Porosity.jl

julia

get Cco2_m(ps_nt)

returns the amount of CO₂ in melt

Arguments

ϕ : melt fraction
Cco2 : bulk CO₂ conc.
Cco2_sat : saturation limit of CO₂ conc. in melt

Usage

The inputs should be in the form of a NamedTuple

julia

ϕ = 0.05
Cco2 = 1000
Cco2_sat = 38e4
ps_nt = (; ϕ, Cco2, Cco2_sat)
get_Cco2_m(ps_nt)

# output

(Cco2_m = 20000.0,)

source

Porosity.get_Ch2o_m Method

julia

get Ch2o_m(ps_nt)

returns the amount of CO₂ in melt and water in the form of NamedTuple

Arguments

ϕ : melt fraction
Cco2 : bulk water conc.
D : partition coefficient

Usage

The inputs should be in the form of a NamedTuple

julia

ϕ = 0.05
Ch2o = 1000
D = 0.005
ps_nt = (; ϕ, Ch2o, D)
get_Ch2o_m(ps_nt)

# output

(Ch2o_m = 18264.840182648404, Ch2o_ol = 91.32420091324202)

source

Porosity.get_melt_fraction Method

julia

get_melt_fraction(ps_nt; H2O_suppress_fn = ΔT_h2o_Blatter2022, CO2_suppress_fn= ΔT_co2_Blatter2022)

returns the melt fraction that is thermodynamically stable at given water conc. and CO₂ conc. for a given dry solidus temperature and pressure

Arguments

Cco2 : bulk CO₂ conc. (ppm), defaults to 0 ppm
Cco2_sat : saturation limit of melt CO₂ conc. (ppm), defaults to 38 wt %
Ch2o : bulk water conc. (ppm), defaults to 0 ppm
T : temperature (K)
T_solidus : solidus temperature (K)
P : Pressure (GPa)
D : water partition coefficient between water and olivine, defaults to 0.005

Keyword Arguments

H2O_suppress_fn : function to calculate suppressed solidus due to presence of water, defaults to ΔT_h2o_Blatter2022
CO2_suppress_fn : function to calculate suppressed solidus due to presence of CO₂, defaults to ΔT_co2_Dasgupta2013

Usage

The inputs should be in the form of a NamedTuple

julia

P = [3.0]
T = (1440:10:1480) .+ 273.0
T_solidus = [1450.0] .+ 273
Ch2o = 100.0
Cco2 = 1000.0

ps_nt = (; P, T, T_solidus, Ch2o, Cco2)
get_melt_fraction(ps_nt)

# output

(ϕ = [0.041345720244193085, 0.05481061353960702, 0.072300827427471, 0.09337629457529527, 0.1171677298066955],)

source

Porosity.solidus_Hirschmann2000 Method

julia

solidus_Hirschmann2000(ps_nt)

returns pressure-dependent dry solidus (in K)

Arguments

P : Pressure in GPa

Optional Arguments

params : variables that parameterize the solidus

Usage

The inputs should be in the form of a NamedTuple, and the output will be a NamedTuple as well with T_solidus as the only field

julia

P = [3.0, 4.0, 5.0]
ps_nt = (; P)
solidus_Hirschmann2000(ps_nt)

References

Marc M. Hirschmann (2000) : Mantle solidus: Experimental constraints and the effects of peridotite composition https://doi.org/10.1029/2000GC000070

source

Porosity.solidus_Katz2003 Method

julia

solidus_Katz2003(ps_nt)

returns pressure-dependent dry solidus (in K)

Arguments

P : Pressure in GPa

Usage

The inputs should be in the form of a NamedTuple, and the output will be a NamedTuple as well with T_solidus as the only field

julia

P = [3.0, 4.0, 5.0]
ps_nt = (; P)
solidus_Katz2003(ps_nt)

References

Katz, R. F., Spiegelman, M., & Langmuir, C. H. (2003) : A new parameterization of hydrous mantle melting. Geochemistry, Geophysics, Geosystems, 4(9), 1–19. https://doi.org/10.1029/2002GC000433

source

Porosity.ΔT_co2_Dasgupta2007 Method

julia

ΔT_co2_Dasgupta2007(ps_nt)

updates solidus with the depressed one because of CO₂ in melt

Arguments

Cco2_m : CO₂ conc. in melt (ppm.)
T_solidus : Temperature of solidus (K)

Usage

The inputs should be in the form of a NamedTuple

julia

P = [3.0]
T_solidus = [1400.0] .+ 273
Cco2_m = 0:200:1000
ps_nt = (; P, T_solidus, Cco2_m)
ΔT_co2_Dasgupta2007(ps_nt)

References

Rajdeep Dasgupta; Marc M. Hirschmann; Neil D. Smith (2007) : Water follows carbon: CO 2 incites deep silicate melting and dehydration beneath mid-ocean ridges, Geology, 2007 https://doi.org/10.1130/G22856A.1

source

Porosity.ΔT_co2_Dasgupta2013 Method

julia

ΔT_co2_Dasgupta2013(ps_nt)

updates solidus with the depressed one because of CO₂ in melt

Arguments

Cco2_m : CO₂ conc. in melt (ppm.)
T_solidus : Temperature of solidus (K)

Usage

The inputs should be in the form of a NamedTuple

julia

P = [3.0]
T_solidus = [1400.0] .+ 273
Cco2_m = 0:200:1000
ps_nt = (; P, T_solidus, Cco2_m)
ΔT_co2_Dasgupta2013(ps_nt)

References

Dasgupta, R., Mallik, A., Tsuno, K. et al. (2013) : Carbon-dioxide-rich silicate melt in the Earth’s upper mantle. Nature 493, 211–215 (2013). https://doi.org/10.1038/nature11731

source

Porosity.ΔT_h2o_Blatter2022 Method

julia

ΔT_h2o_Blatter2022(ps_nt)

updates solidus with the depressed one because of water in melt

Arguments

Ch2o_m : water conc. in melt (ppm.)
T_solidus : Temperature of solidus (K)

Usage

The inputs should be in the form of a NamedTuple

julia

P = [3.0]
T_solidus = [1400.0] .+ 273
Ch2o_m = 0:200:1000
ps_nt = (; P, T_solidus, Ch2o_m)
ΔT_h2o_Blatter2022(ps_nt)

References

Blatter D, Naif S, Key K, Ray A (2022) : A plume origin for hydrous melt at the lithosphere-asthenosphere boundary. Nature. 2022 Apr;604(7906):491-494. doi: 10.1038/s41586-022-04483-w

source

Porosity.ΔT_h2o_Katz2003 Method

julia

ΔT_h2o_Katz2003(ps_nt)

updates solidus with the depressed one because of water in melt

Arguments

P : Pressure (GPa)
T_solidus : solidus temperature (K)
Ch2o_m : melt fraction

Usage

The inputs should be in the form of a NamedTuple, and the output will be a NamedTuple as well with T_solidus as the only field

julia

P = [3.0]
T_solidus = [1400.0] .+ 273
Ch2o_m = 0:200:1000
ps_nt = (; P, T_solidus, Ch2o_m)
ΔT_h2o_Katz2003(ps_nt)

References

Katz, R. F., Spiegelman, M., & Langmuir, C. H. (2003) : A new parameterization of hydrous mantle melting. Geochemistry, Geophysics, Geosystems, 4(9), 1–19. https://doi.org/10.1029/2002GC000433

source

Porosity.Dai_Karato2009 Type

julia

Dai_Karato2009(T, Ch2o_opx)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_opx : water concentration in orthopyroxene (in ppm)

References

Dai, Lidong and Karato, Shun-ichiro (2009), "Electrical conductivity of orthopyroxene: Implications for the water content of the asthenosphere", Proceedings of the Japan Academy, Series B, doi:10.2183/pjab.85.466

Usage

julia

julia> model = Dai_Karato2009(1000 + 273.0, 2e4)
Model : Dai_Karato2009
Temperature (K) : 1273.0
Water concentration in orthopyroxene (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : -1.4966847149880984

source

Porosity.Dai_Karato2009Distribution Type

julia

Dai_Karato2009Distribution(T, Ch2o_opx)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_opx : water concentration in orthopyroxene (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.GAL Type

julia

GAL(m)

Generalized Archie's law for multiple phases

Usage

References

julia

- Glover, P.W.J (2010), A generalized Archie’s law for n phases
https://doi.org/10.1190/1.3509781

source

Porosity.Gaillard2008 Type

julia

Gaillard2008(T)

Electrical conductivity model for melt dependent on Temperature.

Usage

julia

julia> model = Gaillard2008(1000 + 273.0)
Model : Gaillard2008
Temperature (K) : 1273.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : 2.2275677836002115

Arguments

T : Temperature of melt (should be greater than 1146.8 K)

References

Gaillard, Fabrice & Malki, Mohammed & Iacono-Marziano, Giada & Pichavant, Michel & Scaillet, Bruno. (2008), "Carbonatite Melts and Electrical Conductivity in the Asthenosphere", Science (New York, N.Y.). 322. 1363-5, doi: 10.1126/science.1164446.

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Porosity.Gaillard2008Distribution Type

julia

Gaillard2008Distribution(T)

Model Distribution for Gaillard2008[@ref].

Arguments

T : Temperature of melt (in K)

Usage

Refer to the documentation for usage examples.

source

Porosity.HK2003 Type

julia

HK2003(T, P, dg, σ, ϕ, Ch2o_ol = 0.)

Calculate strain rate and viscosity for steady state olivine flow, per Hirth and Kohlstedt (2003), using the three creep mechanisms, i.e., diffusion, dislocation, grain boundary sliding

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity

Optional Arguments

julia

- `Ch2o_ol` : Water concentration in olivine (ppm), defaults to 0 ppm.

Keyword Arguments

julia

- `params` : Various coefficients required for calculation.
Coefficients for different mechanisms (stored in `mechs` field):
    - `diff` : Diffusion creep
    - `disl` : Dislocation creep
    - `gbs`  : Grain boundary sliding 
To investigate coefficients, call `default_params(Val{HK2003})`. 
To modify coefficients, check the relevant documentation page. This
will also users to get any particular type of mechanism, eg. `diff` only
by setting the `A` in `disl` and `gbs` to `0f0`.

`params` for `HK2003` holds another important field:
- `melt_enhancement` : TODO

Usage

julia

julia> T = collect(1073.0f0:40:1273.0f0);

julia> P = 2 .+ zero(T);

julia> dg = collect(3.0f0:8.0f-1:7.0f0);

julia> σ = collect(7.5f0:1.0f0:12.5f0) .* 1.0f-3;

julia> ϕ = collect(1.0f-2:2.0f-3:2.0f-2);

julia> model = HK2003(T, P, dg, σ, ϕ)
Model : HK2003
Temperature (K) : Float32[1073.0, 1113.0, 1153.0, 1193.0, 1233.0, 1273.0]
Pressure (GPa) : Float32[2.0, 2.0, 2.0, 2.0, 2.0, 2.0]
grain size(μm) : Float32[3.0, 3.8, 4.6, 5.4, 6.2, 7.0]
Shear stress (GPa) : Float32[0.0075000003, 0.0085, 0.009500001, 0.010500001, 0.011500001, 0.0125]
Porosity : Float32[0.01, 0.012, 0.014, 0.016, 0.018, 0.02]
Water concentration in olivine (ppm) : 0.0

julia> forward(model, [])
Rock physics Response : RockphyViscous
Strain rate : Float32[3.152961f-11, 9.076501f-11, 2.643556f-10, 7.560147f-10, 2.093749f-9, 5.5805227f-9]
Viscosity (Pa s) : Float32[2.3787166f17, 9.364843f16, 3.5936449f16, 1.3888621f16, 5.4925405f15, 2.2399335f15]

References

Hirth and Kohlstedt, 2003, "Rheology of the Upper Mantle and the Mantle Wedge: A View from the Experimentalists", Inside the Subduction Factory, J. Eiler (Ed.). https://doi.org/10.1029/138GM06

source

Porosity.HK2003Distribution Type

julia

HK2003(T, P, dg, σ, ϕ, Ch2o_ol)

Model Distribution for HK2003[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `Ch2o_ol` : Water concentration in olivine (ppm), defaults to 0 ppm.

Usage

Refer to the documentation for usage examples.

source

Porosity.HS1962_minus Type

julia

HS1962_minus

Hashim-Strikman lower bound for mixing 2 phases

Usage

julia

m = two_phase_modelType(Yoshino2009, Sifre2014, HS1962_minus())

Check out the relevant rock physics documentation.

References

Paul W. J. Glover (2010), "A generalized Archie's law for n phases", Geophysics 2010; 75 (6): E247–E265, doi: https://doi.org/10.1190/1.3509781

source

Porosity.HS1962_plus Type

julia

HS1962_plus

Hashim-Strikman upper bound for mixing 2 phases

Usage

julia

m = two_phase_modelType(Yoshino2009, Sifre2014, HS1962_plus())

Check out the relevant rock physics documentation.

References

Paul W. J. Glover (2010), "A generalized Archie's law for n phases", Geophysics 2010; 75 (6): E247–E265. doi: https://doi.org/10.1190/1.3509781

source

Porosity.HS_minus_multi_phase Type

Hashim-Strikman lower bound for multiple phases

References

julia

- Berryman, J. G. (1995), Mixture Theories for Rock Properties
 https://doi.org/10.1029/RF003p0205

source

Porosity.HS_plus_multi_phase Type

Hashim-Strikman upper bound for multiple phases

References

julia

- Berryman, J. G. (1995), Mixture Theories for Rock Properties
 https://doi.org/10.1029/RF003p0205

source

Porosity.HZK2011 Type

julia

HZK2011(T, P, dg, σ, ϕ)

Calculate strain rate and viscosity for steady state olivine flow, per Zimmerman and Kohlstedt (2011), using the three creep mechanisms, i.e., diffusion, dislocation, grain boundary sliding

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity

Keyword Arguments

julia

- `params` : Various coefficients required for calculation.
Coefficients for different mechanisms (stored in `mechs` field):
    - `diff` : Diffusion creep
    - `disl` : Dislocation creep
    - `gbs`  : Grain boundary sliding 
To investigate coefficients, call `default_params(Val{HZK2011})`. 
To modify coefficients, check the relevant documentation page. This
will also users to get any particular type of mechanism, eg. `diff` only
by setting the `A` in `disl` and `gbs` to `0f0`.

`params` for `HZK2011` holds another important field:
    - `melt_enhancement` : TODO

Usage

julia

julia> T = collect(1073.0f0:40:1273.0f0);

julia> P = 2 .+ zero(T);

julia> dg = collect(3.0f0:8.0f-1:7.0f0);

julia> σ = collect(7.5f0:1.0f0:12.5f0) .* 1.0f-3;

julia> ϕ = collect(1.0f-2:2.0f-3:2.0f-2);

julia> model = HZK2011(T, P, dg, σ, ϕ)
Model : HZK2011
Temperature (K) : Float32[1073.0, 1113.0, 1153.0, 1193.0, 1233.0, 1273.0]
Pressure (GPa) : Float32[2.0, 2.0, 2.0, 2.0, 2.0, 2.0]
grain size(μm) : Float32[3.0, 3.8, 4.6, 5.4, 6.2, 7.0]
Shear stress (GPa) : Float32[0.0075000003, 0.0085, 0.009500001, 0.010500001, 0.011500001, 0.0125]
Porosity : Float32[0.01, 0.012, 0.014, 0.016, 0.018, 0.02]

julia> forward(model, [])
Rock physics Response : RockphyViscous
Strain rate : Float32[8.3687815f-13, 2.4096476f-12, 7.02197f-12, 2.0106366f-11, 5.5824817f-11, 1.4951564f-10]
Viscosity (Pa s) : Float32[8.961879f18, 3.5274867f18, 1.3528968f18, 5.222227f17, 2.060016f17, 8.36033f16]

References

Hansen, Zimmerman and Kohlstedt, 2011, "Grain boundary sliding in San Carlos olivine: Flow law parameters and crystallographic-preferred orientation", J. Geophys. Res., https://doi.org/10.1029/2011JB008220

source

Porosity.HZK2011Distribution Type

julia

HZK2011Distribution(T, P, dg, σ, ϕ)

Model Distribution for HZK2011[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity

Usage

Refer to the documentation for usage examples.

source

Porosity.Jones2012 Type

julia

Jones2012(T, Ch2o_ol)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : water concentration in olivine (in ppm)

Usage

julia

julia> model = Jones2012(1000 + 273.0, 2e4)
Model : Jones2012
Temperature (K) : 1273.0
Water concentration in olivine (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : 0.15504093485137044

References

Jones, A. G., J. Fullea, R. L. Evans, and M. R. Muller (2012), "Water in cratonic lithosphere: Calibrating laboratory-determined models of electrical conductivity of mantle minerals using geophysical and petrological observations", Geochem. Geophys. Geosyst., 13, Q06010, doi:10.1029/2012GC004055.

source

Porosity.Jones2012Distribution Type

julia

Jones2012Distribution(T, Ch2o_ol)

Model Distribution for Jones2012[@ref].

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : Water concentration in olivine (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.MAL Type

julia

MAL

Modified Archie's law for mixing 2 phases

Usage

julia

m = two_phase_modelType(Yoshino2009, Sifre2014, MAL(0.2))

Check out the relevant rock physics documentation.

References

julia

- Glover, P. W. J., Hole, M. J., & Pous, J. (2000),
"A Modified Archie’s Law for two conducting phases", Earth and Planetary Science Letters, 180(3–4), 369–383, 
doi: https://doi.org/10.1016/S0012-821X(00)00168-0

source

Porosity.Ni2011 Type

julia

Ni2011(T, Ch2o_m)

Electrical conductivity model for basaltic melt dependent on Temperature and water content in melt.

Arguments

T : Temperature of melt (should be greater than 1146.8 K)
Ch2o_m : water concentration in melt (in ppm)

Usage

julia

julia> model = Ni2011(1000 + 273.0, 2e4)
Model : Ni2011
Temperature (K) : 1273.0
Water concentration in melt (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : -2.3578741895190163

References

Ni, H., Keppler, H. & Behrens, H. (2011), "Electrical conductivity of hydrous basaltic melts: implications for partial melting in the upper mantle.", Contrib Mineral Petrol 162, 637–650 (2011), doi: https://doi.org/10.1007/s00410-011-0617-4

source

Porosity.Ni2011Distribution Type

julia

Ni2011Distribution(T, Ch2o_m)

Model Distribution for Ni2011[@ref].

Arguments

T : Temperature of melt (in K)
Ch2o_m : Water concentration in melt (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.Poe2010 Type

julia

Poe2010(T, Ch2o_ol)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : water concentration in olivine (in ppm)

Usage

julia

julia> model = Poe2010(1000 + 273.0, 2e4)
Model : Poe2010
Temperature (K) : 1273.0
Water concentration in olivine (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : 3.4473300721921056

References

Brent T. Poe, Claudia Romano, Fabrizio Nestola, Joseph R. Smyth (2010), "Electrical conductivity anisotropy of dry and hydrous olivine at 8GPa", Physics of the Earth and Planetary Interiors,Volume 181, Issues 3–4, 2010, Pages 103-111, ISSN 0031-9201, https://doi.org/10.1016/j.pepi.2010.05.003.

source

Porosity.Poe2010Distribution Type

julia

Poe2010Distribution(T, Ch2o_ol)

Model Distribution for Poe2010[@ref].

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : Water concentration in olivine (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.SEO3 Type

julia

SEO3(T)

Electrical conductivity model for olivine dependent on temperature.

Arguments

julia

- `T` : Temperature of olivine (in K)

Usage

julia

julia> model = SEO3(1000 + 273.0)
Model : SEO3
Temperature (K) : 1273.0

julia> forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : -4.0571856119909375

References

Constable, S (2006), "SEO3: A new model of olivine electrical conductivity", Geophysical Journal International, Volume 166, Issue 1, July 2006, Pages 435–437, https://doi.org/10.1111/j.1365-246X.2006.03041.x

source

Porosity.SEO3Distribution Type

julia

SEO3Distribution(T)

Model Distribution for SEO3[@ref].

Arguments

T : Temperature of olivine (in K)

Usage

Refer to the documentation for usage examples.

source

Porosity.SLB2005 Type

julia

SLB2005(T, P)

Calculate upper mantle shear velocity using Stixrude and Lithgow‐Bertelloni (2005) fit of upper mantle Vs.

Warning

Note that the other parameters (elastic moudli and Vp) are populated with zeros.

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)

Keyword Arguments

julia

- `params` : Various coefficients required for calculation. 
Does not have any coefficients that can be changed and hence is an empty `NamedTuple`

Usage

julia

julia> T = collect(1273.0f0:40:1473.0f0);

julia> P = 2 .+ zero(T);

julia> model = SLB2005(T, P)
Model : SLB2005
Temperature (K) : Float32[1273.0, 1313.0, 1353.0, 1393.0, 1433.0, 1473.0]
Pressure (GPa) : Float32[2.0, 2.0, 2.0, 2.0, 2.0, 2.0]

julia> forward(model, [])
Rock physics Response : RockphyElastic
Elastic shear modulus (Pa) : Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
Elastic bulk modulus (Pa) : Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
Elastic P-wave velocity (m/s) : Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
Elastic S-wave velocity (m/s) : [4478.205990493298, 4463.085990846157, 4447.965991199017, 4432.845991551876, 4417.725991904736, 4402.605992257595]

References

Stixrude and Lithgow‐Bertelloni (2005), "Mineralogy and elasticity of the oceanic upper mantle: Origin of the low‐velocity zone." JGR 110.B3, https://doi.org/10.1029/2004JB002965

source

Porosity.SLB2005Distribution Type

julia

SLB2005Distribution(T, P)

Model Distribution for SLB2005[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)

Usage

Refer to the documentation for usage examples.

source

Porosity.Sifre2014 Type

julia

Sifre2014(T, Ch2o_m, Cco2_m)

Electrical conductivity model for melt dependent on Temperature, water content and CO₂ content in melt.

Arguments

T : Temperature of melt (should be greater than 1146.8 K)
Ch2o_m : water concentration in melt (in ppm)
Cco2_m : Co2 concentration in melt (in ppm)

Usage

julia

julia> model = Sifre2014(1000 + 273.0, 2e4, 2e4)
Model : Sifre2014
Temperature (K) : 1273.0
Water concentration in melt (ppm) : 20000.0
CO₂ concentration in melt (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : -0.012765453025208906

References

Sifré, D., Gardés, E., Massuyeau, M. et al. (2014), "Electrical conductivity during incipient melting in the oceanic low-velocity zone." Nature 509, 81–85 (2014), doi: https://doi.org/10.1038/nature13245

source

Porosity.Sifre2014Distribution Type

julia

Sifre2014Distribution(T, Ch2o_m, Cco2_m)

Model Distribution for Sifre2014[@ref].

Arguments

T : Temperature of melt (in K)
Ch2o_m : Water concentration in melt (in ppm)
Cco2_m : CO₂ concentration in melt (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.UHO2014 Type

julia

UHO2014(T, Ch2o_ol)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : water concentration in olivine (in ppm)

References

Gardés, E., F. Gaillard, and P. Tarits (2014), "Toward a unified hydrous olivine electrical conductivity law", Geochem. Geophys. Geosyst., 15, 4984–5000, doi:10.1002/2014GC005496.

Usage

julia

julia> model = UHO2014(1000 + 273.0, 2e4)
Model : UHO2014
Temperature (K) : 1273.0
Water concentration in olivine (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : 1.2727662435353444

source

Porosity.UHO2014Distribution Type

julia

UHO2014Distribution(T, Ch2o_ol)

Model Distribution for UHO2014[@ref].

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : Water concentration in olivine (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.Wang2006 Type

julia

Wang2006(T, Ch2o_ol)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : water concentration in olivine (in ppm)

Usage

julia

julia> model = Wang2006(1000 + 273.0, 2e4)
Model : Wang2006
Temperature (K) : 1273.0
Water concentration in olivine (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : -0.383209519477097

References

Wang, D., Mookherjee, M., Xu, Y. et al. (2006), "The effect of water on the electrical conductivity of olivine", Nature 443, 977–980 (2006), doi: https://doi.org/10.1038/nature05256

source

Porosity.Wang2006Distribution Type

julia

Wang2006Distribution(T, Ch2o_ol)

Model Distribution for Wang2006[@ref].

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : Water concentration in olivine (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.Yang2011 Type

julia

Yang2011(T, Ch2o_cpx)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_cpx : water concentration in olivine (in ppm)

References

Yang, Xiaozhi and Keppler, Hans and McCammon, Catherine and Ni, Huaiwei and Xia, Qunke and Fan, Qicheng (2011), "Effect of water on the electrical conductivity of lower crustal clinopyroxene", Journal of Geophysical Research, doi:https://doi.org/10.1029/2010JB008010

Usage

julia

julia> model = Yang2011(1000 + 273.0, 2e4)
Model : Yang2011
Temperature (K) : 1273.0
Water concentration in clinopyroxene (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : 1.0103884511392625

source

Porosity.Yang2011Distribution Type

julia

Yang2011Yang2011Distribution(T, Ch2o_cpx)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_cpx : water concentration in olivine (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.Yoshino2009 Type

julia

Yoshino2009(T, Ch2o_ol)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : water concentration in olivine (in ppm)

Usage

julia

julia> model = Yoshino2009(1000 + 273.0, 2e4)
Model : Yoshino2009
Temperature (K) : 1273.0
Water concentration in olivine (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : -0.6428765173222217

References

Takashi Yoshino, Takuya Matsuzaki, Anton Shatskiy, Tomoo Katsura (2009), "The effect of water on the electrical conductivity of olivine aggregates and its implications for the electrical structure of the upper mantle, Earth and Planetary Science Letters", Volume 288, Issues 1–2, 2009, Pages 291-300, ISSN 0012-821X, https://doi.org/10.1016/j.epsl.2009.09.032

source

Porosity.Yoshino2009Distribution Type

julia

Yoshino2009Distribution(T, Ch2o_ol)

Model Distribution for Yoshino2009[@ref].

Arguments

T : Temperature of olivine (in K)
Ch2o_ol : Water concentration in olivine (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.Zhang2012 Type

julia

Zhang2012(T, Ch2o_opx)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_opx : water concentration in olivine (in ppm)

References

todo

Usage

julia

julia> model = Zhang2012(1000 + 273.0, 2e4)
Model : Zhang2012
Temperature (K) : 1273.0
Water concentration in orthopyroxene (ppm) : 20000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : -0.045414286402875675

source

Porosity.Zhang2012Distribution Type

julia

Zhang2012Distribution(T, Ch2o_opx)

Electrical conductivity model for olivine dependent on temperature and water concentration.

Arguments

T : Temperature of olivine (in K)
Ch2o_opx : water concentration in olivine (in ppm)

Usage

Refer to the documentation for usage examples.

source

Porosity.andrade_analytical Type

julia

andrade_analytical(T, P, dg, σ, ϕ, ρ, f)

Calculate anelastic properties stored in RockPhyAnelastic using the Master curve maxwell scaling per McCarthy, Takei and Hiraga (2011)

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `Ch2o_ol` : water concentration in olivine (in ppm), only used when using `HK2003` for viscosity calculations
- `T_solidus` : Solidus temperature (K), only used when using `xfit_premelt` for viscosity calculations
- `f` : frequency

Keyword Arguments

julia

- `params` : Various coefficients required for calculation. 
Also holds coefficients and the type of `RockphyElastic` model and `RockphyViscous model` to be used.

To investigate coefficients, call `default_params(Val{xfit_premelt}())`. 
To modify coefficients, check the relevant documentation page. This
will also users to pick any particular type of `RockphyElastic` model, defaults to `anharmonic`,
as well as `RockphyViscous` model (for diffusion-derived viscosity), defaults to `HK2003`

Usage

Note

Make sure that the dimension of vector f is one more than the other parameters. Check relevant tutorials. Note the transpose on f when making the model in the following eg.

julia

julia> T = [800, 1000] .+ 273.0f0;

julia> P = 2 .+ zero(T);

julia> dg = 4.0f0;

julia> σ = 10.0f-3;

julia> ϕ = 1.0f-2;

julia> ρ = 3300.0f0;

julia> Ch2o_ol = 0.0f0;

julia> T_solidus = 900 + 273.0f0;

julia> f = [1.0f0, 1.0f1];

julia> model = andrade_analytical(T, P, dg, σ, ϕ, ρ, Ch2o_ol, T_solidus, f')
Model : andrade_analytical
Temperature (K) : Float32[1073.0, 1273.0]
Pressure (GPa) : Float32[2.0, 2.0]
grain size(μm) : 4.0
Shear stress (GPa) : 0.01
Porosity : 0.01
Density (kg/m³) : 3300.0
Water concentration in olivine (ppm) : 0.0
Solidus Temperature (K) : 1173.0
Frequency (Hz) : Float32[1.0 10.0]

julia> forward(model, [])
Rock physics Response : RockphyAnelastic
Real part of dynamic compliance (Pa⁻¹) : Float32[1.3498141f-11 1.34976925f-11; 1.4012593f-11 1.4012127f-11]
Imaginary part of dynamic compliance (Pa⁻¹) : Float32[3.2687721f-16 1.5162017f-16; 6.353883f-16 1.8700414f-16]
Attenuation : Float32[2.4216462f-5 1.1233044f-5; 4.534409f-5 1.3345877f-5]
Modulus (Pa) : Float32[7.408428f10 7.4086736f10; 7.136438f10 7.1366754f10]
Anelastic S-wave velocity : (m/s) : Float32[4738.12 4738.1987; 4650.33 4650.4077]
Frequency averaged S-wave velocity (m/s) : Float32[4738.159, 4650.369]

References

Andrade, 1910, "On the viscous flow in metals, and allied phenomena", Proceedings of the Royal Society of London, https://doi.org/10.1098/rspa.1910.0050
Cooper, 2002, "Seismic Wave Attenuation: Energy Dissipation in Viscoelastic Crystalline Solids", Reviews in mineralogy and geochemistry, https://doi.org/10.2138/gsrmg.51.1.253,
Lau and Holtzman, 2019, "“Measures of Dissipation in Viscoelastic Media” Extended: Toward Continuous Characterization Across Very Broad Geophysical Time Scales", Geophysical Research Letters, https://doi.org/10.1029/2019GL083529

source

Porosity.andrade_analyticalDistribution Type

julia

andrade_analyticalDistribution(T, P, dg, σ, ϕ, ρ, f)

Model Distribution for xfit_mxw[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `Ch2o_ol` : water concentration in olivine (in ppm), only used when using `HK2003` for viscosity calculations
- `T_solidus` : Solidus temperature (K), only used when using `xfit_premelt` for viscosity calculations
- `f` : frequency

Usage

Refer to the documentation for usage examples.

source

Porosity.andrade_psp Type

julia

andrade_psp(T, P, dg, σ, ϕ, ρ, f)

Calculate anelastic properties stored in RockPhyAnelastic using the Andrade model with pseudo-scaling per Jackson and Faul (2010)

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `f` : frequency

Keyword Arguments

julia

- `params` : Various coefficients required for calculation.
Also holds coefficients and the type of `RockphyElastic` model to be used.

To investigate coefficients, call `default_params(Val{andrade_psp}())`. 
To modify coefficients, check the relevant documentation page. This
will also users to pick any particular type of `RockphyElastic` model, defaults to `anharmonic`.

Usage

Note

Make sure that the dimension of vector f is one more than the other parameters. Check relevant tutorials. Note the transpose on f when making the model in the following eg.

julia

julia> T = [800, 1000] .+ 273.0f0;

julia> P = 2 .+ zero(T);

julia> dg = 4.0f0;

julia> σ = 10.0f-3;

julia> ϕ = 1.0f-2;

julia> ρ = 3300.0f0;

julia> f = [1.0f0, 1.0f1];

julia> model = andrade_psp(T, P, dg, σ, ϕ, ρ, f')
Model : andrade_psp
Temperature (K) : Float32[1073.0, 1273.0]
Pressure (GPa) : Float32[2.0, 2.0]
grain size(μm) : 4.0
Shear stress (GPa) : 0.01
Porosity : 0.01
Density (kg/m³) : 3300.0
Frequency (Hz) : Float32[1.0 10.0]

julia> forward(model, [])
Rock physics Response : RockphyAnelastic
Real part of dynamic compliance (Pa⁻¹) : Float32[1.35194625f-11 1.35077696f-11; 1.4162938f-11 1.4082101f-11]
Imaginary part of dynamic compliance (Pa⁻¹) : Float32[1.259776f-14 5.8473344f-15; 8.712478f-14 4.0431112f-14]
Attenuation : Float32[0.00093182403 0.00043288674; 0.006151603 0.0028710994]
Modulus (Pa) : Float32[7.39674f10 7.403146f10; 7.060549f10 7.1011836f10]
Anelastic S-wave velocity : (m/s) : Float32[4734.381 4736.4307; 4625.538 4638.8296]
Frequency averaged S-wave velocity (m/s) : Float32[4735.406, 4632.1836]

References

Jackson and Faul, 2010, "Grainsize-sensitive viscoelastic relaxation in olivine: Towards a robust laboratory-based model for seismological application", Phys. Earth Planet. Inter., https://doi.org/10.1016/j.pepi.2010.09.005

source

Porosity.andrade_pspDistribution Type

julia

andrade_pspDistribution(T, P, dg, σ, ϕ, ρ, f)

Model Distribution for andrade_psp[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `f` : frequency

Usage

Refer to the documentation for usage examples.

source

Porosity.anharmonic Type

julia

anharmonic(T, P, ρ)

Calculate unrelaxed elastic bulk moduli, shear moduli, Vp and Vs using anharmonic scaling

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `ρ` : Density of the rock (kg/m³)

Keyword Arguments

julia

- `params` : Various coefficients required for calculation. 
Available options are 
    - `params_anharmonic.Isaak1992`
    - `params_anharmonic.Cammarono2003`
Defaults to the ones provided by Isaak (1992), check references. 
To investigate coefficients, call `default_params(Val{anharmonic}())`. 
To modify coefficients, check the relevant documentation page.

Usage

julia

julia> T = collect(1273.0f0:40:1473.0f0);

julia> P = 2 .+ zero(T);

julia> ρ = collect(3300.0f0:200.0f0:4300.0f0);

julia> model = anharmonic(T, P, ρ)
Model : anharmonic
Temperature (K) : Float32[1273.0, 1313.0, 1353.0, 1393.0, 1433.0, 1473.0]
Pressure (GPa) : Float32[2.0, 2.0, 2.0, 2.0, 2.0, 2.0]
Density (kg/m³) : Float32[3300.0, 3500.0, 3700.0, 3900.0, 4100.0, 4300.0]

julia> forward(model, [])
Rock physics Response : RockphyElastic
Elastic shear modulus (Pa) : Float32[7.136702f10, 7.082302f10, 7.027902f10, 6.9735014f10, 6.919102f10, 6.864702f10]
Elastic bulk modulus (Pa) : Float32[1.1894502f11, 1.18038364f11, 1.1713171f11, 1.1622502f11, 1.1531837f11, 1.1441169f11]
Elastic P-wave velocity (m/s) : Float32[8054.7563, 7791.3696, 7548.708, 7324.0913, 7115.3057, 6920.496]
Elastic S-wave velocity (m/s) : Float32[4650.416, 4498.3496, 4358.2485, 4228.5664, 4108.0234, 3995.5503]

References

Cammarano et al. (2003), "Inferring upper-mantle temperatures from seismic velocities", Physics of the Earth and Planetary Interiors, Volume 138, Issues 3–4, https://doi.org/10.1016/S0031-9201(03)00156-0
Isaak, D. G. (1992), "High‐temperature elasticity of iron‐bearing olivines", J. Geophys. Res., 97( B2), 1871– 1885, https://doi.org/10.1029/91JB02675

source

Porosity.anharmonicDistribution Type

julia

anharmonicDistribution(T, P, ρ)

Model Distribution for anharmonic_poro[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `ρ` : Density of the rock (kg/m³)

Usage

Refer to the documentation for usage examples.

source

Porosity.anharmonic_poro Type

julia

anharmonic_poro(T, P, ρ, ϕ)

Calculate unrelaxed elastic bulk moduli, shear moduli, Vp and Vs after applying correction for poro-elasticity using Takei (2002) on anharmonic scaling

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `ρ` : Density of the rock (kg/m³)
- `ϕ` : Porosity of the rock

Keyword Arguments

julia

- `params` : Various coefficients required for calculation. 
Contains a `p_anharmonic` which have the coefficients for [`anharmonic`](@ref)
calculations. 
To investigate coefficients, call `default_params(Val{anharmonic_poro}())`. 
To modify coefficients, check the relevant documentation page.

Usage

julia

julia> T = collect(1273.0f0:40:1473.0f0);

julia> P = 2 .+ zero(T);

julia> ρ = collect(3300.0f0:200.0f0:4300.0f0);

julia> ϕ = collect(1.0f-2:2.0f-3:2.0f-2);

julia> model = anharmonic_poro(T, P, ρ, ϕ)
Model : anharmonic_poro
Temperature (K) : Float32[1273.0, 1313.0, 1353.0, 1393.0, 1433.0, 1473.0]
Pressure (GPa) : Float32[2.0, 2.0, 2.0, 2.0, 2.0, 2.0]
Density (kg/m³) : Float32[3300.0, 3500.0, 3700.0, 3900.0, 4100.0, 4300.0]
Porosity : Float32[0.01, 0.012, 0.014, 0.016, 0.018, 0.02]

julia> forward(model, [])
Rock physics Response : RockphyElastic
Elastic shear modulus (Pa) : Float32[6.90533f10, 6.8138574f10, 6.723185f10, 6.633203f10, 6.5438487f10, 6.4550883f10]
Elastic bulk modulus (Pa) : Float32[1.1665774f11, 1.1534928f11, 1.1405562f11, 1.127763f11, 1.11511036f11, 1.102595f11]
Elastic P-wave velocity (m/s) : Float32[7953.0596, 7675.5776, 7419.807, 7182.9395, 6962.659, 6757.0347]
Elastic S-wave velocity (m/s) : Float32[4574.4116, 4412.2744, 4262.7188, 4124.1016, 3995.0728, 3874.5107]

References

Takei, 2002, "Effect of pore geometry on VP/VS: From equilibrium geometry to crack", JGR Solid Earth, https://doi.org/10.1029/2001JB000522

source

Porosity.anharmonic_poroDistribution Type

julia

anharmonic_poroDistribution(T, P, ρ, ϕ)

Model Distribution for anharmonic[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `ρ` : Density of the rock (kg/m³)
- `ϕ` : Porosity of the rock

Usage

Refer to the documentation for usage examples.

source

Porosity.const_matrix Type

julia

const_matrix(σ)

Fixed electrical conductivity model for the phase.

Arguments

σ : Conductivity of the phase

Usage

julia

julia> model = const_matrix(1000.0)
Model : const_matrix
Conductivity (S/m) : 1000.0

julia> log_cond = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : 3.0

source

Porosity.const_matrixDistribution Type

julia

const_matrixDistribution(σ)

Model Distribution for const_matrix[@ref].

Arguments

σ : Conductivity of the phase

Usage

Refer to the documentation for usage examples.

source

Porosity.eburgers_psp Type

julia

eburgers_psp(T, P, dg, σ, ϕ, ρ, Ch2o_ol, T_solidus, f)

Calculate anelastic properties stored in RockphyAnelastic using the Extended Burgers model with pseudo-scaling per Jackson and Faul (2010)

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `Ch2o_ol` : water concentration in olivine (in ppm)
- `T_solidus` : Solidus temperature (K), only used when using `xfit_premelt` for viscosity calculations, when scaling from Jackson and Faul (2010) for maxwell time calculations is not used
- `f` : frequency

Keyword Arguments

julia

- `params` : Various coefficients required for calculation.
Also holds coefficients and the type of `RockphyElastic` model and `RockphyViscous model` to be used.

To investigate coefficients, call `default_params(Val{eburgers_psp}())`. 
To modify coefficients, check the relevant documentation page. This
will also users to pick any particular type of `RockphyElastic` model, defaults to `anharmonic`,
as well as `RockphyViscous` model (for diffusion-derived viscosity), defaults to `xfit_premelt`

`params` for `eburgers_psp` holds a few important fields:
    - `params_btype` : fitting parameters from Jackson and Faul (2010) to be used, defaults to `bg_only`. 
    Available options are : 
        - `bg_only` : multiple sample best high-temp background only fit
        - `bg_peak` : multiple sample best high-temp background + peak fit
        - `s6585_bg_only` : single sample 6585 fit, HTB only
        - `s6585_bg_peak` : single sample 6585 fit, HTB + dissipation peak

    - `melt_enhancement` : TODO

    -  `JF10_visc` : Whether to use scaling from Jackson and Faul (2010) for maxwell time calculations,
    otherwise calculate them using the `RockphyViscous` model provide. **Defaults to `true`.**

    - `integration_params` : Tells which integration option to be used, 
    and the number of points (Should not be touched ideally!)
    Available options are `quadgk`, `trapezoidal` and `simpson`, defaults to `quadgk`.

Usage

Note

Make sure that the dimension of vector f is one more than the other parameters. Check relevant tutorials. Note the transpose on f when making the model in the following eg.

julia

julia> T = [800, 1000] .+ 273.0f0;

julia> P = 2 .+ zero(T);

julia> dg = 4.0f0;

julia> σ = 10.0f-3;

julia> ϕ = 1.0f-2;

julia> ρ = 3300.0f0;

julia> Ch2o_ol = 0.0f0;

julia> T_solidus = 900 + 273.0f0;

julia> f = [1.0f0, 1.0f1];

julia> model = eburgers_psp(T, P, dg, σ, ϕ, ρ, Ch2o_ol, T_solidus, f')
Model : eburgers_psp
Temperature (K) : Float32[1073.0, 1273.0]
Pressure (GPa) : Float32[2.0, 2.0]
grain size(μm) : 4.0
Shear stress (GPa) : 0.01
Porosity : 0.01
Density (kg/m³) : 3300.0
Water concentration in olivine (ppm) : 0.0
Solidus Temperature (K) : 1173.0
Frequency (Hz) : Float32[1.0 10.0]

julia> forward(model, [])
Rock physics Response : RockphyAnelastic
Real part of dynamic compliance (Pa⁻¹) : Float32[1.3524236f-11 1.3499646f-11; 1.42722735f-11 1.413697f-11]
Imaginary part of dynamic compliance (Pa⁻¹) : Float32[2.754988f-14 8.080778f-15; 1.29419f-13 7.1557296f-14]
Attenuation : Float32[0.0020370746 0.00059859187; 0.009067862 0.0050617135]
Modulus (Pa) : Float32[7.394117f10 7.4076004f10; 7.006304f10 7.073561f10]
Anelastic S-wave velocity : (m/s) : Float32[4733.5415 4737.8555; 4607.7354 4629.7983]
Frequency averaged S-wave velocity (m/s) : Float32[4735.698, 4618.7666]

References

Faul and Jackson, 2015, "Transient Creep and Strain Energy Dissipation: An Experimental Perspective", Ann. Rev. of Earth and Planetary Sci., https://doi.org/10.1146/annurev-earth-060313-054732
Jackson and Faul, 2010, "Grainsize-sensitive viscoelastic relaxation in olivine: Towards a robust laboratory-based model for seismological application", Phys. Earth Planet. Inter., https://doi.org/10.1016/j.pepi.2010.09.005

source

Porosity.eburgers_pspDistribution Type

julia

eburgers_pspDistribution(T, P, dg, σ, ϕ, ρ, f)

Model Distribution for eburgers_psp[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `f` : frequency

Usage

Refer to the documentation for usage examples.

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Porosity.multi_phase_model Type

julia

multi_phase_model(m1, m2, m3, m4, m5, m6, m7, m8, mix)
multi_phase_model(m1, ..., mix)

Rock physics model Type to combine multiple (upto 8) phases.

Arguments

m1 : model corresponding to phase 1
m2 : model corresponding to phase 2 (optional)
m3 : model corresponding to phase 3 (optional)
m4 : model corresponding to phase 4 (optional)
m5 : model corresponding to phase 5 (optional)
m6 : model corresponding to phase 6 (optional)
m7 : model corresponding to phase 7 (optional)
m8 : model corresponding to phase 8 (optional)
mix : mixing type, available options are HS_plus_multi_phase(), HS_minus_multi_phase, GAL(m)

Usage

julia

julia> m = multi_phase_modelType(SEO3, Ni2011, Yang2011, HS_plus_multi_phase);

julia> T = [900.0f0, 1000.0f0] .+ 273;

julia> P = 3.0f0;

julia> ρ = 3300.0f0;

julia> Ch2o_m = 1000.0f0;

julia> Ch2o_cpx = 100.0f0;

julia> ϕ = [0.8f0, 0.1f0];

julia> ps_nt = ps_nt = (; T, P, ρ, Ch2o_m, Ch2o_cpx, ϕ);

julia> model = m(ps_nt)
multi-phase composition using HS_plus_multi_phase()

*    m₁ : 
Model : SEO3
Temperature (K) : Float32[1173.0, 1273.0]
ϕ : 0.8

*    m₂ : 
Model : Ni2011
Temperature (K) : Float32[1173.0, 1273.0]
Water concentration in melt (ppm) : 1000.0
ϕ : 0.1

*    m₃ : 
Model : Yang2011
Temperature (K) : Float32[1173.0, 1273.0]
Water concentration in clinopyroxene (ppm) : 100.0
ϕ : 0.099999964

julia> forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : Float32[-26.768837, -3.9526708]

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Porosity.multi_phase_modelDistribution Type

julia

multi_phase_modelDistribution(m1, m2, m3, m4, m5, m6, m7, m8, mix)
multi_phase_modelDistribution(m1, ..., mix)

Rock physics model Type to combine multiple (upto 8) phases.

Arguments

m1 : model distribution corresponding to phase 1
m2 : model distribution corresponding to phase 2 (optional)
m3 : model distribution corresponding to phase 3 (optional)
m4 : model distribution corresponding to phase 4 (optional)
m5 : model distribution corresponding to phase 5 (optional)
m6 : model distribution corresponding to phase 6 (optional)
m7 : model distribution corresponding to phase 7 (optional)
m8 : model distribution corresponding to phase 8 (optional)
mix : mixing type, available options are HS_plus_multi_phase(), HS_minus_multi_phase, GAL(m_GAL)

Usage

TODO

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Porosity.multi_phase_modelDistributionType Type

julia

multi_phase_modelDistributionType(m1, m2, m3, m4, m5, m6, m7, m8, mix)
multi_phase_modelDistributionType(m1, ..., mix)

Rock physics model Type to combine multiple (upto 8) phases.

Arguments

m1 : model distribution type corresponding to phase 1
m2 : model distribution type corresponding to phase 2 (optional)
m3 : model distribution type corresponding to phase 3 (optional)
m4 : model distribution type corresponding to phase 4 (optional)
m5 : model distribution type corresponding to phase 5 (optional)
m6 : model distribution type corresponding to phase 6 (optional)
m7 : model distribution type corresponding to phase 7 (optional)
m8 : model distribution type corresponding to phase 8 (optional)
mix : mixing type, available options are HS_plus_multi_phase, HS_minus_multi_phase, GAL

Usage

julia

multi_phase_modelDistributionType(
    SEO3Distribution, Ni2011Distribution, Yang2011Distribution, HS_plus_multi_phase)

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Porosity.multi_phase_modelType Type

julia

multi_phase_modelType(m1, m2, m3, m4, m5, m6, m7, m8, mix)
multi_phase_modelType(m1, ..., mix)

Rock physics model Type to combine multiple (upto 8) phases.

Arguments

m1 : model type corresponding to phase 1
m2 : model type corresponding to phase 2 (optional)
m3 : model type corresponding to phase 3 (optional)
m4 : model type corresponding to phase 4 (optional)
m5 : model type corresponding to phase 5 (optional)
m6 : model type corresponding to phase 6 (optional)
m7 : model type corresponding to phase 7 (optional)
m8 : model type corresponding to phase 8 (optional)
mix : mixing type, available options are HS_plus_multi_phase, HS_minus_multi_phase, GAL

Usage

julia

multi_phase_modelType(SEO3, Ni2011, Yang2011, HS_plus_multi_phase)

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Porosity.multi_rp_model Type

julia

multi_rp_model(cond, elastic, visc, anelastic)

Rock physics model to capture multiple rock physics models, usually constructed through multi_rp_modelType[@ref]

Arguments

cond : conductivity rock physics model
elastic : elastic rock physics model
visc : viscous rock physics model
anelastic : anelastic rock physics model

Usage

julia

m = multi_rp_modelType()(SEO3, anharmonic, Nothing, Nothing)
ps_nt = ps_nt = (;
    T=[800.0f0, 1000.0f0] .+ 273, P=3.0f0, ρ=3300.0f0, Ch2o_m=1000.0f0, ϕ=0.1f0)
model = m(ps_nt)

resp = forward(model)

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Porosity.multi_rp_modelDistribution Type

julia

multi_rp_model(con, elastic, visc, anelastic)

Rock physics model to capture multiple rock physics model, susually constructed through multi_rp_modelDistributionType[@ref]

Arguments

cond : conductivity rock physics modelDistribution
elastic : elastic rock physics modelDistribution
visc : viscous rock physics modelDistribution
anelastic : anelastic rock physics modelDistribution

Usage

julia

m = multi_rp_modelDistributionType()(SEO3Distribution, anharmonicDistribution, Nothing, Nothing)
ps_nt_dist = (; T=product_distribution(Uniform(1200.0f0, 1400.0f0)), P=[3.0f0],
    ρ=product_distribution(Uniform(80.0f0, 120.0f0)), ϕ=[0.1f0])
model = m(ps_nt_dist)

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Porosity.multi_rp_modelDistributionType Type

julia

multi_rp_modelDistributionType(con, elastic, visc, anelastic)

Rock physics model distribution type to capture multiple rock physics model distribution

Arguments

cond : conductivity rock physics modeldistribution type, subtype of AbstractCondModelDistributionType
elastic : elastic rock physics distribution model type, subtype of AbstractElasticModelDistributionType
visc : viscous rock physics distribution model type, subtype of AbstractViscousModelDistributionType
anelastic : anelastic rock physics distribution model type, subtype of AbstractAnelasticModelDistributionType

Usage

Similar to multi_rp_modelDistributionType but instead accepts Distribution or Nothing

julia

multi_rp_modelDistributionType()(SEO3Distribution, anharmonicDistribution, HK2003Distribution, Nothing)

Pass Nothing for the types you do not want responses of, eg. above does not compute for the anelastic type

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Porosity.multi_rp_modelType Type

julia

multi_rp_modelType(con, elastic, visc, anelastic)

Rock physics model type to capture multiple rock physics models

Arguments

cond : conductivity rock physics model type, subtype of AbstractCondModel
elastic : elastic rock physics model type, subtype of AbstractElasticModel
visc : viscous rock physics model type, subtype of AbstractViscousModel
anelastic : anelastic rock physics model type, subtype of AbstractAnelasticModel

Usage

julia

multi_rp_modelType()(SEO3, anharmonic, HK2003, Nothing)

Pass Nothing for the types you do not want responses of, eg. above does not compute for the anelastic type

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Porosity.premelt_anelastic Type

julia

premelt_anelastic(T, P, dg, σ, ϕ, ρ, T_solidus, Ch2o_ol, f)

Calculate anelastic properties stored in RockPhyAnelastic using the Master curve maxwell scaling per near-solidus parametrization of Yamauchi and Takei (2016), with optional extension to include direct melt effects of Yamauchi and Takei (2024)

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `Ch2o_ol` : water concentration in olivine (in ppm)
- `T_solidus` : Solidus temperature (K)
- `f` : frequency

Keyword Arguments

julia

- `params` : Various coefficients required for calculation.
Also holds coefficients and the type of `RockphyElastic` model and `RockphyViscous model` to be used.

To investigate coefficients, call `default_params(Val{xfit_premelt}())`. 
To modify coefficients, check the relevant documentation page. This
will also users to pick any particular type of `RockphyElastic` model, defaults to `anharmonic`.

`params` for `premelt_anelastic` holds another important field:
    - `include_direct_melt_effect` : Whether to include the melt effect of Yamauchi and Takei (2024), defaults to false

Usage

Note

Make sure that the dimension of vector f is one more than the other parameters. Check relevant tutorials. Note the transpose on f when making the model in the following eg.

julia

julia> T = [800, 1000] .+ 273.0f0;

julia> P = 2 .+ zero(T);

julia> dg = 4.0f0;

julia> σ = 10.0f-3;

julia> ϕ = 1.0f-2;

julia> ρ = 3300.0f0;

julia> Ch2o_ol = 0.0f0;

julia> T_solidus = 900 + 273.0f0;

julia> f = [1.0f0, 1.0f1];

julia> model = premelt_anelastic(T, P, dg, σ, ϕ, ρ, Ch2o_ol, T_solidus, f')
Model : premelt_anelastic
Temperature (K) : Float32[1073.0, 1273.0]
Pressure (GPa) : Float32[2.0, 2.0]
grain size(μm) : 4.0
Shear stress (GPa) : 0.01
Porosity : 0.01
Density (kg/m³) : 3300.0
Water concentration in olivine (ppm) : 0.0
Solidus Temperature (K) : 1173.0
Frequency (Hz) : Float32[1.0 10.0]

julia> forward(model, [])
Rock physics Response : RockphyAnelastic
Real part of dynamic compliance (Pa⁻¹) : Float32[1.3508699f-11 1.3501298f-11; 1.7620908f-11 1.6476176f-11]
Imaginary part of dynamic compliance (Pa⁻¹) : Float32[8.801486f-15 2.5916762f-15; 8.878848f-13 6.8378257f-13]
Attenuation : Float32[0.0006515421 0.00019195756; 0.050388142 0.041501287]
Modulus (Pa) : Float32[7.402635f10 7.406695f10; 5.6678855f10 6.0641493f10]
Anelastic S-wave velocity : (m/s) : Float32[4736.267 4737.566; 4144.3228 4286.748]
Frequency averaged S-wave velocity (m/s) : Float32[4736.9165, 4215.535]

References

Yamauchi and Takei, 2016, "Polycrystal anelasticity at near-solidus temperatures", J. Geophys. Res. Solid Earth, https://doi.org/10.1002/2016JB013316
Yamauchi and Takei, 2024, "Effect of Melt on Polycrystal Anelasticity", J. Geophys. Res. Solid Earth, https://doi.org/10.1029/2023JB027738

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Porosity.premelt_anelasticDistribution Type

julia

premelt_anelasticDistribution(T, P, dg, σ, ϕ, ρ, f)

Model Distribution for premelt_anelastic[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `f` : frequency

Usage

Refer to the documentation for usage examples.

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Porosity.single_phase Type

julia

single_phase

Single phase only conductivity. Assumes the rock matrix is composed of a single phase only.

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Porosity.tune_rp_modelType Type

julia

tune_rp_modelType(fn_list, mtype)

Arguments

fn_list : Vector of functions applied to the parameters in the same sequence
mtype : model type that will constructed using the given and estimated parameters

Usage

julia

julia> T = (800:200:1200) .+ 273.0;

julia> P = 2.0;

julia> T_solidus = 1000.0 + 273;

julia> ps_nt = (; T=T, P=P, T_solidus=T_solidus);

julia> fn_list = [get_melt_fraction];

julia> m_type = two_phase_modelType(SEO3, Gaillard2008, HS1962_plus);

julia> m = tune_rp_modelType(fn_list, m_type)
Tuning rock physics with function list :
[Porosity.get_melt_fraction]
to obtain the rock physics model of type two_phase_modelType{SEO3, Gaillard2008, HS1962_plus}

julia> model = m(ps_nt)
Two phase composition using HS1962_plus()

*    m₁ (solid phase) : 
Model : SEO3
Temperature (K) : 1073.0:200.0:1473.0
ϕ : [1.0, 1.0, 0.4594594594594593]

*    m₂ (liquid phase) : 
Model : SEO3
Temperature (K) : 1073.0:200.0:1473.0
ϕ : [0.0, 0.0, 0.5405405405405407]

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Porosity.two_phase_model Type

julia

two_phase_model(ϕ, m1, m2, mix)

Rock physics model to combine two phases, usually constructed through two_phase_modelType[@ref]

Arguments

ϕ : Vol. fraction of the second phase
m1 : model corresponding to phase 1
m2 : model corresponding to phase 2
mix : mixing type, available options are HS_1962_plus(), HS1962_minus, MAL(m)

Usage

julia

julia> m = two_phase_modelType(SEO3, Ni2011, HS1962_plus);

julia> T = [900.0f0, 1000.0f0] .+ 273;

julia> P = 3.0f0;

julia> ρ = 3300.0f0;

julia> Ch2o_m = 1000.0f0;

julia> ϕ = 0.1f0;

julia> ps_nt = ps_nt = (; T, P, ρ, Ch2o_m, ϕ);

julia> model = m(ps_nt)
Two phase composition using HS1962_plus()

*    m₁ (solid phase) : 
Model : SEO3
Temperature (K) : Float32[1173.0, 1273.0]
ϕ : 0.9

*    m₂ (liquid phase) : 
Model : SEO3
Temperature (K) : Float32[1173.0, 1273.0]
ϕ : 0.1

julia> resp = forward(model, [])
Rock physics Response : RockphyCond
log₁₀ conductivity (S/m) : Float32[-5.800449, -4.128538]

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Porosity.two_phase_modelDistribution Type

julia

two_phase_modelDistribution(ϕ, m1, m2, mix)

Rock physics model distribution to combine two phases, usually constructed through two_phase_modelDistributionType[@ref]

Arguments

ϕ : distribution (or value) of vol. fraction of the second phase
m1 : model distribution corresponding to phase 1
m2 : model distribution corresponding to phase 2
mix : mixing type, available options are HS_1962_plus, HS1962_minus, MAL(m_MAL)

Usage

julia

m = two_phase_modelType(SEO3Distribution, Ni2011Distribution, HS1962_plus)
ps_nt_dist = (; T=product_distribution(Uniform(1200.0f0, 1400.0f0)),
    Ch2o_m=MvNormal([100.0f0], diagm([20.0f0])), ϕ=[0.1f0])
model = m(ps_nt_dist)

resp = forward(model)

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Porosity.two_phase_modelDistributionType Type

julia

two_phase_modelDistributionType(m1, m2, mix)

Rock physics model distribution type to combine two phases.

Arguments

m1 : model corresponding to phase 1
m2 : model distribution type corresponding to phase 2
mix : mixing type, available options are HS_1962_plus, HS1962_minus, MAL

Usage

julia

two_phase_modelType(SEO3Distribution, Ni2011Distribution, HS1962_plus)

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Porosity.two_phase_modelType Type

julia

two_phase_modelType(m1, m2, mix)

Rock physics model Type to combine two phases.

Arguments

m1 : model type corresponding to phase 1
m2 : model type corresponding to phase 2
mix : mixing type, available options are HS_1962_plus, HS1962_minus, MAL

Usage

julia

two_phase_modelType(SEO3, Ni2011, HS1962_plus)

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Porosity.xfit_mxw Type

julia

xfit_mxw(T, P, dg, σ, ϕ, ρ, T_solidus, Ch2o_ol, f)

Calculate anelastic properties stored in RockPhyAnelastic using the Master curve maxwell scaling per McCarthy, Takei and Hiraga (2011)

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `Ch2o_ol` : water concentration in olivine (in ppm)
- `T_solidus` : Solidus temperature (K), only used when using `xfit_premelt` for viscosity calculations
- `f` : frequency

Keyword Arguments

julia

- `params` : Various coefficients required for calculation. 
Available options are `fit1` and `fit2`, defaults to `fit1`, i.e, `params_xfit_mxw.fit1`
Also holds coefficients and the type of `RockphyElastic` model and `RockphyViscous model` to be used.

To investigate coefficients, call `default_params(Val{xfit_premelt}())`. 
To modify coefficients, check the relevant documentation page. This
will also users to pick any particular type of `RockphyElastic` model, defaults to `anharmonic`,
as well as `RockphyViscous` model (for diffusion-derived viscosity), defaults to `xfit_mxw`

Usage

Note

Make sure that the dimension of vector f is one more than the other parameters. Check relevant tutorials. Note the transpose on f when making the model in the following eg.

julia

julia> T = [800, 1000] .+ 273.0f0;

julia> P = 2 .+ zero(T);

julia> dg = 4.0f0;

julia> σ = 10.0f-3;

julia> ϕ = 1.0f-2;

julia> ρ = 3300.0f0;

julia> Ch2o_ol = 0.0f0;

julia> T_solidus = 900 + 273.0f0;

julia> f = [1.0f0, 1.0f1];

julia> model = xfit_mxw(T, P, dg, σ, ϕ, ρ, Ch2o_ol, T_solidus, f')
Model : xfit_mxw
Temperature (K) : Float32[1073.0, 1273.0]
Pressure (GPa) : Float32[2.0, 2.0]
grain size(μm) : 4.0
Shear stress (GPa) : 0.01
Porosity : 0.01
Density (kg/m³) : 3300.0
Water concentration in olivine (ppm) : 0.0
Solidus Temperature (K) : 1173.0
Frequency (Hz) : Float32[1.0 10.0]

julia> forward(model, [])
Rock physics Response : RockphyAnelastic
Real part of dynamic compliance (Pa⁻¹) : Float32[1.4031399f-11 1.3812445f-11; 1.6433199f-11 1.57985f-11]
Imaginary part of dynamic compliance (Pa⁻¹) : Float32[1.6107535f-13 1.3877004f-13; 5.1549807f-13 3.6455504f-13]
Attenuation : Float32[0.011479636 0.01004674; 0.031369306 0.023075296]
Modulus (Pa) : Float32[7.1264035f10 7.2394826f10; 6.0822508f10 6.3280304f10]
Anelastic S-wave velocity : (m/s) : Float32[4647.0596 4683.783; 4293.141 4379.024]
Frequency averaged S-wave velocity (m/s) : Float32[4665.4214, 4336.0825]

References

McCarthy, Takei, Hiraga, 2011, "Experimental study of attenuation and dispersion over a broad frequency range:

The universal scaling of polycrystalline materials", Journal of Geophy Research, http://dx.doi.org/10.1029/2011JB008384

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Porosity.xfit_mxwDistribution Type

julia

xfit_mxwDistribution(T, P, dg, σ, ϕ, ρ, f)

Model Distribution for xfit_mxw[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `ρ` : Density (kg/m³)
- `f` : frequency

Usage

Refer to the documentation for usage examples.

source

Porosity.xfit_premelt Type

julia

xfit_premelt(T, P, dg, σ, ϕ)

Calculate viscosity for steady state olivine flow for pre-melting, i.e., temperatures are just below and above the solidus, per Yamauchi and Takei (2016)

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `T_solidus` : Solidus temperature

Keyword Arguments

julia

- `params` : Various coefficients required for calculation.
Coefficients for different mechanisms (stored in `mechs` field):
    - `diff` : Diffusion creep
    - `disl` : Dislocation creep
    - `gbs`  : Grain boundary sliding 
To investigate coefficients, call `default_params(Val{xfit_premelt}())`. 
To modify coefficients, check the relevant documentation page. This
will also users to get any particular type of mechanism, eg. `diff` only
by setting the `A` in `disl` and `gbs` to `0f0`.

Usage

julia

julia> T = collect(1073.0f0:40:1273.0f0);

julia> P = 2 .+ zero(T);

julia> dg = collect(3.0f0:8.0f-1:7.0f0);

julia> σ = collect(7.5f0:1.0f0:12.5f0) .* 1.0f-3;

julia> ϕ = collect(1.0f-2:2.0f-3:2.0f-2);

julia> T_solidus = 1200 + 273 .+ zero(T);

julia> model = xfit_premelt(T, P, dg, σ, ϕ, T_solidus)
Model : xfit_premelt
Temperature (K) : Float32[1073.0, 1113.0, 1153.0, 1193.0, 1233.0, 1273.0]
Pressure (GPa) : Float32[2.0, 2.0, 2.0, 2.0, 2.0, 2.0]
grain size(μm) : Float32[3.0, 3.8, 4.6, 5.4, 6.2, 7.0]
Shear stress (GPa) : Float32[0.0075000003, 0.0085, 0.009500001, 0.010500001, 0.011500001, 0.0125]
Porosity : Float32[0.01, 0.012, 0.014, 0.016, 0.018, 0.02]
Solidus Temperature (K) : Float32[1473.0, 1473.0, 1473.0, 1473.0, 1473.0, 1473.0]

julia> forward(model, [])
Rock physics Response : RockphyViscous
Strain rate : Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
Viscosity (Pa s) : Float32[7.6341115f18, 2.2587335f18, 6.6676584f17, 2.024383f17, 6.40973f16, 2.1291828f16]

References

Yamauchi and Takei, 2016, "Polycrystal anelasticity at near-solidus temperatures", J. Geophys. Res. Solid Earth, https://doi.org/10.1002/2016JB013316

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Porosity.xfit_premeltDistribution Type

julia

xfit_premeltDistribution(T, P, dg, σ, ϕ, Ch2o_ol)

Model Distribution for `xfit_premelt[@ref].

Arguments

julia

- `T` : Temperature of the rock (K)
- `P` : Pressure (GPa)
- `dg`: Grain size (μm)
- `σ` : Shear stress (GPa)
- `ϕ` : Porosity
- `T_solidus` : Solidus temperature

Usage

Refer to the documentation for usage examples.

source