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 Paleointensity estimates based on the high quality Thellier-Thellier data from the early Brunhes (420–780 ka) are rare (only 30 in the published literature). The Second Hawaiian Scientific Drilling Project (HSDP2) drill hole recovered submarine volcanics spanning the approximate time period of 420–550 ka. These are of particular interest for absolute paleointensity studies owing to the abundance of fresh submarine basaltic glass, which can preserve an excellent record of ancient geomagnetic field intensity. We present here new results of Thellier-Thellier paleointensity experiments that nearly double the number of reliable paleointensity data available for the early Brunhes. We also show that the magnetizations of the associated submarine basalts are dominated by viscous magnetizations and therefore do not reflect the true ancient geomagnetic field intensity at the time of extrusion. The viscous contamination is particularly severe because of a combination of low blocking temperatures in the basalts and relatively high temperatures in the deeper parts of the drill core. Our new data, when placed on the approximate timescale available for HSDP and HSDP2, are at odds with other contemporaneous paleointensity data. The discrepancy can be reconciled by adjusting the HSDP timescales to be younger by about 35 kyr.
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 Information about past variations in the strength of the geomagnetic field can be derived from records of two fundamentally different types: absolute paleointensity estimates based on thermally blocked remanences and relative paleointensity estimates based on normalized records of sediments [see, e.g., Tauxe, 1993] or marine magnetic anomalies [Gee et al., 1996]. Despite major effort, the average geomagnetic field intensity during the early Brunhes Chron remains poorly constrained. The Hawaiian Scientific Drilling Project (HSDP) penetrated several kilometers of submarine extrusives and hyaloclastites which are thought to be of early Brunhes age. Of particular interest is the recovery of abundant fresh submarine basaltic glass, a material that often retains an excellent record of paleofield strength [see, e.g., Pick and Tauxe, 1993]. In this paper, we review the available data for the Brunhes Chron and present the results of paleointensity experiments on submarine basaltic glass samples obtained from the HSDP2 drill core.
2. Published Brunhes Paleointensity
 A compilation of absolute paleointensity data is described by Perrin et al.  and is available on line: http://www.ngdc.noaa.gov/seg/potfld/paleo.html. We have updated the so-called PINT00 database with absolute paleointensities based on the Thellier-Thellier technique [Thellier and Thellier, 1959] that have been published since 1996. A list of all data from the Brunhes Chron (<780 kyr) and the references are listed in the auxiliary material (appendix 1 and appendix 2). We have checked the data in the data base against the original publication and corrected information as appropriate. The ages used here correspond to ages implied or stated in the original references. In many cases, these are nominal ages based on interpolation or correlation. In such cases, we have assigned uncertainty to zero. We have (re)calculated the virtual axial dipole moment (VADM) based on the latitudes and paleofield information included in the data table.
 Databases are intended to be inclusive so each investigator must decide on a set of criteria that will exclude data likely to be erroneous. In Figure 1a we plot the VADMs from the data in auxiliary material (appendix 1) that were based on at least three specimens per cooling unit with a standard deviation of less than 15% of the mean value. (Please note that we use units of ZAm2 where one Zetta (Z) is 1021. These are therefore a factor of ten larger than the usual units of 1022Am2). Of the 295 paleointensity estimates published for the Brunhes that meet these minimal reliability criteria, only 30 are older than 420 kyr. In Figure 1b we plot the record of relative paleointensity obtained by Guyodo and Valet  by stacking many individual sedimentary paleointensity records placed on the astronomical timescale (SINT800). These data, while likely to represent variations in paleofield strength, are inherently relative. They were calibrated to approximate VADM by comparison with absolute data over the recent past.
 We re-normalized the stack derived from deep-towed magnetic anomaly profiles of Gee et al.  to have the same mean as the calibrated SINT800 record and plot them in Figure 1b for comparison. The correspondence between the independent two relative paleointensity records is remarkably good. We have numbered several prominant paleointensity lows (PLs) and lettered several paleointensity highs (PHs) for easy reference. PLs are often referred to by the names of geomagnetic excursions defined by directional aberrations observed elsewhere [see, e.g., Valet and Meynadier, 1993]. For example, PL1 is thought to be correlative to the Laschamp Excursion. Given the difficulty of the absolute age assignments in many of the excursional records [see, e.g., Kent et al., 2002], it is premature to make a definitive correlation of each PL with an associated excursion.
 The absolute paleointensity data are less continuous than the relative paleointensity data and are likely to have larger uncertainties in age assignment. It appears that in time periods of dense smapling, however, the absolute paleointensity data record some of the prominant features in the relative paleointensity records (e.g., PHa and PL1). Nonetheless a direct comparison between the absolute and relative paleointensity records for the entire Brunhes must await more and better dated absolute paleointensity data.
 There are very few absolute paleointensity data points prior to 420 ka, hence more data from the early Brunhes are especially needed. The second Hawaii Scientific Drilling Project has recently completed drilling a hole (HSDP2) at 19°42′N and 155°3′W. HSDP2 recovered several thousand meters of submarine basaltic lavas and hyaloclastites [DePaolo et al., 2001] including significant amounts of fresh submarine basaltic glass that range in age from about 420 to 550 kyr [DePaolo and Stolper, 1996; W. Sharp, personal communication, 2002].
 Submarine basaltic glass is well suited for paleointensity measurements [see, e.g., Selkin and Tauxe, 2000] for a recent compilation). The magnetic remanence is carried by single-domain (titano)magnetite often with excellent rock magnetic behavior during the paleointensity experiment. The NRM was acquired during initial quenching of the glass, hence the cooling rate can be approximated to within an order of magnitude in the laboratory. Finally, magnetite encased in glass can avoid pervasive alteration for very long periods of time [see, e.g., Zhou et al., 1997, 1999a, 1999b; Xu et al., 1997a, 1997b]. In this study we seized the opportunity to augment the early Brunhes geomagnetic field intensity variations by exploiting the unaltered submarine basaltic glasses recovered from HSDP2.
3. Thellier-Thellier Experiment
 The most common method for obtaining estimates of paleofield strength from thermally blocked remanences is the so-called “Thellier-Thellier technique” [Thellier and Thellier, 1959]. Thellier-Thellier experiments rely on several implicit assumptions including:
The thermal remanence (TRM) acquired is linearly related to the field in which the rock cools.
The pTRM acquired during laboratory heating is equivalent to the pTRM acquired during initial cooling.
A partial thermal remanence (pTRM) acquired by cooling in an applied field from a given temperature is entirely removed by reheating to the same temperature in a null field.
 There is a great variety in approaches to paleointensity determination. This derives to some extent from the fact that the original Thellier and Thellier  article contained a description of several different experimental protocols. The protocol used in this study is based on the “Coe variant” described by Coe . We heat a specimen to a temperature Ti and cool it in a null magnetic field (the “first zero field step”). After measuring the natural magnetic remanence (NRM) the specimen is re-heated to the same temperature and cooled in a controlled magnetic field (the “first in-field step”). After the first zero field step we can repeat an in-field step at a lower temperature to determine if the capacity to acquire pTRM has changed (the “pTRM check”). In addition to the standard pTRM check, we can conduct a second test. After the first in-field step, the specimen is heated again to Ti and cooled in zero magnetic field. This measurement checks whether all the pTRM acquired in the intervening in-field step was removed by re-heating to the same temperature and cooling in zero field. This procedure is briefly described by Dunlop and Özdemir  and in more detail by Riisager and Riisager . Because a difference in blocking and unblocking temperature (the latter being higher) is characteristic of multi-domain pTRM, we call this the “MD check”.
 Ideally, the assumptions inherent in the Thellier-Thellier technique would be verified by the experimental protocol. The assumption that the natural remanence is a linear function of the ancient field strength is almost certainly true for thermal remanence magnetizations in fields less than about 100 μT. The validity of this assumption in a particular paleomagnetic specimen would be compromised if the magnetization was not in fact an original TRM, but some other magnetization acquired later in the history of the sample (for example a viscous remanence, VRM, or chemical remanence, CRM). To verify the origin of remanence, some investigators demand that the portion of the NRM used in the Thellier-Thellier paleofield calculation trend to the origin. This “origin test” is necessary but not sufficient to establish the applicability of assumption 1. We calculate the scatter of the NRM measurements about the best fit line (MAD of Kirschvink ) and the deviation from the origin of this direction (α of Selkin and Tauxe ).
 The assumption that a given laboratory pTRM accurately reproduces the original pTRM acquired between two temperatures can be erroneous for several reasons. First, if the cooling rate in the laboratory is different from the original cooling rate this assumption is demonstrably false [e.g., Aitken et al., 1981; Dodson and McClelland-Brown, 1980; Halgedahl et al., 1980] Furthermore, if the rock undergoes chemical alteration during laboratory heating the laboratory pTRM will also differ from the original pTRM. Compensating for differences in cooling rate is relatively straight forward if the original cooling rate is well known and the samples behave according to single domain theory (see, e.g., Selkin and Tauxe  for a simple graphical correction method). Recognizing changes in mineralogy can be accomplished using the pTRM checks, monitoring susceptibility, etc. We use the difference ratio or DRAT parameter which is the ratio of the difference between repeat in field steps normalized by the length of selected line used in the paleofield calculation [see Selkin and Tauxe, 2000]. The pTRM checks are quite powerful, but also must be considered necessary but not sufficient tests for the validity of assumption 2 (see below).
 The assumption that the blocking and unblocking temperatures for a given pTRM are equivalent may not always be true for multi-domain (MD) remanences [e.g., Levi, 1977; Bol'shakov and Shcherbakova, 1979; Dunlop and Xu, 1994]. Because the blocking temperature Tb of MD remanence is lower than the unblocking temperature Tub, the plots of remanence remaining versus pTRM gained (“Arai diagrams” [Nagata et al., 1963]) are not linear, but are concave upward. Removal of a viscous remanence also leads to non-linear Arai diagrams. For these reasons we use two criteria. The β parameter (β = σ/∣b∣ where σ is the standard error of the slope and ∣b∣ is its absolute value) ensures linearity of the NRM/pTRM data. The MD check tests the equivalence of the blocking and unblocking temperatures in the specimen.
 Our experimental protocol will detect most errors caused by secondary remanences, MD remanences and alteration of the magnetic mineralogy during the experiment. There are several pathological cases, however, that will generate erroneous results that are not explicitly anticipated by the protocol. Let us consider three scenarios of alteration and the consequences to the Thellier-Thellier experiment. The first scenario is that a magnetic mineral produced has a discrete blocking temperature Tb > Ta (sketched in Figure 2a). The second is that a magnetic mineral is produced with a distribution of blocking temperatures all above Ta (sketched in Figure 2b). The third scenario is the more usual one in which a magnetic mineral is produced with a broad distribution of blocking temperatures that includes Ta and the lower temperature of the pTRM check Tp (sketched in Figure 2c). In all of these scenarios we assume that Tb = Tub rendering the MD test blind to the alteration.
 A flow chart of an experiment in which the first scenario occurs is sketched in Figure 3. Several double heating steps occur, including one at Tp at which we plan to do a pTRM check eventually. At temperature Ta a secondary magnetic mineral is produced with a blocking temperature Tb > Ta. No erroneous pTRM will be acquired until the temperature Ta is reached for the first in-field step. The first zero field step is always done at a higher temperature than the previous in-field step, hence the NRM will never be affected. The erroneous pTRM will appear in the Arai plot as a discrete offset at Ta, followed by “normal” NRM/pTRM behavior as shown in Figure 2d. Such a plot would fail the β criterion if the temperature steps included Ta. Otherwise, the estimated paleofield would in fact be correct.
 In the second scenario depicted in Figure 2b, there are a range of blocking temperatures in the new magnetic phase, all above Ta. In such a case, there would be a continuous increase in the erroneous pTRM acquired, yet both pTRM (triangles) and MD (squares) checks would pass. Nonetheless, these data would fail the β test for linearity.
 The third, less worrisome scenario, is depicted in Figure 2c whereby the blocking temperature spectrum of the new mineral is quite broad and includes Tp. In this case the pTRM checks would fail as well as the test for linearity.
 In summary, while not infallible, the basic Coe  experimental protocol, with the addition of the MAD, origin and MD checks that have been added over the years, is quite robust. Most sources of error can be detected. Other sources of error, for example, large and variable local magnetic anomalies near the specimen as it cools [see Carlut and Kent, 2002], can be detected by also demanding that replicate measurements be made on several specimens from the same cooling unit.
 In the following section, we describe our experimental efforts on samples of submarine basaltic glass recovered from the Hawaiian Scientific Drilling Project core, HSDP2. We start with a description of the lithologic log, including downhole temperature and an age model. We will then discuss the effect of elevated temperature on the paleomagnetic behavior of the specimens. Finally, we will present results from our Thellier-Thellier experiments and discuss the implications of our data on the age model and for the paleointensity behavior of the early Brunhes.
4. Paleomagnetic Data From HSDP2
Figure 4 shows the lithologic log of HSDP2, sampling levels for the present study, temperature versus depth and an age model. A list of the sample names used here and the Box/Run/Unit information for each sample is in appendix 3 of the auxiliary material. The lithologic log and temperature profile are redrawn from DePaolo et al.  and the age model is from DePaolo and Stolper . This age model is consistent with age information from HSDP2 itself (W. Sharp, personal communication, 2002). The dashed line is the best-fitting quadratic relating age and depth by the equation Age (ka) = 367 + 0.0746D − 0.00000462D2 where D is depth in meters below sea level (mbsl). We sampled submarine basaltic glass within the lower part of the section (see Figure 4). Sample depths have been converted to nominal ages using the age model in Figure 4 of DePaolo and Stolper  for consistency with other research efforts on HSDP2. According to this age model, our samples range from approximately 420 ka to 550 ka.
4.1. Rock Magnetic Considerations
4.1.1. Viscous Remanence
 Because the samples from HSDP2 have been at elevated temperature for an extended period of time (see Figure 4), it is necessary to consider what viscous remanence (VRM) may have been acquired and what laboratory blocking temperature would be expected for such a component. At the bottom of the hole, the samples are some 550 ka with an in situ temperature of ∼40°C. According to single domain theory developed by Pullaiah et al. , a VRM acquired over a half a million years at 40°C would not be removed in the laboratory until approximately 220°C. Therefore, the maximum blocking temperature of the NRM component used to estimate paleofield strength must be higher than that. Above about 1500 mbsl, the temperatures in the drill hole have been lower, so the blocking temperature required to remove a VRM would be approximately 125°C.
4.1.2. Magnetic Mineralogy and Grain Size: Transects From Pillow Margin Toward Interior
 Another rock magnetic concern is the variability in grain size and magnetic mineralogy as a function of distance from the glassy margin. Carlut and Kent  have examined this issue by performing Thellier-Thellier experiments on transects of samples from the glassy margins of submarine basaltic pillows inward toward the increasingly coarse grained basaltic interiors. They demonstrated a profound dependence of the estimated paleointensity on the position of the sample with respect to the glassy margin. As this was done on very recent MORB pillow fragments, the actual paleofield was known. The glassy sub-samples reproduced this field very well, while data from the pillow interiors overestimated the paleofield. To understand the origin of this overestimate, they performed a test whereby the pTRM acquired at a given temperature step was demagnetized in several successive zero field steps with increasing temperature. They demonstrated that pTRMs in their pillow interiors failed to be demagnetized at the temperatures in which the magnetization was acquired. This is a characteristic of MD remanences as discussed previously. The cause of the overestimate was therefore attributed to both differences in cooling rate and the failure of pTRM independence in the coarser grained material (an MD effect).
 The methodology Carlut and Kent  provides a useful means for interpreting paleointensity data from basalts. In the case of the HSDP2 material, we have performed a similar experiment on a pillow margin. We chose a fragment near the bottom of HSDP2 as a “worst case” scenario. We sliced the pillow fragment shown in Figure 5 into 5 mm sub-samples from the glass rim toward the center into several transects. One transect was subjected to hysteresis analysis; another was subjected to Thellier-Thellier paleointensity experiments.
 We consider first the results of the Thellier-Thellier experiments. Specimens from the pillow margin transect were fixed into non-magnetic glass tubes. The sample tubes were then subjected to the Thellier-Thellier experiment as described earlier. Our results are in some respects similar to those of Carlut and Kent  but differ in significant ways owing to the elevated temperatures in the Hawaiian crust. Thellier-Thellier experiments on specimens a–d from the HSDP2 pillow margin transect specimens are shown in Figure 6. The results of specimens “e–j” are virtually identical to specimen “d”. Experimental results were evaluated using the criteria of Selkin and Tauxe  and assigned a grade of “A” through “F” depending on the number of criteria failed. Grade “A” specimens met all of the criteria (DRAT ≤ 10%, β ≤ 0.1, α ≤ 15°, MAD ≤ 15°, and the Coe  “quality index” Q > 1). All of the interpretations shown in Figure 6 are grade “A”. However, specimens “c–e” have no blocking temperatures above about 200°C and the remanence removed during the Thellier-Thellier experiment is therefore entirely viscous in origin.
4.1.3. Hysteresis Behavior
 In order to investigate the cause(s) of the differences in the Thellier-Thellier experiment between the glassy margin and the pillow interior, we performed hysteresis measurements on specimens from the parallel transect. Representative hysteresis behavior is plotted in Figure 7. Specimen “b” (Figure 7a) demonstrates a slightly “wasp-waisted” effect characteristic of many glass samples. This is thought to be the result of a strong superparamagnetic (SP) contribution combined with an essentially single domain population dominated by uniaxial anisotropy [Pick and Tauxe 1993, 1994; Tauxe et al., 1996]. The hysteresis behavior of the specimen just inside the basalt glass margin (specimen “c” in Figure 7b) exhibits the enhanced saturation remanence to saturation magnetization rato (here called squareness) and high coercive fields noted by Gee and Kent . Moving away from the glassy margin, the hysteresis loops of the basalt chips have the lower squareness and coercivity characteristic of so-called “pseudo-single domain” type behavior [e.g., Day et al., 1977].
 To summarize the hysteresis behavior of the specimens from the pillow margin transect, we plot the squareness versus coercive field data in Figure 8a for the specimens in the transect. These data trace out a large loop with the largest squareness-coercive field behavior belonging to specimen “c”, just inside the glassy margin. In order to help understand these data, we employ the squareness-coercive field diagram of Tauxe et al.  in Figure 8b. This diagram shows the interpretations of squareness-coercive field space based on micromagnetic modelling of magnetite assemblages of grains with various sizes and shapes. The heavy solid line with an arrow pointing to the right (labelled “uniaxial single domain”) is the trend expected for uniaxial particles with increasing aspect ratios [Stoner and Wohlfarth, 1948] starting with an aspect ratio of approximately 1.5:1 and increasing to the right (to a maximum of about 300 mT at infinite aspect ratio). The point labelled “cubic single domain” is based on the theoretical predictions of Joffe and Heuberger . The solid arrow originating in the uniaxial field and trending toward the origin (labelled “uniaxial + SP”) is based on the numerical simulations of Tauxe et al. . The dotted curve originating in the cubic single domain field and trending toward the origin (labelled “cubic + SP”) is based on the numerical simulations of Walker et al. . The trends labelled “PSD” are based on simulations of random assemblages of magnetite particles of cubes and 2:1 parallelepipeds of sizes ranging from 20 nm up to 115 nm [Tauxe et al., 2002]. PSD behavior in hysteresis loops has been tied to grains whose remanent magnetization is in the “vortex” state and were found to be in the size range of approximately 100 to 140 nm. The dash-dot line is predicted for single domain particles that are slightly elongate (aspect ratios of less than ∼1.5:1). These had elevated squareness values (above the 0.5 expected for strictly uniaxial behavior) and coercivities higher than those allowed by strictly cubic (about 10 mT) behavior. Tauxe et al.  also found that more complex shapes than cubes and parallelepipeds (for example three intersecting rods) could explain the elevated squareness values with exceptionally high coercive fields (indicated by the gold cross labelled “intersecting rods” in Figure 8b).
 The glassy specimens “a” and “b” plot directly on top of the uniaxial plus superparamagnetic (SP) trend, consistent with the slightly wasp-waisted hysteresis loops (Figure 7a). Specimens “c–j” fall on a trajectory starting with quite high squareness (above the 0.5 expected for uniaxial behavior) and high coercivities (much higher than those allowed for cubic anisotropy) and trending in a curve through the field labelled “PSD” toward the expected MD point (essentially, the origin). Thus the trend from specimens “c” to “j” is consistent with increasing grain sizes of populations of either slightly elongate particles or more complex shapes (e.g., skeletal titanomagnetites). A thin section of the pillow margin revealed no visible grains under an optical microscope, so the magnetic crystals in all of these specimens are probably sub-micron in size.
 Blocking temperature spectra from the zero field steps in the Thellier-Thellier experiments for the specimens from the pillow margin transect are plotted in Figure 9a. The blocking temperatures change dramatically from a maximum of over 400°C in the glassy part (a,b) to less than 200° in the pillow interior (d–j). This behavior is most likely the result of a change in titanium substitution from quite low in the glassy portion to TM60 in the pillow interior [see, e.g., Zhou et al., 1997]. Because of the relatively high ambient temperature in the lower part of the drill core (see Figure 4) and the relatively low blocking temperatures in the basalts, the ancient geomagnetic field estimates Banc derived from the pillow margin transect are a strong function of distance from the pillow margin. We plot the estimated “Banc” for the pillow transect in Figure 9b and show the strong over-estimate of the paleofield from the pillow interiors.
 As already mentioned, paleofield estimates can be in error for a variety of reasons, including differences in cooling rate, multi-domain behavior, alteration during the experiment, and overprinting by viscous (or chemical) remanences. The pillow interior specimens (“c–j”) studied here are from within a few centimeters of the pillow margin, so differences in cooling rate cannot account for the factor of two change in paleofield estimate. The specimens do not exhibit any indication for MD behavior, either in the MD-checks (shown as squares in Figure 6) or in the hysteresis loops (see Figure 7), so multi-domain behavior is unlikely to be responsible for the behavior shown in Figure 9b. Instead, because of the very low blocking temperatures of the pillow interiors and the high ambient temperatures of the drill core at that depth, we suspect that the pillow interiors in our transect are dominated by viscous remanence and have no relationship to the geomagnetic field at the time of formation. This is a different mechanism than that inferred for the zero age pillow studied by Carlut and Kent  who found a significant MD signature in their results.
 In the following section we will present results from the rest of the samples of submarine basaltic glasses from HSDP2. These were obtained from pillow rinds and from hyaloclastites from the sampling levels shown in Figure 4.
 Three to five specimens from each sampling horizon from HSDP2 (see Figure 4) were prepared for a Thellier-Thellier experiment. Small glassy chips were broken from the sample, soaked in dilute HCl and examined under the microscope for evidence of alteration. Unaltered specimens with magnetic moments of at least 0.1 nAm2 were placed in non-magnetic glass tubes. These then were subjected to the Thellier-Thellier experiment as described before with the exception that not all the experiments on glassy specimens included the MD-checks. Examples of representative grade “A” results are shown in Figure 10. We list all of the results from this study in appendix 4 of the auxiliary material.
 Many specimens yielded Grade “A” results with maximum blocking temperatures of 225°C or less. We have argued that these paleointensity estimates, while appearing to be of “high quality”, are actually dominated by viscous contamination. In order to underscore the effect these low temperature estimates would have on estimates of the average geomagnetic field, we have calculated paleointensity estimates for the components isolated between 100 and 225°C as well. The grade “A” estimates calculated in this way have the cumulative distribution function shown as the thin line in Figure 11. The cumulative distribution function of the grade “A” data having a maximum blocking temperature of at least 300°C is shown as the heavy line. These two data sets are significantly different, based on a Kolmogorov-Smirnov test, at well above the 99.9% level of confidence. Therefore, in addition to the usual criteria, we have added the criterion that the maximum blocking temperature of acceptable results had to be at least 300°C. Finally, we have calculated average paleointensity data for sampling horizons that had at least three specimens meeting our minimum criteria. These are listed in appendix 5 in the auxiliary material. Those samples having standard deviations of less than or equal to 15% are plotted as triangles in Figure 12.
 The new data shown in Figure 12 nearly double the absolute paleointensity data available for the early Brunhes that meet minimum selection criteria. The magnetic anomaly inversion of Gee et al.  is shown as the thin line. It appears that the new data are quite a bit higher than other data from the same age, in particular, both the data from HSDP2 (triangles) and HSDP (dots within circles [Laj et al., 1999]) appear to be offset from the relative paleointensity stack. In Figure 12b we replot the HSDP and HSDP2 data using an age model that is offset to younger ages by 35 kyr. This offset brings the data into better agreement with the relative paleointensity pattern, yet is consistent with the age constraints available for HSDP2 (W. Sharp, personal communication, 2002). Moreover, the calibration of the relative paleointensity data to approximate VADM appears to be consistent with our data. The data from the basalts from the subaerial section (HSDP [Laj et al., 1999]) are much higher than the calibrated anomaly inversion stack.
Juarez and Tauxe  compiled paleointensity data spanning the last 5 million years and concluded that the average dipole moment was approximately 55 ZAm2. They excluded the period of time 0–0.3 Ma from the average because they suspected that the geomagnetic field was unusually strong during that interval and the overwhelming majority of data points come from that period; hence the average value would be heavily biassed toward a potentially unusual field state. We see from Figure 12a that, while there is no abrupt jump from low to high values of the field during the Brunhes, the latter half does appear to be stronger on average than the early half. To quantify this, we divide the data into “early Brunhes” (0.4–0.78 Ma) and “late Brunhes” (0–0.4 Ma). Cumulative distribution functions for both data sets are shown in Figure 13 illustrating that the two are indeed different at above the 99.9% level of confidence. The late Brunhes average is virtually identical to the present field (∼80 ZAm2) and the early Brunhes (65 ± 21 ZAm2) is compatible with the five million year average of Juarez and Tauxe .
 The data presented in this paper support the following conclusions:
Submarine basaltic glass appears to give high quality estimates of the ancient geomagnetic field strength in the Hawaiian submarine section of the HSDP2 drill core.
Submarine basalts from the hole appear to give estimates that are too high and are contaminated by a strong viscous remanence acquired by low blocking temperature magnetic phases subjected to elevated temperatures over a significant period of time. The submarine basalts from HSDP2 cannot be used for paleointensity studies.
The average paleointensity for Hawaii over the time interval 420 to 550 ka is in broad agreement with the calibrated relative paleointensity records, but agreement improves significantly by adjusting the age model to be younger by 35 kyr.
In order to estimate the average geomagnetic field intensity, one must avoid sampling bias of anomalous states of the geomagnetic field. The preponderance of data from the latter half of the Brunhes is a likely source of bias in average paleofield estimates.
 We are indebted to Carlo Laj for original inspiration for this work and help in sampling. We also would like to thank Joe Kirschvink for help at CalTech, Jeff Gee, Julie Bowles, Peter Selkin and Agnes Genevey for helpful discussions, and Steve Didonna and Winter Miller for making most of the measurements. Julie Carlut and two anonymous reviewers made numerous constructive suggestions. This work was partially supported by an NSF grant to LT.