1. Playing with radioactive decay equations- =
multiply each side by elt
substitute N=N0-D
substitute N0=N-D

2. U-series Disequilibrium 9/13/10
Lecture outline:
Secular equillibrium and
disequilibrium
2) U-Th systematics
3) U-excess
U-Th disequilbrium dating
232Th “initial” corrections
6) Th excess and sedimentation rates
Zircon
Geological archives dated by U-series disequilibrium:
speleothems (top) and fossil corals (bottom)

3. Secular equilibrium and disequilibrium
Secular equilibrium: all radioactive species in a decay chain have the same activity
Disequilibrium: system is perturbed (removal/enrichment of daughter/parent), and system
decays back to secular equilibrium
And if you know how (disequilibrium)initial, can calculate t since disequilibrium
For U-series decay chain,
what are some examples of
processes that cause
disequilibrium ?
There are two types of disequilibria:
1) Daughter excess (i.e. activity of daughter > activity of parent)
2) Daughter deficit (Ad < Ap)

4. Decay Chain Systematics:
Consider a 3-member decay chain:
Evolution of this system is governed by the coupled equations:
Note that at secular equil,
As you can see, the solution of these differential equations is quite complicated
(except for N1), so we will derive some equations from the disequilibria of 234U and 230Th.

5. 234U Excess NOTE: everything in this lecture will be activities (A),
unless otherwise noted
234U Excess
Given: (234U/238U)A of ocean = 1.15
Explanation: [you tell me]
The activity of (234U)excess decreases with time:
And excess 234U corresponds to the 234U not supported by 238U:
And dividing through by 238U activity, we obtain:
So if you measure 234U/238U,
and know (234U/238U)initial
can calculate age
Note that fixed analytical error (±0.5%)
yields larger and larger age error bars
as you approach secular equilibrium

6. 230Th Deficiency
Given: Many U-rich minerals (such as carbonate) precipitated with virtually no Th
Explanation: [you tell me]
So you grow in 230Th due to decay of 238U and excess 234U (in atom number):
And converting to activity, substituting formula for 234UEx, dividing by 238UA,
and simplifying, we obtain:
So if you measure (230Th/238U), and assume initial (234U/238U)A=1.15, then
you can calculate a sample’s age.
*Or, more realistically, you measure (230Th/238U) and 234U/238U,
and iteratively find an age that satisfies both the measurements
made today. You then are calculating also 234U/238U initial.
So when/where is the
assumption that
initial (234U/238U)A=1.15
not a good one?

7. 230Th-234U activity growth lines
Development of mass
spectrometry techniques
enable U-Th ages to be
measured to ±0.1-5 precisions
(Edwards et al., 1987)
secular
equilibrium
For most samples:
secular
equilibrium

8. Common U-Th series applications:
Cutler et al., 2003
1. Corals
- sea level from fossil terraces
- climate reconstruction
Edwards et al., 1987
2. Cave Stalagmites
- climate reconstruction

9. but what happens when good samples get “dirty”?
FACT: most geological samples contain some “initial” or “detrital” or “nonradiogenic” thorium
PROBLEM: mass specs cannot distinguish between “detrital” 230Th and radiogenic 230Th
SAVING GRACE: “detrital” thorium mostly 232Th (quasi-”stable” on U/Th disequilibrium timescale)
STRATEGY: measure 232Th in samples, correct for detrital 230Th using 230Th/232Th
of contaminant
BUT how do you estimate 230Th/232Th of contaminant?
given: average bulk Earth abundance (230Th/232Th)atom = 4.4e-6
at secular equilibrium (Kaufman, 1993)
complication: in most settings this will not apply…

10. STRATEGY #1: date samples of known age
upper error bar =
analytical error + correction
using (230Th/232Th)atom of 2.0e-5
lower error bar =
analytical error
- especially good for corals
because you can absolutely
date them by counting back
annual density bands
(Cobb et al., 2003a)
if you can identify a well-dated
event in your sample (volcanic
eruption from historic record?),
you may be able to do this for
older samples

11. STRATEGY #2: generate isochrons from samples
IDEA: sample multiple samples of the same age but different 232Th concentrations,
then you know that they all contain the same 230Thrad, and that 230Thnr
will scale with 232Th
“dirty” edges
“clean” middle
“dirty” edges

12. U/Th isochron plots most often used for
stalagmites (Partin et al., 2007)
in these plots,
slope α age
intercept = (230Th/232Th)act
of contaminant phase

13. Usually huge range of values uncovered…
translating into huge age errors for “dirty” samples
LESSON: keep it clean (if possible)

14. 230Th Excess and Deep-Sea sediments
Phenomenon: “excess” 230Th present in ocean sediments
Explanation?
The activity of (230Th)excess decreases with time:
If you assume that delivery of 230ThEx is constant through time, can calculate
age as a function of depth - or - sedimentation rate
We can define sedimentation rate as:
S=distance/time; so t=d/S
and
Depth in sediment core
ln(230Th)ex
Slope = -l/S
and

15. 230Th Excess and sedimentation rate changes

16. 230Th Excess - interpretation
But how can you have an increase of 230Thex with depth,
given constant 230Thex delivery?
Down-core measurements
in Norwegian core show
sedimentation rate changes
Increased scavenging
of 230Th during
interglacials in Norway,
or sediment focusing.
So 230Thex delivery is not
constant.
Changes in the rain-rate of
particles will lead to increases
and decreases in Th
scavenging.
What could change
scavenging rate?