interferences. To account for instrumental mass bias on the measurements from different sessions, a strict standard-sample bracketing protocol was used for all the multicollector inductively coupled plasma source mass spectrometer sessions in this study, that is, to analyse the OL-Ti standard solution before and after every sample analysis. Each analysis of the standard or samples comprises 100 cycles with 8 s integration time. On-peak zeros were measured before each sample/standard analysis in the same 0.5 M HNO3 + 0.01 M HF solution used to dissolve the sample/standard for 75 cycles with 8 s integration time. The typical background for the measurements is about 2–4 mV on 48Ti+. To evaluate data reproducibility, each sample has been normally analysed 4–8 times and four reference materials (that is, BHVO-2, BCR-2, AGV-2 and BIR-1) have been processed several times in parallel with the unknown samples.

Concomitant derivation of Ti-stable isotope composition and nucleosynthetic component from double-spike measurements

An accurate determination of the Ti-stable isotope composition in meteoritic samples through a double-spike technique requires knowledge of the nucleosynthetic composition of the samples for correction. In the past, a separate protocol was needed for measurements of Ti nucleosynthetic components, that is, to analyse the samples purified without introducing a spike68,69,70. Because this approach is time consuming, previous Ti isotope studies33,34 have relied on literature values of the same meteorites or the same meteorite groups for correction. However, this is not ideal, as it can introduce artefacts on the Ti-stable isotope composition if discrepancies in the Ti nucleosynthetic component exist between the new digestion aliquots of meteorites and those in the literature.

It is, however, noteworthy that, after normalization onto the 49Ti/47Ti ratio, meteorites in bulk exhibit anomalies mainly on 46Ti and 50Ti (refs. 69,70), which are correlated following a relation of ε46Ti = (0.184 ± 0.007) × ε50Ti + (0.025 ± 0.009) (ref. 71), in which an epsilon notation is used to describe the magnitude of these isotopic anomalies. In this case, it is possible to derive both the Ti-stable isotope composition and the nucleosynthetic component in samples from the measured results of a sample–spike mixture by means of the following procedures, with the standard composition (that is, \({{\rm{R}}}_{{\rm{standard}}}^{46/47}\), \({{\rm{R}}}_{{\rm{standard}}}^{48/47}\), \({{\rm{R}}}_{{\rm{standard}}}^{49/47}\) and \({{\rm{R}}}_{{\rm{standard}}}^{50/47}\)) and the 47Ti–49Ti double-spike composition (that is, \({{\rm{R}}}_{{\rm{spike}}}^{46/47}\), \({{\rm{R}}}_{{\rm{spike}}}^{48/47}\), \({{\rm{R}}}_{{\rm{spike}}}^{49/47}\) and \({{\rm{R}}}_{{\rm{spike}}}^{50/47}\)) calibrated in advance:

  1. 1.

    The interference-corrected 46Ti/47Ti, 48Ti/47Ti and 49Ti/47Ti ratios from an analysis of either OL-Ti standard or unknown samples can be used for a primary double-spike inversion to obtain solutions for the three unknowns λ (that is, the proportion of 47Ti from the 47Ti–49Ti double spike in the sample–spike mixture), α (that is, the natural mass fractionation factor) and β (that is, the instrumental mass fractionation factor), as defined in a set of three non-linear equations72:

    $${F}_{i}(\lambda ,\alpha ,\beta ,n,m,T)=\lambda {T}_{i}+(1-\lambda ){n}_{i}{{\rm{e}}}^{-\alpha {P}_{i}}-{m}_{i}{{\rm{e}}}^{-\alpha {P}_{i}}=0,$$
    (1)

    in which n, m and T represent the standard, the sample–spike mixture and the 47Ti–49Ti double spike, respectively, and each of them further comprises three known or measured Ti isotopic ratios (that is, 46Ti/47Ti, 48Ti/47Ti and 49Ti/47Ti), and Pi stands for a natural log of the atomic masses included in the selected isotope ratio i, for example, P1 = ln(45.9526316/46.9517631) for the 46Ti/47Ti ratio.

  2. 2.

    The 50Ti/47Ti ratio of the sample (\({{\rm{R}}}_{{\rm{sample}}}^{50/47}\)) can be derived from the measured 50Ti/47Ti ratio of the mixture (\({{\rm{R}}}_{{\rm{mixture}}}^{50/47}\)) and that of the 47Ti–49Ti double spike (\({{\rm{R}}}_{{\rm{spike}}}^{50/47}\)) using the defined λ and β values:

    $${{\rm{R}}}_{{\rm{sample}}}^{50/47}=\left[{{\rm{R}}}_{{\rm{mixture}}}^{50/47}\times {{\rm{e}}}^{-\beta \times {\rm{ln}}\left({m}_{50}/{m}_{47}\right)}-\lambda \times {{\rm{R}}}_{{\rm{spike}}}^{50/47}\right]/(1-\lambda ).$$
    (2)
  3. 3.

    Afterwards, in the case that instrumental mass bias follows the exponential mass fractionation law as assumed in equations (1) and (2), deviation of the 50Ti/47Ti ratio of sample (\({{\rm{R}}}_{{\rm{sample}}}^{50/47}\)) from that of the standard composition (\({{\rm{R}}}_{{\rm{standard}}}^{50/47}\)) would be a combined result of the isotopic anomaly on 50Ti and the mass-dependent isotopic fractionation from natural processes, for which the magnitude of the latter can be quantified from the α value of the sample for correction. In this case, the 50Ti anomaly of the sample in an epsilon notation (ε50Ti) would be the same as the preliminary calculated values (that is, ε50Tiprelim):

    $${\varepsilon }^{50}{{\rm{T}}{\rm{i}}}_{{\rm{p}}{\rm{r}}{\rm{e}}{\rm{l}}{\rm{i}}{\rm{m}}}=[{{\rm{R}}}_{{\rm{s}}{\rm{a}}{\rm{m}}{\rm{p}}{\rm{l}}{\rm{e}}}^{50/47}\times {{\rm{e}}}^{-\alpha \times {\rm{l}}{\rm{n}}({m}_{50}/{m}_{47})}/{{\rm{R}}}_{{\rm{s}}{\rm{t}}{\rm{a}}{\rm{n}}{\rm{d}}{\rm{a}}{\rm{r}}{\rm{d}}}^{50/47}-1]\times \mathrm{10,000}.$$
    (3)

    in which m47 and m50 stand for the atomic masses of 47Ti and 50Ti, respectively.

    In the other case that the instrumental mass bias may slightly differ from the exponential mass fractionation law, mass-independent Ti isotopic effects would be created from double-spike inversion and, therefore, a secondary normalization onto the bracketing OL-Ti standards would be necessary to obtain the correct 50Ti anomalies for unknown samples, in which a spline with the minimal mean squared weighted deviation value on the ε50Tiprelim values of the OL-Ti standard can be used for the normalization:

    $${\varepsilon }^{50}{\rm{T}}{\rm{i}}={\varepsilon }^{50}{{\rm{T}}{\rm{i}}}_{{\rm{p}}{\rm{r}}{\rm{e}}{\rm{l}}{\rm{i}}{\rm{m}}-{\rm{s}}{\rm{a}}{\rm{m}}{\rm{p}}{\rm{l}}{\rm{e}}}-{\varepsilon }^{50}{{\rm{T}}{\rm{i}}}_{{\rm{O}}{\rm{L}}-{\rm{T}}{\rm{i}}{\rm{s}}{\rm{p}}{\rm{l}}{\rm{i}}{\rm{n}}{\rm{e}}}.$$
    (4)
  4. 4.

    It is, however, notable that the primary double-spike inversion includes no correction of the 46Ti anomaly. Following equation (4), a ε50Ti value can be obtained for an unknown sample from averaging the results from duplicate measurements, after which a ε46Ti value can be further inferred on the basis of the correlation between ε46Ti and ε50Ti, that is, ε46Ti = (0.184 ± 0.007) × ε50Ti + (0.025 ± 0.009) (ref. 71). An ideal way to correct for the 46Ti anomaly is to create an equivalent effect on the standard composition before double-spike inversion:

    $${\left({{\rm{R}}}_{{\rm{standard}}}^{46/47}\right)}_{{\rm{new}}}={{\rm{R}}}_{{\rm{standard}}}^{46/47}\times \left(\frac{{{\rm{\varepsilon }}}^{46}{\rm{Ti}}}{\mathrm{10,000}}+1\right).$$
    (5)
  5. 5.

    As the correction of the 46Ti anomaly would affect the calculated λ, α and β values from double-spike inversion and then the calculated ε46Ti and ε50Ti values, an iteration of procedures (1) to (4) needs to be carried out using the revised standard composition, and the ε50Ti values for unknown samples normally converge after four or five iterations. The preliminary mass-dependent Ti isotopic fractionations (reported as a delta notation on the 49Ti/47Ti ratio relative to the standard composition) can be obtained from α:

$${{\rm{\delta }}}^{49}{{\rm{Ti}}}_{{\rm{prelim}}}=\left({{\rm{e}}}^{-\alpha \times {\rm{ln}}\left({m}_{49}/{m}_{47}\right)}-1\right)\times \mathrm{1,000},$$
(6)

in which m47 and m49 stand for the atomic masses of 47Ti and 49Ti, respectively. In the case that the instrumental mass fractionation bias did not follow exactly an exponential mass fractionation law, a secondary normalization onto the bracketing OL-Ti standard is necessary to obtain the correct mass-dependent Ti isotopic fractionations for unknown samples, in which a spline with the minimal mean squared weighted deviation value on the δ49Tiprelim values of the OL-Ti standard can be used for the normalization:

$${{\rm{\delta }}}^{49}{\rm{T}}{\rm{i}}={{\rm{\delta }}}^{49}{{\rm{T}}{\rm{i}}}_{{\rm{p}}{\rm{r}}{\rm{e}}{\rm{l}}{\rm{i}}{\rm{m}}-{\rm{s}}{\rm{a}}{\rm{m}}{\rm{p}}{\rm{l}}{\rm{e}}}-{{\rm{\delta }}}^{49}{{\rm{T}}{\rm{i}}}_{{\rm{O}}{\rm{L}}-{\rm{T}}{\rm{i}}{\rm{s}}{\rm{p}}{\rm{l}}{\rm{i}}{\rm{n}}{\rm{e}}}.$$
(7)

Propagation of uncertainty from anomaly correction

The uncertainties from the derivation of 46Ti anomalies from the measured 50Ti anomalies and the subsequent correction need to be propagated onto the results. Main uncertainties on the derived 46Ti anomalies should come from (1) uncertainties on the 50Ti measurements and (2) uncertainties from the assumed relation between ε46Ti and ε50Ti, that is, ε46Ti = (0.184 ± 0.007) × ε50Ti + (0.025 ± 0.009). We consider that the 2 s.e. value of the ε50Tiprelim values from duplicate measurements of each sample to represent the uncertainty on the 50Ti measurements for this sample, that is, σ(ε50Tiprelim). The uncertainty on the inferred 46Ti anomaly can be approximated to:

$$\sigma \left({{\rm{\varepsilon }}}^{46}{\rm{Ti}}\right)\approx \sqrt{{\left[\sigma \left({{\rm{\varepsilon }}}^{50}{{\rm{Ti}}}_{{\rm{prelim}}}\right)\times 0.184\right]}^{2}+{0.009}^{2}}.$$
(8)

The effects from 46Ti correction on the δ49Ti and ε50Ti values can be empirically evaluated by assigning various ε46Ti values for correction within the data-processing protocol described above, which follows linear equations of the assigned ε46Ti value:

$${{\rm{\delta }}}^{49}{{\rm{Ti}}}_{{\rm{corr}}}-{{\rm{\delta }}}^{49}{{\rm{Ti}}}_{{\rm{uncorr}}}\approx 0.108\times {{\rm{\varepsilon }}}^{46}{\rm{Ti}},$$
(9)
$${{\rm{\varepsilon }}}^{50}{{\rm{Ti}}}_{{\rm{corr}}}-{{\rm{\varepsilon }}}^{50}{{\rm{Ti}}}_{{\rm{uncorr}}}\approx -0.96\times {{\rm{\varepsilon }}}^{46}{\rm{Ti}}.$$
(10)

The uncertainty on the derived ε46Ti value from equation (8) can be further propagated onto the δ49Ti and ε50Ti results:

$$\sigma \left({{\rm{\delta }}}^{49}{\rm{Ti}}\right)\approx \sqrt{{\left[\sigma \left({{\rm{\varepsilon }}}^{46}{\rm{Ti}}\right)\times 0.108\right]}^{2}+{\left[\sigma \left({{\rm{\delta }}}^{49}{{\rm{Ti}}}_{{\rm{prelim}}}\right)\right]}^{2}},$$
(11)
$$\sigma \left({{\rm{\varepsilon }}}^{50}{\rm{Ti}}\right)\approx \sqrt{{\left[\sigma \left({{\rm{\varepsilon }}}^{46}{\rm{Ti}}\right)\times \left(-0.96\right)\right]}^{2}+{\left[\sigma \left({{\rm{\varepsilon }}}^{50}{{\rm{Ti}}}_{{\rm{prelim}}}\right)\right]}^{2}}.$$
(12)

Note that the pooled uncertainties on the ε50Tiprelim and δ49Tiprelim values from duplicate measurements are ±0.15 and ±0.010‰, respectively. Substituting these values into equations (8), (11) and (12) shows that the propagated uncertainties from anomaly correction are negligible relative to the uncertainties on ε50Tiprelim and δ49Tiprelim.

Results and data reproducibility

Although simulation shows that the use of a 47Ti–49Ti double spike provides optimally small errors on the results for a large spiking range (fsample = 0.20–0.80, in which fsample stands for the sample fraction in the sample–spike mixture73), in practice, there may be systematic offsets in the calculated δ49Ti value when acquiring data at different spiking ratios, for example, up to about 0.18‰ offsets for the spiked Ti Alfa Aesar aliquots that have fsample values between 0.20 and 0.80 (ref. 35). Despite the magnitude of the offsets at different spiking ratios depending on the calibration of the standard composition and the used 47Ti–49Ti double spike in different laboratories, it is worthwhile scrutinizing the effects and, if necessary, optimizing the fsample values between the samples and the bracketing standard. Except for the Cold Bokkeveld sample (fsample = 0.470), all the samples in this study have fsample values within a small range (0.409–0.454), which closely match that of the used bracketing OL-Ti standard solutions (fsample = 0.43–0.44). Several runs of three reference materials (that is, BHVO-2, BCR-2 and AGV-2) and two chondrites (Murchison and Murray) at different spiking ratios show that, within a fsample range of 0.409–0.454, no systematic offset relative to the bracketing OL-Ti standard (fsample = 0.43–0.44) was resolved at a precision of ±0.15 for ε50Ti and of ±0.010‰ for δ49Ti.

Several runs of reference materials BHVO-2, BCR-2 and AGV-2 provide δ49Ti values of +0.024 ± 0.010‰ (n = 9, 2 s.d.), +0.001 ± 0.006‰ (n = 8, 2 s.d.) and +0.097 ± 0.013‰ (n = 4, 2 s.d.), respectively. These are within uncertainty identical to the previously recommended values in the literature3,4,32,34,35. With respect to anomaly measurements, all of the duplicate runs of reference materials BHVO-2, BCR-2, AGV-2 and BIR-1 give a mean ε50Ti value of −0.07 ± 0.14 (n = 19, 2 s.d.). The consistency of the δ49Ti and ε50Ti values from several runs of the same samples suggests a long-term external precision of ±0.010‰ and ±0.15, respectively, on the δ49Ti and ε50Ti data from this study. It is also noteworthy that the ε50Ti values of both terrestrial reference materials and chondrite meteorites, including Murchison, Orgueil, NWA 5697 and SaH 97159, are consistent with the values acquired previously in refs. 69,70 using a non-spike method (Extended Data Fig. 2), which demonstrate that the ε50Ti results derived from double-spike measurements in this study are accurate at the claimed precision.

Precise and accurate determination of the δ49Ti average for whole-rock chondrites

There is notable scatter of the δ49Ti data reported for whole-rock chondrites in the literature, for instance, a δ49Ti average of +0.008 ± 0.039‰ (n = 16, 2 s.d.) from Greber et al.33, of +0.071 ± 0.085‰ (n = 22, 2 s.d.) from Deng et al.34 and of +0.047 ± 0.071‰ (n = 6, 2 s.d.) from Williams et al.35. However, we note that large offsets in δ49Ti (up to 0.100‰) were observed between lithium metaborate fusion digestions of the same komatiite and eucrite powders (for example, 501-1, 501-8, M657, M663, M666, M712, Lakangaon and Ibitira; Extended Data Fig. 3a) in Greber et al.33, and the authors have ascribed the discrepancy to a lack of equilibration of the sample with the double spike that results in lower δ49Ti values33.

For the digestion or spiking protocols involving HF acids, fluoride formation hampers either full-sample dissolution or sample–spike equilibration. Here we have carried out experiments to evaluate the potential effects from fluorides on the δ49Ti data in this study as follows:

  1. 1.

    An approximately 1,425-mg chip of NWA 5697 (L3) meteorite was crushed into a fine powder (NWA 5697-B) and six aliquots with masses of 83 to 99 mg (-01, -02, -03, -04, -05 and -06) were digested following the typical Parr bomb digestion procedure. Aliquots containing about 6 µg Ti were taken from ‘-1’ and ‘-2’ digestions and spiked in 6 M HCl on a hot plate at 120 °C, whereas the other four whole digestions were spiked and placed into a Parr bomb with 14 M HNO3 acids at 190 °C for a day, at which conditions fluorides should decompose. The six experiments provide consistent δ49Ti values (+0.032 ± 0.004‰, n = 6, 2 s.d.) that agree with the results from a roughly 2,000-mg digestion of NWA 5697 (-A) (+0.039 ± 0.001‰, n = 2, 2 s.d.) (Extended Data Fig. 3b). This confirms that the analytical protocol used in this study is sufficient to destroy potential fluorides formed from HF digestions.

  2. 2.

    The robustness of the protocol to eliminate fluorides can be further tested by a second set of experiments, in which fractions (12–14%) of the NWA 530, NWA 1232, NWA 4428 and NWA 1563 digestions were spiked and heated in 6 M HCl on a hot plate, whereas the remaining solutions were spiked and placed into a Parr bomb with 14 M HNO3 acids at 190 °C for a day. All four samples have identical δ49Ti values between the two procedures within an uncertainty of ±0.010‰ (Extended Data Fig. 3c).

As heterogeneity does exist inside chondrites, for example, the large δ49Ti variation of −4‰ to +4‰ in Ca, Al-rich inclusions71, acquiring mass-dependent Ti isotope data for whole-rock chondrites can be subject to a certain degree of such heterogeneity. This can be well corroborated by the larger scatter in published δ49Ti data for whole-rock chondrites with the decreasing digestion masses (Extended Data Fig. 4). In this study, excluding Talbachat n’aït Isfoul (LL3) and NWA 2364 (CV3) that are probably subject to sample heterogeneity and show elevated δ49Ti values, the remaining 22 chondrite samples define an average δ49Ti of +0.053 ± 0.024‰ (2 s.d.) or ±0.005‰ (2 s.e.) (Extended Data Fig. 4). Our new chondrite average is identical to that of Deng et al.34 (+0.071 ± 0.085‰, n = 22, 2 s.d.) and Williams et al.35 (+0.047 ± 0.071‰, n = 6, 2 s.d.), but with a threefold improvement in precision. Considering the large digestion masses for most of the chondrite samples in this study, our new chondrite data should be least affected by sample heterogeneity. The new chondrite average is resolved to be around 0.052‰ higher than that of modern N-MORBs, that is, +0.001 ± 0.015‰ (2 s.d.) or ±0.004‰ (2 s.e.) (refs. 3,4) (Extended Data Fig. 4).

We note that data offset between laboratories also exists for the δ49Ti results from Archaean komatiites, with the substantially lower and more scattered δ49Ti values in Greber et al.33 than those in this study and Deng et al.4 (Extended Data Fig. 5). We emphasize that the presence of data discrepancy between digestion duplicates of the same komatiite powders in Greber et al.33 probably points to a larger analytical uncertainty on the reported δ49Ti dataset for both whole-rock chondrites and Archaean komatiites than the claimed precision of ±0.030–0.034‰ (95% confidence interval) for individual samples.

Quantifying mass exchange between mantle and crustal reservoirs in deep time

Assuming that the continental crust (CC) at time ti and the mantle equilibrated with the recycled crustal melting residues from continental crust formation (thereafter called the contaminated mantle, that is, CM) together form a primitive mantle (PM) reservoir with respect to TiO2 content and δ49Ti, the TiO2 fraction from continental crust in the CC-CM combination at time ti (that is, \({{\rm{X}}}_{{{\rm{TiO}}}_{2}\_{\rm{CC}}\_{t}_{i}}\)) should be:

$${{\rm{X}}}_{{{\rm{TiO}}}_{2}\_{\rm{CC}}\_{t}_{i}}=\frac{{{\rm{C}}}_{{{\rm{TiO}}}_{2}\_{\rm{CC}}}\times {q}_{{\rm{CC}}\_{t}_{i}}\times {m}_{{\rm{CC}}}}{{{\rm{C}}}_{{{\rm{TiO}}}_{2}\_{\rm{PM}}}\times \left({q}_{{\rm{CC}}\_{t}_{i}}\times {m}_{{\rm{CC}}}+{m}_{{\rm{CM}}}\right)},$$
(13)

in which \({{\rm{C}}}_{{{\rm{TiO}}}_{2}}\) represents the TiO2 content and m stands for the mass. We note that \({q}_{{\rm{CC}}\_{{\rm{t}}}_{i}}\) defines the fraction of the total continental crust (mCC) that has been produced until time ti, which has been provided in the continental crust growth models from refs. 43,44. The Ti isotopic composition of the contaminated mantle at time ti should approximately follow:

$${{\rm{\delta }}}^{49}{{\rm{Ti}}}_{{\rm{CM}}\_{t}_{i}}=\frac{{{\rm{\delta }}}^{49}{{\rm{Ti}}}_{{\rm{PM}}}-{{\rm{\delta }}}^{49}{{\rm{Ti}}}_{{\rm{CC}}}\times {{\rm{X}}}_{{{\rm{TiO}}}_{2}\_{\rm{CC}}\_{t}_{i}}}{\left(1-{{\rm{X}}}_{{\rm{Ti}}{{\rm{O}}}_{2}\_{\rm{CC}}\_{t}_{i}}\right)}.$$
(14)

Assigning δ49TiPM = +0.053 ± 0.005‰ (this study) and the δ49Ti average of Archaean TTGs to be δ49TiCC (+0.381 ± 0.056‰, 2 s.e., n = 19; this study and refs. 5,7), \({{\rm{\delta }}}^{49}{{\rm{Ti}}}_{{\rm{CM}}\_{t}_{i}}\) is controlled by \({{\rm{X}}}_{{\rm{Ti}}{{\rm{O}}}_{2}\_{\rm{CC}}\_{t}_{i}}\). As \({{\rm{C}}}_{{{\rm{TiO}}}_{2}\_{\rm{PM}}}\) and \({{\rm{C}}}_{{{\rm{TiO}}}_{2}\_{\rm{CC}}}\) can be reasonably assumed to be 0.18 wt% and 0.34 wt%, respectively, \({{\rm{X}}}_{{\rm{Ti}}{{\rm{O}}}_{2}\_{\rm{CC}}\_{t}_{i}}\) is further related with two free parameters, that is, mCC and mCM in equation (13). Although modern continental crust is about 0.55% of the BSE in mass (that is, mCC_modern = 0.0055 × mBSE), the total mass of continental crust (mCC) ever produced throughout the Earth’s history remains less clear. To quantify \({{\rm{\delta }}}^{49}{{\rm{Ti}}}_{{\rm{CM}}\_{t}_{i}}\), we can bring in two free parameters, that is, k describing the total mass of continental crust ever produced through the Earth’s history after a normalization to its modern mass (k = mCC/mCC_modern) and f representing the fraction of Earth’s mantle to equilibrate with the recycled melting residues, that is, f = (mCC + mCM)/mBSE. By assuming k and f, we can obtain the evolution of δ49TiCM through time in Fig. 2 based on the continental crust growth models from refs. 43,44.