Isochron calculations

Not giving the isotope ratios and errors actually used in age or isochron calculations (for example, data tables with only °Th/ Th, °Th/ " U, and 234y/238u j-atios but using Th/ Th- W Th and U/ Th- W Th isochrons) so that the reader cannot reproduce the calculations ... 

Vugrinovich RG (1981) A distribution-free alternative to least-squares regression and its application to Rb/Sr isochron calculations. J Math Geol 13 443-454... 

Conforma- Sym- Dihedral angles ) Sets of isochronous Calculated relative ... 

Thus isochron calculations require a suite of cogenedc samples, formed from the same parental material, and assume that there has been no exchange of parent-daughter isotopes other than through radioactive decay. An example of an isochron drawn for the Sm-Nd system from data in Table 6.2 is shown in Figure 6.2. 

Figure 1. Relative change of resislivily during isochronal annealing (AT=10K, At=10min) of completely recrystallized CujAu Tlie LRO-parameter as calculated by Rossiter formalism (A=0 5) is given on second axis ( ) increasing, (0) decreasing temperature (o) plateau values of small step annealing procedure.

Figure 7. Two examples of whole-rock isochrons, (a) Isochron obtained on a lava nnit of the Vico volcano (Central Italy) (Villemant and Flehoc 1989). (b) Isochron defined by glass and groundmass analyses of the Laacher See phonolite (Bonidon et al. 1994). In both examples, differentiation occurred shortly before eraption since calculated ages are indistinguishable from eraption ages.

Th- U dating of samples from subaerial volcanoes. When several volcanic rocks covering a significant period of the eruptive activity of a volcano can be dated (either by mineral isochrons or by other dating methods), the evolution through time of the ( °Th/ Th)o or ( °Th/ U)o initial ratios will be revealed (see section 3.4). If these ratios remain nearly constant, then they may be used to calculate the ages of other lavas... 

Weighted regression of U- " U- °Th- Th isotope data on three or more coeval samples provides robust estimates of the isotopic information required for age calculation. Ludwig (2003) details the use of maximum likelihood estimation of the regression parameters in either coupled XY-XZ isochrons or a single three dimensional XYZ isochron, where A, Y and Z correspond to either (1) U/ Th, °Th/ Th and... 

Figure 6. Rosholt (A) and Osmond (B) isochron diagrams for the same, synthetic AS data, shown as their lo error ellipses. Apparent age is 115.7 9.7 ka (MSWD = 1.7), calculated from either the slopes of the Rosholt isochrons or the intercepts of the Osmond isochrons.

ThAJ age is calculated. Mathematically, however, the choice of ratios is unimportant, provided that there is a common-denominator isotope to all three axes, and the errors and error correlations for the data points are correctly calculated. Note that, unlike paired x-y isochrons, not only can the errors of the detrital-corrected Th/ U and be... 

Kaufman A, Broecker W (1965) Comparison of " C and °Th ages for carbonate minerals from Lakes Lahontan and Boimeville. J Geophys Res 70 4039-4054 Ludwig KR, Titterington DM (1994) Calculation of Th/U Isochrons, ages, and errors Geochim Cosmochim Acta 58 5031-5042... 

The resulting corrected age of 59.8 3.8 ka can be calculated either from the two-point isochron defined by the data, or by application of Equations (16)-(18) of this chapter. 

Figure 2 was constructed by contouring of values calculated from the flow net of figure 1. Much more complex diagrams are possible provided sufficient information concerning the aquifer and fluid-flow conditions can be obtained. For simple boundary conditions and homogeneous aquifers, a direct analytical solution for isochronal surfaces is available [2]. 

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