4.1. Assessing the Magnitude of Chronological Improvement
 Ideally, a sediment core would possess either easily datable foram tests or enough fresh organic material to separate specific compounds at an adequate yield for radiocarbon dating. Near KC-49, at the low-latitude reaches of the Antarctic Peninsula, the latter seemed a viable option in terms of the amount of organic material. Dates from specific compounds as well as compound classes proved to be highly ambiguous indicating significant reworking of the sediment and mixing of organic material of different ages [Ohkouchi et al., 2000]. In the sub-ice shelf sediments of KC-5, fresh sterols were not extractable from any horizon below the surface sediments due to both low productivity below the ice shelf and dilution of organic material by diagenetically altered material [Roe et al., 2006]. In both cases, reworked organic material has likely attained a higher degree of diagenetic stability, yielding leverage by which fresh organic material could be isolated and dated.
 The aim of this experiment was to release fresher material first. Neither combustion nor pyrolysis is perfect in this regard. Pyrolysis was chosen as preferable because it is less purely a chemical distinction. Fresh organic debris was expected to yield more volatile products than diagenetically altered organic material. The results in Figures 4–6 illustrate success in separating, to a first order, components of different ages.
 The results in Figures 4–6 also indicate the significant improvement in chronology achieved by this method. Despite the improvement, the results show that the actual ages of these sediment horizons, while better constrained, remain unknown (KC-49) or unresolved (KC-5). Pyrolysis of NaHCO3 illustrates an ideal situation where the pyrolysis products of carbon sources (one source from dehydration of NaHCO3 at ∼180°C, and another from decomposition of Na2CO3 at ∼850°C) with different thermal stabilities are well separated and easily differentiable (Figure 3). It is unrealistic to expect such an ideal resolution of carbon components when dealing with multiple sources of organic material. Instead, an optimistic expectation for our approach would be the resolution of a low-temperature age plateau. The significant differences between low-temperature ages in KC-49 244–245 (i.e., the lack of a low-temperature age plateau) indicate that even the lowest-temperature fraction contains at least some older, allochthonous material, and the proportion of this material increases from a value greater than zero in the lowest-temperature fraction. Greater mixing of pre-aged carbon into the first temperature interval would be expected of less finely resolved KC-5. Thus the youngest age from this approach represents a maximum age constraint for the autochthonous material in this particular core horizon, and it is likely that the actual age of autochthonous material may be younger. In order to apply this method to compare sedimentary records to high-resolution paleoclimate archives, a means to estimate the maximum likelihood ages of the autochthonous carbon fraction must be established.
 A two-point mixing model with both an autochthonous and an allochthonous end-member would be desirable; however, neither core lends enough clues for success with such a simplified approach. Figures 4b and 5 illustrate that the method confidently determines the isotope ratios of the allochthonous end-member in KC-49 244–245 cm (i.e., there is a high-temperature age plateau), with a δ13C ratio of −26.8 ± 0.6‰ and a fM of 0.079 ± 0.012 calculated from the averages and standard deviations of the final four temperature intervals. In the absence of either a complementary low-temperature plateau or knowledge of the mixture proportions, however, a mixing model cannot be constructed. If ages were known with better confidence either up-core or down core as in KC-5, an extrapolation could be made to 244–245 cm and used to estimate the absolute age of the young AIOM and, subsequently, the proportion of older material present. Although sediment deposited in diatomaceous horizons above 244–245 cm in the core may yield higher proportions of autochthonous organic material, the sediment core KC-49 contains no horizons with datable material other than AIOM, rendering this approach to establishing a mixing model unwieldy. The situation in KC-5 is not much improved despite knowledge of foraminifer ages. Here, the subsampling of pyrolysis products was not of high enough resolution to estimate either a pre-aged or autochthonous end-member. Furthermore, in presence of differential deposition [Mollenhauer et al., 2005] and bioturbation relative to particle size [Bard, 2001], the question of the true age of AIOM would remain in spite of a foramifer age.
4.2. An Objective Estimate of the Autochthonous Component
 Without the necessary information for construction of a simple mixing model, an independent method by which ages, isotope ratios, and relative contributions of AIOM components can be conceived using only the structure of the thermograph in Figure 5. Even in the absence of discrete peaks such as those provided by NaHCO3 (Figure 3), the KC-49 thermograph demonstrates the presence of multiple components simply in terms of variations in the radiocarbon and stable isotopic compositions of individual temperature fractions. In absence of the low-temperature plateau, two inflection points on the rising limb of the thermograph can be conceived to signify changes in proportions of young, intermediate, and old sources of carbon. An estimation of the amounts of these components can be used to approach the maximum likelihood age and the relative proportion of the young AIOM component with an assumption about the pyrolysis kinetics of the individual AIOM components.
 In similar stable isotopic measurements of pyrolysis products, a Gaussian distribution of pyrolysis activation energies constituted a workable first-order approximation where the pyrolysis kinetics of the chemical classes present within the substrate were not precisely known [Cramer, 2004]. The thermograph of KC-49 244–245 (Figure 5) can be decomposed into three Gaussian curves using a nonlinear regression procedure (Figure 7). An attempt to decompose the thermograph into four Gaussian curves resulted in an increase in iterations of the model from 18 to 111, which supports the significance of the inflection points suggested by the structure of the thermograph and illustrates the futility of trying to discern minor components (components that are small enough to not cause thermograph inflection points) despite the likelihood of their presence. Although several local minimizations exist, the two most plausible solution sets are shown in Table 2.
Figure 7. Gaussian decomposition of KC-49 thermograph. A nonlinear least squares technique was used to decompose the thermograph (heavy red line in both panels) into reaction components, assuming Gaussian distribution of pyrolysis activation energies. To apply this technique, a first guess must be made (cyan line, top panel) to initiate an iterative process to minimize the model residuals. The result (black line, top panel) displays good fit and represents the absolute minimum residual of several solutions. The individual components of this model are shown with the calculated isotope ratios of each one (bottom panel).
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Table 2. Gaussian Parameters of Plausible Solution Sets to the Nonlinear Regression of the Thermograph Dataa
|Component 1|| || |
| Height, μmol/mol||606||308|
| Center, °C||324||286|
| Width, °C||82||57|
|Component 2|| || |
| Height, μmol/mol||569||2296|
| Center, °C||409||473|
| Width, °C||47||120|
|Component 3|| || |
| Height, μmol/mol||2814||805|
| Center, °C||505||532|
| Width, °C||95||64|
 With three significant components of unknown age and δ13C, the nine measurements of these quantities can be used to describe an overdetermined system of linear equations:
where superscripts M and C refer to measurements and significant components, respectively. In this case, i is the number of measurements and j is the number of components. Vectors [A] can be either fractions modern of radiocarbon (uncorrected for δ13C) or stable isotope compositions, with the component fraction matrix [f] determined by the nonlinear regression of Gaussian solutions to the thermograph with the minimum residual summed between temperature divisions used during the experiment. To account for all CO2 evolved during each ith temperature interval of each pyrolysis, we use the equality,
whereby each ith row of the component fraction matrix [f] must sum to 1.
 Radiocarbon solutions of equation (1) for the proportions in Table 3 must be constrained to prevent negative fractions modern. Further, fractions modern uncorrected for stable isotope composition are used in vector [AM], but fractions modern are re-corrected to specific component δ13C values from vector [AC] after equation (1) has been solved for both isotopes measured. No constraints were applied to the stable isotope solutions to the system. For both the radiocarbon and δ13C systems, a constrained nonlinear routine was employed, with initial guesses similar to the simple algebraic solutions. Equation (1) was solved for [f] constructed from two plausible Gaussian regression solution sets (Table 2) despite one set producing a significantly lower residual. The solution of equation (1) using Gaussian regression 2 (Table 2) includes a component with fM < 0, rendering it unstable and confirming the lesser root mean square of the residuals of solution 1 as an indicator of the most realistic solution.
Table 3. Component Proportions of Gaussian Decomposition, Solution 1a
 At an age of 10,520 years, the youngest component in the solution to equation (1) is indistinguishable from the maximum age constraint provided by direct measurement of the low-temperature pyrolysis age. All of the stable isotope values in the δ13C solution set are within published measurements on compound class carbon isotopic values from nearby Antarctic seas [Ohkouchi and Eglinton, 2006]. The model is consistent, but how accurate is this objective estimate of the actual age and proportion of autochthonous material at this core depth in KC-49? The answer lies in the assumptions about reaction kinetics for the pyrolysis of sedimentary organic material from the east coast of the Antarctica Peninsula. It is prudent, therefore, to constrain the autochthonous age with an independent approach for comparison in absence of knowledge of the exact reaction kinetics.
 Comparing end-member characteristics with inverse cumulative yield normally results in a linear relationship if the model is of simple mixing. Assuming the amount of autochthonous carbon is negligible in the temperature intervals after the first, this relationship (Figure 8) can provide further constraint on the age of the autochthonous component. The slope of this linear relationship (b) is related to the autochthonous age (expressed here as Δ14C) by
where subscripts s and t refer to autochthonous and allochthonous components, respectively, and N is the number of micromoles of carbon in the lowest-temperature interval, assuming that only negligible amounts of the autochthonous component were present in temperature intervals 2–9 and that the final four intervals are representative of the pre-aged end-member. In other words, the age difference between the autochthonous component and the oldest allochthonous carbon is related to the slope of the linear relationship in Figure 8, in proportion to the amount of autochthonous material in the lowest-temperature interval. Given information about the age of the allochthonous component and the proportion of autochthonous component in the lowest-temperature interval, an additional age constraint on the autochthonous component can be derived. Again, Figure 5 illustrates that a fair estimate of the allochthonous fraction is provided by the final four temperature intervals (fM = 0.079 ± 0.012). Further, the Gaussian decomposition approach allows a viable estimate of the fraction of autochthonous material in the first temperature fraction (0.96, Table 3); however, it does not provide a straightforward uncertainty (the largest uncertainty is likely the model selection, in any case). If the first temperature interval was entirely autochthonous carbon, these values would yield an age of 9650 ± 330 14C years. This age decreases to 9020 ± 300 14C years if it is assumed that the lowest-temperature interval consisted of only 90% autochthonous carbon. Such a range in compositions is not entirely out of the question, especially in the case where our assumption of Gaussian reaction kinetics is not accurate. The range in ages of these scenarios varies from the maximum likelihood Gaussian component age of 10,520 14C years by significantly more than the analytical uncertainties of radiocarbon dates in this age range. Still, the difference between these maximum likelihood ages is much less than the difference between bulk dates and the maximum age constraint directly measured from the low-temperature fraction.
Figure 8. Inverse cumulative yield plot of Δ14C measurements. A linear relationship between the inverse cumulative yield and the Δ14C values measured for each temperature interval provides an independent maximum age constraint for the autochthonous AIOM. Following equation (3), this approach constrains the age of the autochthonous component between 9320 and 9980 14C years, assuming that the first temperature interval is entirely autochthonous carbon. Assuming a proportion less than 1 decreases this constraint. This constraint is comparable to the maximum likelihood age of 10,520 14C years from the Gaussian decomposition method, especially in light of the large differences between these ages and the bulk AIOM age.
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 The KC-5 sub-ice shelf core provides an additional test of the pyrolysis method against known ages from foraminifer tests in each horizon. Figure 9 shows a Gaussian decomposition for both horizons using the same initial guess. The resulting four Gaussian distributions of major components does well to fit the thermograph of this core which is significantly more descriptive in both horizons than the analyzed horizon of KC-49. Gaussian components from each horizon in KC-5 are centered on the same temperatures indicating a geochemical significance of the components. Unfortunately, only 2–3 actual measurements were made on these horizons rendering the system of equations (equation (1)) underdetermined (i < j). This has two consequences. First, equation (1) cannot be explicitly solved for either isotope measurement. Second the inverse yield mixing model discussed above would be in violation of its assumptions of no mixing in the first temperature interval due to the higher temperature defining that interval. This is not to say that every one radiocarbon date must become nine to employ this method; rather enough measurements need to be made to equal or be greater than the amount of major components and at least one sample must come from at or near the cutoff temperature where pre-aged carbon begins to volatilize to alleviate the two consequences, respectively.
Figure 9. Gaussian decompositions of the KC-5 thermographs. Using the initial guess (blue curves, left side), a nonlinear Gaussian regression (black curves, left side) reproduces the raw data (thick red curves, both sides) very well. Major components brought forth by this analysis (individual Gaussians on right side) are centered at the same temperatures despite being from different core horizons. This implies a geochemical significance to the assumption of Gaussian reaction distributions. The thermographs from KC-5 are more descriptive than KC-49 244-245 cm, and they warrant 4 major components. Because only 2-3 measurements were made on each KC-5 horizon, these systems are underdetermined (after equation (1)) and the maximum likelihood ages of each of the individual components could not be calculated.
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4.3. Improving the Method
 Evaluation of these two mathematical approaches relative to each other aids in determining which one is more accurate; however, the question is immaterial in comparison to the difference between these age estimations and the bulk AIOM age. The Gaussian approach relays a maximum likelihood age estimation, which is as likely as the assumption of Gaussian pyrolysis activation energies. The linear model approach yields another maximum age constraint which is lower than this maximum likelihood age. The linear mixing model approach makes the assumption of two components in the mixture with negligible amounts of the low-temperature component in subsequent intervals. Conceptually this is favorable, and the Gaussian approach supports the second assumption with only 4% of the autochthonous component being distributed over the remaining 8 temperature intervals. However, the Gaussian approach strongly suggests a third major component which depicts reality more complex than the two component linear model. The difference between these two estimates, however insignificant relative to our assumptions and the bulk age, illustrates that more must be understood about the pyrolysis reactions, but it is not large enough to discredit the significant improvement in chronology offered by this analytical method. Furthermore, improvement of the method is tangible.
 Analytically, sampling resolution is ultimately limited by sample size. Our effort to choose a target sample size of 12 μmol C in the proof of concept experiment (KC-49) minimized counting error on AMS analysis of small samples while maximizing the amount of temperature bins analyzed. Sampling at shorter temperature intervals than this is certainly possible but involves a proportional decrease in precision. Short of establishing a maximum likelihood age from the nine radiocarbon measurements, the Gaussian decomposition of the thermograph provides a first-order estimate of the low-temperature cutoff point at which allochthonous C becomes mixed with the youngest major component (Figures 4 and 9). The amount of CO2 evolved from KC-49 before this temperature (250°C) is approximately 5 μmol (a small but measurable amount), whereas the next 60°C resulted in an additional 7 μmol C.
 Sampling at a higher resolution in the temperature domain without sacrificing AMS measurement precision of robust small samples (>10 μmol C) would be ideal. Simply increasing the amount of sediment loaded into the reactor does not seem a viable option. Larger sediment weights either carry enough thermal inertia even during exceedingly slow temperature ramps and/or are volumetrically large enough to be differentially heated by thermal heterogeneities within the furnace to blur the resolution between components. This was observed by the lack of return to baseline levels of CO2 evolution measured photometrically, even at temperatures as high as 1000°C for several tens of minutes, during pyrolysis of larger samples (∼0.5 g). Without increasing sample size, the mathematical approach laid out above illustrates that it is likely that we can analyze a nearly pristine sample of autochthonous C, with some sacrifice in precision on a 5 μmol sample. Attempts to observe any low-temperature plateau in multiple aliquots of the first 5 μmol for an unequivocal estimate of this age is unlikely due to the higher statistical counting error associated with sample sizes less than 5 μmol. Of course, our estimation of 275°C as the temperature at which mixing of pre-dated C begins to happen during pyrolysis would benefit greatly from a critical assessment of the assumption of Gaussian pyrolysis activation energies of the components.
4.4. Differential Deposition and Bioturbation
 Our data corroborate a number of recent reports [Mollenhauer and Eglinton, 2007; Mollenhauer et al., 2005, 2006; Villinski et al., 2008] demonstrating that sediment being immobilized at the bottom of the infaunal mixing zone at a given time can have disparate age distributions. Several studies have focused both on the roles of differential bioturbation [Bard, 2001] and differential deposition [Mollenhauer et al., 2003, 2005] in producing varying age distributions of different particle classes (e.g., forams versus alkenones) in the same sediment core horizon. In these reports, age differences within a sediment horizon vary up to 4500 years [Mollenhauer et al., 2005]. In addition, Mollenhauer and Eglinton  have presented a conceptual model with differential degradation of organic components as cause for large differences in Δ14C. Our resolution of different AIOM components for radiocarbon dating demonstrates age differences between components (∼10,000 years) that significantly exceed typical infaunal mixing increments. This poses the question of how the age distributions of differently aged, contemporaneously immobilized sediment components change under the actions of bioturbating infauna. Since the first published work concerning bioturbation [Darwin, 1881], the reigning assumption has been of uniform sediment age distributions at the time of deposition into the infaunal mixing horizon. Questions of individual sediment components with different ages have not normally been considered.
 Figure 10 shows a series of scenarios involving sediment deposited with different components having age distributions and component proportions similar to those in core KC-49, 244–245 cm (Figure 7 and Table 3). The homogenized increment of sediment represents an amount of time,
where m is the depth of the homogeneous, or bioturbated, layer and rd is the increment of sediment deposited in a unit time (rd = dL/dT based on the formulation of Berger and Heath , where dL is the thickness of sediment deposited per unit time, dT). Varying this ratio varies the magnitude of the bioturbation footprint on the original sediment age distributions (Figure 10, right side). At the large homogenized increment Tm = 2400 years (Figure 10), the age distribution of the bulk sediment begins to resemble a nonnormal unimodal distribution, but is far from the original component age distributions because considerable blending has occurred.
Figure 10. Bioturbation scenarios for coevally deposited sediment components having different age distributions. The left of the figure shows the age distribution of three different particle types (bottom) with notation based on Figure 1 of Berger and Heath  (top left). The right of the figure displays the age distribution of sediments taken from this layer after deposition from the homogeneous layer m into the historical layers, assuming constant deposition rate. The three probability density functions on the right (thick black lines represent sum of three components, shown in respective colors) correspond to bulk age distributions of different homogeneous increments as determined by the relation m/rd (see text).
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 The age distribution centroids of the falling sediments as well as their relative proportions in Figure 10 were identical to those in calculated from Gaussian decomposition of KC-47 244–245 cm (Figure 10 and Table 3). The widths of the component distributions were chosen on the basis of the assumption that allochthonous organic material (Figure 10, blue and green distributions) is associated with fine particles which have a relatively large lateral component to their settling velocities and are more likely to have been entrained and re-settled numerous times. The sharp distribution employed on the youngest sediment component (Figure 10, red distributions) corresponds to a narrower distribution of ages that would best describe a coarse sediment component (such as a foraminiferal test relative to a clay particle) having a similar settling history to organic material which could be considered autochthonous. The model shown Figure 10 does not incorporate differential sedimentation rates, differential bioturbation, nor environmental signals as in the work by Bard , but the establishment of first-order effects of bioturbation on different age distributions of sediments within a single historical layer provides a foundation on which to incorporate differential bioturbation approaches with the abundant evidence of differential deposition. With evidence of differentially aged sedimentary components increasing as dating techniques are refined, it is important to provide improved models dealing with signal deconvolution as paleoceanographers and paleoclimatogists aim to compare sedimentary records from different regions during important, dynamic epochs of Earth history.