j.m. abril department of applied physics (i); university of seville (spain)

J.M. AbrilDepartment of Applied Physics (I); University of Seville (Spain)

IAEA Regional Training Course on Sediment Core Dating Techniques. RAF7/008 Project

J.M. Abril, University of Seville

Lecture 3:Clasical dating models using 210Pb

210Pbex fluxes

Radionuclide profiles and inventories

Radiometric dating modelsCIC CF-CSR, CRS, CMZ-CSR , CD-CSR IMZ (*)-CSR

1

2J.M. Abril, University of Seville2

z

aw

222Rn

210Pb

137Cs

J.M. Abril, University of Seville

3

y = 9,3 1 x - 1,87

R2 = 0,689*

0

10

20

30

40

50

60

70

1 2 3 4 5 6

ETo (mm/d)

222 R

n E

xh

ala

tio

n (

Bq

h-1

m-2

)

Abril et al. (JENVRAD, 2009)

222Rn exhalation depends, among other factors, on 226Ra content in soil, soil texture and structure, water content, and the forcing factors…

4J.M. Abril, University of Seville

4

Author: Israel López, Univ. Huelva (Spain)J.M. Abril, University of Seville5

J.M. Abril, University of Seville6

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

Figures from P.G. Appleby, STUK-A145


Some reference values for annual fallout of excess 210Pb (Bq m-2 y-1) 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)

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.

Inputs and Inventories (Bq m-2 ) in sediments Inputs and Inventories (Bq m-2 ) in sediments


Z [cm]

210Pb

[Bq/kg]

226Ra

total210Pb (unsupported)

Radiometric dating with 210Pb: Basic aspects

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

Supported fraction


Basic Concepts and definitionsBasic Concepts and definitions

z

aw


Compaction and bulk density

As depth increases in the sediment core, water pores are replaced by solids

Saturated porous media

V

ms

Bulk density

z

Vmw

ms


Practical measurement of bulk densities

w

s

s

s

w

wsw

mmVVV

w

s

s

w

s

s

s

w

w

s

mmm

m

1

mw

ms

m

Drying and gravimetric method


Practical measurement of bulk densities. Refinement

mw

ms,om

Drying and gravimetric method and loss by ignition

w

s,0

ms,i s,i

is

is

os

os

w

wisosw

mmmVVVV

,

,

,

,,,

is

is

os

os

w

w

isos

mmm

mm

,

,

,

,

,,

is

is

os

os

w

w

isos

mmm

mm

,

,

,

,

,,


Bulk density versus depth profiles in sediment cores

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 5 10 15 20

(g

/cm

3)

Depth [cm]

ze 1

ze 1


z

Mass thickness, Δm , and mass depth:, m

zm z

dzm0

'

[ g dry weight cm-2]

Δz


(Mass) Sedimentation rate : w

dt

dmw [ g dry weight cm-2 y-1]

Time versus m for constant w (*)

w

dmdt w

mt

Z

≈

ZiA (Zi, t)

A (Zi+1, t)

A (Zi-1, t)

w (Zi-1, t)

w (Zi+1, t)


Basic processes

Z

≈

ZiA (Zi, t)

A (Zi+1, t)

A (Zi-1, t)

w (Zi-1, t)

w (Zi+1, t)


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

Fundamental equationsFundamental equations

BOUNDARY CONDITIONS

Mass conservation for a particle-associated radiotracer

Mass conservation for solids


[Bq L-2 T-1]

Constant Flux and Constant Sedimentation rate (CF-CSR)

Activity concentration at interface(non post-depositional mixing) Constant A0 w

FA 0

w

F incoming flux

sedimentation rate


(non post-depositional mixing)

Layer at time t=0

The sediment-water interface displaces upwards

Specific activity A0

time = 0

z=z(t)

time = t =m/w

toeAA

m=m(t)


m

Ln(A)

Validation:

Goldberg first validated the 210Pb dating method in varved sediments

Curve-fitting model , free parameters : Ao , w

wmt

eAA w

m

/0

Think about: Any implicit assumption concerning compaction?


Schweiz. Z. Hydrol. 49/3, 1987

ZF = 172 Bq m-2 y-1

EXAMPLE from a case study


Don't forget:

Estimated sedimentation rates, ages and dates have to be provided with the corresponding uncertainties.

Don't forget:

Estimated sedimentation rates, ages and dates have to be provided with the corresponding uncertainties.

Age : T(m) or T(z) , from m(z)/w

w , (mass) sedimentation rate

Dates or chronology: Year of sampling – Age

W = 0.115 ± 0.014 g cm-2 y-1


Associated uncertainties in 210Pb chronology

is

is

os

os

w

w

isos

mmm

mm

,

,

,

,

,,

is

is

os

os

w

w

isos

mmm

mm

,

,

,

,

,,

iii zm

i

imm

i

im2

2,

2, zrrii m

,r

,...),,( 321 xxxf

...,;,;, 332211 xxx

i

ji

f x

f2

General formulae for error propagation

G.F.

mm


bxaAxf

mx

ln)(

11

2

/1

2

2

2

RN

a

x

a

ab

2,

2, brrw w

bw

2,

2, wrmrt

w

mt t

t

Associated uncertainties in 210Pb chronology


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


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, 1989Data from Axelsson and El-Daoushy, 1989


10

100

1000

10000

0 0.2 0.4 0.6 0.8 1

210 P

b (B

q/kg

)

Mass depth (g cm-2)

RedóGossenkollesee

1.- Many unsupported 210Pb profiles do not follow a simple exponential decay pattern

More complex models are required

PROBLEMS:


CIC model (Constant Initial Concentration)

w

F incoming flux

Activity concentration at interface(no post-depositional mixing) w

FAo

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

sedimentation rate


CIC model can equally be formulated in terms of actual depth (z) or mass depth (m)

Chronology (one date per data point)

Alternative estimation of sedimentation rates (one per data point) – only for cores with high spatial resolution-

CAUTION !•Estimation of the initial concentration, Ao, is not a trivial task !

A0

A(m)

m

A

-Unknowns for CIC: Ao and wi (N+1; N= number of sections in the core)

- It is a “mapping” model




CF-CSR CIC


ZF (recent) = 76 Bq m-2 y-1

CRS model (Constant Rate of Supply)

w

F incoming flux

Initial concentration w

FAo

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


CRS model

Inventory under the horizon z

z

dzzzAz ')'()'()(

After a time t, the horizon now at z=0 will be located at depth z(t), and because of the radioactive decay.

tez 0)(tez 0)(

0

0 ')'()'()0( dzzzAz

At “geological” timescale the inventory is steady state; thus,

000

Fdt

dz 0F 0F

Z

z


)(

ln1

)( 0

zzt

)(

ln1

)( 0

zzt

CRS Chronology:

Once the chronology is established, sedimentation rates can be obtained for each two adjacent layers:

t

zw

dtwdzdm

t

zw

dtwdzdm

z

Alternatively, from the mass balance in the steady state inventory below depth z

CRS model

-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)

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30

Uns

uppo

rted

Pb-

210

(pC

i/g)

Depth (cm)

MARINE SEDIMENT- GOTEBORG-

"data2"2*exp(-0.09*(x-9))

2


ZF = 170 Bq m-2 y-1

from CF-CSR w = 0.115 ± 0.014 g cm-2 y-1


Complete mixing zone model with constant sedimentation rate and constant flux.

Mixing ma

w

F

F

Aama

Radioactive decay

wAa Sediment growth

aa mw

FA

aa mw

FA

Steady-state mass balance

w

mm

aa

a

eAmmA

)( w

mm

aa

a

eAmmA

)(

Curve-fitting model , free parameters : Aa, w, ma


0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30

Un

sup

po

rte

d P

b-2

10

(p

Ci/g

)

Depth (cm)

MARINE SEDIMENT- GOTEBORG-

"data2""cmz"

Example CMZ-1

mixing

ma=9.5 g cm-2; w=0,374 g cm-2 y-1ma=9.5 g cm-2; w=0,374 g cm-2 y-1


Acceleration or mixing?10

100

1000

10000

0 0.2 0.4 0.6 0.8 1

210 P

b (B

q/kg

)

Mass depth (g cm-2)

RedóGossenkollesee

2.- Many times unsupported 210Pb profiles can be equally explained by different models

210Pb chronologies must be validated against an independent dating method

PROBLEMS:



Think about:

What other hypothesis are implicitly assumed in all the previous models ?

Constant flux, CSR and constant difussion Model

Demonstration will be provided within lecture 6

Curve-fitting model , free parameters : ZF, km , w

Data: CF-CS-C DiffusionFit : CF-CSR Model

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)


J. N. Smith proposed a protocol for research journals for theacceptance 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’’.


ZFo=10 mBq/(cm^2 y) , w=0.1+0.1 t/150 g/(cm^2 y) D=0

Examples generated with numerical solutions

Constat aceleration, constant diffusion or CF-CSR?


Effect of “episodic” changes in sedimentation rates?



Numerical algorithm: MSOU

T= - 50 y sgt= 5 y


λ=0

Ts =150 y


T= - 20 y sgt= 2 y

Ts =150 y

λ=0

Numerical algorithm: MSOU

Periodic changes in w with T=7 y

When data are smooth enough to apply CSR models?



j.m. abril department of applied physics (i); university of seville (spain)

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