Melt migration in continental crust modeling of two-phase

Petra Maierová – Pavlína Hasalová – Karel Schulmann

Melt migration in continental crust –modeling of two-phase flow in ASPECT

Migrace taveniny zemskou kůrou – modely dvoufázového tečení v ASPECTu

KG MFF UK 19/5/2021

Motivation – typical view of melt migration through crust

• segregation and migration of melt through interconnected network of veins and/or melt-rich layers and zones (leucosomes)

Himalayan migmatites, formed at 15–20 km depth [Searle et al., 2010]

• a continuous sequence of migmatites in the Bohemian Massif

• change in microstructure from monomineralic bands to isotropic distribution

• lack of segregation structures

gradual change by percolating melt

Motivation – observed sequence of migmatites

• formed from orthogneiss by open-system melt infiltration [Hasalová et al., 2008a,b,c]

• increasing amount of small grains of felsic minerals – crystallized from granitic melt

• small melt fraction (<10 mol.%)

• changes in whole rock composition towards more silica-rich, changes in trace and RE elements

• recorded PT conditions change

from 800°C at 0.8 GPa to 700°C

at 0.5 GPa (15–25 km depth)

• dating shows 10 Myr duration

of the process

[Hasalová et al., 2008a,b,c]

Motivation – observed sequence of migmatites

Motivation – melt imaged by geophysical methods

[Ward et al., 2014]

[Unsworth et al., 2005]

• electric resistivity and seismic data

• high surface heat flow, xenoliths in volcanics show high temperature in MC

Motivation – numerical models

[Keller et al., 2013]

• different styles of melt migration studied numerically – visco-elasto-plastic deformation

• low viscosity (basic) melt, no melting/freezing, only mechanical model

Motivation – numerical models

[Babeyko et al., 2002; Schmeling et al., 2019]

• What are possible styles of melt migration in the hot continental crust?

• At what conditions can melt migrate through the crust without segregating to veins or other conduits?

• Can numerical models of two-phase flow mimic these processes?

Motivation – questions

Goals

• Set up a model of melting and melt migration in thickened continental crust.

• Study the effect of material parameters, temperature conditions...

• Compare obtained models with available data and models.

Basic characteristics of the model

• Two phase flow (solid rock and melt), melting and freezing and temperature evolution.

• Crustal-scale model; deformation at km-scale.

• Focus on the middle–lower crust – only viscous deformation, no description of fracturing.

• Crust-like material properties.

Motivation – goals

• ASPECT code version 2.2.0 https://aspect.geodynamics.org/ • Advanced Solver for Problems in Earth’s ConvecTion • 2D/3D, finite element, parallelized using MPI • installation – compilation from source, installing a virtual machine, using a docker

container • text file with model parameters .prm • definition of material parameters, initial and boundary conditions, postprocessors –

plugins in C++ that can be modified, compiled and linked to ASPECT

[ASPECT: Kronbichler et al., 2012; Heister et al., 2017; Bangerth et al., 2020; Two-phase flow in ASPECT: Dannberg and Heister, 2016]

Model setup

Model setup – conservation of mass

• conservation of mass (fluid and solid):

combined into:

where the fluid velocity is expressed from the Darcy’s law:

ρs,f ... density us,f ... velocity ... porosity Γ ... melting rate KD ... Darcy’s coefficient k ... permeability ηf ... fluid viscosity pf ... fluid pressure

g ... gravity

[McKenzie, 1984; ... Dannberg and Heister, 2016]

• conservation of momentum:

where compaction pressure is defined as:

Model setup – momentum equation

ηs ... shear viscosity ηb ... bulk viscosity pc ... compaction pressure

• heat equation including radiogenic heating and latent heat of melting:

• temperature is the same in the fluid and matrix

• adiabatic and shear heating neglected

Model setup – heat equation

T ... temperature cp ... heat capacity kT ... thermal conductivity H ... volumetric heat sources ΔS ... melting entropy change Γ ... melting rate

• advection of porosity (from conservation of mass):

• advection of depletion/enrichment D:

Model setup – advection of porosity and depletion/enrichment

Model setup – density, thermal parameters

• reference solid density: ρs0 =2700 kg m-3

• depletion dependence: ΔρD = 200 kg m-3

• reference melt density: ρf 0 = 2400 kg m-3

• thermal expansivity: α = 2x10-5 K-1

• thermal conductivity kT: 3 Wm-1K-1

• radiogenic heat sources ρsH: exponential decay with depth

3x10-6 Wm-3 at the surface

background productivity 5x10-7 Wm-3 at depth

• latent heat – melting entropy change ΔS: 300 Jkg-1K-1

Model setup – permeability

[Miller et al., 2014]

• depends on porosity

• permeability prefactor C=200 [Wark and Watson, 1998] – an order of magnitude higher than for mantle rocks

• spacing of pores d corresponds to grain size or to spacing of leucosomes [Schmeling et al., 2018]

• different values tested: d=~10-3–10-1 m, k0=10-8–10-5 m2

• granite flow law assumed representative for crustal rheology – accounts for weak minerals

• depletion dependence of viscosity mimics change to granulitic residuum

Flow laws for granite [Mackwell et al. 1998; Ranalli, 1995], quartz [Gleason and Tullis, 1995; wet and dry quartz: Ranalli, 1995], felsic granulite [Wilks and Carter, 1990], black dashed – applied flow law (=0, D=0)

Model setup – shear viscosity of solid

Model setup – porosity dependence of viscosity

• reduction of shear viscosity by 1–2 orders of magnitude for porosity of 0.1–0.2

• viscosity of ~1016 Pa s estimated from geophysical data from Tibet and Altiplano [Clark and Royden, 2000; Unsworth et al., 2005]

• minimum shear viscosity 1016 Pa s

[Schmeling et al., 2012, for two different geometries of pores]

Model setup – porosity dependence of viscosity

• reduction of shear viscosity by 1–2 orders of magnitude for porosity of 0.1–0.2

• viscosity of ~1016 Pa s estimated from geophysical data from Tibet and Altiplano [Clark and Royden, 2000; Unsworth et al., 2005]

• minimum shear viscosity 1016 Pa s

• bulk viscosity:

or

[Schmeling et al., 2012, for two different geometries of pores; logarithmic limit of bulk viscosity for =0 proposed by Rudge, 2018]

• temperature-dependent relationship valid for a given composition and water content

• calculated 7–8 wt.% of water in melt in Bohemian migmatites; similar as for Himalayan granites

Approximation of experimentally determined felsic melt viscosity [Whittington et al., 2004] for temperature above ~700°C

Model setup – viscosity of melt

• solidus and rock fertility depends on rock composition (dehydration melting) and available fluid (water-fluxed melting) – no simple relationship

[Weinberg and Hasalová, 2015] [after Clemens, 2005]

Model setup – melting parametrization

• prescribed maximum equilibrium melt fraction of 0.3

• equilibrium melt fraction x is used for calculation of the melting rate:

• testing of different values of TS,P=0 , ΔTLS ,

ΔTP , ΔTD

Model setup – melting parametrization

• solidus and liquidus temperatures depend on pressure and depletion:

• initial conditions on temperature:

analytical solution for BCs and radiogenic heat sources

• bottom temperature:

asymmetrically placed Gaussian anomaly of 100 or 200 °C

Model setup – model domain

• quadrilateral finite elements – quadratic us, linear pc, pf, quadratic , D, T, post-processed quadratic uf

• adaptive time-stepping using CFL criterion

• adaptive mesh refinement – finer resolution in sites where melt is present, finest element size ~200 m

• operator splitting method – shorter time step for computation of reaction terms (terms with Γ) in equations for , D and T

Model setup

Results

Example of computational grid

Porosity (= melt fraction)

We tested the effect of:

• permeability

• temperature boundary condition

• melting parametrization

• viscosity

Results – model evolution – low permeability

k0=10-8 m2 (d=~1 mm) • diapirs form and merge into melt-enhanced convection • motion of melt with respect to the solid matrix is slow, but for quick

deformation (high porosity) it can still reach cm per year

maximum velocity of solid: ~10–20 cm/yr

maximum velocity difference between melt and solid: ~1 cm/yr

(at 9 Myr)

time 1 Myr 4 Myr 9 Myr 9 Myr

Depletion/enrichment D

600°C

700°C 800°C

Example: model with TS,P=0 = 600°C, ΔTLS = 1000°C, ΔTP = 100°C/GPa, ΔTD = 300°C and 100°C anomaly at bottom boundary

Porosity

Results – model evolution – medium permeability

k0=10-6 m2 (d=~1 cm) • melt segregates into high-porosity channels • melt-enhanced convection • formation of melt-rich zone in middle crust and depleted lower crust

maximum velocity of solid: ~10 cm/yr


(at 2.6 Myr)

time 0.5 Myr 1 Myr 2.6 Myr 2.6 Myr

Depletion/enrichment D

600°C

700°C 800°C


Porosity

k0=10-5 m2 (d=~5 cm) • quick melt extraction in vertical porosity channels • formation of melt-rich zone in middle crust and depleted lower crust

Results – model evolution – high permeability

maximum velocity of solid: ~20 cm/yr (in the melt-rich middle crust), ~5 cm/yr in the lower crust


(at 0.8 Myr)

time 0.2 Myr 0.5 Myr 0.8 Myr 0.8 Myr

Porosity Depletion/enrichment D

600°C

700°C 800°C


• low solidus, small solidus–liquidus difference, large temperature anomaly at bottom boundary => more melting, melt accumulation in middle crust

• fixed parameters: k0=10-7 m2, ΔTP = 100°C/GPa, ΔTD = 300°C

Results – effect of melting parametrization – temperature

TS,P=0 = 600°C ΔTLS = 1000°C anomaly 100°C





(Snapshots after 2 Myr of model evolution)

Poro

sity

600°C

700°C

800°C

• stronger pressure dependence => more melt in middle crust

• fixed parameters: k0=10-7 m2, ΔTLS = 1000°C, ΔTD = 300°C and 200°C anomaly at bottom boundary; solidus shifted to obtain the same melting temperature at the bottom boundary

Results – effect of melting parametrization – pressure dependence

ΔTP = 100°C/GPa TS,P=0 = 700°C

ΔTP = 150°C/GPa TS,P=0 = 630°C

ΔTP = 50°C/GPa TS,P=0 = 770°C


Poro

sity

600°C

700°C 800°C

fixed parameters: k0=10-7 m2, TS,P=0 =700°C, ΔTLS = 1000°C, ΔTP = 100°C/GPa and 200°C anomaly

fixed parameters: k0=10-6 m2, TS,P=0 =600°C, ΔTLS = 1000°C, ΔTP = 100°C/GPa and 100°C anomaly

Results – effect of melting parametrization – depletion dependence


ΔTD = 0°C ΔTD = 400°C

600°C

700°C

800°C 900°C

ΔTD = 300°C

ΔTD = 0°C ΔTD = 100°C ΔTD = 300°C

• depletion dependence => focusing of melt to high-porosity conduits

Results – effect of viscosity

fixed parameters: k0=10-6 m2, TS,P=0 =600°C, ΔTLS = 1000°C, ΔTD = 300°C, ΔTP = 100°C/GPa and 100°C anomaly

fixed parameters: k0=10-5 m2, TS,P=0 =600°C, ΔTLS = 500°C, ΔTD = 300°C, ΔTP = 100°C/GPa and 100°C anomaly

linear b 0 = 2x1014 Pa s

logarithmic b 0 = 2x1014 Pa s

linear b s increased 5x


• linear vs logarithmic bulk viscosity – small effect • higher viscosity => slower deformation

linear b s cropped at 1016 Pa s

logarithmic b s cropped at 1016 Pa s

linear b s cropped at 1015 Pa s

• The models show different styles of melt migration and solid matrix deformation: diapirism, melt-enhanced convection, km-scale high porosity zones gathering to melt conduits.

• In all models, melt is efficiently removed from the lower crust, with or without significant deformation of the matrix.

• In models, where relative motion between melt and solid is significant, depleted lower crust and enriched upper–middle crust form.

• High velocities are observed in hot partially-molten crust in models with melt-enhanced convection. It is a direct consequence of the low viscosity prescribed.

Summary – melt migration styles

• Permeability of the solid matrix and depletion dependence of melting are the key parameters.

• For a low permeability (spacing of pores = grain size) diapirism and convection occur. Velocity of the melt with respect to the matrix is ~1 cm yr-1 at maximum. For a high permeability (spacing of pores = spacing of melt-rich layers in rock) melt segregates and forms high-porosity conduits and zones.

• Without depletion dependence of melting, the high-porosity conduits and zones do not form.

• Melt flow without segregation as observed in the Bohemian migmatites is obtained in models with low permeability and/or small dependence of melting temperature on depletion.

Summary – segregation of melt and solid

• The applied modeling approach works only for low to medium melt fractions. Disintegration of the solid matrix and magmatic flow is not modeled.

• Linear viscous rheology is assumed. Brittle fracturing and elasticity are not taken into account. Anisotropy of the rock, which might be important especially in the case of metasedimentary rocks, is neglected.

• The applied parametrization of melting is rather artificial – a more natural parametrization based on the rock composition should be tested. Determination of proper depletion dependence is required.

• Gravity is the driving force for deformation and melt migration in our models. Stresses induced by plate motions and variable surface topography may contribute to deformation and influence the style of melt migration.

• Resolution, composition of melt ...

Summary – limitations and future work

Thank you!

This contribution was funded by the Grant Agency of the Czech Republic – grant GAČR EXPRO GX19-27682X. We thank the Computational Infrastructure for Geodynamics (geodynamics.org) which is funded by the National Science Foundation under award EAR-0949446 and EAR-1550901 for supporting the development of ASPECT. References Babeyko et al. (2002). Numerical models of crustal scale convection and partial melting beneath the Altiplano–Puna plateau. Earth and Planetary Science Letters 199.3-4, 373–388. Bangerth et al. (2020). ASPECT v2.2.0. (version v2.2.0). Zenodo. https://doi.org/10.5281/ZENODO.3924604. Bangerth et al. (2020). ASPECT: Advanced Solver for Problems in Earth's ConvecTion, User Manual. https://doi.org/10.6084/m9.figshare.4865333 Beaumont et al. (2004). Crustal channel flows: 1. Numerical models with applications to the tectonics of the Himalayan‐Tibetan orogen. Journal of Geophysical Research: Solid Earth 109.B6 (2004). Clark and Royden (2000). Topographic ooze: Building the eastern margin of Tibet by lower crustal flow. Geology, 28(8), 703-706. Cruden and Weinberg (2018). Mechanisms of magma transport and storage in the lower and middle crust—magma segregation, ascent and emplacement. Volcanic and igneous plumbing systems 13–53. Dannberg and Heister (2016). Compressible Magma/mantle Dynamics: 3-D, Adaptive Simulations in ASPECT. Geophysical Journal International 207 (3) 1343–1366. Gleason and Tullis (1995). A flow law for dislocation creep of quartz aggregates determined with the molten salt cell. Tectonophysics, 247(1-4), 1–23. Hasalová et al. (2008a). From orthogneiss to migmatite: geochemical assessment of the melt infiltration model in the Gföhl Unit (Moldanubian Zone, Bohemian Massif). Lithos, 102(3-4), 508-537. Hasalová et al. (2008b). Origin of migmatites by deformation‐enhanced melt infiltration of orthogneiss: A new model based on quantitative microstructural analysis. Journal of Metamorphic Geology, 26(1), 29-53. Hasalová et al. (2008c). Transforming mylonitic metagranite by open‐system interactions during melt flow. Journal of Metamorphic Geology, 26(1), 55-80.

References and Acknowledgements I

Heister et al. (2017). High Accuracy Mantle Convection Simulation through Modern Numerical Methods – II: Realistic Models and Problems. Geophysical Journal International 210 (2), 833–851. Keller et al. (2013) Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust. Geophysical Journal International 195.3, 1406-1442. Kronbichler et al. (2012). High Accuracy Mantle Convection Simulation through Modern Numerical Methods. Geophysical Journal International 191 (1), 12–29. Mackwell et al. (1998). High‐temperature deformation of dry diabase with application to tectonics on Venus. Journal of Geophysical Research: Solid Earth, 103(B1), 975-984. Miller et al. (2014) Experimental quantification of permeability of partially molten mantle rock. Earth and Planetary Science Letters 388, 273-282. Ranalli (1995). Rheology of the Earth. Springer Science & Business Media. Rudge (2018) The viscosities of partially molten materials undergoing diffusion creep. Journal of Geophysical Research: Solid Earth 123.12, 10–534. Searle et al. (2010) Crustal melt granites and migmatites along the Himalaya: melt source, segregation, transport and granite emplacement mechanisms. Earth and environmental science transactions of the Royal Society of Edinburgh 100.1-2, 219-233. Schmeling et al. (2012). Effective shear and bulk viscosity of partially molten rock based on elastic moduli theory of a fluid filled poroelastic medium. Geophysical Journal International, 190(3), 1571-1578. Schmeling et al. (2019). Modelling melting and melt segregation by two-phase flow: new insights into the dynamics of magmatic systems in the continental crust. Geophysical Journal International, 217(1), 422-450. Unsworth et al. (2005). Crustal rheology of the Himalaya and Southern Tibet inferred from magnetotelluric data. Nature, 438(7064), 78-81. Weinberg and Hasalová (2015). Water-fluxed melting of the continental crust: A review. Lithos, 212, 158-188. Ward et al. (2014) Seismic imaging of the magmatic underpinnings beneath the Altiplano-Puna volcanic complex from the joint inversion of surface wave dispersion and receiver functions. Earth and Planetary Science Letters 404, 43–53. Wark and Watson (1998). Grain-scale permeabilities of texturally equilibrated, monomineralic rocks. Earth and Planetary Science Letters, 164(3-4), 591-605. Wilks and Carter (1990). Rheology of some continental lower crustal rocks. Tectonophysics, 182(1-2), 57-77. Whittington et al. (2005). Experimental temperature-X (H2O)-viscosity relationship for leucogranites and comparison with synthetic silicic liquids. Geol. Soc. Am. Spec. Pap, 389, 59-71.

References and Acknowledgements II

Documents

Melt migration in continental crust modeling of two-phase