Long-term changes of geomagnetic field intensity, including possible dependence on lengths of polarity intervals, provide fundamentally important information for understanding the geodynamo. A positive correlation between paleointensity and polarity interval length was previously suggested from an Oligocene (ca. 23–34 Ma) relative paleointensity record at Deep Sea Drilling Program Site 522 in the Atlantic Ocean, which is the only continuous paleointensity data set published so far for this age interval. We have conducted a paleomagnetic study of Eocene to Oligocene sediments at three sites in the eastern equatorial Pacific Ocean. Our objectives include revisiting the issue of the paleointensity-polarity length correlation. Magnetic properties of the sediments meet the frequently used criteria for reliable relative paleointensity estimation. Although short-wavelength normalized remanence intensity fluctuations associated with polarity boundaries and possible geomagnetic excursions agree among the three sites, long-term changes are inconsistent. Apparent positive correlation between normalized intensity and polarity length was observed, but the normalized intensity has an obvious anti-correlation with the ratio of anhysteretic remanent magnetization (ARM) to isothermal remanent magnetization (IRM), which is mainly controlled by the relative abundance of biogenic and terrigenous magnetic minerals. Furthermore, the normalized intensity correlates with sedimentation rate. These facts indicate a lithological contamination on the normalized intensity records. The dependence on ARM/IRM and sedimentation rate is also evident at Site 522. It is inferred that variations in sedimentation rate and the relative abundance of biogenic magnetite on depositional remanent magnetization acquisition efficiency may not be well compensated by the normalization. It is therefore premature to conclude that stronger geomagnetic fields were recorded during longer polarity intervals from currently available normalized intensity records.
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 Estimating the strength of the past geomagnetic field is fundamentally important for understanding the geodynamo. The frequency of geomagnetic polarity reversals has changed through geologic time [e.g., Tauxe, 2010]. Reversals have occurred ~4 times per million years on average for the last ca. 20 Ma, whereas no reversal occurred for about 35 Ma during the Cretaceous Normal Superchron (CNS) between 83 and 118 Ma [Cande and Kent, 1995; Lowrie and Kent, 2004]. Reversal frequency appears to have gradually increased since the end of the CNS. Cox  proposed that reversals could be inhibited when the geomagnetic field is strong. Some numerical simulations have been used to suggest that during a stable polarity period like the CNS, the geodynamo may be in a high efficiency state with an elevated dipole moment that may be controlled by the thermal structure of the lower mantle [Glatzmaier et al., 1999; Courtillot and Olson, 2007; Driscoll and Olson, 2011]. To test these ideas, it is desirable to accumulate reliable paleomagnetic data that enable examination of any relationship between paleointensity and polarity interval length.
 Compilation of absolute paleointensity data from volcanic rocks indicates that the geomagnetic field was stronger on average and highly variable during the CNS and that it was relatively weaker between about 20 and 55 Ma, although there is no clear paleointensity trend associated with increased reversal frequency since the CNS [Tauxe and Yamazaki, 2007]. To understand the relationship between paleointensity and polarity interval length, it is desirable to obtain average paleointensity data for each polarity interval, but the number of reliable absolute paleointensity data and their age resolution is insufficient for this purpose. Furthermore, data reliability and possible bias depending on paleointensity determination methods and the materials analyzed are matters of active debate [Yamamoto and Tsunakawa, 2005; Tarduno et al., 2006, Tauxe and Yamazaki, 2007; Granot et al., 2007; Biggin, 2010].
 Continuous records from sediments are indispensable for discussing long-term geomagnetic field intensity changes and power spectral features. Stacked relative paleointensity curves have been established back to only about 3 Ma [Valet et al., 2005; Yamazaki and Oda, 2005; Channell et al., 2009; Ziegler et al., 2011], and they are too short to enable discussion of the relationship between paleointensity and polarity interval length, although this was done by Valet and Meynadier . The sole exception is the relative paleointensity record from Deep Sea Drilling Project (DSDP) Site 522, Walvis Ridge, South Atlantic Ocean. This is the only Oligocene record available so far, and covers ~11 Ma almost continuously [Hartl et al., 1993; Tauxe and Hartl, 1997]. In the late Oligocene, the polarity reversal frequency of ~4 per million years was similar to that of the last 5 Ma, whereas in the early Oligocene reversal frequency was about half this value. Based on this record, weak positive relationships between geomagnetic field intensity and polarity interval length and between intensity and field variability were proposed [Tauxe and Hartl, 1997; Constable et al., 1998], and power spectral features of the ancient geomagnetic field have been discussed [Constable et al., 1998; Smith-Boughner et al., 2011].
 Possible influences of sediment lithological changes on relative paleointensity estimation have long been discussed [e.g., Kok, 1999; Hofmann and Fabian, 2009; Valet et al., 2011; Roberts et al., 2012]. Criteria to establish rock-magnetic homogeneity have been proposed and used widely in an attempt to ensure reliable relative paleointensity estimation [King et al., 1983; Tauxe, 1993; Tauxe and Yamazaki, 2007]. The criteria seem to work well for studies that use relative paleointensity variations for stratigraphic correlations and age estimation of marine sediment cores, so-called paleointensity-assisted chronostratigraphy [e.g., Stoner et al., 2000; 2002; Kiefer et al., 2001; Evans et al., 2007]. However, when discussing the relationship between paleointensity and polarity interval length, more rigorous checks are required to detect possible lithological contamination.
 In this study, we aimed to assess long-term relative paleointensity variations for the Eocene and Oligocene using sediment cores from the eastern equatorial Pacific Ocean that were recovered during Integrated Ocean Drilling Program (IODP) Expeditions 320/321. Our intention is to test the DSDP Site 522 record and the possible correlation between paleointensity and polarity interval length. Relative paleointensity variations on shorter timescales, of the order of 105 years, from the same cores are presented and discussed elsewhere (Yamamoto et al., manuscript in preparation).
2 Geological Setting and Samples
 The sites cored during IODP Exp. 320/321, the Pacific Equatorial Age Transect (PEAT), were selected along the northwestward Pacific plate trajectory to recover continuous Cenozoic sediment sequences that were deposited in the equatorial high-productivity zone [Pälike et al., 2009]. Sites U1331, U1332, and U1333 are the three northwesternmost sites among the eight sites of the PEAT expeditions (Figure 1).
 At Site U1331 (12°04.09′N, 142°09.71′W; 5116 m in water depth), ~53 Ma crust is overlain by pelagic sediments (187 m in thickness) that were cored with the Advanced Piston Corer (APC) down to 157 m below seafloor (mbsf). In the upper 80 m, late middle Eocene to Oligocene sediments were deposited at upward decreasing rates of 6 to 3 m/m.y. except for an ~7 m interval of Pliocene-Pleistocene surface clay. At Site U1332 (11°54.72′N, 141°03.74′W; 4924 m), ~50 Ma seafloor is overlain by pelagic sediments (150 m thick) that were cored with the APC down to ~126 mbsf. Middle Eocene to early Miocene sediments were deposited at upward decreasing rates of 7–3 m/m.y. except for the uppermost interval (~13 m) of late Miocene to Pliocene-Pleistocene clay. At Site U1333 (10°31.00′N, 138°25.16′W; 4853 m), ~46 Ma seafloor is overlain by pelagic sediments (183 m in thickness) that were cored with the APC down to ~163 mbsf. Except for the uppermost few meters, middle Eocene to early Miocene sediments were deposited at average rates of ~4 m/m.y. in the Eocene, ~12 m/m.y. in the early Oligocene, and ~6 m/m.y. in the late Oligocene and early Miocene. Radiolarian ooze is the main Eocene lithology at all sites, whereas nannofossil oozes and chalks dominate the Oligocene sequences. The Eocene-to-Oligocene transition is characterized by a major lithological change from radiolarian oozes to nannofossil oozes, which reflects a major deepening of the carbonate compensation depth (CCD) in the equatorial Pacific Ocean at that time [Pälike et al., 2012]. Increased carbonate content at the Eocene-Oligocene transition was also observed at Site 522 in the South Atlantic Ocean [Mead et al., 1986; Hartl et al., 1995]. Sedimentation rates at Site 522 were similar to those of Sites U1331 to U1333; the rates decreased upward in general from ~10 to ~4 m/m.y., but increased near the Eocene-Oligocene transition [Mead et al., 1986].
 Shipboard paleomagnetic measurements on archive-half cores revealed a clear magnetic polarity reversal sequence that correlates with the geomagnetic polarity timescale (GPTS) [Pälike et al., 2010]. All studied core sections have a brownish color that is indicative of an oxic depositional and post-depositional environment. It is hence considered that the cores did not undergo Fe reduction and that alteration of magnetic minerals by reduction diagenesis is unlikely. These observations indicate that the sediments are potentially useful for relative paleointensity estimation. Thus, u-channel samples [e.g., Weeks et al., 1993] were taken at the IODP Core Repository at Texas A&M University along the revised composite section [Westerhold et al., 2012]. For Sites U1332 and U1333, u-channels were taken down to the bottom of the sediment sequences that were cored with the APC. For Site U1331, core sections below ~80 mbsf were not used in this study because of frequent intercalation of turbidite layers. The age of the sediments at ~80 mbsf is ~41 Ma, which is close to the ages near the bottom of the other two studied sites.
 The natural remanent magnetization (NRM) of archive-half core sections was initially measured onboard JOIDES Resolution with alternating-field (AF) demagnetization up to 20 mT [Pälike et al., 2010]. For u-channel samples, measurements were conducted at the paleomagnetism laboratories of the Geological Survey of Japan (GSJ), National Institute of Advanced Industrial Science and Technology (AIST), for Site U1331, Kochi University for Site U1332, and University of California, Davis, for Site U1333. The instruments and experimental procedures, including acquisition and demagnetization of anhysteretic remanent magnetization (ARM) and isothermal remanent magnetization (IRM), are reported in Guidry et al.  and Yamamoto et al. (in prep.). For u-channels of Sites U1331 and U1332, a DC biasing field of 0.1 mT was used for ARM acquisition. For Site 1333, a DC field of 0.05 mT was used and ARM values were doubled to enable comparison with the other two sites. For imparting IRM to u-channels, slightly different fields were used among the laboratories (0.7–0.9 T) due to the limitation of the instruments. Data from the first and last 4 cm of each u-channel sample were eliminated to avoid erroneous results due to edge effects.
 For Sites U1331 and U1332, further rock-magnetic measurements were conducted on discrete samples taken onboard JOIDES Resolution at intervals of about 1.5 m. The ARM was imparted with a peak AF of 80 mT and a DC bias field of 0.1 mT and was measured using 2G Enterprises cryogenic magnetometers at the GSJ for Site U1331 and at Kochi University for Site U1332. An IRM was imparted to the samples with a 2.5 T inducing field using pulse magnetizers (2G Enterprises model 660 at the GSJ and Magnetic Measurements MMPM-10 at Kochi University). The IRM acquired in a 2.5 T induction is regarded as the saturation IRM (SIRM). IRMs of 0.1 and 0.3 T were then successively imparted in the direction opposite to the initial IRM. The IRMs were measured using Natsuhara-Giken spinner magnetometers. S-ratios (S−0.1T and S−0.3T) were calculated according to the definition of Bloemendal et al. .
 Measurements of magnetic hysteresis loops and first-order reversal curves (FORCs) [Pike et al., 1999; Roberts et al., 2000] were conducted at the GSJ using an alternating gradient magnetometer (AGM, Princeton Measurements Corporation MicroMag 2900) on dried specimens at stratigraphic intervals of about 1.5 m for Site U1331 and 3 m for Site U1332. For high-resolution FORC diagrams, the field spacing between measurements was set to 0.5 mT. A total of 191 FORCs were measured, with Hc between 0 and 60 mT, and Hu between −15 and 15 mT. For some selected specimens, normal-resolution FORC measurements were also made; the field spacing between measurements was set to 1.3 mT, and 150 FORCs were measured, with Hc between 0 and 80 mT, and Hu between −50 and 50 mT. The average time spent at each data point was 200 ms for all measurements.
4 Normalized Remanence Intensity
 Stepwise AF demagnetization demonstrated the presence of a stable, well-defined characteristic remanent magnetization (ChRM) for most samples [Pälike et al., 2010; Guidry et al., 2012; Yamamoto et al., in prep.]. Secondary magnetizations that are probably acquired during coring, which are sometimes serious for ODP/IODP APC cores [e.g., Herr et al., 1998], could generally be removed by a peak AF of 20–25 mT. The ChRMs, which were determined using principal component analysis [Kirschvink, 1980], have maximum angular deviation (MAD) values that are generally only a few degrees except for stratigraphic intervals associated with polarity transitions. Ages were assigned to the cores by correlating reversals to the GPTS [Guidry et al., 2012; Yamamoto et al., in prep.] and are similar to those based on shipboard half-core measurements [Pälike et al., 2010].
 Magnetic mineral concentrations, represented by IRM, vary by less than an order of magnitude [Pälike et al., 2010; Guidry et al., 2012; Yamamoto et al., in prep.]. S-ratios (S−0.3T) measured on discrete samples have minor variations, from 0.95 to 0.97 for Site U1331 and from 0.96 to 0.99 for Site U1332, which suggests that the magnetic mineral assemblages of the studied sediments are dominated by low-coercivity minerals like magnetite and that their compositional variations are small (Yamamoto et al., in prep.). Low-temperature measurements also indicate little variation of magnetic mineralogy, with subdued Verwey transitions that suggest maghemitization (Yamamoto et al., in prep.). Magnetic hysteresis parameters, the ratio of saturation remanence to saturation magnetization (Mrs/Ms) and the ratio of coercivity of remanence to coercivity (Hcr/Hc), tightly cluster in the pseudo-single-domain (PSD) region of a Day plot [Day et al., 1977] as shown in Figure 2 for Sites U1331 and U1332 and as shown by Guidry et al.  for Site U1333. This suggests that magnetic grain-size variations are not significant for the studied sediments. The data distribution in the PSD range on the Day plot does not necessarily mean that the majority of magnetic grains in a sample have a PSD size; alternatively the magnetic mineral assemblage can be a mixture of single-domain (SD) and multi-domain (MD) grains [Dunlop, 2002]. These observations meet the frequently used criteria of rock-magnetic homogeneity required for reliable paleointensity estimation [King et al., 1983; Tauxe, 1993]. However, changes in the magnetic properties of the sediments represented by ARM/IRM are not necessarily small, as discussed later.
 The IRM was used to normalize the NRM for relative paleointensity estimation in this study. ARM is also often used as a normalizer, but here we prefer IRM because ARM acquisition efficiency is sensitive to the strength of magnetostatic interactions among magnetic particles [Yamazaki, 2008]. IRM has a drawback in that it includes contributions from coarse MD grains that do not carry a stable remanent magnetization, in addition to the contribution from fine SD grains. However, the contribution of MD grains would be relatively small in a pelagic environment such as at the studied sites. For Sites U1331 and U1333, normalized intensities are calculated from NRM and IRM intensities after AF demagnetization at a peak field of 30 mT. For Site U1332, NRM and IRM demagnetization slopes were used for paleointensity normalization [Channell et al., 2002; Yamamoto et al., in prep.]. The preference of IRM as the normalizer is supported by the observation that correlation coefficients between the normalized intensity and the normalizer are smaller when IRM is used compared with ARM for Sites U1331 and U1332 (Yamamoto et al., in prep.).
 Normalized remanence intensity records for the three sites are presented in Figure 3, in which the record from Site 522 [Hartl et al., 1993] is included for comparison. The age model for Site 522, which was originally based on the GPTS of Cande and Kent , was changed to the timescale used in the PEAT program [Expedition 320/321 Scientists, 2010], which is based on the orbitally tuned chronology of Pälike et al.  for the late Eocene and Oligocene. IRM was also chosen as the normalizer for the Site 522 relative paleointensity record because the normalized intensity is less correlated to the normalizer when IRM is used compared to ARM or magnetic susceptibility [Hartl et al., 1993; Constable et al., 1998].
 Normalized intensity variations of the order of 105 years are consistent among Sites U1331, U1332, and U1333 (Yamamoto et al., in prep.). Common features include minima within stable polarity periods as well as at polarity boundaries, which are similar to paleointensity variations during the last 3 Ma, which are often associated with geomagnetic excursions [Laj and Channell, 2007; Roberts, 2008].
 There are consistencies and inconsistencies in the normalized intensity records with timescales of a few million years or longer (Figure 3). During the long (~2.2 Ma) reversed polarity Chron 12r (31.021–33.232 Ma), normalized intensities are higher on average than before and/or after this chron at the three studied sites and also at Site 522. A major normalized intensity peak also occurs from the lower part of Chron C18n to the upper part of Chron C18r at all three sites. However, conspicuous differences are evident in long-term changes before and after the Eocene-Oligocene boundary at 33.8 Ma in the uppermost part of Chron C13r (Figure 3). At Site U1331, the normalized intensity after the Eocene-Oligocene boundary is lower than that before the boundary on average. At Site U1333, on the contrary, the normalized intensity tends to be higher after the boundary than before. At Site U1332, on the other hand, average values before and after the boundary are not remarkably different.
5 FORC Diagrams and kARM/SIRM Ratios
 High-resolution FORC diagrams for all specimens from Sites U1331 and U1332 have a narrow ridge along the Hc axis with negligible vertical spread (Figures 4a and 4c). This indicates weak magnetostatic interactions [Roberts et al., 2000] and is a characteristic of biogenic magnetite [Egli et al., 2010; Roberts et al., 2011; Li et al., 2012]. Biogenic magnetites preserved in sediments as isolated chains are magnetically equivalent to non-interacting SD particles because all magnetite crystals in individual chains simultaneously switch magnetically at a critical field [Penninga et al., 1995; Hanzlik et al., 2002]. Hc values at the peak of the FORC distributions range from 25 to 30 mT, which is typical of the coercivity of SD magnetite. Until recently, documentation of biogenic magnetite from pre-Quaternary sediments was relatively rare [Kopp and Kirschvink, 2008]. However, Roberts et al.  reported biogenic magnetites in Eocene sediments from the Southern Ocean, and Larrasoaña et al.  obtained similar results from Paleocene-Eocene thermal maximum sediments at the same site. They inferred that biogenic magnetite can be preserved for geologically long periods of time where organic carbon flux was low and where diagenetic environments never became anoxic. Our results support this idea and suggest that biogenic magnetite may be common in pre-Quaternary pelagic sediments. This conclusion has also been reached by Roberts et al.  based on an analysis of many sediment types of variable ages from around the world.
 In addition to the narrow ridge along the Hc axis, a weak and broad signal with considerable vertical spread is recognized on the FORC diagrams (Figure 4). This broad component is estimated to be carried by a mixture of interacting SD, PSD, and MD grains. In the normal-resolution FORC diagrams, FORC distributions of the broad component tend to diverge from the Hu = 0 axis (Figures 4b and 4d), which is interpreted to be carried mainly by PSD and MD grains [Roberts et al., 2000; Pike et al., 2001]. The broad component with significant magnetostatic interactions contrasts with the central-ridge component representing biogenic magnetite, and it is estimated to be of terrigenous origin [Yamazaki, 2008; 2009; Yamazaki and Ikehara, 2012]. A contribution from interacting SD grains is also estimated from elliptical FORC distributions at the lower coercivity end of the central ridge on the high-resolution FORC diagrams, which could include contribution from disrupted magnetosome chains [Kind et al., 2011; Li et al., 2012].
 For semi-quantitative estimation of the relative abundance of the non-interacting (N-I) biogenic-magnetite component, a procedure similar to that of Yamazaki [2008, 2009] was adopted, by curve fitting of a cross-section that parallels the local interaction field (Hu) axis and that crosses the peak coercivity (Hc), assuming that the profile consists of three components, each with a Gaussian Hu distribution. The first component is the N-I SD component that corresponds to the central ridge. The second and third are interacting components, the I-1 and I-2 components, with different standard deviations of Hu (5 and 23 mT, respectively), which represent the broad part of the FORC distribution. Mixtures of interacting SD, PSD, and MD grains would constitute the I-1 and I-2 components, although Yamazaki [2008, 2009] interpreted the I-1 component as an interacting SD component and the I-2 component as an MD component, respectively.
 The ratio of ARM susceptibility (kARM) to SIRM correlates with the ratio of the N-I component to the interacting (I) component (the sum of the I-1 and I-2 components) (Figure 5); specimens with high kARM/SIRM values tend to have a larger proportion of the N-I component. Values of the N-I/I component ratio and kARM/SIRM from Sites U1331 and U1332 are comparable to those from Site 1337 in the eastern equatorial Pacific Ocean (3°50.01′N, 123°12.35′W) during the late Pleistocene [Yamazaki, 2012] and are distributed near the upper right-hand end of the trend that is common to pelagic sediments from the Pacific and Indian Oceans, which includes the central North Pacific Ocean along the 175°E line of longitude, the Ontong-Java Plateau in the western equatorial Pacific Ocean, the Manihiki Plateau in the South Pacific Ocean, and the southern Indian Ocean [Yamazaki and Ikehara, 2012]. This correlation indicates that the kARM/SIRM ratio is dominantly controlled by the relative abundance of biogenic and terrigenous magnetic minerals in sediments. High kARM/SIRM values for sediments from Sites U1331 and U1332 as well as Site U1337 suggest that the magnetic mineral assemblage in eastern equatorial Pacific Ocean sediments is dominated by biogenic magnetite and that the proportion of terrigenous magnetic minerals is small. This reflects the locations of the sites; they are far from land and do not lie under major wind systems that transport eolian dust.
 Weak to moderate positive correlations exist between average normalized intensity and polarity interval length in Eocene-Oligocene sediments at Sites U1331, U1332, and U1333, as was proposed at Site 522 in the South Atlantic Ocean (Figure 6) [Tauxe and Hartl, 1997]. Data from Site 522 were re-calculated based on the timescale used in the PEAT program [Expedition 320/321 Scientists, 2010]. The correlation is statistically significant at 95% confidence level for Sites U1332 and U1333. We demonstrate below that rock-magnetic and depositional changes in the sediments significantly influence these normalized intensity values.
6.1 Dependence on ARM/IRM
When temporal variations of normalized intensity and ARM/IRM are compared, the two roughly anti-correlate for considerable parts of the studied time span (Figure 3). Long-term normalized intensity variations at Sites U1331 and U1332 have a generally decreasing trend from 40 to 30 Ma, whereas ARM/IRM has the opposite trend. Long-range variations of both normalized intensity and ARM/IRM from 40 to 36 Ma at Site U1333 are similar to those at Sites U1331 and U1332. At Site U1331, the average ARM/IRM ratio in the Oligocene is much higher than that in the Eocene, whereas there is no remarkable difference at Site U1333; the difference at Site U1332 is intermediate between the case for Sites U1331 and U1333. These differences may have caused the different average normalized intensity values before and after the Eocene-Oligocene boundary. Yamamoto et al. (in prep.) therefore divided the normalized intensity records into Eocene and Oligocene sections and focused discussion on short-wavelength variations. The long-term anti-correlation between the normalized intensity and ARM/IRM is also recognized at Site 522 between 35 and 31 Ma.
For variations on shorter timescales, prominent peaks in normalized intensity at 40–41 Ma occur at all three sites and are associated with major ARM/IRM minima (Figure 3). A large decrease in normalized intensity at ~34.5 Ma is observed only at Site 1333, where there is a prominent peak in ARM/IRM that only occurs at this site. A similar, but less conspicuous, inverse correlation between normalized intensity and ARM/IRM is also evident at ~23.5 Ma at Site U1332, at ~25 and ~30.5 Ma at Site U1333, and at ~28 Ma at Site 522.
When normalized intensity is plotted against ARM/IRM, the amplitude of normalized intensity variations is subdued for larger ARM/IRM values (Figure 7), which is a natural consequence of the frequent occurrence of inverse correlation between these parameters. It should be noted that direct comparison of ARM/IRM values above and below 104 mbsf (30.5 Ma) at Site 522 might not be possible because of the factor of two differences in DC bias field strength for ARM acquisition above and below 104 mbsf. The difference in the DC field strength was corrected assuming linear dependence of ARM acquisition to the strength of a DC field, but linearity is not necessarily guaranteed in the presence of magnetostatic interactions [Moskowitz et al., 1993; Kopp et al., 2006]. Absolute values of ARM/IRM also cannot necessarily be compared among the four sites because ARM acquisition is sensitive to instrumental conditions, including the frequency and decay rate of the applied AF [Sagnotti et al., 2003; Yu and Dunlop, 2003], which was not necessarily the same among the laboratories in which the measurements were conducted, in addition to the problem concerning the correction for differences in a DC biasing field, and because the applied fields used for imparting IRM are slightly different among the sites.
The apparent dependence of normalized intensity on ARM/IRM indicates that magnetic property changes in the sediments have contaminated the normalized intensity records. The observed anti-correlation between normalized intensity and ARM/IRM is not caused by the choice of the normalizer for the relative paleointensity estimation. If ARM is used as the normalizer instead of IRM, the anti-correlation is stronger because normalization with ARM makes the normalized intensity smaller when ARM/IRM is higher. kARM/SIRM correlates with the N-I/I component ratio for pelagic sediments (Figure 5), which means that it represents the relative abundance of biogenic and terrigenous magnetic minerals [Yamazaki, 2008, 2009, 2012; Yamazaki and Ikehara, 2012]. This indicates that kARM/SIRM can be used as a proxy for the relative abundance of biogenic magnetite in pelagic sediments, as well as a magnetic grain-size proxy [Banerjee et al., 1981; King et al., 1982]. When the proportion of biogenic magnetite increases, average magnetic grain size should decrease because the biogenic component is finer than the terrigenous component and kARM/SIRM is expected to increase. It should be noted that in pelagic sediments, kARM/SIRM indicates not merely differences in average magnetic grain size, but also variations in the proportion of two magnetic-mineral populations with contrasting magnetic properties (biogenic versus terrigenous). We conclude that such compositional changes may not be well compensated for by normalization with either IRM or ARM in paleointensity estimations and that they will contaminate normalized intensity.
6.2 Dependence on Sedimentation Rate
Comparison of time variations in normalized intensity and sedimentation rate suggests an influence of sedimentation rate on normalized intensity (Figure 8). A constant sedimentation rate between polarity boundaries is assumed. Calculation of averages is based on the GPTS used in the PEAT program; possible excursions that may have occurred within polarity chrons were not considered. The stronger normalized intensities during Chron C12r and near the boundary between Chrons C18n and C18r correspond to intervals with higher sedimentation rates (Figure 8). Different average normalized intensity values before and after the Eocene-Oligocene boundary at Sites U1331, U1332, and U1333 parallel differences in sedimentation rates. Sedimentation rates at Site U1331 are higher in general below the boundary, where normalized intensity is higher. At Site U1333, on the contrary, sedimentation rates and normalized intensity are lower below the boundary (Figure 8). Positive correlation can be recognized between the mean normalized intensity and sedimentation rate averaged for each polarity chron (Figure 9); the correlation is statistically significant at 95% confidence level for all sites. This implies that it is premature to conclude that the geomagnetic field had stronger average intensities during longer polarity intervals. A possible control of sedimentation rate on normalized intensity has been suggested by Yamazaki and Oda  for calcareous ooze from the Manihiki Plateau, the South Pacific Ocean. This suggests that the influence of sedimentation rate is not limited to a particular sedimentary environment, but that such an influence widely occurs in pelagic environments.
We suggest that NRM acquisition efficiency and, thus, normalized remanence intensities in pelagic marine sediments depend on the relative abundance of biogenic and terrigenous magnetic components, although the underlying mechanism for this influence is not clear. The observed anti-correlation between normalized intensity and ARM/IRM suggests that the normalizer, either ARM or IRM, may overestimate the efficiency of NRM acquisition by biogenic magnetite. Furthermore, NRM acquisition efficiency also depends on sedimentation rate, for which the normalizers fail to compensate. Any relationship between sedimentation rate and magnetic properties remains unclear. For example, in the Southern Ocean, a causal link between higher sedimentation rate and lower kARM/SIRM has been proposed [Yamazaki and Ikehara, 2012]. Ocean productivity is limited by iron depletion in the Southern Ocean, and increased eolian dust input in glacial periods causes higher productivity fueled by iron fertilization. This leads to higher glacial sedimentation rates and an increase in relative abundance of terrigenous magnetic minerals compared with biogenic magnetite, which results in lower kARM/SIRM. In the equatorial Pacific Ocean, however, correspondence between sedimentation rate and ARM/IRM is not remarkable except for the interval near the boundary of Chrons C18n and C18r at ~40 Ma, where normalized intensity and sedimentation rate are high and ARM/IRM is low (Figures 3 and 8). Thus, variations in sedimentation rate and the relative abundance of biogenic and terrigenous magnetic components are considered to be largely independent. No evidence for iron fertilization in the equatorial Pacific Ocean has ever been presented.
In relative paleointensity studies, the possibility of correlation between normalized intensity and sedimentation rate or ARM/(S)IRM has not often been examined in detail. Bi-plots of ARM versus SIRM (or versus magnetic susceptibility) have been used frequently to make inference about the homogeneity of magnetic mineral grain size. On such bi-plots, slopes of ARM/SIRM usually vary within a finite, but sometimes broad, range. Such variations are often ignored as consistent with “homogeneous” grain size distributions unless the variations are relatively large. We have demonstrated that, when discussing long-term relative paleointensity changes, it is necessary to seriously consider possible contamination from variations in sedimentation rate and the relative abundance of biogenic and terrigenous magnetic components. The possibility of correlation between normalized intensity and ARM/SIRM should be checked using plots of variations with depth and/or age, not merely on bi-plots of ARM and SIRM. Hofmann and Fabian  also provided evidence for higher efficiency of NRM acquisition for smaller ARM/IRM values in sediment cores from the South Atlantic Ocean. The anti-correlation between normalized intensity and ARM/SIRM may occur widely in pelagic sediments, which we suggest results from differences in NRM acquisition efficiency between biogenic and terrigenous magnetic components. For recovering long-term relative paleointensity variations, it is imperative to establish a method for detecting and correcting for the effects of such lithological and magnetic changes in sediments [Valet et al., 2011; Roberts et al., 2012].
 Paleomagnetic and rock-magnetic analyses of Eocene-Oligocene sediment cores from IODP Sites U1331, U1332, and U1333 in the eastern equatorial Pacific Ocean and comparison with results from DSDP Site 522 in the South Atlantic Ocean, from which positive correlation between paleointensity and polarity interval length was proposed by Tauxe and Hartl , have led to the following conclusions.
The magnetic properties of the studied sediments meet the frequently used criteria for reliable relative paleointensity estimation [King et al., 1983; Tauxe, 1993]. However, normalized intensity records from the three sites are not consistent over long periods, particularly before and after the Eocene-Oligocene boundary.
Relative paleointensity estimation is influenced by ARM/IRM variations. When temporal variations of normalized intensity and ARM/IRM are compared, anti-correlation between the two is recognized for considerable parts of the studied time interval. On a plot of normalized intensity against ARM/IRM, the amplitude of normalized intensity variations is subdued for larger ARM/IRM values. ARM/IRM variations in pelagic sediments represent changes in the relative abundance of biogenic and terrigenous magnetic minerals.
Sedimentation rate also influences relative paleointensity estimation. Significant correlation occurs between normalized intensity and sedimentation rate averaged for each polarity interval.
It is premature to conclude that stronger geomagnetic fields were recorded during longer polarity intervals from currently available normalized intensity records. It is inferred that the effect of changes in sedimentation rate and the relative abundance of biogenic and terrigenous magnetic minerals on NRM acquisition efficiency may not be well compensated by commonly used normalizers in relative paleointensity studies. When discussing long-term changes in relative paleointensity, which are relatively small compared to paleointensity fluctuations associated with polarity boundaries and geomagnetic excursions, it is necessary to carefully examine the possibility of lithological contamination due to variable mixture of biogenic and terrigenous magnetic minerals and sedimentation rate.
 We thank Jim Channell and Christian Ohneiser for jointly conducting paleomagnetic measurements onboard JOIDES Resolution during Integrated Ocean Drilling Program (IODP) Expeditions 320/321 and Emi Kariya for help with the measurements at the Geological Survey of Japan, AIST. We also thank Lisa Tauxe for providing us with rock magnetic data from Site 522. Thoughtful review by Andrew Roberts greatly improved the manuscript. This research used samples provided by IODP and was partly supported by a Grant-in-Aid for Scientific Research ((B) 22340129) from the Japan Society for the Promotion of Science. Participation of T.Y. and Y.Y. in IODP Exp. 320/321 was supported by J-DESC and CDEX/JAMSTEC.