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AN ELECTRONIC JOURNAL OF THE EARTH SCIENCES Published by AGU and the Geochemical Society

Article Volume 11, Number 2 11 February 2010 Q02Z12, doi:10.1029/2009GC002804 ISSN: 1525-2027

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Paleointensity determination using anhysteretic remanence and saturation isothermal remanence Yongjae Yu Department of Geology and Earth Environmental Sciences, Chungnam National University, Daejeon 305-764, South Korea

[1] Determining the strength of ancient planetary magnetic field is pivotal to understanding the evolution of planets and asteroids in the solar system. While the Thellier-type double heating technique provides the most faithful field strength information for rocks carrying a thermoremanent magnetization (TRM), many extraterrestrial rock samples respond unfavorably to heat treatment. The present study systematically examined the two well-known normalization techniques that avoid any heating by comparing the ratios of TRM/anhysteretic remanent magnetization (ARM) and TRM/saturation isothermal remanent magnetization (SIRM). Both the ratios of TRM/ARM and TRM/SIRM are dependent on the grain size as well as the volume concentration of magnetite. The remanence ratios also were found to increase as the alternating field increased during demagnetization for fine-grained magnetite. A new calibration relation of 2.60 ± 1.32 for the TRM/ARM and of (3.62 ± 1.28) 102 for the TRM/SIRM was defined for an external field of 50 mT. The TRM/SIRM is superior to TRM/ARM because the former showed less dispersion in the grain size dependence, the volume concentration dependence, and the stability against AF demagnetization. In addition, the standard error of the mean for the TRM/SIRM ratio was smaller than that for the TRM/ARM ratio. Thus, whenever heating is inapplicable, the SIRM method seems to be a better choice than the ARM method. However, it should be emphasized that the uncertainty of TRM/ARM and TRM/SIRM is still nearly an order of magnitude larger than that of the high-fidelity Thellier estimation and thus must be limited in use only when samples are irreversibly altered during heating. In practice, the best approach is to carry out both ARM and SIRM methods and check whether the two estimations agree within the uncertainties. Components: 7526 words, 5 figures, 1 table. Keywords: magnetic field; paleointensity; anhysteretic remanence; saturation; isothermal remanence; thermoremanence. Index Terms: 1521 Geomagnetism and Paleomagnetism: Paleointensity; 1540 Geomagnetism and Paleomagnetism: Rock and mineral magnetism; 1594 Geomagnetism and Paleomagnetism: Instruments and techniques. Received 25 August 2009; Revised 30 November 2009; Accepted 9 December 2009; Published 11 February 2010. Yu, Y. (2010), Paleointensity determination using anhysteretic remanence and saturation isothermal remanence, Geochem. Geophys. Geosyst., 11, Q02Z12, doi:10.1029/2009GC002804. ————————————

Theme: Magnetism From Atomic to Planetary Scales: Physical Principles and Interdisciplinary Applications in Geoscience Guest Editors: J. Feinberg, F. Florido, B. Moskowitz, and A. P. Roberts

Copyright 2010 by the American Geophysical Union

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yu: paleointensity using sirm and arm

1. Introduction [2] Ever since the discovery of ancient stable natural remanent magnetization (NRM) in extraterrestrial materials, it has been recognized that rock magnetic characterization holds an important clue for deciphering the evolutionary paths of planets and asteroids in the solar system [e.g., Banerjee and Hargraves, 1971, 1972]. In 1970s, intensive paleomagnetic investigation and paleointensity determination were carried out on the Apollo lunar samples (see Fuller [1974, 1998] for details). For instance, Apollo 11 lunar samples were analyzed [Doell et al., 1970; Helsley, 1970; Nagata et al., 1970; Runcorn et al., 1970; Strangway et al., 1970] with the aim of understanding the evolution of lunar interior. There is now undisputable evidence that a lunar magnetic field was present at the time when the lunar rocks were formed [e.g., Fuller, 1974, 1998; Banerjee and Swits, 1975; Banerjee and Mellema, 1976a, 1976b; Banerjee et al., 1977; Cisowski, 1983; Cisowski et al., 1983]. However, it is controversial whether the estimates of the lunar magnetic field intensity were reliable [e.g., Brecher, 1977; Lawrence et al., 2008; Garrick-Bethell et al., 2009]. Such dispute mostly results from the fact that lunar rocks alter irreversibly when heated [e.g., Pearce et al., 1976; Sugiura et al., 1978, 1979]. [3] It is a general consensus that the most faithful paleointensity estimate is obtained from a double heating Thellier-type technique [Thellier and Thellier, 1959] where the relative proportionality between the loss of NRM and the gain of partial thermoremanent magnetization (pTRM) should remain constant throughout entire heating steps. Application of the classical Thellier technique on lunar rocks was unprecedented [e.g., Collinson et al., 1973; Gose et al., 1973; Stephenson and Collinson, 1974; Sugiura et al., 1979; Sugiura and Strangway, 1980, 1983] although the reliability remains debatable if a modern paleointensity technique with stringent alteration check [e.g., Coe, 1967; Aitken et al., 1988; Yu et al., 2004] is applied. As a matter of fact, a modern variation of Thellier analysis was only once performed on lunar rocks [Lawrence et al., 2008]. Such a limited application of the Thelliertype paleointensity determination is somewhat natural because lunar rocks respond unfavorably to conventional heating methods even in a hard vacuum [e.g., Pearce et al., 1976; Sugiura et al., 1978, 1979] with a delicate sample preparation of double-buffered encapsuling [e.g., Taylor, 1979]. That is why an alternative normalization technique with no or little heating was seriously considered.

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As a result, three well-known alternative methods were all developed in 1970s. These are the anhysteretic remanent magnetization (ARM) method [Markert and Heller, 1972], the saturation isothermal remanent magnetization (SIRM) method [Cisowski et al., 1975] and the Shaw method [Shaw, 1974]. While the ARM and SIRM methods are simple normalization techniques, the Shaw method [Shaw, 1974] and its modern variations [Rolph and Shaw, 1985; Tsunakawa and Shaw, 1994; Yamamoto et al., 2003] require construction of a detailed coercivity spectra for NRM, artificial ARM(s), and laboratory-produced thermoremanent magnetizations (TRMs) [see Yamamoto and Shaw, 2008, and references therein]. Because the present study focuses only on the normalization techniques, the Shaw method and its variations will not be discussed any further. [4] The ARM method was once extensively used in extraterrestrial paleointensity determination [e.g., Markert and Heller, 1972; Collinson et al., 1973; Banerjee and Mellema, 1974a, 1974b; Stephenson and Collinson, 1974; Bagina and Petrova, 1977; 1Sugiura and Strangway, 1980]. In terms of physical principles, replacing NRM (by implication TRM) with artificial ARM was intuitive because thermal fluctuation in TRM is analogous to alternating field (AF) in ARM. In addition, ARM and TRM share similar behavior under AF demagnetization [Rimbert, 1959; Dunlop and West, 1969; Levi and Merrill, 1976]. However, the uncertainty of the ratio R ( = TRM/ARM or NRM/ARM) was experimentally found to be as large as an order of magnitude [e.g., Dunlop et al., 1975; Bailey and Dunlop, 1977]. Since then, the ARM method nearly vanished in practical paleointensity determination except for fundamental rock magnetic comparisons [e.g., Dunlop and Argyle, 1997; Yu et al., 2003] and for relative paleointensity for sediments [e.g., Guyodo and Valet, 1999]. However, two recently published articles successfully employed the ARM method in extraterrestrial magnetic investigation [Weiss et al., 2008; Garrick-Bethell et al., 2009]. [5] Contrary to the ARM method, the SIRM method (REM = TRM/SIRM or NRM/SIRM) followed a slightly different path. Despite limited use, it has been mostly applied to extraterrestrial material to determine the ancient planetary magnetic field strength [e.g., Wasilewski, 1981; Cisowski, 1986; Fuller et al., 1988; Wasilewski and Kletetschka, 1999; Wasilewski and Dickinson, 2000; Wasilewski et al., 2002; Gattacceca et al., 2003, 2008; Kletetschka et al., 2003, 2004, 2006; Gattacceca and Rochette, 2 of 12

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Table 1. Physical Properties of Synthetic Powdersa Powder

Counts

4000 5099 112978 M 5000 3006 112982 041183

884 1300 1022 532 1262 1471 1618 870

q ± sq 1.48 1.44 1.33 1.29 1.65 1.62 1.61 1.57

± ± ± ± ± ± ± ±

0.42 0.42 0.29 0.28 0.63 0.54 0.58 0.54

d ± sd, mm

Tc

R

0.065 ± 0.036 0.21 ± 0.10 0.44 ± 0.20 0.24 ± 0.07 0.34 ± 0.21 1.06 ± 0.71 16.9 ± 8.3 18.3 ± 12.0

582 586 582 583 585 585 579 580

0.29 0.27 0.30 0.27 0.34 0.38 0.47 0.48

a

Powders 4000, 112978, 5000, 3006, 112982, and 041183 are from the Wright Company; powders 5099 and M are the products of Pfizer and Mapico Companies; q is the axial ratio; d is the estimated mean grain size; uncertainty corresponds to one standard deviation; Tc is a Curie point; and R is a crossover point as in the work by Cisowski [1981].

2004]. Recently, it has been observed that the ratio of TRM/SIRM was dependent on the grain size of magnetite [Yu, 2006]. Furthermore, the TRM/ SIRM ratio increased during progressive AF demagnetization for fine-grained magnetite [Yu, 2006]. In an extreme case of acicular magnetite, TRM/SIRM can be two orders of magnitude higher than the average calibration relation due to high efficiency of acquiring TRM along the grain elongation [Yu et al., 2007]. Similarly, TRM/ARM is also dependent on the mean aspect ratio of magnetic material [Egli and Lowrie, 2002; GarrickBethell et al., 2009]. [6] Recent increase in using the TRM/SIRM in planetary magnetic field intensity determination drew one fundamental unanswered question whether the SIRM method is really superior to the ARM method. The present study was intended to test whether such a proposition is true using well-defined synthetic and natural samples. In detail, the grain size dependence, the volume concentration dependence, and the stability against AF demagnetization of TRM/ARM versus TRM/ SIRM will be discussed. A parallel goal in the present study is to provide a better calibration relation for the TRM/ARM and TRM/SIRM.

2. Samples and Experiments [7] To compare the ratios of TRM/ARM and TRM/SIRM, well-defined magnetite-carrying samples were used whose rock magnetic information was previously published elsewhere. A total of forty synthetic samples were prepared using eight different magnetite powders whose mean grain sizes range from single-domain (SD) to small multidomain (MD). For each powder, five different sets of volume dispersions (0.1%, 0.5%, 1%, 5%,

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and 20%) of magnetite were prepared in a matrix of CaF2 (Table 1). Cylindrical pellets 8.8 mm in diameter and 8.6 mm in height were pressed and then tightly wrapped with quartz wool inside quartz capsules. The capsules were vacuum sealed and annealed for 6 h at 650°C to stabilize the magnetic properties (see Yu et al. [2002] for details). [8] Sixty-three gabbro samples were used to define a calibration relation for the TRM/ARM and TRM/ SIRM. All the samples were thermally stabilized previously. The samples selected have magnetic and paleomagnetic properties that are well documented [e.g., Yu and Dunlop, 2001, 2002]. They were chosen from a much larger collection of over a thousand cores on the basis of their low magnetic fabric anisotropy, their reproducible ARM and TRM intensities, and minimal viscous magnetic changes. For instance, intensities of ARM and TRM were reproducible within 3% to the initial ARM and TRM in multiple heatings. In addition, principal components of the anisotropy of ARM (AARM) tensor are indistinguishable within 2%, suggesting their low degree of magnetic anisotropies. Samples were cylindrical, 2.3 cm in diameter and 2.0 cm in height. In particular, these 63 gabbro samples yielded apparently excellent paleointensity data in previous studies [Yu and Dunlop, 2001, 2002]. All these gabbro samples have a very narrow unblocking temperature spectrum with most of the remanence unblocked between 500°C and 580°C, hallmarks for SD magnetite. Such restricted unblocking mainly results from the magnetic grains embedded within the plagioclase as inclusions (Appendix A). [9] TRM was produced along z (cylindrical axis of the sample) by cooling from 600°C in a laboratory field B = 50 mT using an MMTD furnace. ARM was imparted along z in an AF decaying from 100 mT with a superimposed steady field B = 50 mT using a Molspin AF demagnetizer. In other words, B was always parallel to the axis of the AF. SIRM was produced by exposing samples in a field of 1 T using ASC-10 impulse magnetometer. All the remanence was produced along the consistent direction, pivotal to avoid the effect of remanence anisotropy caused by uniaxial sample compactions.

3. TRM/ARM Versus TRM/SIRM 3.1. Background [10] TRM is acquired when the magnetic minerals are cooled from the Curie point in the presence of 3 of 12


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given temperature and then reducing the field to zero. [11] The rationale for the use of normalization methods relies on the fact that the TRM/ARM and TRM/SIRM can be expressed as a simple ratio R and REM, respectively. The TRM/ARM ratio is MTRM ðB0 Þ Ms0 TB n =M (T0 ) with the value of expressed as M ARM ðB0 Þ sB n depending on the models. Model type 1 defined n = 0 for SD [Dunlop and West, 1969] with rough experimental support from Fe3O4, gFe2O3, and fine-grained terrestrial rocks. Model type 1 was extended for pseudo-single-domain (PSD) grains [Gillingham and Stacey, 1971] with practical application in lunar rocks [Stephenson and Collinson, 1974]. Model type 2 used n = 0.5 for SD grains [Jaep, 1971] with decent experimental support from SD CrO2 [Banerjee and Mellema, 1974a].

Figure 1. The ratios of (a) cTRM/cARM and (b) cTRM/cSIRM were displayed as a function of grain size of magnetite (and Cr oxide). The cTRM/cARM and cTRM/cSIRM showed more than an order of dispersion with maxima at 0.2 mm.

an external field over an interval of blocking temperatures. ARM is an artificially produced magnetization that does not exist in nature. ARM is produced by applying a small inducing d.c. field on which a slowly decaying AF is superimposed. As the AF decreases, the remanence is blocked in when the peak value of AF falls below the microcoercivity of the magnetite grains. On the basis of qualitative similarity (thermal fluctuation versus AF) and quantitative comparison (similar demagnetization behavior), ARM is considered to be the analog of TRM [e.g., Rimbert, 1959; Dunlop and West, 1969; Levi and Merrill, 1976; Bailey and Dunlop, 1983]. SIRM is applied by exposing the sample deliberately to a large saturating field at a

[12] Neél’s thermal fluctuation theory [Neél, 1949] states that the TRM/SIRM ratio is expressed as MTRM ðBv Þ SIRM = tanh [VMs (TB)B0/kTB] for noninteracting SD grains where V is grain volume, Ms is spontaneous magnetization ( = 480 kA/m for magnetite at T0 = 23°C), TB is blocking temperature, B0 is the applied field, and k is the Boltzmann’s constant. Of course, Neél’s theory requires modification when applied to magnetic material other than non– interacting SD grains (see Dunlop and Argyle [1997] for details). A complimentary mathematical and experimental treatment on the various models of ARM, TRM, and SIRM was provided by Dunlop et al. [1975] and Dunlop and Argyle [1997].

3.2. Grain Size Dependence [13] In rock magnetism, properties of ARM versus TRM, ARM versus SIRM, or TRM versus SIRM were intensively compared for magnetite. However, it is surprising that only a limited number of studies combined all three pairs from the same set of magnetite with well-defined grain volume information [e.g., Hartstra, 1982; Dunlop, 1986; Argyle and Dunlop, 1990; Dunlop and Argyle, 1997; Muxworthy and McClelland, 2000; Yu et al., 2002, 2003; Yu, 2006]. Instead, information on limited pairs (TRM/ARM for Levi and Merrill [1976]; TRM/SIRM for Hartstra [1983]) was available in some studies. [14] In Figure 1, a compilation of the ratio of TRM/ ARM and TRM/SIRM are displayed as a function of grain size of magnetite. Results for chromium oxide [Banerjee and Mellema, 1974a] were also inserted as a comparison (Figure 1). For a fair 4 of 12


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comparison, cARM, cTRM, and cSIRM were used because some studies used different values of B in producing ARM and/or TRM. In Figures 1–4, the ratios of TRM/ARM and TRM/SIRM are displayed on a logarithmic scale because the TRM/ SIRM often extends up to two orders of magnitude and because TRM was smaller than ARM for

Figure 2. The volume concentration dependence of the (a) cTRM/cARM, (b) cTRM/cSIRM, and (c) cARM/ cSIRM for magnetite (and Cr oxide). For fine-grained magnetite, the cTRM/cARM increased while the cTRM/ cSIRM and cARM/cSIRM decreased as the volume concentration increased. For MD magnetite, the ratio of cTRM/cARM, cTRM/cSIRM, and cARM/cSIRM remained constant regardless of the volume concentration of magnetite. BM74, Banerjee and Mellema [1974a]; S79, Sugiura [1979].

Figure 3. Testing the stability of the (a) TRM/ARM, (b) TRM/SIRM, and (c) ARM/SIRM against the AF demagnetization. The TRM/ARM and TRM/SIRM increased as the AF increased for SD and PSD magnetite. For MD magnetite, the TRM/SIRM was virtually consistent while the TRM/ARM decreased as AF increased. 5 of 12


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for both the cTRM/cARM and cTRM/cSIRM trends, there is no obvious offset between the synthetically produced [Levi and Merrill, 1976; Dunlop and Argyle, 1997; Muxworthy and McClelland, 2000; this study] and naturally crushed [Hartstra, 1982, 1983] grains, suggesting that the effect of internal stress on these ratios is minimal at least for magnetite grains larger than 1 mm (Figure 1). Sixth, despite limited quantity, Cr oxide showed similar ratios of cTRM/cARM and cTRM/cSIRM to those for magnetite (Figure 1).

Figure 4. Comparison of the ratios of TRM/ARM and TRM/SIRM for 63 gabbro samples. Specimens are sorted out in ascending order of the TRM/SIRM. The average ratios of TRM/ARM and TRM/SIRM are 2.60 ± 1.32 and (3.61 ± 1.28) 102, respectively.

cm-sized samples (Figure 1). Otherwise, several interesting aspects would be masked if the results are displayed on a linear scale. [15] The grain size dependence of cTRM/cARM and cTRM/cSIRM displayed six remarkable features (Figure 1). First, both the ratios of cTRM/cARM and cTRM/cSIRM vary over an order of magnitude. Such a wide range suggests that the cTRM/cARM and cTRM/cSIRM are equally uncertain in paleointensity determination unless a strong constraint on the grain size characterization is provided. Second, both the cTRM/cARM and cTRM/cSIRM reach peak values at 0.2–0.4 mm (Figure 1). Presence of such peaks has been attributed to difference in magnetic microstates between field-treated ARM or SIRM (e.g., vortex spin states) [e.g., Halgedahl, 1991; Dunlop and Argyle, 1997; Winklhofer et al., 1997] versus thermally treated TRM (e.g., two domain states). Third, the effect of volume concentration is substantial for fine-grained magnetite, as evidenced by a noticeable vertical gap between the highest and the lowest cTRM/cARM for the same nominal grain size (Figure 1a). Such contrast is somewhat diminished for the cTRM/cSIRM (Figure 1b), suggesting that the effect of volume concentration affects ARM (see section 3.3 for details). Fourth, except for the two outliers of cmsized magnetite, TRM was always larger than ARM, indicating that thermal fluctuations are much more efficient than the alternating fields in switching magnetic polarity of domains. Fifth,

[16] Neél’s thermal fluctuation theory for TRM [Neél, 1949, 1955] and analogous ARM counterpart [Egli and Lowrie, 2002; Yu and Dunlop, 2003] all predict a decreasing TRM or ARM as the grain size of magnetite increases. Empirical experimental determination confirms such a prediction with three interesting features. First, the highest TRM and ARM occurs in the range of 50 – 80 nm, possibly indicating SD threshold for magnetite [Dunlop and Argyle, 1997]. Second, both TRM and ARM varied as d1 for 1 mm [Dunlop and Argyle, 1997]. Third, the two trends below 1 mm and above 1 mm merge smoothly only for TRM. Whereas they showed substantial offset for ARM, implying that the effect of internal stress was less significant for TRM. Different degree of grain size dependence and the presence of offset 1 mm provide reasonable explanation for the observed varying ratios of cTRM/cARM (Figure 1). However, it is currently unobvious why the cTRM/cSIRM follows a similar trend to that of cTRM/cARM.

3.3. Volume Concentration Dependence [17] Both ARM and TRM are known to be strongly concentration-dependent [e.g., Banerjee and Mellema, 1974a; Sugiura, 1979]. Thus, it is important to compare the strength of TRM, ARM, and SIRM for the samples with different volume concentration in a given grain size. The ratios of cTRM/cARM, cTRM/cSIRM, and cARM/cSIRM were plotted against the volume concentration of magnetite (or chromium oxide). For synthetic magnetite used in this study, representative results for 0.065 mm, 0.24 mm, 0.44 mm, and 18.3 mm are shown (Figure 2). Two sets of PSD magnetite were selected because the largest cTRM/cARM and cTRM/cSIRM ratios were observed for 0.24 mm and 0.44 mm, respectively (Figure 1). In addition, results for the smallest (0.065 mm) and the largest grain size (18.3 mm) were included (Figure 2). 6 of 12


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[18] For SD (0.065 mm) and PSD magnetites (0.24 mm and 0.44 mm), the cTRM/cARM increased (Figure 2a) while the cTRM/cSIRM decreased (Figure 2b) as the volume concentration increased. As expected from Jaep’s theory [Jaep, 1971], higher grain interaction (i.e., higher volume concentration) reduces the efficiency of remanence acquisition. Then it is natural to observe an increasing cTRM/cARM with decreasing volume concentration for PSD magnetites (Figure 2c). Results from previously documented magnetite [Sugiura, 1979] and Cr oxide [Banerjee and Mellema, 1974a] shared similar trends (Figure 2). Contrary to PSD magnetite, MD magnetite showed nearly constant cTRM/cARM, cTRM/cSIRM, and cARM/cSIRM ratios regardless of the volume concentration, indicating a lack of grain interaction in MD grains (Figure 2).

[Dunlop and West, 1969]. For nonuniformly magnetized samples, IRMs are definitely softer than the ARM and TRM due to an intrinsic distribution of energy barriers toward a self-demagnetized configuration [Lowrie and Fuller, 1971]. The ratios of TRM/ARM, TRM/SIRM, and ARM/SIRM are not constant against AF coercivity because ARM, SIRM, and TRM possess different domain (or micromagnetic spin) configurations (Figure 3). Predominance of relatively softer fraction (i.e., relatively easy to demagnetize) is developed in the order of SIRM, ARM, and TRM for finegrained magnetite [Yu et al., 2003], providing reasonable explanation for the observed AF stability (Figure 3). An opposite trend for coarser grained magnetite (Figure 3) results from the AF resisting ARM (Figure 3).

3.4. Stability of TRM/ARM and TRM/SIRM

3.5. Calibrating the TRM/ARM and TRM/SIRM

[19] For extraterrestrial material, univectorial decay of entire NRM is far less common than the NRMs with composite magnetic vectors. Regardless of the origin of nonprimary remanence for extraterrestrial material such as viscous contamination and shockinduced effect, partial AF demagnetization is required to isolate the primary remanence. Then, it is necessary to check whether the TRM/ARM and TRM/SIRM is stable against AF demagnetization. It has been recently demonstrated that the TRM/SIRM increased as the AF increased for finegrained magnetite [Yu, 2006]. To test whether the TRM/ARM and TRM/SIRM shared similar AF stability, stepwise AF demagnetization was carried out for ARM, TRM and SIRM at 2.5, 5, 7.5, 10, 15, 20, 25, 30, 35, 40, and 50 mT.

[22] To provide the best calibration relation, it is necessary to estimate dispersion of the TRM/ARM and TRM/SIRM. If the dispersion is reasonably small, then an approximate calibration law can be provided. Although the Thellier-type work is recommended from the first place for all paleointensity investigation, providing a better calibration relation is still useful as long as the normalization techniques are utilized for samples that are unstable during heating.

[20] There is a tendency that the TRM/ARM remained relatively constant at low AF < 20 mT (Figure 3a). However, the TRM/ARM increased as the AF increased over 20 mT for SD and PSD magnetite (Figure 3a). Similar increasing trends of the TRM/SIRM were observed for SD and PSD magnetite (Figure 3b). For MD magnetite, the TRM/SIRM was virtually constant while the TRM/ARM decreased as AF increased (Figure 3). The ratio of ARM/SIRM increased as the AF increased for MD only (Figure 3c). [21] According to Neél’s theory, there is no reason to expect substantially different AF coercivity spectra among ARM, TRM, and SIRM for SD magnetite, although weak field TRM would have slightly softer coercivity spectra due to lesser contribution from the high coercivity fraction

[23] The TRM/ARM and TRM/SIRM ratio for 63 gabbro samples are plotted in Figure 4 where specimens are sorted out in ascending order for the ratio of TRM/SIRM. The average ratios of TRM/ ARM and TRM/SIRM are 2.60 ± 1.32 and (3.61 ± 1.28) 102, respectively. In particular, the TRM/ SIRM calibration factor of 0.036 for B = 50 mT is in excellent agreement with the previously reported calibration relation (0.032 ± 0.007 for B = 46.8 mT) from the historic Showa lava [Yu, 2006]. A roughly similar calibration relation was obtained for other iron- or spinel-bearing extraterrestrial material except for the hematite [e.g., Cisowski, 1983; Fuller and Cisowski, 1987; Kletetschka et al., 2003, 2004; Gattacceca and Rochette, 2004].

4. Discussion [24] Three fundamental assumptions embedded in using normalization paleointensity techniques are the grain size independence, the volume concentration independence, and a linear field dependence of weak field remanences. Unfortunately, the first 7 of 12


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two conditions appear to be invalidated (Figures 1 and 2). For instance, a compilation of the TRM/ ARM and TRM/SIRM displayed strong grain size dependence with more than an order of dispersion (Figure 1). In addition, the TRM/ARM and TRM/ SIRM were far from being constant as the volume concentration varied (Figure 2). [25] Another source of ambiguity in using normalization paleointensity technique is the instability of TRM/ARM and TRM/SIRM against AF demagnetization. As clearly shown in Figure 3, values of TRM/ARM and TRM/SIRM did not remain constant during AF demagnetization (Figure 3). Stability of the TRM/ARM and TRM/SIRM during AF demagnetization must be treated seriously in normalization techniques because composite NRMs are common for extraterrestrial material. Such instability of the TRM/ARM and TRM/SIRM against AF demagnetization results from the fact that ARM, TRM, and SIRM possess different AF demagnetization spectra. While the instability of the TRM/SIRM is easily anticipated for SD and PSD where TRM and SIRM share distinctively different coercivity spectra [Lowrie and Fuller, 1971], the instability of the TRM/ARM is unexpected because TRM and ARM are known to share similar AF coercivity spectra for SD and PSD. However, close examination for SD and PSD magnetite from available data showed that ARM is less resistant to AF demagnetization than TRM in most (if not all) samples [e.g., Dunlop and West, 1969; Levi and Merrill, 1976; Muxworthy and McClelland, 2000; Yu et al., 2003]. If so, such difference of the AF coercivity spectra between ARM and TRM may explain slight increase of the TRM/ARM for SD and PSD magnetite (Figure 3). Of course, highly acicular samples showed an opposite trend where ARM is considerably more resistant to AF demagnetization than the TRM [e.g., Dunlop and West, 1969; Levi and Merrill, 1976]. [26] An objective of this study is to compare the ratio of TRM/ARM and TRM/SIRM for the same set of magnetite samples as a mean to determine ancient planetary magnetic field strength. Is the SIRM method superior to the ARM method? In terms of the grain size dependence, both the ratios of TRM/ARM and TRM/SIRM showed roughly similar trends but with substantial dispersion, although the dispersion was slightly narrower for the TRM/SIRM (Figure 1). The TRM/SIRM showed weaker volume concentration dependence

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than the TRM/ARM (Figure 2). Such contrast is natural because ARM and TRM are much more sensitive to the volume concentration of finegrained magnetic material than SIRM. The ratios of TRM/ARM and TRM/SIRM increase as peak AF increases for fine-grained magnetite, whereas MD magnetite showed exceptionally constant TRM/SIRM (Figure 3). The TRM/SIRM showed better statistical clustering than the TRM/ARM when applied to rock samples that yielded reliable paleointensities in past studies. So far as the present work is concerned, the scatters in the mean ratio estimated from 63 gabbro samples are 51% and 35% for the TRM/ARM and TRM/SIRM, respectively (see the gray bars in Figure 4a). [27] When the grain size dependence, volume concentration dependence, and stability against AF demagnetization are all taken together, the TRM/SIRM is a better paleointensity estimator than TRM/ARM (Figures 1–3). In addition, the mean TRM/SIRM ratio had a smaller scatter than the mean TRM/ARM ratio for the same set of natural samples (Figure 4). Another discouraging aspect of using the ARM method would be the difficulty of intercalibration because the ARM intensity is strongly dependent on the instrument [Sagnotti et al., 2003] as well as on the decay rate of AF [Yu and Dunlop, 2003]. Thus, whenever heating is inapplicable, the SIRM method seems to be a better choice than the ARM method. [28] In planetary magnetism, a major hope for using the TRM/ARM and TRM/SIRM is to acquire reliable paleointensity estimation. This is analogous to relative geomagnetic field intensity determination from the sediments [e.g., Tauxe, 1993]. For instance, the ARM/SIRM has been applied in relative paleointensity study as a granulometric proxy [e.g., Doh et al., 1988; Valet and Meynadier, 1993] because uniform grain size distribution of magnetic material is a prerequisite for the reliable relative paleointensity [e.g., Tauxe, 1993]. However, a notable discrepancy lies on the fact that the relative paleointensity seeks an optimal normalizer from various rock magnetic parameters such as magnetic susceptibility, ARM, SIRM, and/or partially demagnetized ARM or SIRM. Instead, such an optimization process is neglected when the TRM/ARM or TRM/SIRM is applied to extraterrestrial material to determine ancient planetary magnetic field strength. A major success of applying the ARM/SIRM in relative paleointensity work

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Figure A1. Typical backscattered SEM (scanning electron microscopy) images of Tudor Gabbro for (a and b) accepted paleointensity and (c) rejected paleointensity. Figure A1a shows submicron magnetites (bright) embedded within plagioclase (dark). In Figure A1b, in a magnified scale, magnetites are mostly elongated. In Figure A1c, large multidomain magnetite (bright) exists for the samples which were rejected from the paleointensity.

is partially supported in Figure 3 where the ARM/ SIRM showed the best stability against AF.

5. Conclusion [29] Information on the strength of ancient planetary magnetic field is essential for understanding the evolution of planetary bodies in the solar system. It is true that for terrestrial rocks, the most reliable field strength determination technique is the Thellier-type double heating method and its variations. However, alternative normalization techniques (e.g., the ARM and SIRM method) with no heating are worthy for examination when rock samples contain unstable material under heating. In the present study, quantitative evaluation for the ARM and SIRM methods was provided by comparing the ratios of TRM/ARM and TRM/SIRM. A similar grain size dependence of the TRM/ARM and TRM/SIRM for magnetite was observed (Figure 1). Both the ratios of TRM/ARM and TRM/SIRM for magnetite vary over an order of magnitude with noticeable peaks between 0.2 and 0.4 mm (Figure 1). For PSD magnetites (0.24 mm and 0.44 mm), the TRM/ARM increases while the TRM/SIRM decreases as the volume concentration increases (Figure 2). The ARM/SIRM increases with decreasing concentration for SD and PSD magnetites (Figure 2). Contrary to PSD magnetite, MD magnetite shows nearly constant values of TRM/ARM, TRM/SIRM, and ARM/SIRM regardless of the volume concentration of magnetite (Figure 3). The ratio of TRM/ARM increases as the AF increases for SD and PSD magnetite. Similar increasing trends of the TRM/SIRM are observed for SD and PSD magnetite (Figure 3).

For MD magnetite, the TRM/SIRM was virtually consistent while the TRM/ARM decreased as AF increased. For magnetite, the TRM/ARM of 2.60 ± 1.32 and the TRM/SIRM of (3.61 ± 1.28) 102 can be correlated with B = 50 mT (Figure 4). This new calibration relation is in agreement with the previously reported calibration relation of 0.032 ± 0.007 for B = 46.8 mT for magnetite. The TRM/SIRM is superior to TRM/ ARM because the former showed less dispersion for the grain size dependence and the volume concentration dependence (Figures 1–3). In addition, the uncertainty calculated from the scatter of the data in calibration relation was smaller for the SIRM method than the ARM method (Figure 4). Thus, whenever heating is inapplicable, the SIRM method seems to be a better choice than the ARM method. However, it should be highlighted that the uncertainty of normalization methods is still nearly an order of magnitude larger than that of the highfidelity Thellier estimation, thus must be limited in use only when samples are irreversibly alter during heating. In practice, the best approach is to carry out both ARM and SIRM methods and check whether the two estimations agree within the uncertainties.

Appendix A [30] Sixty-three gabbro samples used in the present study showed a very narrow unblocking temperature spectrum (Figure A1). Such restricted unblocking from 500°C to 580°C originates from the magnetite embedded within the plagioclase as inclusions. 9 of 12


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Acknowledgments [31] Despite his fragile health, Subir Banerjee kindly attended my doctoral degree defense as an external committee member on 20 October 2002. On completion of my dissertation presentation, Subir Banerjee inspired me to explore the two widely used normalization paleointensity methods in the 1970s. Bruce Moskowitz, John Tarduno, and Benjamin Weiss provided insightful and constructive reviews. David J. Dunlop, Gunther Kletetschka, Adrian Muxworthy, Ozden Ozdemir, and Lisa Tauxe shared fruitful discussions. This research was supported by Korea Polar Research Institute grant PP09020.

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