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Intro to Quantitative Geology www.helsinki.fi/yliopisto
Introduction to Quantitative Geology Lesson 13.1
Basic concepts of thermochronology
Lecturer: David [email protected]
4.12.17
3
www.helsinki.fi/yliopistoIntro to Quantitative Geology
Goals of this lecture
• Introduce the basic concepts of thermochronology
• Discuss the closure temperature concept and how closure temperatures are estimated
4
www.helsinki.fi/yliopistoIntro to Quantitative Geology
Why thermochronology?
• Popular dating technique for studying long-term tectonic and erosional processes (i.e., stuff we’ve been learning)
5
Spanish Pyrenees
www.helsinki.fi/yliopistoIntro to Quantitative Geology
Why thermochronology?
• Inherently linked to crustal heat transfer processes (advection, diffusion, production, etc.)
6
www.helsinki.fi/yliopistoIntro to Quantitative Geology
�2 =X (Oi � Ei)2
�2i
Why thermochronology?
• Incorporates many equations we’ve seen and many other concepts presented earlier in the course (hillslope processes, river erosion, heat conduction/advection, basic geostatistics)
7
Age
Measured age
Predicted ages
www.helsinki.fi/yliopistoIntro to Quantitative Geology
Geochronology versus thermochronology
• Geochronology is the science of dating geological materials, and in many ways most radioisotopic chronometers are also thermochronometers
• An important distinction lies in what the ages mean and their interpretation
• Geochronological ages are generally interpreted as ages of the materials (crystallization ages)
• Thermochronological ages are often interpreted as the time since the material cooled below a given temperature (cooling ages)
8
www.helsinki.fi/yliopistoIntro to Quantitative Geology
General thermochronology terms
• Thermochronometer A radioisotopic system consisting of:
• a radioactive parent
• a radiogenic daughter isotope or crystallographic feature
• the mineral in which they are found
9
Chapter 1: Introduction - Figure 1
T0
Tectonics + Surface Processes = Exhumation = Cooling
Spontaneous Nuclear Reaction
Solid-State Diffusion
Time
Tem
per
atu
reTemperature History
Quantitative Thermochronology – p. 3/103
Fig 1.1, Braun et al., 2006
www.helsinki.fi/yliopisto December 4, 2017Low-temperature thermochronology
Geochronology versus thermochronology
• Geochronology is the science of dating geological materials, and in many ways most radioisotopic chronometers are also thermochronometers
• An important distinction lies in what the ages mean and their interpretation
• Geochronological ages are generally interpreted as ages of the materials (crystallization ages)
• Thermochronological ages are often interpreted as the time since the material cooled below a given temperature (cooling ages)
10
www.helsinki.fi/yliopistoIntro to Quantitative Geology
General thermochronology terms
• Thermochronometry The analysis, practice, or application of a thermochronometer to understand thermal histories of rocks or minerals
• Thermochronology The thermal history of a rock, mineral, or geologic terrane.
11
Chapter 1: Introduction - Figure 1
T0
Tectonics + Surface Processes = Exhumation = Cooling
Spontaneous Nuclear Reaction
Solid-State Diffusion
Time
Tem
per
atu
reTemperature History
Quantitative Thermochronology – p. 3/103
Fig 1.1, Braun et al., 2006
www.helsinki.fi/yliopistoIntro to Quantitative Geology
General thermochronology terms
• Thermochronometry The analysis, practice, or application of a thermochronometer to understand thermal histories of rocks or minerals
• Thermochronology The thermal history of a rock, mineral, or geologic terrane.
12
Chapter 1: Introduction - Figure 1
T0
Tectonics + Surface Processes = Exhumation = Cooling
Spontaneous Nuclear Reaction
Solid-State Diffusion
Time
Tem
per
atu
reTemperature History
Quantitative Thermochronology – p. 3/103
Fig 1.1, Braun et al., 2006
www.helsinki.fi/yliopistoIntro to Quantitative Geology
The aim of thermochronology
• In most modern applications of thermochronology, the goal is to use the recorded thermal history to provide insight into past tectonic or erosional (surface) processes
• To do this, it is essential to link the temperature to which a thermochronometer is sensitive to a depth in the Earth
• This is not easy, and the field of quantitative thermochronology is growing rapidly as a result
13
Chapter 1: Introduction - Figure 1
T0
Tectonics + Surface Processes = Exhumation = Cooling
Spontaneous Nuclear Reaction
Solid-State Diffusion
Time
Tem
per
atu
reTemperature History
Quantitative Thermochronology – p. 3/103
Fig 1.1, Braun et al., 2006
www.helsinki.fi/yliopistoIntro to Quantitative Geology
The essence of thermochronology
• Daughter products are continually produced within a mineral as a result of radioactive decay
• Daughter products may be lost due to thermally activated diffusion
• The temperature below which the daughter product is retained depends on the daughter product and host mineral
14
Fig 1.3, Braun et al., 2006
Chapter 1: Introduction - Figure 3
Parent
Daughter
decay
Open SystemClosed System
Quantitative Thermochronology – p. 5/103
www.helsinki.fi/yliopistoIntro to Quantitative Geology
The essence of thermochronology
• Daughter products are continually produced within a mineral as a result of radioactive decay
• Daughter products may be lost due to thermally activated diffusion
• The temperature below which the daughter product is retained depends on the daughter product and host mineral
15
Chapter 1: Introduction - Figure 3
Parent
Daughter
decay
Open SystemClosed System
Quantitative Thermochronology – p. 5/103
Low T High T Fig 1.3, Braun et al., 2006
www.helsinki.fi/yliopistoIntro to Quantitative Geology
The concept of a closure temperature
• The transition from an open to a closed system does not occur instantaneously at a given temperature, but rather over a temperature range known as thepartial retention (or partial annealing) zone
16
Chapter 1: Introduction - Figure 3
Parent
Daughter
decay
Open SystemClosed System
Quantitative Thermochronology – p. 5/103
Fig 1.3, Braun et al., 2006
Fig 1.6a, Braun et al., 2006
Chapter 1: Introduction - Figure 6
Dep
th /
Tem
per
atu
re
partialretention
zone
Exhumed PRZ
Present-dayPRZ
Apparent age Apparent age
Elev
atio
n
Present-dayMean surface
elevation
Ro
ck u
plif
t
Den
ud
atio
nSu
rfac
eu
plif
t
Paleo-surfaceelevation
Iso
stat
icre
bo
un
dTe
cto
nic
up
lift
a
b
t1
t
t1+ t
Den
ud
atio
n
Modified from Fitzgerald et al. (1995) - Reproduced with permission from the American Geophysical Union
Quantitative Thermochronology – p. 8/103
Daughter concentration /Apparent age
Partial retention/annealing zone
www.helsinki.fi/yliopistoIntro to Quantitative Geology
The concept of a closure temperature
• The transition from an open to a closed system does not occur instantaneously at a given temperature, but rather over a temperature range known as thepartial retention (or partial annealing) zone
• The partial retention zone temperature range spans from the point at which nearly all produced daughter products are lost to diffusion to where they are nearly all retained
17
Chapter 1: Introduction - Figure 3
Parent
Daughter
decay
Open SystemClosed System
Quantitative Thermochronology – p. 5/103
Fig 1.3, Braun et al., 2006
Fig 1.6a, Braun et al., 2006
Chapter 1: Introduction - Figure 6
Dep
th /
Tem
per
atu
re
partialretention
zone
Exhumed PRZ
Present-dayPRZ
Apparent age Apparent age
Elev
atio
n
Present-dayMean surface
elevation
Ro
ck u
plif
t
Den
ud
atio
nSu
rfac
eu
plif
t
Paleo-surfaceelevation
Iso
stat
icre
bo
un
dTe
cto
nic
up
lift
a
b
t1
t
t1+ t
Den
ud
atio
n
Modified from Fitzgerald et al. (1995) - Reproduced with permission from the American Geophysical Union
Quantitative Thermochronology – p. 8/103
Daughter concentration /Apparent age
Partial retention/annealing zone
www.helsinki.fi/yliopistoIntro to Quantitative Geology
Effective closure temperature, defined
• Defined by Dodson (1973), the closure temperature is the ‘temperature of a thermochronological system at the time corresponding to its apparent age’
• This concept is quite useful, as we can thus relate a measured age to a temperature in the Earth
• Unfortunately, closure temperatures vary as a function of the thermochronological system, mineral size, chemical composition and cooling rate
• This definition also only works when cooling is monotonic (no reheating)
18
Fig 1.6a, Braun et al., 2006
Chapter 1: Introduction - Figure 6
Dep
th /
Tem
per
atu
re
partialretention
zone
Exhumed PRZ
Present-dayPRZ
Apparent age Apparent age
Elev
atio
n
Present-dayMean surface
elevation
Ro
ck u
plif
t
Den
ud
atio
nSu
rfac
eu
plif
t
Paleo-surfaceelevation
Iso
stat
icre
bo
un
dTe
cto
nic
up
lift
a
b
t1
t
t1+ t
Den
ud
atio
n
Modified from Fitzgerald et al. (1995) - Reproduced with permission from the American Geophysical Union
Quantitative Thermochronology – p. 8/103
Daughter concentration /Apparent age
Partial retention/annealing zone
Effective closuretemperature
Tc
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Influence of cooling rate on effective Tc
• In general, the effective closure temperature for a given thermochronometer system will increase with increasing cooling rate
• For the retention of 4He in apatite, the effective closure temperature is ~40°C at a cooling rate of 0.1 °C/Ma and ~80°C at a rate of 100°C/Ma
• The absolute difference in effective closure temperature is also larger for higher temperature thermochronometers
• ~40°C for 4He in apatite
• ~130°C for 40Ar in hornblende
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ANRV273-EA34-14 ARI 17 April 2006 23:42
KsArZHe
AFT
THe
AHe
ZFT
radiation-damaged
zirconBiAr
zero-damagezircon
Tagami et al.
HbAr
Apatite FT
Zircon FT
0.1 1 10 1000
50
100
150
200
250
300
350
400
0.1 1 10 1000
100
200
300
400
500
600
Eff
ectiv
e cl
osur
e te
mpe
ratu
re (°
C)
Eff
ectiv
e cl
osur
e te
mpe
ratu
re (°
C)
Cooling rate (°C Myr-1) Cooling rate (°C Myr-1)
Renfrew
averagecompostion
Tioga
MuAr
Figure 2Effective closure temperature (Tc) as a function of cooling rate for common He, FT, and Arthermochronometers. Estimates shown here are based on Equation 7 and parameters inTables 1–2. Results were calculated using the CLOSURE program.
such cases, the closure temperature concept does not strictly apply, and this couldpotentially confound attempts to relate thermal and exhumational histories. This un-derscores the need to consider the conditions of a mineral’s formation, as well as itscooling path, in interpreting thermochronologic histories.
Figure 2b provides a comparison of the various Tc estimates for apatite and zirconFT dating. Tc for the average apatite is only ∼10◦C higher than that for an end-member fluorapatite, as represented by the Renfrew apatite. In contrast, the Tc forthe Tioga apatite is ∼60◦C above that for the average apatite. This range in Tc
would give a 7 Myr spread of FT ages for a typical orogenic cooling rate of ∼10◦CMyr−1. FT dating of detrital apatites in thermally reset sandstones commonly yieldsover-dispersed grain ages, which means that the range of grain ages is much greaterthan expected owing to analytical errors alone. This result is probably a consequenceof a mix of apatite compositions, which gives a mix of retention behaviors. The Tc
estimates shown here indicate that the youngest grains in a grain age distributionshould be dominated by low-retentivity apatites. Peak-fitting methods can be usedto isolate the minimum age, which is the age of the youngest fraction of grain ages(Galbraith & Green 1990; Galbraith & Laslett 1993; Brandon 2005, as summarized
www.annualreviews.org • Thermochronology of Orogenic Erosion 433
Ann
u. R
ev. E
arth
Pla
net.
Sci.
2006
.34:
419-
466.
Dow
nloa
ded
from
ww
w.a
nnua
lrevi
ews.o
rgby
Dal
hous
ie U
nive
rsity
on
10/2
3/12
. For
per
sona
l use
onl
y.
Reiners and Brandon, 2006
www.helsinki.fi/yliopistoIntro to Quantitative Geology
What causes cooling?
• With the idea of an effective closure temperature, we now have the main concept of thermochronology - a date will ideally reflect the time since the rock sample was at Tc
• But, what causes cooling?
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Erosional exhumation
• Occurs as a result of erosion and removal of overlying rock bringing relatively warm rock to the surface
• Can take place in convergent, extensional, strike-slip or inactive tectonic settings
• Most common “cooling type” for thermochronology
2121
Erosion at surface
Rivers/glaciersLandslides, hillslope
diffusion, etc.
Mountains
Crustal block
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Erosional exhumation
• Occurs as a result of erosion and removal of overlying rock bringing relatively warm rock to the surface
• Can take place in convergent, extensional, strike-slip or inactive tectonic settings
• Most common “cooling type” for thermochronology
2222
Rock uplift
Erosion at surface
Rivers/glaciersLandslides, hillslope
diffusion, etc.
Mountains
Crustal block
www.helsinki.fi/yliopistoIntro to Quantitative Geology
Erosional exhumation
• Occurs as a result of erosion and removal of overlying rock bringing relatively warm rock to the surface
• Can take place in convergent, extensional, strike-slip or inactive tectonic settings
• Most common “cooling type” for thermochronology
2323
Rock uplift
Erosion at surface
Rivers/glaciersLandslides, hillslope
diffusion, etc.
Rock exhumation path
Mountains
Crustal block
www.helsinki.fi/yliopistoIntro to Quantitative Geology
Tectonic exhumation
• Generally occurs in extensional settings
• Uplifted footwall will also experience some erosional exhumation in most cases
24
Exhumed rocks
Crustal block
Rock uplift
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Other cases of rock cooling
• Rock cooling can also occur
• Following emplacement of an igneous body or volcanic deposit
• Typically, thermochronology is not useful in these cases as the cooling is rapid and geochronological and thermochronological ages will be similar
• Following reheating by
• Burial in a sedimentary basin and subsequent exhumation
• Emplacement of proximal igneous intrusions or volcanics
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t =1
�ln
✓1 +
Nd
Np
◆
Radioisotopic chronometer ages
• The general equation for an isotopic age iswhere ! is the isotopic age, " is the radioactive decay constant,
#d is the concentration of the daughter product and #p is the concentration of the parent isotope
• For thermochronometers, we know that the concentration of the daughter product will vary not only as a result of radioactive decay, but also due loss via solid-state diffusion
26
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@Nd
@t
= D(T )@
2Nd
@x
2+ P
Solid-state diffusion
• Thermochronometer daughter products are not suitable to be incorporated in the host mineral’s crystal lattice
• As ‘foreign’ isotopes, they are thus mobile and will diffuse within the crystal
• Their diffusion can be modelled using the standard diffusion equation where $(%) is the temperature dependent diffusivity (see next
slide), ∂2#d/∂&2 is the second derivative of the daughter
product concentration and ' is the daughter production rate
27
1-D
Parent and daughterisotopes in a crystal
Alpha decay
Parent isotope
“Normal” atomDaughter isotope
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D(T )
a2=
D0
a2e�Ea/(RTK)
Temperature-dependent diffusion
• Temperature dependence for diffusion is typically modelled aswhere $0 is the diffusivity at infinite temperature (diffusion
constant), ( is the diffusion domain, )a is the activation energy,
* is the gas constant and %K is temperature in Kelvins
• For simple systems, the diffusion domain ( is typically the size of the mineral itself
• The activation energy )a is the minimum energy that must be put into the system in order for diffusion to occur
28
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Temperature-dependent diffusion
• With the temperature-dependent diffusion concept in mind, there are essentially 3 different temperatures we might consider
• The ‘open system’ temperature %o The time/temperature that corresponds to the lower limit to the fully open system
• The closure temperature %cThe temperature of the system at the time corresponding to its age (Dodson)
• The blocking temperature %bThe upper temperature limit of fully closed system behavior
29
Chapter 2: Basics of Thermochronology - Figure 1
Tem
pe
ratu
re
tc
Tc
tb
Tb
to
To
time
time
D/P
rat
io
measuredD/P ratio
Modified from Dodson (1973)
Quantitative Thermochronology – p. 11/103
Fig 2.1, Braun et al., 2006
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D(t) = D(0)e�t/⌧
Dodson’s effective closure temperature
• Dodson (1973) introduced a method for calculating the closure temperature of a thermochronological system based on the observed diffusion parameters and the rock/mineral cooling rate
• If we assume that once a rock enters the partial retention zone, the temperature will vary as the inverse of time (%∝1/!), it is possible to find an approximate solution to the temperature-dependent diffusion equation with a diffusivity where , is is the time taken for the diffusivity to decrease by a factor of 1/e
30
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Tc =Ea
R ln(A⌧D0/a2)
⌧ = �RT 2
EaT
Dodson’s effective closure temperature
• After some mathematical manipulation we can solve for , and findwhere Ṫ is the cooling rate (negative by convention)
• Dodson’s closure temperature equation iswhere - is a geometry factor (25 for a sphere, 27 for a cylinder and 8.7 for a plane sheet)
• We can find the closure temperature as a function of cooling rate by assuming %=%c in the equation for , and iterating
31
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Pseudo-code for solving Dodson’s equation
• Define constants
• Define initial “guess” for value of ,
• Loop over some range to iterate on values of , and %c
• Calculate new %c with current value of ,
• Calculate new value of , for new %c value
• Check to see how much value of %c has changed since last iteration
• If value has not changed more than some very small number, exit loop and output calculated ‘final’ %c value
32
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Dodson’s effective closure temperature
• The effective closure temperature %c increases significantly at higher cooling rates
33
Chapter 2: Basics of Thermochronology - Figure 3
Cooling rate (oC Myr-1)
1 10 100
Clo
sure
te
mp
era
ture
(oC
)
55
60
65
70
75
80
85
90
95
Quantitative Thermochronology – p. 13/103
Fig 2.3, Braun et al., 2006
Estimated %c for apatite (U-Th)/He
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From age to process
• Using Dodson’s equations, we’re able to calculate closure temperatures as a function of cooling rate
• This does not provide any information about the depth of the closure temperature in the Earth
• There are several possibilities for determining the depth (or position) of %c, such as assuming a constant geothermal gradient
• As quantitative geologists, we can do better…
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Recap
• What is the basic idea for thermochronology?
• What is an effective closure temperature and how does it relate to the rate of cooling of a mineral sample?
35
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Recap
• What is the basic idea for thermochronology?
• What is an effective closure temperature and how does it relate to the rate of cooling of a mineral sample?
36
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References
Braun, J., der Beek, van, P., & Batt, G. E. (2006). Quantitative Thermochronology. Cambridge University Press.
Reiners, P. W., and M. T. Brandon (2006), Using Thermochronology to Understand Orogenic Erosion, Annual Review of Earth and Planetary Sciences, 34, 419–466.
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