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paper_onefit.py
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paper_onefit.py
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# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit for the Earth and Planetary Sciences
# Copyright (C) 2012 - 2015 by the BurnMan team, released under the GNU
# GPL v2 or later.
"""
paper_onefit
------------
This script reproduces :cite:`Cottaar2014`, Figure 7.
It shows an example for a best fit for a pyrolitic model within mineralogical error bars.
"""
from __future__ import absolute_import
from __future__ import print_function
import os.path
import sys
if not os.path.exists("burnman") and os.path.exists("../../burnman"):
sys.path.insert(1, os.path.abspath("../.."))
import numpy as np
import matplotlib.pyplot as plt
import numpy.ma as ma
import numpy.random
import burnman
import pickle
from burnman import minerals
from contrib.CHRU2014.helper_solid_solution import HelperSolidSolution
import matplotlib.cm
import matplotlib.colors
from scipy import interpolate
from scipy.stats import norm
import matplotlib.mlab as mlab
import contrib.CHRU2014.colors as colors
def make_rock():
# approximate four component pyrolite model
x_pv = 0.67
x_fp = 0.33
pv_fe_num = 0.07
fp_fe_num = 0.2
mg_perovskite = minerals.SLB_2011_ZSB_2013.mg_perovskite()
fe_perovskite = minerals.SLB_2011_ZSB_2013.fe_perovskite()
wuestite = minerals.SLB_2011_ZSB_2013.wuestite()
periclase = minerals.SLB_2011_ZSB_2013.periclase()
perovskite = HelperSolidSolution(
[mg_perovskite, fe_perovskite], [1.0 - pv_fe_num, pv_fe_num]
)
ferropericlase = HelperSolidSolution(
[periclase, wuestite], [1.0 - fp_fe_num, fp_fe_num]
)
pyrolite = burnman.Composite([perovskite, ferropericlase], [x_pv, x_fp])
pyrolite.set_method("slb3")
anchor_temperature = 1935.0
return pyrolite, anchor_temperature
def output_rock(rock, file_handle):
for ph in rock.staticphases:
if isinstance(ph.mineral, HelperSolidSolution):
for mineral in ph.mineral.endmembers:
file_handle.write("\t" + mineral.to_string() + "\n")
for key in mineral.params:
file_handle.write(
"\t\t" + key + ": " + str(mineral.params[key]) + "\n"
)
else:
file_handle.write("\t" + ph.mineral.to_string() + "\n")
for key in ph.mineral.params:
file_handle.write(
"\t\t" + key + ": " + str(ph.mineral.params[key]) + "\n"
)
def realization_to_array(rock, anchor_t):
arr = [anchor_t]
names = ["anchor_T"]
for ph in rock.staticphases:
if isinstance(ph.mineral, burnman.minerals_base.helper_solid_solution):
for mineral in ph.mineral.endmembers:
for key in mineral.params:
if (
key != "equation_of_state"
and key != "F_0"
and key != "T_0"
and key != "P_0"
):
arr.append(mineral.params[key])
names.append(mineral.to_string() + "." + key)
else:
for key in ph.mineral.params:
if (
key != "equation_of_state"
and key != "F_0"
and key != "T_0"
and key != "P_0"
):
arr.append(ph.mineral.params[key])
names.append(ph.mineral.to_string() + "." + key)
return arr, names
def array_to_rock(arr, names):
rock, _ = make_rock()
anchor_t = arr[0]
idx = 1
for phase in rock.phases:
if isinstance(phase, HelperSolidSolution):
for mineral in phase.endmembers:
while mineral.to_string() in names[idx]:
key = names[idx].split(".")[-1]
if (
key != "equation_of_state"
and key != "F_0"
and key != "T_0"
and key != "P_0"
):
assert mineral.to_string() in names[idx]
mineral.params[key] = arr[idx]
idx += 1
else:
raise Exception("unknown type")
return rock, anchor_t
if __name__ == "__main__":
# set up the seismic model
seismic_model = burnman.seismic.PREM()
npts = 10
depths = np.linspace(850e3, 2700e3, npts)
pressure, seis_rho, seis_vp, seis_vs, seis_vphi = seismic_model.evaluate(
["pressure", "density", "v_p", "v_s", "v_phi"], depths
)
pressures_sampled = np.linspace(pressure[0], pressure[-1], 20 * len(pressure))
names = [
"anchor_T",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.Gprime_0",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.K_0",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.G_0",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.q_0",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.Kprime_0",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.grueneisen_0",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.V_0",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.Debye_0",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.molar_mass",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.n",
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.eta_s_0",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.Gprime_0",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.K_0",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.G_0",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.q_0",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.Kprime_0",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.grueneisen_0",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.V_0",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.Debye_0",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.molar_mass",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.n",
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.eta_s_0",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.Gprime_0",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.K_0",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.G_0",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.q_0",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.Kprime_0",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.grueneisen_0",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.V_0",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.Debye_0",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.molar_mass",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.n",
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.eta_s_0",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.Gprime_0",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.K_0",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.G_0",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.q_0",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.Kprime_0",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.grueneisen_0",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.V_0",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.Debye_0",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.molar_mass",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.n",
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.eta_s_0",
"err",
"err_rho",
"err_vphi",
"err_vs",
]
# those are the literature values:
mymaplit = {
"anchor_T": 2000,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.Gprime_0": 1.74, # r:1.74
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.K_0": 250.5e9,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.G_0": 172.9e9,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.q_0": 1.09,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.Kprime_0": 4.01, # r:4.01
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.grueneisen_0": 1.44,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.V_0": 24.45e-6,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.Debye_0": 9.059e2,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.molar_mass": 0.1,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.n": 5,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.eta_s_0": 2.13,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.Gprime_0": 1.4,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.K_0": 2.72e11, # b: 2.637e11, r:2.72e11
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.G_0": 1.33e11,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.q_0": 1.1,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.Kprime_0": 4.1, # r: 4.1
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.grueneisen_0": 1.57,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.V_0": 2.549e-05,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.Debye_0": 8.71e2,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.molar_mass": 0.1319,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.n": 5,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.eta_s_0": 2.3,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.Gprime_0": 2.1,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.K_0": 161e9,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.G_0": 1.310e11,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.q_0": 1.700,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.Kprime_0": 3.8, # b: 3.718 r:3.8
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.grueneisen_0": 1.36,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.V_0": 1.124e-05,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.Debye_0": 767,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.molar_mass": 0.0403,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.n": 2,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.eta_s_0": 2.8,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.Gprime_0": 1.4, # r: 1.4
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.K_0": 1.790e11,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.G_0": 59.0e9,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.q_0": 1.7,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.Kprime_0": 4.9,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.grueneisen_0": 1.53,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.V_0": 1.226e-05,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.Debye_0": 4.54e2,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.molar_mass": 0.0718,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.n": 2,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.eta_s_0": -0.1,
"err": 0,
"err_rho": 0,
"err_vphi": 0,
"err_vs": 0,
}
# those are the values we use:
mymap = {
"anchor_T": 2000,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.Gprime_0": 1.779, # r:1.74
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.K_0": 250.5e9,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.G_0": 172.9e9,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.q_0": 1.09,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.Kprime_0": 3.917, # r:4.01
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.grueneisen_0": 1.44,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.V_0": 24.45e-6,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.Debye_0": 9.059e2,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.molar_mass": 0.1,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.n": 5,
"'burnman.minerals.SLB_2011_ZSB_2013.mg_perovskite'.eta_s_0": 2.13,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.Gprime_0": 1.4,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.K_0": 2.637e11, # b: 2.637e11, r:2.72e11
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.G_0": 1.33e11,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.q_0": 1.1,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.Kprime_0": 3.428, # r: 4.1
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.grueneisen_0": 1.57,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.V_0": 2.549e-05,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.Debye_0": 8.71e2,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.molar_mass": 0.1319,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.n": 5,
"'burnman.minerals.SLB_2011_ZSB_2013.fe_perovskite'.eta_s_0": 2.3,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.Gprime_0": 2.1,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.K_0": 161e9,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.G_0": 1.310e11,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.q_0": 1.700,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.Kprime_0": 3.718, # b: 3.718 r:3.8
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.grueneisen_0": 1.36,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.V_0": 1.124e-05,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.Debye_0": 767,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.molar_mass": 0.0403,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.n": 2,
"'burnman.minerals.SLB_2011_ZSB_2013.periclase'.eta_s_0": 2.8,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.Gprime_0": 1.4, # r: 1.4
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.K_0": 1.790e11,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.G_0": 59.0e9,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.q_0": 1.7,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.Kprime_0": 4.9,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.grueneisen_0": 1.53,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.V_0": 1.226e-05,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.Debye_0": 4.54e2,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.molar_mass": 0.0718,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.n": 2,
"'burnman.minerals.SLB_2011_ZSB_2013.wuestite'.eta_s_0": -0.1,
"err": 0,
"err_rho": 0,
"err_vphi": 0,
"err_vs": 0,
}
# make table:
rows = [
"V_0",
"K_0",
"Kprime_0",
"G_0",
"Gprime_0",
"molar_mass",
"n",
"Debye_0",
"grueneisen_0",
"q_0",
"eta_s_0",
]
for row in rows:
val = []
for n in names:
if "." + row in n:
val.append(mymap[n])
print(row, "& %g && %g && %g && %g & \\" % (val[0], val[1], val[2], val[3]))
dashstyle2 = (7, 3)
dashstyle3 = (3, 2)
fit = []
lit = []
for n in names:
fit.append(mymap[n])
lit.append(mymaplit[n])
rock, anchor_t = array_to_rock(fit, names)
temperature = burnman.geotherm.adiabatic(pressure, anchor_t, rock)
rock.set_averaging_scheme(burnman.averaging_schemes.HashinShtrikmanAverage())
rho, vp, vs, vphi, K, G = rock.evaluate(
["rho", "v_p", "v_s", "v_phi", "K_S", "G"], pressure, temperature
)
err_vs, err_vphi, err_rho = burnman.utils.math.compare_l2(
depths / np.mean(depths),
[vs / np.mean(seis_vs), vphi / np.mean(seis_vphi), rho / np.mean(seis_rho)],
[
seis_vs / np.mean(seis_vs),
seis_vphi / np.mean(seis_vphi),
seis_rho / np.mean(seis_rho),
],
)
error = np.sum([err_rho, err_vphi, err_vs])
print("errors:", error, err_rho, err_vphi, err_vs)
figsize = (6, 5)
prop = {"size": 12}
plt.rc("text", usetex=True)
plt.rcParams["text.latex.preamble"] = r"\usepackage{relsize}"
plt.rc("font", family="sans-serif")
figure = plt.figure(dpi=100, figsize=figsize)
# plot v_s
plt.plot(
pressure / 1.0e9,
seis_vs / 1.0e3,
linestyle="-",
color="k",
linewidth=2.0,
label="PREM",
)
# plot v_phi
plt.plot(
pressure / 1.0e9, seis_vphi / 1.0e3, linestyle="-", color="k", linewidth=2.0
)
# plot density
plt.plot(
pressure / 1.0e9, seis_rho / 1.0e3, linestyle="-", color="k", linewidth=2.0
)
plt.plot(
pressure / 1.0e9,
vphi / 1.0e3,
linestyle="-",
color=colors.color(3),
linewidth=1.0,
marker="s",
markerfacecolor=colors.color(3),
label="vphi",
)
plt.plot(
pressure / 1.0e9,
vs / 1.0e3,
linestyle="-",
color=colors.color(4),
linewidth=1.0,
marker="v",
markerfacecolor=colors.color(4),
label="vs",
)
plt.plot(
pressure / 1.0e9,
rho / 1.0e3,
linestyle="-",
color=colors.color(2),
linewidth=1.0,
marker="o",
markerfacecolor=colors.color(2),
label="rho",
)
rock, anchor_t = array_to_rock(lit, names)
temperature = burnman.geotherm.adiabatic(pressure, anchor_t, rock)
rock.set_averaging_scheme(burnman.averaging_schemes.HashinShtrikmanAverage())
rho, vp, vs, vphi, K, G = rock.evaluate(
["rho", "v_p", "v_s", "v_phi", "K_S", "G"], pressure, temperature
)
plt.plot(
pressure / 1.0e9,
vs / 1.0e3,
dashes=dashstyle2,
color=colors.color(4),
linewidth=1.0,
)
plt.plot(
pressure / 1.0e9,
vphi / 1.0e3,
dashes=dashstyle2,
color=colors.color(3),
linewidth=1.0,
label="literature",
)
plt.plot(
pressure / 1.0e9,
rho / 1.0e3,
dashes=dashstyle2,
color=colors.color(2),
linewidth=1.0,
)
plt.xlabel("Pressure (GPa)")
plt.ylabel("Velocities (km/s) and Density ($\cdot 10^3$ kg/m$^3$)")
plt.legend(bbox_to_anchor=(1.0, 0.9), prop={"size": 12})
plt.xlim(25, 135)
# plt.ylim(6,11)
if "RUNNING_TESTS" not in globals():
plt.savefig("onefit.pdf", bbox_inches="tight")
print("wrote onefit.pdf")
# plt.show()