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 210 Pb
210 Pb 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

J.M. Abril, University of Seville

a w
3 z
137 Cs
222 Rn
210 Pb
J.M. Abril, University of Seville

222 Rn exhalation depends, among other factors, on 226 Ra content in soil, soil texture and structure, water content, and the forcing factors…
70
60
50
40
30
20
10
0
1 2 y = 9,3 1 x - 1,87
R
2
= 0,689*
3 4
ETo (mm/d)
5 6
Abril et al. (JENVRAD, 2009)
J.M. Abril, University of Seville

5
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 210 Pb ex fallout
•Predominant west-east movement of air masses  210 Pb ex fallout is low in the western areas of the continents
• 210 Pb ex fallout is higher in the North hemisphere
• 210 Pb ex fallout is positively correlated with rainfall
Figures from P.G. Appleby, STUK-A145
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J.M. Abril, University of Seville

Some reference values for annual fallout of excess 210 Pb (Bq m -2 y -1 )
Global scale , F ~ 23-367 Bq m -2 y -1 (Robbins, 1978)
8
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 210 Pb

= ln2/T
1/2 with T
1/2
= 22.26 y.
J.M. Abril, University of Seville

Radiometric dating with 210 Pb: Basic aspects
210 Pb
[Bq/kg] total
210 Pb (unsupported)
226 Ra
Supported fraction
Z [cm]
If we assume that there is no Rn exhalation from the sediment, then the total
9 activity of 210 Pb total will be 210 Pb total
= 210 Pb supported and 210 Pb supported
+ 210 Pb unsupported
= 226 Ra activity
J.M. Abril, University of Seville

Basic Concepts and definitions a w
10 z
J.M. Abril, University of Seville

z
Compaction and bulk density
As depth increases in the sediment core, water pores are replaced by solids

V
Saturated porous media
 
 m s

V
Bulk density
 m w
 m s
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J.M. Abril, University of Seville

Practical measurement of bulk densities
 m
 m w
 m s
Drying and gravimetric method

V
 
V w
 
V s

 m w
 w

 m s
 s
12
 

 w w
 m s

 m s
 s

1

 s
 m w
 m s

 w s
J.M. Abril, University of Seville
 w
 s

Practical measurement of bulk densities. Refinement
 m
 m w
 m s,o
 m s,i
 w
 s,0
 s,i
Drying and gravimetric method and loss by ignition

V
 
V w
 
V s , o
 
V s , i

 m w
 w

 m s , o
 s , o

 m s , i
 s , i
 
 m w
 w
 m s

 s

, o
 m s
, o
 m s
, o 
, i

 m s s i ,
, i
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J.M. Abril, University of Seville

Bulk density versus depth profiles in sediment cores
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
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J.M. Abril, University of Seville
  

 
1 e
  z
15 5 10
Depth [cm]
20

z
Mass thickness, Δm , and mass depth
:, m
Δz
 m
   z m
 z

0
 dz '
[ g dry weight cm -2 ]
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J.M. Abril, University of Seville

(Mass) Sedimentation rate : w w
 dm dt
[ g dry weight cm -2 y -1 ]
Time versus m for constant w (*) dt
 dm w t
 m w
16
J.M. Abril, University of Seville
Z
Z i w (Z i-1
, t) w (Z i+1
, t)
A (Z i-1
, t)
A (Z i
, t)
A (Z i+1
, t)

Basic processes
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J.M. Abril, University of Seville
Z
Z i
w (Z i-1
, t)
A (Z i-1
, t)
A (Z i
, t) w (Z i+1
, t)
A (Z i+1
, t)

Mass conservation for a particle-associated radiotracer
Mass conservation for solids
BOUNDARY CONDITIONS
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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
J.M. Abril, University of Seville

Flux
F incoming flux [Bq L -2 T -1 ] w sedimentation rate
Activity concentration at interface
( non post-depositional mixing )  Constant A
0
A

0
F w
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J.M. Abril, University of Seville

The sediment-water interface displaces upwards m=m(t) z=z(t)
Specific activity A
0
Layer at time t=0
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A

A o e
  t
(non post-depositional mixing)
J.M. Abril, University of Seville

Ln(A) t
A

A
0 e
  m w
 m / w
21 m
Curve-fitting model , free parameters : A o , w
:
Goldberg first validated the 210 Pb dating method in varved sediments
Think about : Any implicit assumption concerning compaction?
J.M. Abril, University of Seville

EXAMPLE from a case study
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J.M. Abril, University of Seville
ZF = 172 Bq m -2 y -1
Schweiz. Z. Hydrol. 49/3, 1987

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

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Associated uncertainties in 210 Pb chronology
General formulae for error propagation f ( x
1
, x
2
, x
1
,

1
; x
2
,

2 x
3
,...)
; x
3
,

3
...
 f
  i


  f
 x i
 j


 2
 m i m
 m


  i
  i
 z i m i
 i
 i
2
 i
 r ,

  m i




 r
2
,

 
2 r , z
 
 m w
 w
 m s

 s

, o
 m s
, o
 m s
, o 
, i
 m s
 s , i
, i


G.F.
J.M. Abril, University of Seville
 m

Associated uncertainties in 210 Pb chronology x
 m f ( x )
 ln
 
 a
 bx
Lest squares fitting a, b, R 2  easily produced with excel or other shifts
 b
  a
 a

1 /
 x
2 
N a
2

2
1
R
2

1

 w w

 b
 w
 w
 r
2
,

 
2 r , b
 t t
 m w
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J.M. Abril, University of Seville
 t
 
2 r , m
 
2 r , w

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

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Data from Axelsson and El-Daoushy, 1989
J.M. Abril, University of Seville
CAUTION !
•Estimation of the supported fraction is not a trivial task !
• 226 Ra may be non uniform in depth and being different from the 210 Pb baseline
•Settling particles can be depleted in 226 Ra in the water column while enriched in 210 Pb

10000
Redó
Gossenkollesee
1000
100
1.- Many unsupported 210 Pb profiles do not follow a simple exponential decay pattern
 More complex models are required
10
0 0.2
0.4
0.6
0.8
1
Mass depth (g cm -2 )
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J.M. Abril, University of Seville

F incoming flux w sedimentation rate
Activity concentration at interface
(no post-depositional mixing)
A o

F w
CIC model assumes constant A o;
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
A
0
A
(m)
Chronology (one date per data point) m
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Alternative estimation of sedimentation rates
(one per data point) – only for cores with high spatial resolution-
Unknowns for CIC: A o and w i
(N+1; N= number of sections in the core)
It is a “mapping” model
CAUTION !
•Estimation of the initial concentration, A o
, is not a trivial task !
J.M. Abril, University of Seville

EXAMPLE from a case study
CF-CSR
CIC
ZF (recent) = 76 Bq m -2 y -1
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J.M. Abril, University of Seville
Schweiz. Z. Hydrol. 49/3, 1987

w
F incoming flux
Initial concentration A o

F w
assumes constant F, independently of w . A o
Also assumes non post-depositional mixing.
can vary.
Reasonable when F is not coupled with inputs of matter
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J.M. Abril, University of Seville

33
Inventory under the horizon z

( z

0 )
 
0



0
A ( z ' )

( z ' ) dz ' z

( z )


 z
A ( z ' )

( z ' ) dz '
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 z

0

F
  
0

0
F
  
0
J.M. Abril, University of Seville

CRS Chronology: t ( z )

1
 ln



0

( z )


Once the chronology is established, sedimentation rates can be obtained for each two adjacent layers: dm w

  dz
  z
 t
 w dt
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, w i
(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)
3
2.5
2
1.5
1
0.5
0
0
MARINE SEDIMENT- GOTEBORG-
"data2"
2*exp(-0.09*(x-9))
2
5 10 15
Depth (cm)
20 25 30
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J.M. Abril, University of Seville

EXAMPLE from a case study
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J.M. Abril, University of Seville
Schweiz. Z. Hydrol. 49/3, 1987

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

F w
Steady-state mass balance
F
Mixing m a

A a m a
Radioactive decay w A a Sediment growth
A a
 w

F
 m a
A ( m
 m a
)

A a e
  m
 m a w
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J.M. Abril, University of Seville
Curve-fitting model , free parameters :
A a
, w, m a

Example CMZ-1
3
2.5
2
1.5
MARINE SEDIMENT- GOTEBORG-
"data2"
"cmz" mixing
1
0.5
39
0
0 5
J.M. Abril, University of Seville
10 15
Depth (cm)
20 25 30 m a
=9.5 g cm -2 ; w=0,374 g cm -2 y -1

10000
1000
100
Redó
Gossenkollesee
2.- Many times unsupported
210 Pb profiles can be equally explained by different models
 210 Pb chronologies must be validated against an independent dating method
10
0 0.2
0.4
0.6
0.8
1
Mass depth (g cm -2 )
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J.M. Abril, University of Seville

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, k m , w w 0,1 g cm^(-2) y^(-1) km 6 g^2 cm^(-4) y^(-1)
ZF 200
Bq m^(-2) y^(-1) w 0,49 g cm^(-2) y^(-1)
ZF 200,6
Bq m^(-2) y^(-1)
Data: CF-CS-C Diffusion
Fit : CF-CSR Model
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J.M. Abril, University of Seville

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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 210 Pb dating to establish a sediment core geochronology:
‘‘The 210 Pb geochronology must be validated using at least one independent tracer which separately provides an unambiguous timestratigraphic horizon’’.
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J.M. Abril, University of Seville

Examples generated with numerical solutions
Constat aceleration, constant diffusion or CF-CSR?
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ZFo=10 mBq/(cm^2 y) , w=0.1+0.1 t/150 g/(cm^2 y) D=0
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
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J.M. Abril, University of Seville
Ts =150 y
T= - 50 y sgt= 5 y
Numerical algorithm: MSOU

λ=0
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J.M. Abril, University of Seville
Ts =150 y
T= - 20 y sgt= 2 y
Numerical algorithm: MSOU

Examples generated with numerical solutions
When data are smooth enough to apply CSR models?
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J.M. Abril, University of Seville
Periodic changes in w with T=7 y