Palaeointensity, core thermal conductivity and the unknown age of the inner core

Abstract

Data on the evolution of Earth's magnetic field intensity are important for understanding the geodynamo and planetary evolution. However, the paleomagnetic record in rocks may be adversely affected by many physical processes, which must be taken into account when analysing the palaeointensity database. This is especially important in the light of an ongoing debate regarding core thermal conductivity values, and how these relate to the Precambrian geodynamo. Here, we demonstrate that several data sets in the Precambrian palaeointensity database overestimate the true paleofield strength due to the presence of non-ideal carriers of palaeointensity signals and/or viscous re-magnetizations. When the palaeointensity overestimates are removed, the Precambrian database does not indicate a robust change in geomagnetic field intensity during the Mesoproterozoic. These findings call into question the recent claim that the solid inner core formed in the Mesoproterozoic, hence constraining the thermal conductivity in the core to ‘moderate’ values. Instead, our analyses indicate that the presently available palaeointensity data are insufficient in number and quality to constrain the timing of solid inner core formation, or the outstanding problem of core thermal conductivity. Very young or very old inner core ages (and attendant high or low core thermal conductivity values) are consistent with the presently known history of Earth's field strength. More promising available data sets that reflect long-term core structure are geomagnetic reversal rate and field morphology. The latter suggests changes that may reflect differences in Archean to Proterozoic core stratification, whereas the former suggest an interval of geodynamo hyperactivity at ca. 550 Ma.

Dynamo: theories and simulations, Magnetic field, Palaeointensity, Rock and mineral magnetism, Core, outer core and inner core, Planetary interiors

INTRODUCTION

Earth's magnetic field is generated by convection of iron in the liquid outer core. Today, the compositional gradient and latent heat associated with the crystallizing inner core helps fuel this convection. But thermal models predict Earth has not always had an inner core (e.g. Aubert et al.2010). The geodynamo has existed for at least the last 3.45 billion years (Usui et al.2009; Tarduno et al.2010; Biggin et al.2011), with new evidence suggesting an age as old as 4.2 billion years (Tarduno et al.2015). Prior to the onset of inner core nucleation, the field must have been generated by thermal convection or an alternate source of compositional convection such as the recently proposed precipitation of magnesium (O'Rourke & Stevenson 2016). Thus, the time when inner core growth commenced is a fundamental parameter important for understanding evolution of the core and the long-term energetics of the dynamo.

The onset time of the inner core crystallization depends critically on core thermal conductivity (Olson 2013), and conventional values allowed inner core ages that extended well into Archean times (e.g. Gubbins et al.2004). However, recent diamond anvil-cell experiments and first principles-calculations suggest thermal conductivities ranging from 90 to 150 W m⁻¹ K⁻¹, several times greater than the classical values (e.g. de Koker et al.2012; Pozzo et al.2012; Gomi et al.2013; Davies 2015). These values in turn suggest ages less than 1 Ga for the onset of inner core growth (Nimmo 2015). However, debate continues, as some first-principle calculations incorporating electron-electron scattering suggest lower values, consistent with classical core thermal conductivities (Zhang et al.2015). This debate naturally raises the question of whether some paleomagnetic observable might be able to detect independently inner core growth and in so doing constrain core thermal conductivity.

In a recent paper, Biggin et al. (2015) argued that the solid inner core formed in the Mesoproterozoic (ca. 1300 Ma), and that this onset time constrains the thermal conductivity in the core to ‘moderate’ values. Their interpretations are based on Precambrian palaeointensity data selected using a set of criteria (Biggin & Patterson 2014) vitiated so that more data pass screening, allowing for a statistical analysis (i.e. as few as three of eight criteria were employed). Here we argue that critical data underlying these conclusions significantly overestimate the true paleofield strength due to rock magnetic effects and are affected by a statistical bias. If the biased data are removed, the remaining values do not indicate a robust change in geomagnetic field intensity during the Mesoproterozoic. We conclude that the presently available palaeointensity data of Precambrian age are insufficient in number and quality to constrain the timing of solid inner core formation or the outstanding problem of core thermal conductivity. In contrast, we highlight that the available data set of paleodirections (and associated geomagnetic reversal frequency) is a more fruitful probe of early core evolution.

PRECAMBRIAN PALAEOINTENSITY

The gold standard for the determination of past field strength remains the Thellier double-heating method (Thellier & Thellier 1959; Coe 1967; Dunlop & Özdemir 1997; Tauxe 2010) which compares demagnetization of a natural remanent magnetization (NRM) with the acquisition of a partial thermal remanent magnetization (pTRM) in a series of paired heating steps. Conventionally, the points corresponding to each temperature step are evaluated with an NRM-lost versus pTRM-gained plot (Arai plot; Nagata et al.1963). The palaeointensity is calculated from the slope of a linear segment on the plot corresponding to the unblocking temperature range of the primary remanent magnetization, which must be a thermal remanent magnetization (Thellier & Thellier 1959; Fig. 1a). To monitor possible alteration during the Thellier experiment, partial thermoremanent magnetization (pTRM) checks are commonly utilized by repeating several on-field steps at lower temperatures (Coe 1967).

Figure 1.

Examples of normalized Arai plots measured from (a) the Lake Shore Traps (Kulakov et al.2013) and (b) the Gardar lava flows (Thomas 1993). Squares show natural remanent magnetization (NRM) lost versus partial thermoremanent magnetization (pTRM) gained. Numbers specify temperatures (°C) for selected heating steps; R: rejected points. Triangles are pTRM checks. (a) While the primary magnetization unblocks above 375 °C for the LST sample, the corresponding Arai plot has a concave (double slope) shape typical for multidomain magnetic carrier. The palaeointensity was determined from the high-temperature segment of the plot (solid line). The use of low-temperature segment (dashed line) would result in a more than twofold palaeointensity overestimate. (b) An example of the low-temperature segment fitting (dashed line) used to determine palaeointensity for most Gardar lava flows (Thomas 1993). (c) The site-mean data based on bulk rock (triangles) or single crystal (diamonds) samples with Q_PI ≥ 3 used by Biggin et al. (2015) (Supporting Information Fig. S1a) with the palaeointensity overestimates removed (see the text). The arrow shows a potential 50 per cent overestimate correction for the corresponding data point (Salminen et al.2006). The large/small black circles show the study-means based on three or more sites or two sites, respectively. The error bars are 1σ. The red and blue lines show the mean palaeointensity values for the 0.05–5 Ma and 10–15 Ma time intervals (see the text) with the uncertainties (1σ) shown by pink and purple boxes, respectively.

A fundamental requirement for the successful application of the Thellier method is that the palaeointensity signal is carried by single-domain magnetic grains. However, rocks used in palaeointensity analyses commonly contain large magnetic grains in the multidomain (MD) state. Arai plots from such rocks typically show a ‘concave-up’ (or double slope) shape (Shcherbakova & Shcherbakov 2001; Xu & Dunlop 2004; Fig. 1a). Nominal palaeointensity values defined by the low-temperature range on such Arai plots are overestimates (Shcherbakova & Shcherbakov 2001; Fig. 1a). Another common effect that yields two slopes on the Arai plots and nominal palaeointensity values isolated at low unblocking temperatures that greatly overestimate the true field value is the acquisition of secondary viscous magnetization.

The high nominal palaeointensity values critical to the interpretation of a Mesoproterozoic age for the inner core (Biggin et al.2015) come from only two localities: (1) the ∼1300 Ma Gardar lava flows (Thomas & Piper 1992, 1995; Thomas 1993) in Greenland, and (2) rocks associated with the ∼1100 Ma North American Midcontinent Rift (MCR; Pesonen & Halls 1983; Kulakov et al.2013; Supporting Information Fig. S1a). The primary remanence in the Gardar lavas is mainly carried by magnetite, or low-Ti magnetite, and in some samples hematite. This remanence unblocks after treatment to ∼450 to 690 °C (Thomas & Piper 1992, 1995; Thomas 1993). However, for most of the Gardar lava samples, palaeointensity was calculated by fitting low-temperature Arai segments (below 450 °C, to as low as 100 °C) (Thomas 1993; Thomas & Piper 1995; Fig. 1b). We interpret these values as overestimates of the true field due to MD effects (Shcherbakova & Shcherbakov 2001). In addition, most Gardar samples contain a viscous remanent magnetization (VRM) that unblocks within the same low temperature range used for palaeointensity determination, potentially contributing to the high palaeointensity bias.

One of the MCR sites (R40; Pesonen & Halls 1983) used by Biggin et al. (2015) is based on two samples representing a ∼1100 Ma diabase sill and baked Sibley Formation red beds. Similar to the Gardar rocks, these palaeointensity values are based on fitting low-temperature Arai segments (mostly below 450 °C and as low as 20 °C) and hence are likely overestimates due to MD and VRM effects. Another MCR site (NCG; Pesonen & Halls 1983) from the Copper Harbor Conglomerate baked by the ∼1087 Ma Lake Shore Trap (LST) lavas yields a site-mean value about twice as high as the mean palaeointensity recently obtained from the LST based on a large number of independent cooling units (Kulakov et al.2013). Interestingly, when the specimen data based on low-temperature Arai fitting are removed, the remaining NCG values become indistinguishable from those in the recent study (Kulakov et al.2013), supporting our interpretation that using the low-temperature segments of Arai plots is responsible for the high palaeointensity values. Finally, we note that a high value from a single site at ∼682 Ma defined by low-temperature Arai segments may overestimate the true field by 50 per cent (Salminen et al. 2006; Fig. 1c).

If the palaeointensity overestimates from the Gardar and MCR rocks are excluded, the changes in the field intensity throughout the Proterozoic become less significant (Fig. 1c; Supporting Information Fig. S1b). In particular, the remaining data do not support the ‘natural’ splitting into the ‘Late’ (500–1300 Ma) and ‘Mid’ (1400–2400 Ma) periods (Biggin et al.2015). Furthermore, when the site-means characterized by a high-scatter (the standard deviation to the site-mean ratio exceeds 25 per cent) are removed, the database becomes sparse (Supporting Information Fig. S1c), further questioning the significance of the claim of a clear change in palaeointensity (Biggin et al.2015). Importantly, if study-mean data are used instead of site-mean data (which is a more conservative approach to avoid bias by giving equal weight to time-averaged and non-time-averaged data), any statistically significant differences between the ‘Late’, ‘Mid’, and ‘Early’ (2400–3500 Ma) periods disappear (Table 1).

Table 1.

Results of two-sample Kolmogorov–Smirnov tests for the palaeointensity data sets with biased data removed (see the text) for the Late (500–1300 Ma), Mid (1400–2400 Ma) and Early (2400–3500 Ma) periods. Study-means were calculated for two or more site-means; otherwise site-means were used (Supporting Information Table S1). The null hypothesis: the two samples are drawn from the same underlying population. n₁ and n₂: the sample size, D_KS: the Kolmogorov–Smirnov statistic, D_crit: the critical test value for the 95 per cent confidence level (Sheskin 2004).

					The null hypothesis
Data subsets compared	n1	n2	DKS	Dcrit	not rejected/rejected
All accepted data (study-means and site-means)
Late–Mid	10	14	0.30	0.53	Not rejected
Mid–Early	14	14	0.43	0.57	Not rejected
Late–Early	10	14	0.41	0.53	Not rejected
Study-means only
Late–Mid	3	6	0.67	1.00	Not rejected
Mid–Early	6	5	0.60	0.80	Not rejected
Late–Early	3	5	0.40	0.83	Not rejected

The similarity of palaeointensity data sets (with biased data removed; Supporting Information Table S1) for the 500–1300, 1400–2400 and 2500–3500 Ma periods was evaluated using the two-sample Kolmogorov–Smirnov test (Sheskin 2004). The test statistic was calculated using:

\begin{equation} {D_{{\rm{KS}}}} = \mathop {\sup }\limits_x \left| {{F_{n1}}(x) - {G_{n2}}(x)} \right| \end{equation}

(1)

where F_n1(x) and G_n2(x) are empirical cumulative distribution functions for the samples. The D_KS was compared with the critical value for the 95 per cent confidence level, D_crit, corresponding to the sample sizes (the number of data points) n₁ and n₂. The null hypothesis that both samples are drawn from the same underlying continuous population was not rejected at the 5 per cent significance level if the Kolmogorov–Smirnov statistic (D_KS) was smaller than D_crit (D_KS < D_crit). The Kolmogorov–Smirnov tests indicate that the corresponding palaeointensity data sets are drawn from the same underlying continuous population at the 95 per cent confidence level (Table 1).

DISCUSSION

Our results indicate that, in contrast to the conclusions of Biggin et al. (2015), very young or very old inner core ages (and attendant high or low core thermal conductivity values) are consistent with the available history of Earth's field strength. Data meeting our more rigorous selection criteria are limited, but even if we accept these as adequate measures of the field they should be gauged against field behaviour during times when we know inner core onset did not occur. We note that fluctuations in field intensity similar to those defined by our select data are seen for much younger time periods populated by larger data sets. For example, a comparison of reliable palaeointensity data for the 0.05–5 and 10–15 Ma time intervals results in different mean values (6.87 ± 2.82 × 10²² A m² and 3.63 ± 1.73 × 10²² A m²); this difference exceeds the increase in the field intensity interpreted by Biggin et al. (2015) as the signal of the inner core nucleation.

Is there any signal of core evolution between 3.5 and 0.5 billion years ago (the approximate limits for inner core growth constrained by core conductivity values currently under debate) in paleomagnetic data? Thellier palaeointensity analyses require a comparison of the NRM and a partial thermoremanent magnetization acquired by heating in the presence of an applied field. In contrast, a sample is ideally never exposed to a significant field during demagnetizations applied to collect paleodirectional data. Therefore, palaeointensity data are much more susceptible to laboratory induced alteration than paleodirectional data. Moreover, the grain-size, compositional/remanence acquisition requirements for robust palaeointensity data are much more severe as compared to those needed for directional analyses.

Therefore, because paleodirectional data are, in principle, of higher quality than palaeointensity data, these might be a more fruitful source of changes in core morphology. Potential changes might be recorded in field morphology. In fact, in the first analyses of paleodirectional data to constrain the morphology of the Archean field (Smirnov & Tarduno 2004) evidence was found for a slightly more dipolar field prior to ∼2.5 Ga. This analysis was borne out by subsequent analyses (Biggin et al.2008; Smirnov et al.2011). Although this change could conceivably indicate inner core onset (at ∼2.2 Ga), it might also more simply reflect changes in core stratification following evolution of the core-mantle boundary induced by long-term subduction history (Smirnov et al.2011).

Another higher resolution signal probe of core conditions is geomagnetic reversal frequency (Cox 1968; Lowrie & Kent 1983; Merrill & McFadden 1990; Hulot & Gallet 2003; Driscoll & Evans 2016; Gallet & Pavlov 2016). A low reversal frequency has been suggested for the Archean (Dunlop & Yu 2004). While this conclusion is tentative because of the potential for underestimates in reversal rate related to the spatial and temporal limitations of the Archean geologic record (Tarduno et al.2014), a low reversal rate is nevertheless consistent with a small (or absent) inner core in some numerical geodynamo simulations (e.g. Coe & Glatzmaier 2006). However, a number of recent studies have highlighted an interval of extreme reversal frequency at ca. 550 Ma (Bono & Tarduno 2015; Halls et al.2015; Bazhenov et al.2016). It is fascinating that this interval corresponds with the predicted inner core growth onset age predicted by the high conductivity values (e.g. Nimmo 2015). These inferences on changes in core stratification and inner core formation are testable through continued collection of key directional data sets.

CONCLUSIONS

Just over 30 yr ago, Stevenson et al. (1983) suggested an onset of inner core growth at ca. 2.5 Ga based on a statistically significant increase in the field strength indicated by the palaeointensity data available at that time. However, subsequent data soon demonstrated that that conclusion was premature. Interpretation of the present palaeointensity data set as firm evidence for inner core nucleation in the Mesoproterozoic (Biggin et al.2015) seems to fall into the same trap by accepting the data that do not represent the true paleofield strength readings. If the onset of inner core growth generates a palaeointensity signal large enough to be seen (itself a topic of debate), a much more representative palaeointensity data set for the Precambrian will be needed to differentiate this potential signal from variation inherent to the ancient dynamo.

Palaeointensity data are of prime importance for defining the long-term presence/absence of the field in the Precambrian (e.g. Dunlop & Yu 2004; Macouin et al.2006; Selkin et al.2008; Tarduno et al.2010; Muxworthy et al. 2013; Tarduno et al.2015). However, one should be careful to avoid over-interpretations of these data in terms of constraining inner core growth (and attendant core conductivity values) because the actual signal may be very small relative to the natural variations of the geodynamo (Aubert et al.2010; Reynolds et al.2015). Given their higher signal to noise characteristics relative to palaeointensity data, paleodirections might better define salient aspects of the long-term evolution of the core. In the presently available data, important signals that merit further investigation are Archean to Proterozoic changes in field dipolarity (Biggin et al. 2008; Smirnov et al.2011; Veikkolainen & Pesonen 2014) which could reflect changes in core stratification, and an apparent interval of hypergeomagnetic reversal rate at ca. 550 Ma (Bono & Tarduno 2015; Halls et al.2015; Bazhenov et al.2016) that corresponds to the time of inner core growth onset predicted from high core thermal conductivity values.

We thank David Evans and an anonymous reviewer for their comments. This work was supported by the National Science Foundation.

SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this paper:

Table S1. The palaeointensity data sets (with biased data removed) used in Kolmogorov–Smirnov tests. N_sites: the number of sites per study. VDM: a study-mean/site-mean virtual dipole moment if N_sites ≥ 2/N_sites = 1. Ref. ID: the reference number in the IAGA Palaeointensity Database.

Figure S1. Precambrian palaeointensity data. (a) The Precambrian virtual dipole moment (VDM) site-mean data with Q_PI ≥ 3 used by Biggin et al. (2015). (b) The same data as in (a) with the palaeointensity overestimates removed (see the text). The arrow shows a potential 50 per cent overestimate correction for the corresponding data point (Salminen et al.2006). (c) The same data as in (b) excluding the site-mean determinations with the standard deviation to the site-mean ratio (dF/F) exceeding 25 per cent and those based on a single specimen.

(Supplementary Data).

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