Bulk magnetic domain stability controls paleointensity fidelity.

Nonideal, nonsingle-domain magnetic grains are ubiquitous in rocks; however, they can have a detrimental impact on the fidelity of paleomagnetic records-in particular the determination of ancient magnetic field strength (paleointensity), a key means of understanding the evolution of the earliest geodynamo and the formation of the solar system. As a consequence, great effort has been expended to link rock magnetic behavior to paleointensity results, but with little quantitative success. Using the most comprehensive rock magnetic and paleointensity data compilations, we quantify a stability trend in hysteresis data that characterizes the bulk domain stability (BDS) of the magnetic carriers in a paleomagnetic specimen. This trend is evident in both geological and archeological materials that are typically used to obtain paleointensity data and is therefore pervasive throughout most paleomagnetic studies. Comparing this trend to paleointensity data from both laboratory and historical experiments reveals a quantitative relationship between BDS and paleointensity behavior. Specimens that have lower BDS values display higher curvature on the paleointensity analysis plot, which leads to more inaccurate results. In-field quantification of BDS therefore reflects low-field bulk remanence stability. Rapid hysteresis measurements can be used to provide a powerful quantitative method for preselecting paleointensity specimens and postanalyzing previous studies, further improving our ability to select high-fidelity recordings of ancient magnetic fields. BDS analyses will enhance our ability to understand the evolution of the geodynamo and can help in understanding many fundamental Earth and planetary science questions that remain shrouded in controversy.

The strength of the ancient geomagnetic field (paleointensity) is an invaluable tool for understanding the evolution of the geodynamo and how it interacts with other Earth systems, as well as understanding our solar system. As such, paleointensity data have important applications in understanding the early geodynamo (1, 2) and mantle convection (3), they can be used as a dating tool (4), they have been used to suggest links between the geomagnetic field and climate (5), and paleointensity data can provide important constraints on the evolution of the early solar system (6). However, the interpretation of paleointensity data, and hence their applications, remains controversial due to the difficulty in the acquisition and identification of reliable data. Developing robust methods to enhance paleointensity data fidelity is, therefore, one of the most enduring challenges of solid Earth geophysical studies.

Although progress has been made in this endeavor (7–12), no developed approach represents a direct measure of properties that govern the acquisition of thermoremanent magnetization (TRM). Linking paleointensity results to the fundamental rock magnetic properties that should inform us of the stability of paleomagnetic recordings has been a long-sought-after but unfulfilled goal (13–18). While a qualitative link between magnetic particle grain size (hence magnetic domain state) and paleointensity behavior is established (19, 20) and quantitative measures for such synthetic specimens exist (21), these measures are not unambiguous proxies of fundamental magnetic properties and may be influenced by other detrimental factors (22–24). Quantitative links between direct measures of fundamental rock magnetic properties that can be applied to natural specimens and the fidelity of paleointensity results are lacking.

Magnetic hysteresis measurements of coercivity (B), saturation (M), and remanent (M) magnetizations, combined with back-field saturation remanence demagnetization measurements of remanent coercivity (B), are the most widely used and rapid rock magnetic measurements in paleomagnetic studies (e.g., the 112 studies presented in Datasets S1–S3). As such, these have been extensively investigated as potential tools for preselecting paleointensity specimens for success and postanalyzing paleointensity data (15–18). A well-established method of presenting this type of hysteresis data is to compare M/M to B/B (25). Although frequently misinterpreted as being a definitive indicator of magnetic grain size, this style of plot is also sensitive to grain size distributions, magnetic interactions, mineralogy, and thermal fluctuations, among other factors (26–29). Because of this, an M/M versus B/B plot is only indicative of the relative magnetic stability of a collection of specimens.

Here, we use B/B and M/M data from sized (titano-) magnetite specimens to develop a measure of the relative bulk domain stability (BDS) of a paleomagnetic specimen. Then, using hysteresis and paleointensity data from new laboratory control data and a compilation of historical data, we demonstrate that a quantifiable relationship exists between the BDS of a paleomagnetic specimen and the behavior and accuracy of Thellier-type paleointensity results. This relationship, which may be widespread throughout all paleomagnetic studies, represents an important means of understanding the fundamental controls on paleointensity data and identifying high-fidelity results.

Results

One of the challenges in identifying links between paleointensity data and fundamental rock magnetic properties is that datasets are often small and can be diverse, which means that relationships in one dataset are often not observed in another (cf. refs. 15 and 17). To overcome this, we use a compilation of 303 hysteresis data from a diverse set of sized (titano-) magnetite specimens to define a base trend with which all datasets can be referenced (referred to as the “Sized Dataset”; Dataset S1).

When viewed in log10 space, these hysteresis data form a linear trend that can be decomposed with principal component analysis (PCA). This first principal component accounts for 98.3% of the dataset variance (red line in Fig. 1). The position of hysteresis data projected on this axis can be viewed as a relative measure of “effective BDS” (i.e., an approximate quantitative measure of the effective bulk domain state of an assemblage of magnetic carriers that may be influenced by one or more factor; see for calculation details). This is evidenced by a strong correlation between BDS and the known grain size of these specimens (Fig. 1), as well as strong relations with single-domain (SD) and multidomain (MD) mixing trends (26), and increasing degrees of magnetostatic interactions (27) (Fig. S1). BDS is a relative measure of stability where larger values are indicative of more stable remanence carriers (e.g., an idealized assemblage of Stoner–Wohlfarth particles has a BDS of 0.79) and smaller, more negative values indicate less stable remanence carriers (e.g., a 220-µm grain has a BDS of −0.94; Fig. 1 and Dataset S1).

Fig. 1.

PCA of hysteresis data. (A) The 303 sized magnetite data that define the BDS trend. (B) The relation between BDS and the physical magnetic grain size (n = 303). Hysteresis data from (C) 2,682 geological and (D) 504 archeological specimens typically used for paleointensity studies. The BDS trend is prevalent throughout all datasets.

By defining the BDS trend using the Sized Dataset, any hysteresis data can be projected onto the same BDS trend, irrespective of the material or the number of data available. BDS accounts for 96.3% and 94.0% of the data variances from 2,682 geological specimens (“Geological Dataset”) and 504 archeological specimens (“Archeological Dataset”), respectively—materials that are typically used to obtain paleointensity data (Fig. 1 and Datasets S2 and S3). This BDS trend is therefore dominant throughout paleomagnetic and archeomagnetic datasets, and, irrespective of the underlying mechanisms, BDS represents a relative measure of the magnetic domain stability of a bulk paleomagnetic specimen.

Using hysteresis and paleointensity data from new control data, historical data, and both datasets combined (“Control,” “Historical,” and “Combined” Datasets, respectively), we find clear relationships between BDS and the inaccuracy of the paleointensity results (Fig. 2 ). No consistent relationship is found with respect to inaccuracy and hysteresis ratios B/B and M/M (Table S2). We only consider correlations robust if they are present in the Control, Historical, and Combined Datasets. This suggests that BDS is more robust to the diversity of materials, experimental steps, different laboratory field conditions, and sample heterogeneity (the historical hysteresis data were measured on sister specimens to the paleointensity data). For the Control Dataset, in which all experimental conditions are near-identical, the relation between inaccuracy and BDS is more clearly defined than for the Historical Dataset (Fig. 2). Nevertheless, both indicate that paleointensity accuracy deteriorates as BDS decreases (Fig. 2 ).

Fig. 2.

Comparison between BDS and the inaccuracy and curvature of paleointensity data. Comparison of median inaccuracy and median Arai plot curvature with bulk domain stability, and the median inaccuracy as a function of Arai plot curvature, , for (A–C) the 160 Control data, (D–F) the 112 Historical data, and (G–I) both datasets combined (n = 272). An ideal paleointensity result has a linear Arai plot, which corresponds to a curvature of zero. MIC is the maximal information coefficient of ref. 47 and is a measure of the strength of the relationship between two variables. In parts A–F, the red lines represent best-fit models to the Control Dataset where an exponential function was used for A and B, and a linear function was used in C. In G and H, the boxes denote the IQRs, the whiskers denote the 95% ranges, and the red lines are the median values. The red crosses represent values that lie outside the 95% ranges. Box and whiskers are only shown if ≥5 data are available; otherwise, cross symbols are used.

Median curvature of the fitted analysis, or Arai plot segments (21, 30), increases with decreasing BDS for all datasets (Fig. 2 ). That is, less magnetically stable specimens tend to produce more nonlinear Arai plots (an ideal result is a straight line), which confirms that the trend isolated from high-field hysteresis data corresponds to a low-field bulk remanence stability trend. The inaccuracy of these datasets is strongly correlated with Arai curvature, , indicating that nonlinearity is the source of incorrect results and that inaccuracy, curvature, and BDS are intimately related (Fig. 2 ). These findings illustrate that, when interpreted appropriately, an M/M versus B/B plot is still a valuable rock magnetic tool.

For statistics typically used to quantify partial TRM (pTRM) checks and tails (statistics thought to be sensitive to domain state-related remanence instability), none are consistently correlated with B/B or M/M for all datasets (Table S2). However, both Arai plot curvature and pTRM check “DRAT” are consistently sensitive to BDS. Of all statistics typically used to quantify pTRM checks and tails, only Arai plot curvature is consistently related to the inaccuracy of the paleointensity results (Fig. 2 and Table S3). Arai plot curvature is therefore one of the most useful selection criteria for distinguishing unstable remanence carriers and the inaccurate results they produce.

Discussion

Summary.

We have quantified a trend in hysteresis data that corresponds to the BDS of a paleomagnetic specimen, irrespective of the specific mechanisms that are influencing the specimen’s bulk domain state (i.e., grain size, size distributions, magnetic interactions, etc.). BDS is correlated to the curvature and accuracy of paleointensity results, and therefore also represents a measure of bulk remanence stability. Such relations have long been hypothesized, but have not been conclusively identified for natural materials used for paleointensity studies.

Previous efforts to identify rock magnetic properties related to paleointensity have been applied to relatively small numbers of specimens (31), applied to ancient materials where the true field strength is unknown (15), associated paleointensity and hysteresis data at the site and not sample level, or only considered a single acceptable result per specimen out of many possible acceptable results (15, 17). These factors can make it difficult to identify general trends in complicated datasets (examples of these effects are outlined in ). Our analysis of 272 paleointensity data, application of minimal data selection, and intimately associated paleointensity and hysteresis data, along with consideration of all possible paleointensity results for each specimen, avoids these issues, allowing us to highlight underlying trends.

Robustness of Relationships.

The laboratory Control Dataset is well characterized with consistent paleointensity experiment conditions and clearly illustrates the relationships identified here (e.g., Fig. 2 ). The Historical Dataset, on the other hand, is more complicated. The specimens are fresh (not thermally stabilized) and therefore more likely to chemically alter during experimental heating, they were measured in different laboratories with different experimental steps and applied field strengths and angles, the ratios of the laboratory to ancient field strengths were different, and, furthermore, hysteresis data were measured on sister specimens; hence sample heterogeneity may be important. Despite these complications, we can still identify significant trends in Arai plot curvature and paleointensity inaccuracy that are related to the specimens’ BDS (Fig. 2 ). The “dirtiness” of the Historical Dataset therefore emphasizes the robustness of these relations.

Alternative Quantifications of BDS.

Our analysis characterizes a relative measure of BDS, but cannot reveal the mechanisms that underlie the variability in stability that influences paleointensity results. A number of alternative data measurements and/or analyses may provide more powerful discrimination as to the specific underlying mechanisms leading to low BDS values and poor paleointensity results. The recent rapid advancement of first-order reversal curve analysis looks to be the most promising tool to achieve this (15, 32–34). A future challenge is therefore to develop suitably large datasets to test and develop these ideas.

Other Paleointensity Methods.

All Control and Historical paleointensity data presented here come from the Coe variant of Thellier-type experiments (35), and, although paleointensity results from different Thellier-type methods can have distinct behavior with respect to differing domain state (30), BDS should manifest in some fashion in all paleointensity data. This may not only be related to Arai plot curvature, but may, for example, manifest in Arai plot zigzagging for “IZZI”-protocol experiments (36). At present, however, insufficient data are publically available to explore this in more detail.

Sufficient data are available from nonheating pseudo-Thellier experiments to illustrate the influence of BDS on this paleointensity method (37). We show that the calibration factor used to scale an anhysteretic remanent magnetization (ARM) is dependent on BDS such that lower BDS values yield lower calibration factors (Fig. 3). This relationship could be used for screening out less stable specimens for use in pseudo-Thellier experiments, or, with a larger and more diverse dataset, BDS could be used to determine specimen specific pseudo-Thellier calibrations factors.

Fig. 3.

Relationships between BDS and other paleomagnetic results and how BDS can be used to improve paleointensity results. BDS relationship with (A) calibration of the pseudo-Thellier method (n = 56), (B) ARM MDF from 56 Control data, and (C) TRM MDF from 56 Control and 55 Historical data. In C, MIC values are for the Control and Historical Datasets combined. (D) Median inaccuracy and IQR after rejecting specimens with BDS less than the given thresholds. The selection thresholds are applied to the Control and Historical Datasets combined. The gray shaded area represents a change in the slopes that yields more accurate and less scattered results and may be a useful first-order selection threshold for preselecting paleointensity specimens.

Geological materials form the bulk of our analyses, but the BDS trend is also evident in archeological materials (Fig. 1). A more widespread application of hysteresis to archeological materials would make BDS a valuable tool in archeomagnetic studies.

Impact on Other Paleomagnetic Studies.

The prevalence of the BDS trend in paleomagnetic specimens (Fig. 1) suggests this behavior should impact all paleomagnetic studies on volcanic materials, not just paleointensity data. For the Control Dataset, we find the median destructive field (MDF) of ARM and TRM are both correlated with BDS (Fig. 3 ). For the Historical Dataset, where the natural remanent magnetizations should be TRMs, a similar relation is observed (Fig. 3). Specimens with low BDS will be more susceptible to overprinting and remagnetization, which may influence the interpretation of directional data used for secular variation, magnetostratigraphy, or tectonic reconstructions. This type of information, which is invaluable for asserting directional fidelity, may not be possible to directly extract from the demagnetization data, but the hysteresis analysis outlined in this work would be an alternative approach to assert reliability.

Applications of BDS.

BDS determined from hysteresis data has the potential to be used as a statistic to preselect specimens for paleointensity experiments or to reject results during analysis. Although many such statistics exist (12), all are derived from paleointensity data, and none represent a direct measure of magnetic properties that govern the acquisition of TRM. BDS, however, does reflect fundamental magnetic properties. Deviations from the trends identified here (e.g., specimens with high BDS, but high Arai plot curvature) also provide an approach for identifying specimens strongly influenced by other detrimental factors, such as alteration or chemical magnetizations.

Combining both the Control and Historical Datasets, we explore how different thresholds for BDS influence the median inaccuracy and its interquartile range (IQR) when specimens with low stability are rejected (Fig. 3). For this dataset, there is a change in slope in both the median inaccuracy and IQR at BDS values of ∼0.10, which yield more accurate and less scattered results (Fig. 3). This corresponds to B/B and M/M ratios of ∼3.4 and ∼0.08, respectively. Specimens that are less stable than a BDS of 0.10 are less likely to yield meaningful paleointensity estimates. This first-order threshold can be used as a preselection criterion in combination with other data selection processes. From the compilation of 2,682 geological specimens, ∼18% have BDS values < 0.10, which suggests that less than 20% of paleomagnetic specimens have such low bulk domain stabilities that they can be viewed as poor paleomagnetic carriers that are less likely to yield geophysically meaningful results.

The search to identify reliable paleointensity data is as old as the discipline itself, but, despite this longevity, all current approaches do not directly quantify the fundamental magnetic properties that govern the acquisition of TRM. We have demonstrated that, by quantifying hysteresis data in terms of the BDS of the entire magnetic assemblage in a paleomagnetic specimen, we can relate rock magnetic properties to the behavior and reliability of paleointensity data. This powerful tool will strengthen our ability to probe the workings of our planet’s deep interior in greater detail and with greater confidence.

Methods

Hysteresis Data.

For the sized magnetite data presented in Fig. 1 , 303 hysteresis ratio combinations (i.e., B/B and M/M) were compiled from the published literature. These titanomagnetite and magnetite specimens come from 34 studies and represent a wide range of synthesis methods, grain sizes (and grain size distribution), and grain spacing (magnetic interactions), as well as differing degrees of annealing. So, although dominated by grain size effects, the hysteresis data are influenced by a wide range of other factors. The data and sources are given in Dataset S1. Similarly, 2,682 hysteresis data from geological materials and 504 archeological data were compiled from the literature and are detailed in Datasets S2 and S3, respectively.

For the Control Dataset, some hysteresis and backfield measurements were previously measured (37). New data were measured using a Princeton Measurements Corporation MicroMag 3900 Vibrating Sample Magnetometer at the Institute of Geology & Geophysics, Chinese Academy of Sciences (IGGCAS). For the Historical Dataset, previously published hysteresis data were used, and we refer to the relevant studies (8, 17, 37–41). All hysteresis measurements were reprocessed following ref. 42, except for 11 sized magnetite specimens included in the Control Dataset (8, 41), where the reported hysteresis ratios were used. Where multiple hysteresis data were available per paleointensity specimen, hysteresis data were averaged. Only hysteresis data that have acceptable paleointensity results are analyzed for the Control and Historical Datasets. Additional descriptions of the all of the datasets are given in , Figs. S2 and S3, and Table S1.

BDS.

To identify the BDS trend, the Sized Dataset hysteresis data are log10-transformed and detrended by the mean values, before performing PCA. BDS values are calculated by projecting the hysteresis data onto the first principal component (an illustrative example is given in Fig. S5). We normalize BDS such that a single grain yielding a perfectly square hysteron has a BDS value of 1. If X represents B/B data and Y represents M/M data, BDS values are given by

Since the hysteresis ratios are detrended for the dataset means, the origin of the BDS axis corresponds to center of mass of the Sized Dataset; BDS is therefore only a relative scale. An idealized Stoner−Wohlfarth assemblage (B/B = 1.09, M/M = 0.5) (43, 44) has a BDS of 0.79, while an assemblage of idealized cubic anisotropy dominated particles (B/B = 1.08, M/M = 0.87) (45) has a BDS of 0.95. The lowest value is −∞ and represents a specimen incapable of retaining any magnetic remanence over measurement timescales (i.e., superparamagnetic grains). The full principal component description is given in .

Paleointensity Experiments.

Only the Control and Historical Dataset are associated with paleointensity data. All paleointensity data are from the Coe paleointensity protocol (35), whereby a specimen’s original magnetization is progressively removed and replaced by a laboratory-induced magnetization by heating the specimen to increasingly higher temperatures.

New “control” paleointensity experiments were performed using 62 specimens from refs. 17 and 39, 10 from ref. 46, and 79 new basalts, dikes, granites, and granitoids (see ). All specimens were thermally stabilized before the experiments, to ensure no alteration occurred, and given a full laboratory TRM from 700 °C. Magnetite (with some titanomagnetite) and hematite are the main magnetic carriers in these specimens (37). The paleointensity experiments involved 7 to 12 heating steps up to a peak temperature of 700 °C and included pTRM and tail checks. All remanences were acquired in a field of 32 µT applied along the same axis. Remanence measurements were performed at IGGCAS with a 2G Enterprises superconducting magnetometer. Within the Control Dataset, we also include 11 Coe protocol paleointensity data from previously measured sized magnetite specimens available from the MagIC database (8, 41). With the exception of the sized magnetite specimens, all Control Dataset paleointensities were measured on the same specimen as for the hysteresis measurements following thermal stabilization.

Historical paleointensity data are available from the MagIC database. From a total of 172 Coe protocol paleointensity data, 129 are associated with hysteresis data at the core or clast level (17, 38, 40); hysteresis and paleointensity data were measured on sister specimens. Titanomagnetite with and without hematite are the main magnetic carriers in these specimens (17, 38, 40).

Paleointensity Analysis.

To quantify a specimen’s general behavior, instead of considering only a single Arai plot fit per specimen, we consider all fits. We also apply a minimal set of selection criteria to ensure robust basic fitting: We require that at least four Arai plot points per fit (n ≥ 4), “FRAC” ≥ 0.45, and unanchored “MAD” ≤ 15°. We apply no other criteria to avoid distortion of any relationship with BDS.

For the Historical Dataset, in addition to the above criteria, to minimize the potential impact of magnetomineralogical alteration, each fit is required to have pTRM checks “δpal” ≤ 20 and “δCK” ≤ 10. These thresholds correspond to the 95th percentiles of the accepted fits from the Control Dataset and should therefore be predominantly screening out the effects of alteration.

All paleointensity statistics are calculated following the standard definitions (12) and are calculated as median values of the accepted results. To obtain a reasonable measure of a specimen’s general behavior, we require at least three Arai plot fits per specimen. After applying these requirements, two Control and 17 Historical specimens are rejected.

The inaccuracy of a paleointensity result (B) is based on the deviation (Dev.) from the correct intensity (B): , where negative values are underestimates of the true intensity, and positive values are overestimates (21). Inaccuracy is quantified as the median absolute deviation of all acceptable fits, such that values of 0 are perfectly correct.

Pseudo-Thellier data are taken from ref. 37 and are their unselected results. These are the median calibration factors from all possible fits on the pseudo-Arai plots with at least four data points (37).

MDF Analysis.

Control Dataset results were taken from ref. 37, and Historical results were taken from ref. 17. All remanences are approximately univectoral, so no additional adjustments were made to calculate the MDFs.

Correlations.

All correlations are performed using the maximal information coefficient (MIC) (47), which varies between 0 and 1. The MIC places no constraint on the form of the relationship, which makes it a flexible method for assessing diverse types of relationships. The default grid scaling parameter α = 0.6 was used (47). P values are calculated by interpolating the reference tables and are conservatively reported as p plus its associated 95% confidence interval and are considered significant if ≤ 0.05.