Model age calculation

Figure 9. Lead isotope compositions for Early Bronze Age copper-based alloy artifacts from Troy II and artifacts from Kastri and Chalandriani on Cycladic island of Syros. The lead isotope fields indicated by broken lines are approximate. Model ages calculated in millions of years on the basis of Cummings and Richards (1975) model Jit are indicated for each grouping of lead isotope data. (Reproduced with permission from ref. 6. Copyright 1984 Basil Blackwell...

Cratonic mantle peridotites. Over 230 whole-rock cratonic xenoliths have now been analyzed for Re-Os isotope compositions. Given that many peridotite xenoliths have experienced relatively recent rhenium introduction, it is generally best to use rhenium-depletion model ages (Trd) that do not rely on the measured rhenium content of the rock for model age calculation. For cratonic peridotite xenoliths, the frequency distribution of rhenium-depletion ages shows a wide range, with a pronounced mode at 2.5-2.75 Gyr and some samples that have ages of >3.5 Gyr... 

Figure 44 Frequency distribution plots of Re-Os isotope Trd model ages (calculated assuming Re/Os = 0) for cratonic and off-craton peridotite xenoliths and massifs. The light-shaded field in the off-craton plot shows the range for kimberlite-derived peridotites from Namibia and East Griqualand. Data sources as in Figure 21 plus Pearson (unpublished).

Model age calculations are based, as their name implies, on a particular model of mantle isotopic evolution. They are a measure of the time when a particular sample became separated from its mantle source. They are most commonly used for the Nd-isotopic system, but increasingly are also being used in the Hf-(hafnium] isotope system. 

The time at which melt was extracted from a mantle peridotite. More precisely it is a model age calculated relative to the187Os/188 Os ratio of the BSE, assuming that the Re/Os ratio of the sample is zero. Note, however, that BSE reference... 

The foundations of modern geochronology were laid at the turn of the century in the work of Rutherford and Soddy (1903) on natural radioactivity. They showed that the process of radioactive decay is exponential and independent of chemical or physical conditions. Thus rates of radioactive decay may be used for measuring geological time. Isotopic systems used in age calculations are listed in Table 6.1 and Box 6.1. In this section we discuss two of the most common techniques used in geochronological calculations — isochron diagrams and model age calculations. This is followed by a discussion of the significance of the calculated ages. 

A model age is a measure of the length of time a sample has been separated from the mande from which it was originally derived. Model ages are most commonly quoted for the Sm- d system and are valuable because they can be calculated for an individual nick from a single pair of parent-daughter isotopic ratios. They must, however, be interpreted with care. The basis of all model age calculations is an assumption about the isotopic composition of the mande source region from which... 

TrCHUR model ages The CHUR model assumes that the Earth s primitive mantle had the same isotopic composition as the average chondritic meteorite at the formation of the Earth, which in this case is taken to be 4.6 Ga. For neodymium isotopes CHUR is synonymous with the composition of the bulk Earth. A model age calculated reladve to therefore is the time in the past at which the... 

It is important when calculating model ages to remember the assumptions upon which they are based, for these are not always fulfilled. Firstly, assumptions are made about the isotopic composition of the reservoir which is being sampled — either CHUR or depleted mantle. This aspect of model age calculations in itself raises three further problems. 

A second assumption used in model age calculations is that the Sm/Nd ratio of the sample has not been modified by fractionation after its separation from the mantle source. In the case of Nd isotopes this is a reasonable assumption to make. 

Interesting ice samples from Antarctica and Greenland have been and are being recovered. We studied samples of the Byrd core, which is a 12-cm-diameter core that extended to bedrock at 2100-m depth [1]. This core is presently kept at the Central Ice Core Storage Facility at S.U.N.Y. Buffalo (C. C. Langway, Jr., Curator). Its age-depth relationship has been calculated on the basis of rheological models [3,4,5], and comparisons of the 6180 variations of the core with those in the Camp Century (Greenland) core. The age calculated for the bottom ice is between 50 x 103 and 100 x 103 years. 

The rather constant fractionation of Sm/Nd ratios in upper continental cmstal rock reservoirs is the basis for the widely applied neodymium model age that is illustrated in Figure 3. The Sm-Nd systematics of chondritic meteorites serve as a reference for the parent/daughter ratio of the undifferentiated Earth (Jacobsen and Wasserburg, 1984), labeled as CHUR for chondritic uniform reservoir. The evolution of this undifferentiated Earth is the basis for calculation of CHUR model ages (McCulloch and Wasserburg, 1978), while the neodymium isotopic evolution of the depleted upper part of the mantle is a more valid reference for most cmstal materials, resulting in the DM model age (DePaolo, 1981). Neodymium isotopic compositions are usually given by s d, where the deviations of Nd/ Nd above or below... 

Figure 21 Stratigraphic age versus Nd- and Hf-crustal residence ages. Model ages were calculated using hnear E evolution from 0 to - -10 for Nd and 0 to - -16 for Hf, from 4.56 Gyr to present. The similarity of the model age systematics underscores the overall coherent behavior of the Sm-Nd and Lu-Hf isotopic systems in the sedimentary environment (after Vervoort et al., 1999).

Radiocarbon-model Ages of Gorleben Waters. Based on different assumptions, several sets of C-model ages (t in years before present (BP)) have been calculated from the content of carbonate components (DlC) and DOC (FA and HA) using the following expression ... 

Two sets of C-model ages are shown in Fig 4. The comparison between the calculated ages derived for different carbonate components in each set shows... 

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