Isotope Ratios as Tracers of Sources (and mixing of materials from different sources) in the Solid Earth, Hydrosphere, Biosphere

Transcription

1 Isotope Ratios as Tracers of Sources (and mixing of materials from different sources) in the Solid Earth, Hydrosphere, Biosphere Reading: White, Chapter 7, section titled, Geochemistry of Two-Component Mixtures NOTE for 2014 class: Grey-highlighted areas will not be covered this year. We can sometimes learn where the Sr, Nd, Pb, etc. in a rock, water, or biological sample came from based on isotopic signatures. We have already seen that different reservoirs on earth have different radiogenic isotope contents. For example, old crustal rocks with much Rb have large 87 Sr/ 86 Sr ratios (e.g., >0.712), whereas magmas recently ascended from the mantle have low 87 Sr/ 86 Sr ratios (e.g., <0.707). In some cases, there are two potential sources, and we can determine how much each source contributed to the sample we have. Examples: 1) Groundwater sampled at point S may have originated in 2 potential recharge areas, A and B. If these recharge areas impart different isotope ratios to the water, we may be able to determine the source. 2) A bird s feather may contain isotope ratios inherited from a distant feeding ground and thus the isotopes may be used to track migration. 3) A magma may be a mixture of a) material derived directly from the mantle and b) crustal contamination. We expect the crustal component to contain Sr that is more radiogenic than the mantle component and this we can determine how much of it is in the mixture. Guide Questions: 1. How can we predict whether a given rock will have a highly radiogenic isotope value or a less radiogenic one? 2. How can we use isotopic data to show that the various rocks or waters of a system are formed by mixing of two materials? 3. What is the exact meaning of residence time as applied to a well-mixed reservoir? 4. How has the 87 Sr/ 86 Sr ratio of the oceans evolved over time and how can this be used? 5. Picture a reservoir with inputs and outputs that is NOT at steady state. What equations gives us a model for an isotope ratio of the reservoir over time after some change in the system? Using Radiogenic Isotopes to Find Where Material Came From Different materials on earth have different radiogenic isotope ratios: 87 Sr/ 86 Sr, 206 Pb/ 204 Pb and other Pb ratios, 143 Nd/ 144 Nd, 187 Os/ 188 Os, etc. Examples: Mantle has high 143 Nd/ 144 Nd versus crust Older crust has greater 87 Sr/ 86 Sr and 187 Os/ 188 Os vs. younger crust Carbonate rocks generally have little ingrowth of 87 Sr because they are Rb-poor Granites may be U-rich and thus develop large Pb isotope ratios over time

2 Important general principle for radiogenic isotope tracing: The parent/daughter element ratio and the age are the key variables. Materials that have high Rb/Sr, Sm/Nd, U/Pb etc. ratios AND have aged long enough to build up radiogenic daughter products have high isotope ratios. Material with low Rb/Sr, Sm/Nd, U/Pb etc. ratios OR materials with high ratios but young ages have lower isotope ratios. Precision of the isotope ratio measurements is often very good, so we can measure even small contrasts. Example: East African Rift human artifacts and animals. In side the east African rift, volcanic rocks formed from magmas recently formed in the mantle have low 87 Sr/ 86 Sr ratios (0.703 to 0.706). Very old rocks with relatively high Rb/Sr ratios just outside the rift have much greater 87 Sr/ 86 Sr ratios (0.720 up to as high as 1.500). These ratios can be measured with precision of , so the variation is HUGE compared to the precision. Anthropologists use Sr isotope ratios to determine where materials came from. For example, Prof. Ambrose here at Illinois has traced movement ostrich egg shell beads, possibly used as money long ago, across Africa. Example: Pre-1492 humans in the Midwest. We have done work aimed at tracing human migration and food trading in the Midwest in pre-1492 times (e.g., the Cahokians). This more difficult, because the glaciers have mixed up various rocks types and smeared them around, leaving a landscape with somewhat unpredictable Sr isotope values. Nonetheless, there are difference between sites and these may be used for tracing purposes. Example: The famous ice man who lived 3300 B.C. in northern Italy. He was found frozen in the alps. His origins were traced using Sr isotopes. Bone Sr rapidly turns over and tells where he lived before his death, whereas tooth enamel reflects where he lived during late childhood. Scientists have narrowed these locations down to a few valleys. Example: Bird Migrations. People have done work with various isotope ratios (Sr, C, N, etc.) to trace bird migrations. Example: Pb contamination. Pb is a serious environmental issue- Pb-rich paint chips, soil, and sometimes drinking water are problems. Pb ores have very low U/Pb ratios, so they preserve the original Pb isotope ratios at the time of ore formation. Different ore bodies have different ages and different Pb isotope signatures. Pb in gasoline was taken from certain mines, but the mines used changed over time. One can distinguish gasoline Pb from industrial Pb, usually. Because the Pb from gasoline burning and Pb smelting was carried widely in the atmosphere, one may be able to obtain age dates for materials like peat that accumulate atmospheric Pb. Example: Forensic Geochemistry. Fake wines have been identified using various isotope ratios to see if the values match the known values for strictly controlled wine regions. Criminals have been traced back to murder scenes by analyzing the dirt in their shoes.

3 Recognizing and modeling mixing of two materials with isotope data Mixing occurs when waters meet in aquifers or surface water bodies, when magmas mix, or when magmas acquire material my melting host rock. Here are mathematical tools to analyze data that result from mixing. Binary Mixing How can we analyze data from a system that is a mixture of sources? 1) Binary Mixing: Take two vats, mix them completely, look at the mixture. A + B = M The following equations are derived from simple mass balance statements and algebra. See the appendix at the end of these notes for derivations. The concentration of the mixture is given by: = f + (1-f) where f is the volume fraction of A in the mixture (f = / ) C Pure B Pure A The equation relating concentrations to isotope ratios is: f 1 R R A B + R C R A B B R This is an approximation; to be exact, the concentrations would be of the denominator isotope only (e.g., 86 Sr). But this approximation is so nearly perfect we use it in almost all cases. The form of this equation is a hyperbola: C 1 a + b

4 or it is linear if you plot 1/C on the x axis. So If you think your data array might reflect mixing of two waters (or magmas, sediments, etc.), you can test this hypothesis by plotting the results on this type of diagram: R 1/C Also: Plots of one isotope ratio versus another also produce hyperbolic curves for mixtures. 143 Nd/ 144 Nd 187 Sr/ 86 Sr Note that the curvature depends on the relative concentrations of Sr and Nd in the two end members: See White s notes for equations. Use of these mixing models: If data fit a mixing model, then binary mixing is a plausible explanation for the observed variation. HOWEVER, THIS DOES NOT prove that other explanations (such as mixing of 3 or 4 components) is not possible. Ternary mixing models: with three components mixing together, the procedure is the same. Plot isotope ratios versus 1/C. Binary mixtures of two out of the three components make straight lines. Three such lines exist and they form a triangle. Temporal variation of well-mixed reservoirs with varying inputs Example: 87 Sr/ 86 Sr in the Oceans:

5 See variation of 87 Sr/ 86 Sr over time: White s notes, end of lecture Large variations over time to Some of the changes are fairly rapid 3. Long-term trends, too (e.g., steady increase since 160 Ma) What controls the 87 Sr/ 86 Sr as a function of time? Sr/ 86 Sr of various inputs a) Continental weathering- generally moderate to high o Carbonate rocks to o Silicate Rocks! old granites, shales, metamorphic rocks have high ratios (e.g., >0.712)! younger ones not so large (e.g., to 0.712) b) Mid-ocean ridge hydrothermal systems add Sr to water- low 87 Sr/ 86 Sr (~0.704) c) Dissolution of carbonate buried in ocean sediments may have occurred during some time periods (?) 2. Sizes of these inputs change over time 3. Memory of past 87 Sr/ 86 Sr in the oceans - residence time of Sr is 2-3 Ma 4. Ignore outputs: 87 Sr/ 86 Sr of output = ocean 87 Sr/ 86 Sr; no direct effect on ocean 87 Sr/ 86 Sr (Note this only works when the oceans are well mixed so that the outputs are isotopically identical to the ocean as a whole.) Why is the 87 Sr/ 86 Sr record in the oceans of interest? 1) Weathering changes. We think that continental collisions increase weathering of silicate material, and this extra weathering affects the chemistry of the ocean in ways that decreases CO 2 in the atmosphere and thus leads to cooler climate conditions. 2) Age dating of marine carbonate rocks. 87 Sr/ 86 Sr ratios measured in carbonate rocks can be matched to the record to give precise age dates. The dates are often non-unique (e.g., occurs many times in the last 500 million years), but usually we start with a rough idea of age from the rock layer sequences. Mathematical tools for time series data from systems with constant inputs that may vary over time What if we have a system where small amounts of liquid are added in continuously and mixed, instead of an instantaneous mixing of two vats??? (This is more like a natural situation) Develop differential equations for incremental mixing of inputs into a system. Again: Let s start with 87 Sr/ 86 Sr in the oceans: What determines the 87 Sr/ 86 Sr in the oceans at any given time? 1) The ratios of the various inputs NOW. 2) Their sizes NOW. 3) The 87 Sr/ 86 Sr already in the system from past additions. Model the ocean as a well-mixed reservoir.

6 Well-mixed = completely homogenized each instant. Then we need to understand how mixing in of an input affects the reservoir. We want to know either: 1) The steady-state value of the ocean OR, if the ocean is not in a steady state 2) The ratio as a function of time R(t) Here s a model of the oceans. 2 inputs of Sr, one output. Now, we must formulate an equation that expresses how the system responds to inputs and outputs: The question: How does the isotope ratio of a reservoir of substance A change as an increment of substance B is mixed in? Let c = concentration in A, c in = concentration in B, R = isotope ratio in A, R in = isotope ratio in B. V is the volume of A, is the incremental volume of B added. I use volume so that this is easy to visualize. Here s the differential equation for changes in an isotope ratio with addition of volume increments of B. See appendix for the derivation. In a strict sense, all the concentrations and masses would be of the denominator isotope (e.g., 86 Sr) only, but using total elemental concentrations is a very close approximation. dt = c in dt Vc [ R in R] = added mass 2 mass 2 ( isot. ratio constrast) which can also be expressed dt = dm in dt m [ R R in ] but time is not essential here, added mass is, so = dm in m [ R R in ]

7 dm we can add more terms for multiple inputs = i [ m R i R] i Note: This only applies if outputs have the same R as the reservoir. If isotopic fractionation causes the outputs to have different R than the reservoir, this analysis does not apply. However, for all radiogenic isotopes, it works. For cases where outputs do not have the same isotope ratios as the reservoir (e.g., oxygen isotopes or other light stable isotopes), the output must be included as well. Putting in outputs is not difficult, they can be simply included as negative inputs, with the same mathematics. For the outputs, dm in <0. These equations all work with delta notation too! dδ dt = i dm i dt m [ δ i δ ] What types of systems does this apply to? Examples: 1) The ocean, or lakes. 2) Groundwater or pore fluids that are receiving and losing solute as they react with the host rock 3) Magma contaminated by country rock over some time period. Example #1: What is the steady state 87 Sr/ 86 Sr ratio of a reservoir? We start with the governing equation: dm in dt = 0 = dt [ m R R in ] /dt = 0 because steady state means no change with time. On the left side, the only term that can be zero is the R in -R term. So the system reaches steady state when the reservoir R equals the input (or the weighted average of all inputs if there are multiple inputs). Example #2: Start with a crude model of the ocean: Sr budget 1) Input from weathering 2) Output via carbonates What are the 87 Sr/ 86 Sr ratios of these? Draw the vat model. What do you think will happen to the vat as a function of time, starting with some arbitrary R, if we abruptly change the input to a higher 87 Sr/ 86 Sr value? For simplicity, assume the Sr concentration in the ocean is constant over time and ocean volume is also constant. dt = c in dt Vc [ R in R]OR 1 [ R in R] dt = J inc in, J is input rate, volume per unit time. Vc Solution: Intuitively, you can guess it is a function that asymptotically approaches R Noting that the change in R is closely related to R itself, you might guess the solution is a negative exponential that asymptotically approaches R.

8 R = ( R 0 R in )e ( t/τ ) + R in, τ = Vc 2 NOTE: τ = total mass/mass flux in (= residence time!!!!!) J in c in Definition of Residence time: The time spent in the system by an average atom of the element you are tracking. Calculation of residence time: = total mass in the system divided by the rate of mass input. This assumes the concentrations of the input and the reservoir are constants. In reality, these concentrations would probably change if something caused the isotope ratio of the input to change. How can we model more complex cases? The governing equation can be solved for constantly variable inputs and outputs. We can use numerical integration for the differential equation OR we can use fourier transforms, maybe other techniques as well. Example #3: How does groundwater evolve as it reacts with its host rock and flows along? What do we expect to see in terms of a spatial pattern? Imagine a packet of water moving along. Solute is added to it by dissolution of rock. This can also be modeled as a mixing process. dt = d m dt 1 R R Vc 2 [ ], dt = J R R c 2 [ ] where J is the reaction flux per liter water Same result as before- exponential decay.disequilibrium decreases by a factor of e over some distance- what is that distance? Time constant is c2/j. Distance would then be u*c2/j. What if input is not uniform? Use numerical solution. Appendix 1: Derivation of binary mixing equations. First: Mixing gives linear relationship between volume of each liquid and concentration: m A + m B = m M (1) (m is mass) + = (2) (C is concentration, V is volume) / + / = (3) Define f = / (4) = f + (1-f) (5) This gives us the concentration of the mixture.

9 Then: Isotope Ratios DO NOT mix linearly Write 2 statements of eqn 5: 1 for each isotope:, 1 =, 1 f +, 1 (1-f) (6), 2 =, 2 f +, 2 (1-f) (7) =,1,2 =,1 +,1,2 +,2 (8) =,1 +,1,2 +,2 (9) =,1 +,1,2 (but because R = C 1 /C 2 ) (10) = R A,2,2,2 (11),2 = R A,2,2 (12) (very good approximation), or m M m A m B (13) now get rid of V s, so we can plot R vs. C:, f (1 f ) but, using equation (5) above, f = (1 ) Only variable on right side is. Divide both sides by, collect terms C R A A + 1 R B R C B B R R B A + R C R A B B R B This gives some terms that are constant and some that are 1/ terms. So the form of the equation is: 1 a + b

10 Appendix 2: Derivation of governing equation for the changes of isotope ratio in a reservoir over time: dc dt = 1 dt V (c in c), (makes sense intuitively) define R = c 1 c 2, = 1 dc 1 c 1 c 2 ( ) 2 dc 2 c 2 dc = 1 V (c in c) (1), (using the product rule) = 1 dc 1 R dc 2 c 2 dv, subst. for c derivatives using (1) in = 1 1 ( c 2 V c c 1,in 1) R 1 V c c ( 2,in 2 ), but Rc 2= c 1, also pull out the V term = 1 Vc c 1,in c 1 2 ( ) Rc 2,in + c 1, simplify and pull out c 2, = c 2,in c 1,in R and Vc 2 c 2,in = c 2,in R R Vc 2 [ ] and to a very close approximation c in Vc [ R R]