BurnMan: A Lower Mantle Toolbox

Valentina Magni (Durham)Timo Heister (Texas A&M)Sanne Cottar (Berkeley)

Marc Hirschmann (Minnesota)

Ian Rose(Berkeley)Yu Huang (Maryland)Jiachao Liu (Michigan)

Barbara Romanowitz (Berkeley)

Cayman Unterborn (Ohio State)

What is BurnMan?• Full mineral physics python-based toolbox

for calculating and comparing seismic observables of the lower mantle

• Vs, Vp, Vphi and density along any geotherm

• With or without thermal corrections

• Any material you want

• includes basic (Mg,Fex)-pv and (Mg,Fex)-fp, and many more

• User definition possible at every step

Motivation

•Originally: Constrain the Mg/Si ratio of lower mantle

•Lack of universal methodology (mineral physics) and understanding of interdisciplinary constraints (seismology, geochemistry, geodynamics)

The Basics

User Defined User Defined MineralsMinerals(Pressure (Pressure

range)range)(Geotherm)(Geotherm)

User Defined User Defined MineralsMinerals(Pressure (Pressure

range)range)(Geotherm)(Geotherm)

Equation of Equation of StateState

(K, G, V at P,T)(K, G, V at P,T)BMHBMH

Stixrudian Stixrudian MGDMGD

Equation of Equation of StateState

(K, G, V at P,T)(K, G, V at P,T)BMHBMH

Stixrudian Stixrudian MGDMGD

Vs, Vp, Vϕ, ρVs, Vp, Vϕ, ρPlot? Data file?Plot? Data file?Vs, Vp, Vϕ, ρVs, Vp, Vϕ, ρ

Plot? Data file?Plot? Data file?

BurnMan DeluxeWt%? Pv/Fp Wt%? Pv/Fp

ratio?ratio?(spin transition? (spin transition? [coming soon])[coming soon])

(standard (standard geotherm or geotherm or

input your own?)input your own?)

Wt%? Pv/Fp Wt%? Pv/Fp ratio?ratio?

(spin transition? (spin transition? [coming soon])[coming soon])

(standard (standard geotherm or geotherm or

input your own?)input your own?)

Equation of StateEquation of State(K, G, V at P,T)(K, G, V at P,T)

BMHBMHStixrudian (2nd Stixrudian (2nd or 3rd order) or 3rd order)

MGDMGD

Equation of StateEquation of State(K, G, V at P,T)(K, G, V at P,T)

BMHBMHStixrudian (2nd Stixrudian (2nd or 3rd order) or 3rd order)

MGDMGD

Compare to Compare to seismic data seismic data (PREM, fast, (PREM, fast,

slow)?slow)?

Compare to Compare to seismic data seismic data (PREM, fast, (PREM, fast,

slow)?slow)?

Wt% - build Wt% - build mineralsminerals

Fe partition Fe partition coefficient at coefficient at

each P, Teach P, TVRH end-VRH end-membersmembers

Wt% - build Wt% - build mineralsminerals

Fe partition Fe partition coefficient at coefficient at

each P, Teach P, TVRH end-VRH end-membersmembers

Attenuation? Attenuation? Combine Combine

minerals, VRH minerals, VRH final K,G,Vfinal K,G,V

Attenuation? Attenuation? Combine Combine

minerals, VRH minerals, VRH final K,G,Vfinal K,G,V

Vs, Vp, Vϕ, ρVs, Vp, Vϕ, ρPlot? Data file?Plot? Data file?Vs, Vp, Vϕ, ρVs, Vp, Vϕ, ρ

Plot? Data file?Plot? Data file?

Examples• EOS: Stixrude &

Lithgow-Bertelloni w/ 2nd order thermal corrections

• Minerals: Perovskite (95%) and Ferropericlase (5%)(Murakami, 2012)

• Seismic comparison: PREM

Example 1 cont.

User Defined mineralsAdd to code/minerals.py:

Weight %

Inputs

2+ materialsEnstatite (Javoy, 2010) vs C-Chondrite

(McDonough, 2003)

Mixing?Distribution Coefficent?

Optimize•Compare

Murakami pv and fp at various partition coefficient

•Compare to PREM

•Which partition coefficient works best?

Future Work• Publish BurnMan

• Add in effects of Al

• Include Ca-pv, stishovite

• Mixing wt% phases

• Inverse Model

• Compare fast vs. slow PREM to constrain LLSVPs

• Constrain Mg/Si for whole Lower Mantle

• Mixing models between Upper and Lower mantle

Inverse Model?• Bayesian Inversion

• fit amount perovskite with Murakami pv and fp to prem v_s

• pv = minerals.Murakami_perovskite()

• fp = minerals.Murakami_fp_LS()

• assume 1% error in seismic data

• 32000 samples

• mean: 0.88

Text

Inversions cont.• as before, but track

error in the seismic data as an unknown (normal

• distribution with value sigma in [0,10])

• mean has err=0.31 and perov=0.82 (mean is not that useful...)

• maximum likely answer has err= 0.11 and perov=0.89

• 20000 samples

Yet More Inversionstrack amount perovskite and iron content as unknowns

pv = minerals.mg_fe_perovskite(iron_pv)

fp = minerals.ferropericlase(iron_fp)

only 5000 samples

perov mean: 0.8198

iron_pv mean: 0.1491

iron_fp mean: 0.4413

One More Thing...

•Available Today!

•Includes entire toolbox with ~10 example input files utilizing various aspects of BurnMan

•Ask Cayman for copy from flashdrive

code.google.com/p/burnman/