Interpreting SrÅNd isotopic data from magmatic and metamorphic ...

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Vojtěch Janoušek: Interpreting Sr–Nd isotopic data: numerical recipes Exercise 4-1 Calculate initial ε Nd values for the granitoid samples from the Central Bohemian Pluton (see exercises 1–1 and 2–1) assuming that their age is 350 Ma. Plot the initial 87 Sr/ 86 Sr ratios and ε Nd values into a diagram similar to Fig. 4–2 and briefly discuss the possible sources of individual granitoid bodies, provided no assimilation, magma mixing or later disturbance of the Sr–Nd isotopic system has taken place. [cbp.xls] Hints: ! Epsilon values are calculated using eq. [4.1], ! Note that the intersection of both axes will be in ε Nd = 0 and the 87 Sr/ 86 Sr composition of UR 350 Ma ago (see Page 2 for constants), ! Having trouble with interpretation See Figure 4–2. 5. ND MODEL AGES Single-stage ages The single-stage Nd model ages provide an estimate of the time that a rock unit has had a different Sm/Nd ratio from that of the Earth’s mantle (represented by a model reservoir, typically either DM or CHUR: Fig. 5–1). The equation I = ( 143 Nd/ 144 Nd) SA Sample DM Depleted mantle I 0 DM I 0 SA I = I [5.1] T SA T DM SAMPLE is solved for T (the so-called model age): I T = I T DM SA I 0 SA − R 0 SA λT 0 0 λT ( e −1) = I − R ( e −1) DM DM [5.2] DM Partial melting T 0 T Nd DM 0 0 1 ⎛ I ⎞ SA − I DM = ln ⎜ + 1 ⎟ 0 0 λ ⎝ RSA − RDM ⎠ [5.3] Time Figure 5-1: Theoretical concept of a single-stage Nd model age. Model age is the time in the past, when mantle evolution line (here is assumed depleted mantle) intersects with that for the given sample. – 8 –
Vojtěch Janoušek: Interpreting Sr–Nd isotopic data: numerical recipes Two-stage ages The Nd model ages can be also calculated using the two-stage model of Liew and Hofmann (1988) which accounts for the fact that a great deal of rocks contain a significant proportion of a crustally-derived material. In the following formulae, the indexes DM, CC, SA refer to depleted mantle, average crustal reservoir and the sample, respectively. T = two-stage Nd model age, t = crystallization age of the sample, 0 refers to the present day (Fig. 5–2). As: I 0 CC − R 0 CC I = I [5.4] T CC T DM λT 0 0 λT ( e −1) = I − R ( e −1) DM DM 0 0 1 ⎛ I ⎞ CC − I DM T = ln ⎜ + 1 ⎟ 0 0 λ ⎝ RCC − RDM ⎠ For the crustal and sample evolution lines: t I = I and because: I 0 CC CC I t SA = I = I 0 SA 0 CC 0 SA t CC [5.5] [5.6] − R − R 0 CC 0 SA I = I − λt ( e −1) λt ( e −1) t SA λt 0 0 ( e − )( R − R ) 1 SA CC From [5.6] and [5.10]) we finally get : 0 λt 0 0 0 Nd 1 ⎛ I − ( −1)( − ) − ( ) ⎟ ⎞ SA e RSA RCC I DM T = ln ⎜ DM + 1 0 0 λ ⎝ RCC − RDM ⎠ Where: I t = I t SA CC I T = I T DM CC I = ( 143 Nd/ 144 Nd) ⎛143 Nd⎞ 0 ⎜ ⎟ ⎝144 Nd ⎠DM = 0.513151 ⎝ ⎜⎛ 147 Sm 144 ⎠ ⎟⎞ 0 Nd DM = 0.219 ⎝ ⎜⎛ 147 Sm 144 ⎠ ⎟⎞ 0 Nd CC = 0.12 DM CC SA DM Depleted mantle Average crust Sample CC SAMPLE T t 0 Time Partial melting Figure 5-2: Theoretical concept of a two-stage Nd model age. An intermediate reservoir with Sm/Nd ratio of typical crustal rocks (CC) is assumed. I 0 DM I 0 CC I 0 SA [5.7] [5.8] [5.9] [5.10] [5.11] Exercise 5-1 Calculate single-stage T Nd and two-stage TNd model ages for the granitoid samples CHUR DM from the Central Bohemian Pluton, in the second case assuming the intrusion age of 350 Ma. Hints: [cbp.xls] ! Necessary parameters of both models are given on Page 2, ! Single-stage CHUR Nd model ages are obtained using eq. [5.3], ! Two-stage DM Nd model ages are calculated by eq. [5.11]. – 9 –
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