Continuous Thermal Histories from MDD Modeling of 40Ar/39Ar K-feldspar Analyses and Applications to

Extensional Tectonics

Martin Wong1, Phillip Gans2, Peter Zeitler3, Bruce Idleman3

T-t paths

Synthetic age spectra

1Colgate University, 2UC Santa Barbara, 3Lehigh University

Support from NSF EAR-0948536

Tectonics and thermochronology

Ehlers (2005)

• Most tectonic processes impart thermal signatures

• Thermochronology can be used to address wide range of tectonic questions• Inception• Duration• Magnitude• Rate• Spatial variation

• Offers unique insight that is often inaccessible by other methods

Thermochronology overview

40Ar40K

• Decay of parent to daughter product

• Daughter can diffuse out of the host mineral

• Volume diffusion is a thermally activated process

• Closure temperature (Tc) reflects temp below which daughter is retained

• Isotopic age reflects time since cooling through Tc

How do we measure Tc of minerals in the lab?Diffusion parameters Ea and D0

Where:D = diffusivity (m2 s-1)T = temperature (K)

R = Gas constant

Ea = Activation energy (J mol-1)D0 = frequency factor (m2 s-1)

Modified from Reiners and Brandon (2006)

• Diffusion scales exponentially with temperature

Volume diffusion in minerals follows an Arrhenius relationship

Links reaction rate to temperature

• R is a constant

• Diffusion kinetics controlled by Ea and D0

Using diffusion experiments to measure Tc

Laboratory He diffusion from zircon (Reiners et al., 2004)

• Arrhenius plot• note inverse T on x-axis!

• Linear trend shows a single Arrhenius relationship

• Ea is α to slope D0 = y–intercept

• Suggests one diffusion domain with a given Tc

• Ea and D0 used to calculate Tc via Dodson’s equation

Increasing T

From Pollard et al. (2002) with data from P. Fitzgerald, S. Baldwin, G. Gehrels, P. Reiners, and M. Ducea

Thermochronometers with wide range of Tc are available

• Most common methods:• 40Ar/39Ar• fission track• (U-Th)/He analyses

• Apply multiple thermochronometers to reconstruct T-t path from >500°C to near surface

Problems with this approach:What are we missing between point constraints?

?

?

• Most thermochron data yields point constraints on T–t path

• Uncertainty in how to connect points

• What are we missing in between?

Problems with this approach:How well do we know Tc of our samples?

• Typically use kinetic data from standards and assume they apply (e.g. Ar-Ar biotite Tc = 325 ± 25°C)

• But compositional, grain size, other effects on Tc

• Don’t typically measure the kinetic data, composition, etc. for each sample

• Creates uncertainties in Tc and thus in the T-t path

• To track from 350-120°C:• Ar-Ar musc• Ar-Ar bio• FT zircon• U-Th/He titanite• FT apatite• etc

• Separation time, analytical time, cost, etc.

• Do the rocks have all of these minerals? Some are trace/rare

• Multiply by spatial coverage across a field area…

Problems with this approach:That’s a lot of work!

What would our dream thermochronometer be?

• Record a continuous thermal history rather than point constraints on T-t path

• Tc range applicable to many geologic/tectonic processes

• T½ applicable to wide range of ages

• Present in many rock types

• Abundant in sample (ease of separation)

40Ar/39Ar K-feldspar analyses offer best opportunity to extract continuous thermal histories

K–feldsparKAlSi3O8

• Based on 40K 40Ar (T ½ = 1.25 Ga)

• Common in many basement rocks

• Major mineral constituent • easy to sample and separate!

• Appears to record continuous cooling from ~350-150°C

• Applicable to wide range of tectonic processes from middle to upper crust

Why do we think 40Ar/39Ar K-feldspar analyses yield continuous thermal histories?

Appa

rent

age

(Ma)

Cumulative 39Ar

Single step heating

experiment

Increasing T-steps

500°C 1100°C

Beginning with Lovera et al. (1989), Richter et al. (1991), Harrison et al. (1993) and many othersSee recent review by Harrison et al. (2005)

• 40Ar/39Ar age spectrum - step heat mineral and analyze age at each step

• Basement K-feldspar step ages get progressively older at higher–T steps

• Inconsistent with presence of single diffusion domain and Tc

K-spar diffusion not consistent with a single Tc

Typical K-feldspar Arrhenius plot

Inverse temperature

Diff

usiv

ity

Increasing T

• Initially follows Arrhenius relationship at low-T

• Falls off this line at higher–T steps

• No single E and D0

• Inconsistent with a single diffusion domain with one Tc

Multiple diffusion domain theory

Typical K-feldspar Arrhenius plot

Inverse temperature

Diff

usiv

ity

Increasing T

Schematic model of MDD theory

High Tc domain

Moderate Tc domainLeast retentive domain (Low Tc)

Ar

Ar

Ar

Low Tc domain degasSingle E and D0

Degassing of higher Tc domain

Consistent with presence of multiple diffusion domains, each with unique Tc and volume fraction

• Likely from microstructures such as exsolution lamellae

• MDD behavior not present in high–T K-feldspar such as sanidine that lack these structures

• Creates Ar reservoirs of varying size + diffusivity

• Each K-feldspar has unique domain structure

Ar

Ar

Ar

Source of multiple diffusion domains in K-feldspar?

How do we extract a thermal history from K-feldspar?

• Directly measuring the kinetics of each sample!

• Only goal is to adequately reproduce laboratory 39Ar release with model, not reproduce nature exactly

Domain software – Peter Zeitler (Lehigh)

measuredmodel

E and Do of smallest domain

Melting at ~1100°C

ArAr

Ar

• Linear portion defines E and D0 of smallest domain

• Model # of domains, relative size (Tc) and volume fraction to fit measured data

Model domain structure

Inverse modeling for T-t path – Arvert software (P. Zeitler)

• Generate random T-t paths • impose constraints if desired

• Produce synthetic age spectrum for each T-t path• Via the modeled domain structure• What fraction of Ar does each

domain hold and when did it cool through its Tc?

• Compare synthetic to measured age spectrum

• Take best fit T-t paths and iterate, learning algorithm

Initial Monte Carlo T-t paths

Synthetic age spectra

Measured spectrum

Final model resultsGR-8

• Converge on class of best-fit cooling paths

• Best fit T-t paths reproduce measured age spectrum

• Rapid cooling = flat age spec.• Rapid closure of many domains

• Slow cooing = age gradient

• Alter parameters to test model sensitivity (not just one model)

T-t paths

Synthetic age spectra

Measured age spectrum

Key assumptions of the MDD approach

• Ar loss in K-feldspar occurs by volume diffusion

• Laboratory Ar release adequately mimics diffusion mechanisms and kinetics of sample in nature• K-feldspar is anhydrous so no dehydration reactions in vacuo

• No modification of diffusion domains below the Tc of that domain

• Some issues of secondary importance • Somewhat debated, see Parsons et al., 1999; Lovera et al., 2002

Harrison et al. (2005)

These are key assumptions for many thermochronometers…

Identifying problematic behavior

From Harrison et al. (2005)

• Climbing age gradients at higher T steps required for volume diffusion

• Excess 40Ar can produce anomalously old ages in some samples

• Intermediate age maxima also problematic – source? How to interpret?

• Generally low % of samples affected

• We can identify and screen for problematic behavior!

So that’s the theory… but does it work?

Two case studies applied to extension

in the Basin and Range

Gold Butte normal fault block, NV

Grayback normal fault block, AZ

Thermochronology at tilted normal fault

blocks

• Old ages near surface

• Ages young as depth/temperature increases

• Zero age below the Tc isotherm

• Age-depth inflection shows position of Tc isotherm

Prior to extension:

• Exhumation and cooling of footwall

• Rapid cooling “quenches” thermochron patterns

• Samples above Tc paleo–isotherm keep same age structure

• Samples below Tc at start of extension cool rapidly, record start of extension

After extension and tilting

Some info we can derive from

thermochron

(1) Inception of extension• Inflection in age-

paleodepth relationship

Inception of extension

(2) Exhumation rate• For samples below Tc paleo-

isotherm (open at extension)• Slope of paleodepth vs. age

Exhumation rate

(3) Geotherm prior to extension• Paleodepth of fossil Tc isotherm• Must know paleodepth robustly

– tilt, paleosurface, intact block

Paleo-geotherm

Tc

Paleo-surface

The Grayback fault block, AZ

• Proterozoic and Laramide (ca. 75 Ma) granite

• >100% extension on now gently W-dipping normal faults

• 90° of eastward block tilt during Tertiary extension (domino–style block rotation)

• Preserved Oligocene paleo–surface (paleodepth known)

Wong et al. (accepted) after

Howard and Foster (1996)

Prior thermochronology •Apatite and Zircon FT• (Howard and Foster, 1996)

• (U-Th)/He apatite • (Wong et al., accepted)

• Extension began at ca. 25 ± 3 Ma

25 ± 3 Mainflection

• Tectonic exhumation rate of ~1 mm/yr

~1 mm/yr exhumation rate

• Deepest part of block at 220 ± 20 °C at 25 Ma

Zr. FT PAZ at 25 Ma220 ± 20°C

Prior thermochronology •Apatite and Zircon FT• (Howard and Foster, 1996)

• (U-Th)/He apatite • (Wong et al., accepted)

• Extension began at ca. 25 ± 3 Ma

• Tectonic exhumation rate of ~1 mm/yr

• Deepest part of block at 220 ± 20 °C at 25 Ma

• Paleo-geothermal gradient of 14–17°C/km at start of extension

– Fossil Tc isotherms for AHe, Ap. And Zr. FT

AHe14°C/km Ap. FT

17°C/km

Zr. FT17°C/km

An excellent place to evaluate K-spar MDD continuous thermal histories!

K-spar results

K-spar spectra are systematic – young towards deeper paleodepths

No problematic Ar behavior

Deeper paleodepths

Pre-extensional (~25 Ma) isotherms

• Top of Laramide pluton (75-80 Ma)• K–spar yields flat age spectrum• ~ 58-65 Ma

Moderate paleodepth (central block – GR-1)

GR-1

• MDD models suggest rapid cooling (10-15°C/m.y.) from 300–150°C

• Suggests post-emplacement cooling of pluton in shallow crust

• MDD models suggest <150°C by 25 Ma, matches paleo-geotherm prediction

40Ar/39Ar age spectra

MDD thermal model

Deeper paleodepths (west central block GR-2)

GR-2

• Climbing age gradient from 28–55 Ma

• MDD models suggest slow cooling (2–4°C/m.y.) during early Tertiary

• Deeper than GR–1 so K–spar did not record rapid post-emplacement cooling

• Consistent with tectonic quiescence inferred from geologic studies

40Ar/39Ar age spectrum

MDD thermal model

Deepest paleodepths (western part of block – GR-8)

GR-8

• Age flat at low–T steps, 24–27 Ma

• Climbing age gradient 28–40 Ma

• MDD models suggest slow cooling 27–40 Ma

• Rapid cooling (15-17°C/m.y.) after 27 Ma documents start of extension

• Deeper than GR–2 so catches part of slow cooling but low Tc domains stayed open into Oligocene, record rapid cooling

40Ar/39Ar age spectra

MDD thermal model

MDD thermal models replicate all key aspects of prior thermochron

(1) Extension began at ca. 25 ± 3 Ma

(2) Tectonic exhumation rate of ~1 mm/yr (cooling rate 15-17°C/m.y.)

(3) Oligocene paleo-geothermal gradient of 14–17°C/km

– GR-8 MDD model at 240°C at ~12 km paleodepth

Rapid cooling at 27 Ma

Prior thermochron

K-spar MDD models

Rapid cooling at 25 ± 3 Ma

~ 1 mm/yr

15-17°C/m.y.(1 mm/yr)

GR-8 at ~240°C at 27 Ma

Deep footwall at 220°C at 27

Ma (Zr. FT)

A single K-feldspar sample (GR-8) yielded the same info as a

large array of AHe and FT analyses!

Key points from the Grayback case study

Prior thermochron

K-spar MDD models

• 40Ar/39Ar K-spar MDD thermal models are geologically meaningful

• Well calibrated to other thermochron-ometers (AHe, FT)

• Yields the same (more?) info with fewer samples

A quick look at the Gold Butte fault block, NV

GBT-10 GBT-9

• Proterozoic units and minor Laramide (ca. 75 Ma) granite

• Extension on now gently W-dipping normal faults

• 60° of eastward block tilt during Tertiary extension

• Miocene paleodepths up to 18 km?

Fryxell et al. (1992), Brady et al. (2000)

Prior thermochronology

•Apatite FT (Fitzgerald et al. 1991, 2009)• (U-Th)/He (Reiners et al. 2000)• apatite • Titanite • zircon

•Zircon FT (Bernet, 2002)•40Ar/39Ar (Karlstrom et al., 2010)

• Extension began at ca. 17Ma

• Deepest part of block at 300–350 °C at 17 Ma, assuming an intact block

GBT-10 GBT-9

• Climbing age gradient from 50–700 Ma

• MDD models suggest very slow cooling (<<1°C/m.y.) throughout Paleozoic–Mesozoic

• Lacks any Miocene record (makes sense given its position)

Central part of blockGBT-9

GBT-9

GBT-10 GBT-9

• Some problematic behavior• 40ArE and Int. Age Max.

• Not suitable for MDD modeling

• But shares climbing age gradient 50–300 Ma as GBT–9

• ~20% gas yields Miocene ages at low–T steps

• Low Tc domains recording Miocene rapid cooling

Further west: GBT-10

GBT-10

GBT-10 GBT-9

• Flat age spectrum at 17 Ma • 30-40% of 39Ar released

• Climbing age gradient 17-70 Ma

Further west: GBT-11

GBT-11

Note Y-axis scale change!

GBT-10 GBT-9

• MDD model suggests slow cooling/isothermal residence at ~300 ± 25°C from early to middle Tertiary

• Matches well with projection of Miocene paleo–geothermal gradient

• Captures start of rapid tectonic exhumation at 17 Ma

• Identical to prior thermochron

Further west: GBT-11

GBT-11

17 Ma

GBT-10 GBT-9

Looks good so far, but…There is a K-spar age repetition between GBT-11 and GBT-7

GBT-11

GBT-11

GBT-7

GBT-7GBT-11 shown at

same age scale as GBT–7 for

comparison

GBT-7 is further west (deeper paleodepths) but is older… breaks the pattern

GBT-10 GBT-9

GBT-4/5

• Ages drop younger again

• Remarkably similar form to GBT-11 Kspar

• Age flat at 17 Ma at low–T steps

• Climbing age gradient to 35-50 Ma

Western footwall: GBT-4 and 5

MDD thermal models of GBT–4 and GBT–5 capture the inception and rate of extensional exhumation perfectly…

K-spar MDD: 250–275°C at

17 Ma

GBT-10 GBT-9

GBT-4/5

17 Ma geotherm. projection: 350°C

But MDD models suggest they were 75-100°C colder at 17 Ma than the projected

Miocene geotherm. would suggest…

GBT-10 GBT-9

Two “problems” with Kspar dataset:Age repetition and MDD models of westernmost footwall are too cold

How can we resolve this?

• K–spar ages from GBT-9, 10 and 11 make sense

• Match expected thermal behavior from prior thermochronology

GBT-11

GBT-10GBT-9

GBT-9GBT-10GBT-11

Decreasing ages towards deeper hotter footwall

GBT-10 GBT-9

Two “problems” with Kspar dataset:Age repetition and MDD models of westernmost footwall are too cold

How can we resolve this?

• Data from the deepest footwall repeats this pattern

• GBT–7 matches GBT-10• GBT–4/5 match GBT–11

GBT-11

GBT-10

GBT-11GBT-4/5

GBT-7

GBT-7

GBT-10

GBT-4/5

GBT-10 GBT-9

GBT-11

GBT-7

GBT-10

GBT-4/5

A shallowly west dipping normal fault with ~4-5 km of slip at ~13 km paleo–

depth would match these data exactly

Possible normal fault

• Gold Butte block may not be an intact block• Possibly cut by at least one major normal fault• Max paleodepth at Gold Butte may be ~12 km• May reduce the total required slip on the bounding Lakeside Mine fault• Would explain lack of mylonites in western footwall, lack of Miocene Ar

mica ages

K-feldspar as a tool to ID cryptic faults and quantifying slip?

• Prior thermochronology shows no obvious age repetitions in this part of footwall

• Why? Fault motion above Tc of those thermo-chronometers? Lack of resolution?

• K-feldspar analyses may offer a high-resolution tool for identifying cryptic faults and constraining slip

Conclusions• Laboratory Ar diffusion studies of K-feldspar are consistent

with the presence of multiple diffusion domains (MDD) within a single mineral

• The domain structure from each sample can be modeled based on lab diffusion data

• MDD thermal histories are possible T-t paths when they reproduce the measured 40Ar/39Ar age spectrum via the modeled domain structure

• Two case studies from tilted normal fault blocks document the utility of the MDD approach

Conclusions• The MDD approach can produce highly accurate and geologically

meaningful thermal histories

• MDD results appear well calibrated to other thermochronometers in these two case studies

• 40Ar/39Ar K–feldspar data may be more sensitive than other thermochronometers in some cases – potential utility for identifying cryptic faults and constraining slip

K–feldspar MDD thermal models are a potentially powerful but underutilized tool for addressing a

wide range of tectonic problems

Bonus slides

Using diffusion kinetics to calculate Tc

The Dodson equation

From Harrison et al. (2005) after Dodson (1973)

Where:E = Activation energyD0 = frequency factorR = Gas constantA = Geometry constant (sphere, slab, etc)r = effective diffusion length scaledT/dt = cooling rate

If we know E and D0 for a given thermochronometer, we

can solve for Tc

GBT-10 GBT-9

GBT-10 GBT-9

GBT-11GBT-4/5

• Sample from the deepest footwall gets younger again (GBT 4 and GBT 5)• They look remarkably like GBT-11…