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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, B09101, doi:10.1029/2011JB008388, 2011

Importance of cooling rate dependence of thermoremanence in paleointensity determination Yongjae Yu1 Received 24 March 2011; revised 30 June 2011; accepted 14 July 2011; published 9 September 2011.

[1] The practical effect of cooling rate on the magnitude of thermal remanent magnetization (TRM) is experimentally tested, using both natural and synthetic magnetites. For synthetic and natural single‐domain (SD) magnetites, TRM intensity increases as the cooling rate decreases because a longer exposure time for slower cooling offers more chances to achieve an equilibrium magnetization. Multidomain (MD) magnetites have the opposite response: TRM decreases as the cooling rate increases because slower cooling allows more time to achieve lower magnetization because of self‐demagnetization. For pseudo‐single‐domain (PSD) magnetite, the effect of cooling rate on the remanence intensity appears to be insignificant, intermediate in behavior between SD and MD. For a SD, TRM differences are restricted to lower temperatures but diminish near the Curie point, strongly indicating a serious problem in a conventional treatment of cooling rate correction. On the practical side, merely applying TRM differences as a correction can overcorrect the true paleointensity. Another important significance of the present study is that a cooling rate difference alone can cause a slight nonlinearity in an Arai plot for a SD. Citation: Yu, Y. (2011), Importance of cooling rate dependence of thermoremanence in paleointensity determination, J. Geophys. Res., 116, B09101, doi:10.1029/2011JB008388.

1. Introduction [2] Rocks acquire a thermal remanent magnetization (TRM) produced over an interval of blocking temperatures during cooling in the magnetic field B in planetary lithosphere. Among various techniques that determine the intensity of ancient planetary magnetic field, the Thellier method [Thellier and Thellier, 1959] is considered to be the most reliable because it can test the fundamental principles of additivity, independence, and reciprocity of partial TRM (pTRM) in the experimental design. In the Thellier‐type double‐heating experiments [e.g., Coe, 1967; Aitken et al., 1988; Yu et al., 2004], the natural remanent magnetization (NRM) produced by an original magnetic field (Bnature) is replaced with successive pTRMs produced in a laboratory field (Blab) by repeated heating and cooling. [3] Several factors influence the intensity of TRM. First, TRM is dependent on the grain size of magnetite [e.g., Dunlop and West, 1969; Levi and Merrill, 1976; Dunlop and Argyle, 1997]. It has been shown that TRM is more intense in smaller grains than in larger grains, as is also true for anhysteretic remanent magnetization (ARM) [e.g., Yu et al., 2003; Egli, 2004]. Second, for a fixed grain size of magnetite, TRM depends on the magnetic concentration [e.g., Dunlop and West, 1969]. A low TRM intensity was 1 Department of Geology and Earth Environmental Sciences, Chungnam National University, Daejeon, South Korea.

Copyright 2011 by the American Geophysical Union. 0148‐0227/11/2011JB008388

observed for higher concentrations because of stronger interactions, as in ARM [e.g., Sugiura, 1980; King et al., 1983; Yamazaki and Ioka, 1997]. Third, TRM intensity is dependent on the magnitude of the applied field Blab. It has been commonly assumed that TRM and ARM are proportional to weak inducing fields Blab = 200 mT. For instance, Thellier [1938] showed experimentally that the TRM acquired by baked clays is proportional to the weak magnetic field applied during cooling. However, a linear proportionality is violated at higher fields of Blab > 200 mT [e.g., Dunlop and Argyle, 1997; Muxworthy and McClelland, 2000; Selkin and Tauxe, 2000] or for some exceptionally elongated fine‐grained magnetite [Selkin et al., 2007]. Fourth, TRM intensity is dependent on the cooling rate. In this paper, the practical impact of the cooling rate effect on TRM intensity will be closely examined.

2. Thellier Modeling [4] The intensity of TRM is governed by a cooling condition that determines the blocking temperatures (TB) in a given magnetic system. The time taken for an assemblage of magnetic grains to reach an equilibrium state of magnetization is expressed as a relaxation time (t). If the t in natural cooling is similar to that in a laboratory cooling, the cooling rate effect would be negligible. However, a longer exposure time during slow cooling in plutonic settings allows a closer approach to equilibrium condition, thus lowering the TB. [5] Theoretically the TRM intensity of single‐domain (SD) grains should decrease as the cooling rate increases

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Figure 1. (a) Simulation of Arai plots for different cooling modes and unblocking concentrations. The values of T denote the temperature steps. (b) Cumulative ratio of NRM remaining over pTRM acquisition as a function of temperature. Solid circles, slowly cooled TRMslow; open circles, rapidly cooled TRMlab; open squares, bias interval T0–T5; open triangles, bias interval T5–T10. All the simulated results were normalized to TRMlab. [Néel, 1955; Pullaiah et al., 1975; York, 1978; Halgedahl et al., 1980; Dodson and McClelland‐Brown, 1980; Walton, 1980; Walton and Williams, 1988]. This prediction has been experimentally confirmed by studies on SD hematite [Papusoi, 1972a], archeological baked clay [Fox and Aitken, 1980], fine‐grained archeologic relics [Chauvin et al., 2000], seafloor basaltic glass [Bowles et al., 2005], and volcanic glass [Leonhardt et al., 2006]. In particular, both Papusoi [1972a] and Fox and Aitken [1980] found that the slowly cooled (∼10−3 K/s) magnetization was 5%–14% larger than the rapidly cooled (∼1 K/s) magnetization. Nearly the same outcome was confirmed for pseudo‐single‐domain‐ (PSD‐) sized grains in baked clays or potsherds and glasses in volcanic rocks [e.g., Yang et al., 1993; Biquand, 1994; Genevey and Gallet, 2002; Genevey et al., 2003; Morales et al., 2006a, 2006b; Ferk et al., 2010]. However, exactly the opposite trend of lower magnetization for slower cooling was observed for multidomain (MD) magnetite [Papusoi, 1972b; Brown, 1984; Perrin, 1998] and remains poorly understood. Hereafter, a slower cooling condition represents a cooling slower than a typical laboratory fan cooling. [6] Cooling rate dependence of TRM intensity has an important implication for Thellier‐type paleointensity determination in which the ratio of a laboratory TRM to the NRM is equivalent to the intensity ratio between ancient and laboratory field. For SD magnetite, a common consensus is that the intensity of Bnature would be overestimated if NRM is produced at a slower cooling condition than the laboratory TRM. However, such an argument is extremely superficial in the sense that the detailed blocking and unblocking relation is untested. For example, consider a NRM of a slowly cooled TRM (TRMslow) that is 20% more intense than the laboratory‐produced TRM (TRMlab). Paleointensity would be overestimated by 20% only when thermal demagnetization spectra of TRMslow is 20% more intense than those

of TRMlab at each and every temperature step used in the Thellier analysis. A simple model in Figure 1 explains why so. [7] For mathematical convenience, we assume that additivity and reciprocity of pTRMs are valid. The additivity law means that pTRMs produced in nonoverlapping blocking temperature intervals are additive [Thellier, 1938]. The reciprocity of pTRM represents an equivalence of the blocking and the unblocking temperatures [Thellier, 1938]. Suppose 10 temperature steps from T0 to T10 are defined so that each step increment in temperature destroys 10% of TRMlab. According to the reciprocity law, these temperature steps should also produce 10% step increments of pTRM during remanence acquisition steps. Thus, the NRM remaining versus pTRM acquisition for these 10 thermal steps would fall on an ideal SD line in a conventional Arai plot (see open circles in Figure 1a). All the simulated data points were normalized to TRMlab (Figure 1). [8] If we follow the traditional approach, results for a slowly cooled TRMslow would fall on a straight line whose slope is −1.2 (solid circles in Figure 1a). This is the case that all the paleomagnetists hope to be true. However, it is possible that a difference between TRMslow and TRMlab is restricted only to lower‐temperature ranges (bias from T0 to T5) or to higher‐temperature intervals (bias from T5 to T10). The outcome is surprising in that the former bias from T0 to T5 produces a convex‐down Arai plot (open squares in Figure 1a) while the latter bias from T5 to T10 generates a convex‐up pattern (open triangles in Figure 1a). They both show correct paleointensity only for the temperature steps for which TRMslow and TRMlab yielded identical demagnetization spectra (Figure 1a). Plotting the ratio of NRM lost to pTRM gained is another way of representing the bias between TRMslow and TRMlab (Figure 1b).

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Figure 2. Temperature variation used in the present study during cooling. Fast and slow cooling corresponds to ∼40 K/min and ∼3 K/min, respectively. [9] In particular, it is worth highlighting two important aspects, especially when the difference between TRMslow and TRMlab is restricted to lower temperatures (open squares in Figure 1). First, paleointensity is overestimated between T0 and T5, but it shows a correct slope from T5 to T10 (Figure 1a). In other words, a cooling rate correction is unnecessary as long as the paleointensity is estimated using only the higher‐temperature fraction between T5 and T10. Second, the cooling rate effect alone can produce dual segments in an Arai plot even for SD grains (Figure 1a). [10] A physical rationale for emphasizing the lower‐ temperature‐biased case comes from the analogy between ARM and TRM. ARM is produced by the combination of a slowly decaying alternating field (AF) and a steady unidirectional field B. A decay‐rate dependence of ARM is physically analogous to the cooling rate dependence of TRM. It has been observed that a slow decay rate produces an intense ARM for fine‐grained magnetites [e.g., Yu and Dunlop, 2003; Sagnotti et al., 2003]. Most important, the intensity difference of ARM that is due to varying decay rates is restricted mostly to low and intermediate coercivities [Yu and Dunlop, 2003]. On the basis of a close analogy between ARM and TRM, it is necessary to experimentally demonstrate whether the lower‐temperature‐biased cooling rate effect would occur in a real TRM experiment.

3. Samples and Experiments [11] In the present study, well‐defined magnetite‐carrying synthetic and natural samples were used. Eight synthetic samples were prepared using magnetite powders whose mean grain sizes range from SD (0.065 mm) to small MD (18.3 mm) [Yu et al., 2002]. Grain sizes were determined using a Hitachi S‐4500 scanning electron microscope. These samples are 0.5% by volume dispersions of magnetite in a matrix of CaF2. Cylindrical pellets 8.8 mm in diameter and

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8.6 mm in height were pressed and then tightly wrapped with quartz wool inside quartz capsules. The capsules were sealed under vacuum and annealed for 3 h at 700°C to stabilize the magnetic properties [Yu et al., 2002]. [12] The natural samples selected have magnetic and paleomagnetic properties that are also well documented [Yu et al., 2002]. They were chosen from a much larger collection of several hundred cores on the basis of their low‐ magnetic‐fabric anisotropy, their reproducible ARM and TRM intensities, and minimal viscous magnetic changes. Most important, during the initial paleointensity work, none of the samples showed any indication of alteration during repeated heatings; all the samples passed the pTRM check within 5% at all temperature ranges. Three SD‐analog specimens were used from the Tudor Gabbro (Ontario, Canada), which apparently yielded excellent paleointensity data [Yu and Dunlop, 2001]. In particular, these samples have a very narrow unblocking temperature spectrum (most of the remanence was unblocked between 500°C and 580°C). For PSD‐ and MD‐analog natural sample sets, three basalts [Yu et al., 2002] and three granites [Dunlop et al., 1984] were used, respectively. These PSD‐ and MD‐analog sets were rejected in previous paleointensity work because of their nonlinear behavior in Arai plots. [13] For each specimen, a total of four different TRM acquisitions were applied in the present study. The first and second TRMs were used to characterize demagnetization behavior, and the third and fourth TRMs were for the independent Thellier analysis. First, a total TRM1lab was produced by cooling from 600°C in a laboratory field B = 50 mT in a fast cooling condition (∼40°C/min). The sequential orders of TRM acquisitions and cooling conditions set during TRM acquisition are denoted by superscripts and subscripts, respectively. Unblocking temperature spectra were obtained from a stepwise thermal demagnetization for TRM1lab. Second, exactly the same experiment was repeated for TRM2slow produced in a slow cooling condition (∼3°C/min). On completion of thermal demagnetization experiment, a third TRM3lab was reproduced in a fast cooling condition again. Then, a Coe‐modified Thellier method [Coe, 1967] was applied. After the first zero‐field heating‐cooling step to temperature Ti, the remanence was measured and the NRM lost was calculated. The second heating‐cooling step to Ti was in Blab. Double heatings were carried out at 300°C, 450°C, 500°C, 525°C, 540°C, 550°C, 560°C, 568°C, 572°C, 576°C, and 580°C for the SD and PSD sets. For the MD set, 200°C, 250°C, 300°C, 350°C, 400°C, 450°C, 500°C, 550°C, and 580°C were used. A conventional pTRM check was made at every temperature. Another independent Thellier analysis was repeated for the fourth TRM4slow produced in a slow cooling condition. Results of experimental testings were normalized to TRMfast (see Figures 3–5 in section 4). [14] To get a precise temperature reading during cooling, three thermocouples were attached right next to the pairs of three sample rows. Despite various efforts, cooling from 600°C to lower temperatures does not follow a perfectly linear decrease in temperature but is slightly exponential (Figure 2). Thus, an average cooling rate was determined as ∼40°C/min (= (600°C–197°C)/10 min) and ∼3°C/min (= (600°C–401°C)/64 min) for fast and slow coolings, respectively (Figure 2). Throughout all heat treat-

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Figure 3. Comparison of unblocking temperature spectra for (a) SD magnetite (65 nm), (b) TU1D1 (gabbro), (c) PSD magnetite (1.06 mm), (d) AN2B1 (andesite), (e) MD magnetite (18.3 mm), (f) BU5B1 (granite). Results of thermal demagnetization were normalized to TRMfast. ments, reproducibility and stability of temperatures were better than 1°C. The residual field inside the oven was always less than ∼120 nT. Measurements were carried out in a magnetically shielded space with an ambient field of less than 250 nT.

4. Results 4.1. Demagnetization Behavior [15] A comparison of thermal demagnetization spectra between TRM1fast and TRM2slow is shown in Figure 3. For SD (65 nm) (Figure 3a) and TU1D1 (Figure 3b), TRM is mostly unblocked at temperature intervals from 500°C to 580°C, hallmarks for the presence of SD magnetite (Figures 3a, 3b). At temperatures