Transcript lecture3-JMA

IAEA Regional Training Course on Sediment Core Dating
Techniques. RAF7/008 Project
J.M. Abril
Department of Applied Physics (I); University of Seville (Spain)
Lecture 3:Clasical dating models using 210Pb
210Pb
ex
fluxes
Radionuclide profiles and inventories
Radiometric dating models
CIC
CF-CSR,
CRS, CMZ-CSR , CD-CSR
IMZ (*)-CSR
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J.M. Abril, University of Seville
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J.M. Abril, University of Seville
137Cs
222Rn
aw
210Pb
z
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J.M. Abril, University of Seville
exhalation depends, among other factors, on 226Ra content in
soil, soil texture and structure, water content, and the forcing factors…
222
Rn Exhalation (Bq h -1 m-2)
222Rn
70
60
y = 9,3 1 x - 1,87
R2 = 0,689*
50
40
30
20
10
0
1
2
3
4
5
6
ETo (mm/d)
Abril et al. (JENVRAD, 2009)
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J.M. Abril, University of Seville
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J.M. Abril, University of Seville
Author: Israel López, Univ. Huelva (Spain)
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J.M. Abril, University of Seville
Some global patterns for 210Pbex fallout
•Predominant west-east movement of air masses  210Pbex fallout
is low in the western areas of the continents
•210Pbex fallout is higher in the North hemisphere
•210Pbex fallout is positively correlated with rainfall
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Figures from P.G. Appleby,
J.M. Abril, University of Seville
STUK-A145
Some reference values for annual fallout of excess 210Pb (Bq m-2 y-1)
Global scale , F ~ 23-367 Bq m-2 y-1
(Robbins, 1978)
Tropical Australia , F ~ 50 Bq m-2 y-1
(Brunskill and Pfitzner, 2000)
Inputs and Inventories (Bq m-2 ) in sediments
Catchment concentration factor
(normalization or focusing factor) : Z
Input (*) = ZF
Steady State Inventories Σ = ZF/λ
For 210Pb = ln2/T1/2 with T1/2 = 22.26 y.
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J.M. Abril, University of Seville
Radiometric dating with 210Pb: Basic aspects
210Pb
[Bq/kg]
total
210Pb
(unsupported)
226Ra
Supported fraction
Z [cm]
If we assume that there is no Rn exhalation from the sediment, then the total
activity of 210Pbtotal will be 210Pbtotal = 210Pbsupported + 210Pbunsupported
and 210Pbsupported = 226Ra activity
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J.M. Abril, University of Seville
Basic Concepts and definitions
aw
z
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J.M. Abril, University of Seville
Compaction and bulk density
As depth increases in the sediment core,
water pores are replaced by solids
V
mw
ms
z
Saturated porous media
m s

V
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Bulk density
J.M. Abril, University of Seville
Practical measurement of bulk densities
m
mw
w
ms
s
Drying and gravimetric method
V  Vw  Vs 
mw
w

ms
s
ms
s


 w ms
mw  s

1
w s
ms  w
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J.M. Abril, University of Seville
Practical measurement of bulk densities. Refinement
w
 mw
m
s,0
s,i
 ms,o
 ms,i
Drying and gravimetric method and loss by ignition
V  Vw  Vs ,o  Vs ,i 
mw
w

ms ,o
 s ,o
ms ,o  ms ,i

mw ms ,o ms ,i


w
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J.M. Abril, University of Seville
 s ,o
 s ,i

ms ,i
 s ,i
Bulk density versus depth profiles in sediment cores
0.7
 (g/cm3)
0.6
0.5
0.4
    1 e
0.3
0.2
 z
0.1
0
0
5
10
Depth [cm]
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J.M. Abril, University of Seville
15
20
Mass thickness, Δm , and mass depth:, m
m   z
z
Δz
z
m    dz '
0
[ g dry weight cm-2]
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J.M. Abril, University of Seville
(Mass) Sedimentation rate : w
dm
w
dt
≈
[ g dry weight cm-2 y-1]
A (Zi-1, t)
w (Zi-1, t)
Time versus m for constant w (*)
A (Zi, t)
Zi
dm
dt 
w
m
t
w
w (Zi+1,
t)
A (Zi+1, t)
Z
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J.M. Abril, University of Seville
Basic processes
≈
A (Zi-1, t)
w (Zi-1, t)
A (Zi, t)
Zi
w (Zi+1,
t)
A (Zi+1, t)
Z
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J.M. Abril, University of Seville
Fundamental equations
Mass conservation for a particle-associated radiotracer
Mass conservation for solids
BOUNDARY CONDITIONS
In situations where the tracer is partially carried by pore water or in presence
of selective and/or translocational bioturbation Eqs. has to be revisited
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J.M. Abril, University of Seville
Constant Flux and Constant Sedimentation rate (CF-CSR)
F
incoming flux
[Bq L-2 T-1]
w sedimentation rate
Activity concentration at interface
(non post-depositional mixing)  Constant A0
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J.M. Abril, University of Seville
A0 
F
w
The sediment-water interface displaces upwards
m=m(t)
Specific activity A0
z=z(t)
Layer at time t=0
A  Aoe
time = 0
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 t
(non post-depositional mixing)
J.M. Abril, University of Seville
time = t =m/w
Ln(A)
A  A0 e

m
w
t  m/ w
m
Curve-fitting model , free parameters : Ao , w
Validation:
Goldberg first validated the 210Pb dating method in varved sediments
Think about: Any implicit assumption concerning compaction?
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J.M. Abril, University of Seville
EXAMPLE from a case study
ZF = 172 Bq m-2 y-1
Schweiz. Z. Hydrol. 49/3, 1987
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J.M. Abril, University of Seville
w , (mass) sedimentation rate
Age : T(m) or T(z) , from m(z)/w
Dates or chronology:
Year of sampling – Age
Don't forget:
Estimated sedimentation rates, ages and dates have
to be provided with the corresponding uncertainties.
W = 0.115 ± 0.014 g cm-2 y-1
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J.M. Abril, University of Seville
Associated uncertainties in
210Pb
chronology
General formulae for error propagation
 f


 f     j 
i  xi

f ( x1 , x2 , x3 ,...)
x1 , 1 ; x2 ,  2 ; x3 ,  3 ...
2
mi  i zi
m   mi
i
m 
2

 i
i
m
ms ,o  ms ,i

mw ms ,o ms ,i


w
 s ,o
 s ,i
 i  mi  r2,   r2, z
 r ,
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


J.M. Abril, University of Seville
G.F.

Associated uncertainties in
210Pb
chronology
xm
f ( x)  ln A  a  bx
w
Lest squares fitting
w
a, b, R2 easily produced with
excel or other shifts
a2  1

 2  1
N 2 R

m
t
w
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b
 w  w  r2,   r2,b
 b   a 1/  x2 
a 

J.M. Abril, University of Seville
t  
2
r ,m

2
r ,w
t
Time resolution . Each sectioned layer in the core corresponds to a
time interval Δt = dm/w
Remember: As the analytical method is homogenizing the material
from each layer, it is not possible to solve other time marks within
such an interval (e.g. two 137-Cs peaks).
Note for advanced students:
•Apply lineal regression taking into account the associated uncertainties
in measurements
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J.M. Abril, University of Seville
CAUTION !
•Estimation of the supported
fraction is not a trivial task !
• 226Ra may be non uniform
in depth and being different
from the 210Pb baseline
•Settling particles can be
depleted in 226Ra in the
water column while enriched
in 210Pb
Data from Axelsson and El-Daoushy, 1989
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J.M. Abril, University of Seville
10000
Redó
Gossenkollesee
PROBLEMS:
1.- Many unsupported 210Pb profiles
do not follow a simple exponential
decay pattern
210Pb
(Bq/kg)
1000
 More complex models are
required
100
10
0
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0.2 0.4 0.6 0.8
Mass depth (g cm-2)
J.M. Abril, University of Seville
1
CIC model (Constant Initial Concentration)
F
incoming flux
w sedimentation rate
Activity concentration at interface
(no post-depositional mixing)
F
Ao 
w
CIC model assumes constant Ao; Thus, changes in F must be
compensated with changes in w.
Also , it assumes non post-depositional mixing
-Reasonable when F is associated with inputs of solids
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J.M. Abril, University of Seville
CIC model can equally be formulated in terms of actual depth (z) or
mass depth (m)
A
A0
A(m)
Chronology (one date per data point)
m
Alternative estimation of sedimentation rates
(one per data point) – only for cores with high
spatial resolution-Unknowns for CIC: Ao and wi (N+1; N= number of sections in the core)
- It is a “mapping” model
CAUTION !
•Estimation of the initial concentration, Ao, is not a trivial task !
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J.M. Abril, University of Seville
EXAMPLE from a case study
CF-CSR
CIC
ZF (recent) = 76 Bq m-2 y-1
Schweiz. Z. Hydrol. 49/3, 1987
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J.M. Abril, University of Seville
CRS model (Constant Rate of Supply)
F
incoming flux
w
Initial concentration
F
Ao 
w
CRS model assumes constant F, independently of w. Ao can vary.
Also assumes non post-depositional mixing.
-Reasonable when F is not coupled with inputs of matter
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J.M. Abril, University of Seville
CRS model
Inventory under the horizon z

( z  0)   0   A( z ' )  ( z ' )dz'
0
z

( z )   A( z ' )  ( z ' )dz'
Z
z
After a time t, the horizon now at z=0 will be located at depth z(t),
and because of the radioactive decay.
( z)  0 e
 t
At “geological” timescale the inventory is steady state; thus,
d
dt
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z 0
 F   0  0
J.M. Abril, University of Seville
F   0
CRS model
CRS Chronology:
 0 

t ( z )  ln
  ( z) 
1
Once the chronology is established, sedimentation rates can be obtained
for each two adjacent layers:
dm   dz  w dt
 z
w
t
Alternatively, from the mass balance in the steady state inventory below depth z
z
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J.M. Abril, University of Seville
-Unknowns for CRS: F, wi (N+1; N= number of
sections in the core)
- It is a “mapping” model
CAUTION
•Check for completeness of inventories (sometimes it will be
necessary to estimate the “missing” part of the total inventory)
MARINE SEDIMENT- GOTEBORG3
"data2"
2*exp(-0.09*(x-9))
2
2.5
2
1.5
1
0.5
0
0
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J.M. Abril, University of Seville
10
15
20
Depth (cm)
25
30
EXAMPLE from a case study
Schweiz. Z. Hydrol. 49/3, 1987
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J.M. Abril, University of Seville
ZF = 170 Bq m-2 y-1
from CF-CSR w = 0.115 ± 0.014 g cm-2 y-1
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J.M. Abril, University of Seville
Complete mixing zone model with constant sedimentation rate
and constant flux.
F
Steady-state mass balance
w
F
Aama
ma
Mixing
Radioactive decay
wAa
Aa 
A(m  ma )  Aa e
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
J.M. Abril, University of Seville
mma
w
Sediment growth
F
w   ma
Curve-fitting model , free parameters :
Aa, w, ma
Example CMZ-1
MARINE SEDIMENT- GOTEBORG3
"data2"
"cmz"
2.5
mixing
2
1.5
1
0.5
0
0
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J.M. Abril, University of Seville
10
15
Depth (cm)
20
25
30
ma=9.5 g cm-2; w=0,374 g cm-2 y-1
10000
PROBLEMS:
Redó
Gossenkollesee
2.- Many times unsupported
210Pb profiles can be equally
explained by different models
210Pb
(Bq/kg)
1000
210Pb chronologies must be
validated against an
independent dating method
100
10
0
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0.2 0.4 0.6 0.8
Mass depth (g cm-2)
J.M. Abril, University of Seville
1
Acceleration or mixing?
Think about:
What other hypothesis are implicitly assumed in all the
previous models ?
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J.M. Abril, University of Seville
Constant flux, CSR and constant difussion Model
Demonstration will be provided within lecture 6
Curve-fitting model , free parameters : ZF, km , w
w
km
ZF
0,1
6
200
w 0,49
ZF 200,6
Data: CF-CS-C Diffusion
Fit : CF-CSR Model
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J.M. Abril, University of Seville
g cm^(-2) y^(-1)
g^2 cm^(-4) y^(-1)
Bq m^(-2) y^(-1)
g cm^(-2) y^(-1)
Bq m^(-2) y^(-1)
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J.M. Abril, University of Seville
J. N. Smith proposed a protocol for research journals for the
acceptance of papers that rely on 210Pb dating to establish a
sediment core geochronology:
‘‘The 210Pb geochronology must be validated using at least one
independent tracer which separately provides an unambiguous
time-stratigraphic horizon’’.
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J.M. Abril, University of Seville
Examples generated with numerical solutions
Constat aceleration, constant
diffusion or CF-CSR?
ZFo=10 mBq/(cm^2 y) , w=0.1+0.1 t/150 g/(cm^2 y) D=0
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J.M. Abril, University of Seville
Examples generated with numerical solutions
Effect of “episodic” changes
in sedimentation rates?
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J.M. Abril, University of Seville
λ=0
Ts =150 y
T= - 50 y sgt= 5 y
Numerical algorithm: MSOU
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J.M. Abril, University of Seville
λ=0
Ts =150 y
T= - 20 y sgt= 2 y
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Numerical algorithm: MSOU
J.M. Abril, University of Seville
Examples generated with numerical solutions
When data are smooth enough to apply CSR models?
Periodic changes in w with T=7 y
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J.M. Abril, University of Seville