Transcript Sediment characterization - University of Washington

OCEAN/ESS 410
17. Radiometric dating and
applications to sediment
transport
William Wilcock
Lecture/Lab Learning Goals
• Understand the basic equations of radioactive decay
• Understand how Potassium-Argon dating is used to
estimate the age of lavas
• Understand how lead-210 dating of sediments works
– Concept of supported and unsupported lead-210 in
sediments
– Concept of activity
– Steps to estimate sedimentation rates from a vertical profile
of lead-210 activity
• Application of lead-210 dating to determining
sediment accumulation rates on the continental shelf
and the interpretation of these rates - LAB
Radioactive decay - Basic equation
The number or atoms of an unstable isotope elements
decreases with time
dN
µN
dt
dN
= lN
dt
NT
-ò
N0
N0
N - Number of atoms of an
unstable isotope
 - radioactive decay constant is
the fraction of the atoms that
decay in unit time (e.g., yr-1)
T
dN
dN
= ò
= ò l dt
N N N
0
T
Radioactive decay - Basic equation
NT
-ò
N0
N0
T
dN
dN
= ò
= ò l dt
N N N
0
T
éëln N ùû
N0
NT
T
N0
= ln
= éël t ùû0 = lT
NT
Setting NT = ½N0, the time for half the radioactive atoms
to decay is give by
T1 =
2
ln 2
l
T1/2 - half life is the time for half
the atoms to decay
Potassium-Argon (K-Ar) Dating
• The isotope 40K is one of 3 isotopes of Potassium (39K,
40K and 41K) and is about 0.01% of the natural potassium
found in rocks
• 40K is radioactively unstable and decays with a half life
T½ = 1.25 x 109 years (λ = 1.76 x 10-17 s-1) to a mixture of
40-Calcium (89.1%) and 40-Argon (10.9%).
• Because Argon is a gas it escapes from molten lavas.
Minerals containing potassium that solidify from the lava
will initially contain no argon.
• Radioactive decay of 40K within creates 40Ar which is
trapped in the mineral grains.
• If the ratio of 40Ar/40K can be measured in a rock
sample via mass spectrometry the age of lava can be
calculated.
K-Ar Dating Formula
N0
ln
= lT
NT
If Kf is the amount of 40-Potassium left in the rock and Arf
the amount of 40-Ar created in the mineral then
NT = K f
N 0 = K f + Arf / 0.109
æ K f + Arf / 0.109 ö
T = ln ç
÷
l è
Kf
ø
1
Note that the factor
1 / 0.109 accounts
for the fact that
only 10.9% of the
40K that decays
created 40Ar (the
rest creates 40Ca)
K-Ar dating assumptions
• Ar concentrations are zero when the lava solidifies (in
seafloor basalts which cool quickly Argon can be trapped
in the glassy rinds of pillow basalts violating this
assumption)
• No Ar is lost from the lava after formation (this
assumption can be violated if the rock heats up during a
complex geological history)
• The sample has not been contaminated by Argon from
the atmosphere (samples must be handled carefully).
Lead-210 dating
210Pb
or Pb-210 is an isotope of lead that forms as part of
a decay sequence of Uranium-238
238U 234U
230
226
… Th  Ra
Half Life 4.5 Byr
Rocks
Half life 1600 yrs,
eroded to
sediments
222Rn…210Pb…206Pb
Gas, half life
3.8 days
Half life,
22.3 years
Stable
Pb-210 in sediments
Supported 210Pb
Sediments contain a background level of 210Pb that is
“supported” by the decay of 226Ra (radium is an alkali metal)
which is eroded from rocks and incorporated into sediments.
As fast as this background 210Pb is lost by radioactive decay,
new 210Pb is created by the decay of 226Ra.
Excess or Unsupported 210Pb
Young sediments also include an excess of “unsupported”
210Pb. Decaying 238U in continental rocks generates 222Rn
(radon is a gas) some of which escapes into the atmosphere.
This 222Rn decays to 210Pb which is efficiently washed out of
the atmosphere and incorporated into new sediments. This
unsupported 210Pb is not replaced as it decays because the
radon that produced it is in the atmosphere.
Activity - Definition
In order understand how 210Pb is used to determine
sedimentation rates we need to the activity of a sediment
A
A = cl N
Activity is the number of disintegrations in
unit time per unit mass (units are decays
per unit time per unit mass. For 210Pb the
usual units are dpm/g = decays per minute
per gram )
C - detection coefficient, a value between 0
and 1 which reflects the fraction of the
disintegrations are detected (electrically or
photographically)
Activity - Equations
We know previously defined the equation for the rate of
radioactive decays as
dN
= lN
dt
Multiplying both sides by the constant cλ gives an
equivalent equation in activity
dA
= lA
dt
Pb-210 activity in sediments
AB
Pb-210 activity
Surface mixed layer - bioturbation
Measured Pb-210 activity
Region of radioactive
decay.
Depth, Z
(or age)
Background Pb-210 levels from
decay of Radon in sediments
(“supported” Pb-210)
Excess or unsupported
Pb-210 activity
(measured minus
background)
Excess Pb-210 concentrations
t1
t2
Age of
sediments, t
A1
Excess Pb-210 activity
Work with data in this region
A2
For a constant
sedimentation rate, S
(cm/yr), we can
replace the depth
axis with a time axis
z = St
z
t=
S
Solving the equation - 1
dA
= lA
dt
A2
t2
dA
òA - A = òt l dt
1
The equation relating activity to the
radioactive decay constant
Integrating this with the limits of
integration set by two points
1
A2
t2
éë - ln Aùû = l éët ùû
A1
t1
A1
- ln A2 + ln A1 = ln
= l t2 - t1
A2
(
)
A relationship between age and activity
Solving the equation - 2
A1
ln
= l t2 - t1
A2
z2 - z1
t2 - t1 =
S
A1 l z2 - z1
ln
=
A2
S
(
(
)
(
(
S=
)
)
Substitute in the relationship between
age and depth
)
l ( z2 - z1 )
A1
ln
A2
An expression for
the sedimentation
rate
Pb-210 sedimentation rates
Plot depth against natural logarithm of Pb-210 activity
ln(A)
Ignore data in mixed layer
Depth, z
Slope = -
Ignore data with background levels
S
l
Summary - How to get a sedimentation rate
1.
2.
3.
4.
5.
6.
7.
8.
Identify the background (“supported”) activity AB - the value
of A at larger depths where it is not changing with depth.
Subtract the background activity from the observed activities
at shallower depths
Take the natural logarithm to get ln(A)=ln(Aobserved-AB)
Plot depth z against ln(A).
Ignore in the points in the surface mixed region where ln(A)
does not change with depth.
Ignore points in the background region at depth
(Aobserved ≈ AB).
Measure the slope in the middle region. It will be negative.
Multiply the minus the slope by the radioactive decay
constant ( = 0.0311 yr-1) to get the sedimentation rate.
Limitations
•Assumption of uniform sedimentation
rates. Cannot use this technique
where sedimentation rate varies with
time (e.g., turbidites).
•Assumption of uniform initial and
background Pb-210 concentrations
(reasonable if composition is constant).
Upcoming lab
In the lab following this lecture you are
going to calculate a sedimentation rate for
muds on the continental shelf using
radioactive isotope Lead-210 and you are
going to interpret a data set of many such
measurements obtained off the coast of
Washington.