def fun(r,y,p):
# Eigenvalues
F=p[0]
speed=p[1]
# PREM gravity and density in layer
if model =='prem':
density_seis=lp.premdensity(r*csb_radius)/density0 # dimensionless density
elif model == 'ohtaki':
_,density_seis = lp.ohtaki(r*csb_radius)/density0
gravity_seis=lp.premgravity(r*csb_radius)/csb_gravity # dimensionless gravity
density_grad_seis=np.gradient(density_seis,r)
gravity_grad_seis=np.gradient(gravity_seis,r)
# r derivative of barodiffusion term
term=gravity_seis*density_seis*np.exp(F*(csb_radius*r-icb_radius)/layer_thickness)* \
(F*csb_radius/layer_thickness+2/r-y[3]/y[0]+ \
gravity_grad_seis/gravity_seis+density_grad_seis/density_seis)/y[0]
# liquidus (=dxi/dr)
eq1=-(Lip*density_seis*gravity_seis+y[3]/y[0])*Rrho/(Lix*St*y[0])
# oxygen eqn (=dj/dr)
eq2=(Lip*Rrho*term/(Lix*St*Pe*Rvol) - eq1*(Rrho*speed+y[2]) - \
2*y[1]*y[2]/r)/y[1]
# temp eqn (=d2T/dr2)
eq3=-Pe/Le*((eq2+2/r*y[2])/St + \
(speed+2*Le/(r*Pe))*y[3])
return np.vstack([y[3],eq1,eq2,eq3])
def slurrydensity(radius,temp,xi,solidflux,mol_conc_oxygen_bulk, \
sedimentation_constant,mol_conc_SSi=8,model='prem'):
# Density profile across slurry layer
csb_radius = radius[-1]
if model == 'prem':
csb_density = premdensity(csb_radius)
elif model == 'ohtaki':
_, csb_density = ohtaki(csb_radius)
# Solid fraction
Kphi = getKphi(sedimentation_constant, radius, mol_conc_oxygen_bulk)
phi = (-solidflux / Kphi)**(3 / 5)
# Density fluctuations
deltaV_solid_liquid = getchangevolmeltingFe(csb_density)
temp_denFluc = -csb_density * alphaT * (temp - temp[-1])
xi_denFluc = -csb_density * alphaXi * (xi - xi[-1])
phi_denFluc = csb_density * (csb_density * deltaV_solid_liquid +
alphaXi * xi) * (phi - phi[-1])
density_fluc = temp_denFluc + xi_denFluc + phi_denFluc
# Hydrostatic density
slurry_gravity = premgravity(radius)
density_hydrostatic=1/(slurry_gravity*(radius-csb_radius)/bulk_modulus+ \
1/csb_density)
# Total density
density_slurry = density_hydrostatic + density_fluc
return (density_slurry, phi, temp_denFluc, xi_denFluc, phi_denFluc,
density_fluc)
def getLip(csb_radius, model='prem'):
gravity = premgravity(csb_radius)
if model == 'prem':
density = premdensity(csb_radius)
elif model == 'ohtaki':
_, density = ohtaki(csb_radius)
Lip = deltaV_solidFe_liquidFe * gravity * density * csb_radius / latent_heat
return Lip, gravity, density
def getKphi(sedimentation_constant,
radius,
mol_conc_oxygen_bulk,
mol_conc_SSi=8):
gravity = premgravity(radius)
density = premdensity(radius)
deltaV_solid_liquid = getchangevolmeltingFe(density[-1])
Kphi = sedimentation_constant * gravity * density * deltaV_solid_liquid
return Kphi
def getdimensional(layer_thickness,Pe,St,Le, \
mol_conc_oxygen_bulk=8., mol_conc_SSi=8., \
self_diffusion=0.98e-8):
csb_radius = getcsbradius(layer_thickness)
density0 = premdensity(csb_radius)
mass_conc_O, acore = getcsbmassoxygen(mol_conc_oxygen_bulk, mol_conc_SSi)
freezing_speed = getfreezingspeedfromPe(Pe, csb_radius, self_diffusion)
icb_heatflux = geticbheatflux(freezing_speed)
csb_heatflux = getcsbheatflux(St, freezing_speed, density0, csb_radius)
thermal_conductivity = getthermalconductivity(Le, density0)
return (icb_heatflux, csb_heatflux, thermal_conductivity)
def heatflux(radius,temp,xi,solidflux,phi,temp_grad,xi_grad,density_slurry, \
icb_speed,icb_heatflux,layer_thickness,thermal_conductivity, \
csb_heatflux,n):
csb_radius = radius[-1]
# GRAVITATIONAL POWER
# Gravitational potential
radius_psi = np.linspace(icb_radius, cmb_radius)
gravity_psi = premgravity(radius_psi)
psi = np.zeros(radius_psi.size)
for i in range(radius_psi.size - 1):
psi[i] = -integrate.simps(gravity_psi[i:], radius_psi[i:])
# Slurry
f = interpolate.interp1d(radius_psi, psi)
psi_slurry = f(radius)
oxygen_mass_slurry = 4 * np.pi * density_solidFe * layer_thickness**2 * icb_speed * xi[
-1]
mass_slurry = integrate.simps(density_slurry * 4 * np.pi * radius**2,
radius)
Qg_slurry = -alphaXi*oxygen_mass_slurry/mass_slurry* \
integrate.simps(density_slurry*psi_slurry*4*np.pi*radius**2,radius)
# print('Change in oxygen mass (slurry) is {}'.format(oxygen_mass_slurry))
# print('Mass of slurry is {}'.format(mass_slurry))
print('Qg slurry is {:.2f}TW'.format(Qg_slurry * 1e-12))
# Outer core
radius_oc = np.linspace(csb_radius, cmb_radius)
psi_oc = f(radius_oc)
surf = -psi[0] * alphaXi * density_slurry[-1] * xi[
-1] * icb_speed * 4 * np.pi * csb_radius**2
# Mass of OC
density_oc = premdensity(radius_oc)
mass_oc = integrate.simps(density_oc * 4 * np.pi * radius_oc**2, radius_oc)
oxygen_mass_oc = -density_slurry[
-1] * icb_speed * 4 * np.pi * csb_radius**2 * xi[-1] / mass_oc
bulk = integrate.simps(
alphaXi * psi_oc * oxygen_mass_oc * 4 * np.pi * radius_oc**2,
radius_oc)
# print('Change in oxygen mass (outer core) is {}'.format(oxygen_mass_oc))
# print('Mass of outer core is {}'.format(mass_oc))
print('Qg surface term in outer core is {:.2f}TW'.format(surf * 1e-12))
print('Qg bulk term in outer core is {:.5f}TW'.format(bulk * 1e-12))
# Total gravitational energy
Qg_oc = surf + bulk
Qg = Qg_slurry + Qg_oc
print('Total Qg is {:.2f}TW'.format(Qg * 1e-12))
# LATENT HEAT
Ql = 4 * np.pi * icb_radius**2 * density_solidFe * icb_speed * latent_heat
print('Total Ql is {:.2f}TW'.format(Ql * 1e-12))
# SECULAR COOLING
# Cooling rate
csb_temp = temp[-1]
cooling_rate, cmb_temp, temp_ad = get_cooling(icb_speed, csb_temp,
radius_oc, csb_radius,
cmb_radius)
# Outer core
Qs_oc = - heat_capacity*cooling_rate/cmb_temp \
*integrate.simps(density_oc*temp_ad*4*np.pi*radius_oc**2,radius_oc)
print('Qs in outer core is {:.2f}TW'.format(Qs_oc * 1e-12))
# Slurry
Qs_slurry = csb_heatflux - Qg_slurry - Ql
print('Qs in slurry {:.2f}TW'.format(Qs_slurry * 1e-12))
Qs = Qs_slurry + Qs_oc
print('Total Qs is {:.2f}TW'.format(Qs * 1e-12))
# CMB heat flux
Q_cmb = csb_heatflux + Qs_oc + Qg_oc
print('Qcmb is is {:.2f}TW'.format((Q_cmb) * 1e-12))
return (Q_cmb, Qs, Qs_slurry, Qs_oc, Ql, Qg, Qg_oc, Qg_slurry,
cooling_rate, cmb_temp, temp_ad)
def plot_sensitivity(csb_temp,
csb_oxygen,
csb_temp0,
csb_oxy0,
saveOn,
aspectRatio=0.75):
w, h = plt.figaspect(aspectRatio)
fig1, (ax1, ax2) = plt.subplots(1, 2, figsize=(2 * w, h), sharey=True)
# Temperature
nTemp = csb_temp.size
colors = plt.cm.OrRd(np.linspace(0.4, 1, nTemp))
den_jump = []
for i in range(nTemp):
filename = 'sensitivity/temp_{:.0f}'.format(csb_temp[i]).replace(
'.', '_')
with open(filename, 'rb') as f:
(radius, temp, xi, solidFlux, density) = pickle.load(f)
if i == 0 or i == nTemp - 1:
ax1.plot(radius * 1e-3,
density,
color=colors[i],
linewidth=2,
label=r'$T^{{sl}}=${:.0f} K'.format(csb_temp[i]))
# Reference case
elif csb_temp[i] == csb_temp0:
den_jump0 = density[0] - density[-1]
ax1.plot(radius * 1e-3,
density,
color='silver',
linewidth=2,
label=r'$T^\mathregular{{sl}}=$5457 K')
else:
ax1.plot(radius * 1e-3, density, color=colors[i])
den_jump.append(density[0] - density[-1])
# PREM
density_prem = premdensity(radius)
ax1.plot(radius * 1e-3, density_prem, 'k', linestyle='--')
ax1.legend(fontsize=11.5)
ax1.set_xlim([radius[0] * 1e-3, radius[-1] * 1e-3])
ax1.set(xlabel="Radius (km)", ylabel="Density ($\mathrm{kg m^{-3}}$)")
den_low = (den_jump[0] - den_jump0) / den_jump0 * 100
den_high = (den_jump[-1] - den_jump0) / den_jump0 * 100
print(
'Temperature: Density jump ranges from {:.2f}% to {:.2f}% of reference'
.format(den_low, den_high))
# Oxygen
nOxy = csb_oxygen.size
colors = plt.cm.GnBu(np.linspace(0.4, 1, nOxy))
den_jump = []
for i in range(nOxy):
filename = 'sensitivity/oxy_{:.1f}'.format(csb_oxygen[i]).replace(
'.', '_')
with open(filename, 'rb') as f:
(radius, temp, xi, solidFlux, density) = pickle.load(f)
if i == 0 or i == nOxy - 1:
ax2.plot(radius * 1e-3,
density,
color=colors[i],
linewidth=2,
label=r'$\xi^{{sl}}=${:.1f} mol.%'.format(csb_oxygen[i]))
# Reference case
elif csb_oxygen[i] == csb_oxy0:
den_jump0 = density[0] - density[-1]
ax2.plot(radius * 1e-3,
density,
color='silver',
linewidth=2,
label=r'$\xi^{{sl}}=$8.0 mol.%')
else:
ax2.plot(radius * 1e-3, density, color=colors[i])
den_jump.append(density[0] - density[-1])
# PREM
density_prem = premdensity(radius)
ax2.plot(radius * 1e-3, density_prem, 'k', linestyle='--', label=r'PREM')
ax2.legend(fontsize=11.5)
ax2.set_xlim([radius[0] * 1e-3, radius[-1] * 1e-3])
ax2.set(xlabel="Radius (km)")
den_low = (den_jump[0] - den_jump0) / den_jump0 * 100
den_high = (den_jump[-1] - den_jump0) / den_jump0 * 100
print('Oxygen: Density jump ranges from {:.2f}% to {:.2f}% of reference'.
format(den_low, den_high))
ax1.set_title('(a)', x=0.95, y=1, fontsize=14)
ax2.set_title('(b)', x=0.95, y=1, fontsize=14)
if saveOn == 1:
saveDir = 'figures/sensitivity/'
if not os.path.exists(saveDir):
os.makedirs(saveDir)
fig1.savefig(saveDir + "temp_oxy.pdf",
format='pdf',
dpi=200,
bbox_inches='tight')
fig1.savefig(saveDir + "temp_oxy.png",
format='png',
dpi=200,
bbox_inches='tight')
print('Figure saved as {}'.format(saveDir + "temp_oxy.pdf"))
def plot_CD(layer_thickness,
thermal_conductivity,
icb_heatflux,
csb_heatflux,
saveOn,
figAspect=0.75):
w, h = plt.figaspect(figAspect)
# fig, (ax1,ax2,ax3) = plt.subplots(3,1,figsize=(1.25*w,1.25*h),sharex=True)
fig = plt.figure(constrained_layout=True, figsize=(1.25 * w, 2 * h))
spec = gridspec.GridSpec(ncols=1, nrows=3, figure=fig)
ax1 = fig.add_subplot(spec[0, 0])
ax2 = ax1.twinx()
ax3 = fig.add_subplot(spec[1, 0], sharex=ax1)
n = layer_thickness.size*thermal_conductivity.size \
*icb_heatflux.size*csb_heatflux.size
if n != 1:
fig_label = [r'high $Le$', r'low $Le$']
start = 0.2
stop = 0.5
cm_subsection = np.linspace(start, stop, n)
colors = [cm.gray_r(x) for x in cm_subsection]
# Load data
k = 0
for w, x, y, z in [(w, x, y, z) for w in layer_thickness
for x in icb_heatflux for y in csb_heatflux
for z in thermal_conductivity]:
foldername, filename = get_outputDir(w, x, y, z)
inputDir = "results/{}/{}/".format(foldername, filename)
try:
inputs, outputs, profiles = readdata(inputDir)
except:
print('{} does not exist'.format(inputDir))
return
# Calculate bulk modulus from PREM
bulk_modulus = premvp(profiles.r)**2 * premdensity(profiles.r)
# Calculate vp using slurry density and PREM bulk modulus
vp_slurry = np.sqrt(bulk_modulus / profiles.density)
# Calculate FVW P wave speed (Ohtaki et al. 2015, fig 11a)
x = profiles.r / earth_radius
vp_fvw = 3.3 * x[0] - 3.3 * x + 10.33
max_diff = np.max((vp_fvw - vp_slurry * 1e-3) / vp_fvw * 100)
print('Maximum difference with Ohtaki et al. (2015) is {:.2f}%'.format(
max_diff))
max_diff = np.max(
(premvp(profiles.r) - vp_slurry) / premvp(profiles.r) * 100)
print('Maximum difference with PREM is {:.2f}%'.format(max_diff))
print('Density on slurry side of ICB is {:.2f}'.format(
profiles.density[0]))
density_jump = profiles.density[0] - profiles.density.iloc[-1]
print('Density jump is {:.2f}'.format(density_jump))
rho_bod = density_solidFe - profiles.density[0]
print('Delta rho bod is {:.2f}'.format(rho_bod))
rho_mod = rho_bod + density_jump
print('Delta rho mod is {:.2f}'.format(rho_mod))
# Plot P wave speed
if n == 1:
ax3.plot(profiles.r * 1e-3,
vp_slurry * 1e-3,
color='darkgrey',
lw=2,
label='slurry density') #(km/s)
ax3.vlines(profiles.r[0] * 1e-3,
vp_slurry[0] * 1e-3,
10.4,
color='darkgrey',
lw=2)
else:
ax3.plot(profiles.r * 1e-3,
vp_slurry * 1e-3,
color=colors[k],
lw=2,
label=fig_label[k]) #(km/s)
ax3.vlines(profiles.r[0] * 1e-3,
vp_slurry[0] * 1e-3,
10.4,
color=colors[k],
lw=2)
# Check density
# ax3.plot(profiles.r*1e-3,premdensity(profiles.r),'k--')
# ax3.plot(profiles.r*1e-3,profiles.density)
k += 1
# Plot temperature and composition
ax1.plot(profiles.r * 1e-3,
profiles.temp,
lw=2,
color='red',
label='temperature')
(mass_conc_O, acore) = getcsbmassoxygen(inputs.oxygen_bulk)
acore = float(acore)
ax2.plot(profiles.r * 1e-3,
profiles.oxygen * acore / aO * 100,
lw=2,
color='blue',
label='oxygen')
# Plot FVW, PREM and AK135
ax3.plot(profiles.r * 1e-3,
vp_fvw,
color='black',
lw=2,
ls=':',
label='Ohtaki et al. (2015)')
ax3.vlines(profiles.r[0] * 1e-3,
vp_fvw[0],
10.4,
color='black',
ls=':',
lw=2)
ax3.plot(profiles.r * 1e-3,
premvp(profiles.r) * 1e-3,
color='k',
ls='--',
label='PREM')
ax3.vlines(profiles.r[0] * 1e-3,
premvp(profiles.r[0]) * 1e-3,
10.4,
'k',
linestyle='--')
# ax3.plot(radius_ak135*1e-3,vp_ak135*1e-3,'k',label='ak135')
# ax3.vlines(radius_ak135[0]*1e-3,vp_ak135[0]*1e-3,10.4, 'k')
ax3.legend(fontsize=11.5, loc='upper right')
ax1.set(ylabel="Temperature (K)")
ax1.spines["right"].set_edgecolor('red')
ax1.spines["right"].set_edgecolor('blue')
ax1.yaxis.label.set_color('red')
ax2.set(ylabel="Oxygen (mol.%)")
ax2.spines["left"].set_edgecolor('red')
ax2.spines["right"].set_edgecolor('blue')
ax2.yaxis.label.set_color('blue')
ax2.tick_params(axis='y', colors='blue')
ax1.tick_params(axis='y', which='both', colors='red')
ax3.set(xlabel="Radius (km)")
ax3.set(ylabel="P wave speed (km/s)")
ax3.set_xlim([1200, profiles.r.iloc[-1] * 1e-3])
ax3.set_ylim([10.25, 10.4])
major_xticks = np.arange(1200, 1370, 20)
minor_xticks = np.arange(1200, 1370, 5)
ax1.set_xticks(major_xticks)
ax1.set_xticks(minor_xticks, minor=True)
ax2.set_xticks(major_xticks)
ax2.set_xticks(minor_xticks, minor=True)
ax3.set_xticks(major_xticks)
ax3.set_xticks(minor_xticks, minor=True)
major_yticks = np.arange(5500, 5751, 100)
minor_yticks = np.arange(5500, 5751, 20)
ax1.set_yticks(major_yticks)
ax1.set_yticks(minor_yticks, minor=True)
ax1.grid(which='minor', alpha=0.2)
ax1.grid(which='major', alpha=0.5)
ax1.tick_params(which='major', length=7)
ax1.tick_params(which='minor', length=3.5)
# major_yticks = np.arange(6.5,8.1,0.5)
# minor_yticks = np.arange(6.5,8.1,0.1)
# ax2.set_yticks(major_yticks)
# ax2.set_yticks(minor_yticks, minor=True)
# ax2.grid(which='minor', alpha=0.2)
# ax2.grid(which='major', alpha=0.5)
# ax2.tick_params(which='major',length = 7)
# ax2.tick_params(which='minor',length = 3.5)
major_yticks = np.arange(10.25, 10.4, 0.05)
minor_yticks = np.arange(10.25, 10.4, 0.01)
ax3.set_yticks(major_yticks)
ax3.set_yticks(minor_yticks, minor=True)
ax3.grid(which='minor', alpha=0.2)
ax3.grid(which='major', alpha=0.5)
ax3.tick_params(which='major', length=7)
ax3.tick_params(which='minor', length=3.5)
if saveOn == 1:
saveDir = 'figures/seismic/'
if not os.path.exists(saveDir + foldername):
os.makedirs(saveDir + foldername)
fig.savefig(saveDir + foldername + "/" + filename + "_CD.pdf",
format='pdf',
dpi=200,
bbox_inches='tight')
fig.savefig(saveDir + foldername + "/" + filename + "_CD.png",
format='png',
dpi=200,
bbox_inches='tight')
print('Figure saved as {}'.format(saveDir + foldername + "/" +
filename + "_CD.pdf"))
plt.show()
return profiles.r, vp_slurry, profiles.density, vp_fvw
def plot_compare(layer_thickness,
csb_heatflux,
icb_heatflux,
thermal_conductivity,
saveOn,
saveTag,
mol_conc_oxygen_bulk=8.,
mol_conc_SSi=8.,
self_diffusion=0.98e-8,
aspectRatio=0.75,
tempMin=5400,
tempMax=5800,
xiMin=6,
xiMax=8,
jMin=-3.5e-7,
jMax=0,
denMin=11900,
denMax=12250):
w, h = plt.figaspect(aspectRatio) * 2
fig = plt.figure()
fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2,
2,
sharex=True,
figsize=(w, h))
colors = plt.cm.tab10(np.linspace(0, 1, layer_thickness.size))
plt.rcParams["axes.prop_cycle"] = plt.cycler("color", plt.cm.tab10.colors)
for i in (range(layer_thickness.size)):
foldername, filename = get_outputDir(layer_thickness[i], icb_heatflux,
csb_heatflux,
thermal_conductivity)
inputDir = foldername + "/" + filename
data_in, data_out, data_profiles = readdata(inputDir)
radius = (data_profiles['r']) * 1e-3
oxygen = data_profiles['oxygen']
(mass_conc_O, acore) = getcsbmassoxygen(data_in.oxygen_bulk)
acore = float(acore)
ax1.plot(radius, data_profiles['temp'],
label='_nolegend_') #, color=colors[i])
ax2.plot(radius, oxygen * acore / aO * 100) #, color=colors[i])
ax3.plot(radius, data_profiles['solidflux']) #,color=colors[i])
ax4.plot(radius,
data_profiles['density'],
label='{:.0f} km'.format(layer_thickness[i] *
1e-3)) #,color=colors[i])
# Liquidus
radius_liquidus = np.linspace(icb_radius, icb_radius + 400e3)
temp_liquidus = liquidus(radius_liquidus)
ax1.plot(radius_liquidus * 1e-3,
temp_liquidus,
'k--',
label='Liquidus (Davies et al. 2015)')
# PREM
radius_prem = np.linspace(icb_radius, icb_radius + 400e3)
density_prem = premdensity(radius_prem)
ax4.plot(radius_prem * 1e-3, density_prem, 'k--', label='PREM')
ax4.set(xlabel="Radius (km)", ylabel="Density ($\mathrm{kg m^{-3}}$)")
# Axis titles
ax1.set(ylabel="Temperature (K)")
ax2.set(ylabel="Oxygen (mol.%)")
ax3.set(xlabel="Radius (km)",
ylabel="Solid flux ($\mathrm{kg m^{-2} s^{-1}}$)")
# Legend
ax1.legend(fontsize=11.5, loc=1)
ax4.legend(fontsize=11.5, loc=1)
# Axis limits
ax1.set_ylim([tempMin, tempMax])
ax2.set_ylim([xiMin, xiMax])
ax3.set_ylim([jMin, jMax])
ax4.set_ylim([denMin, denMax])
ax1.set_xlim([1220, (icb_radius + 400e3) * 1e-3])
# Subfigure labels
ax1.text(1225, tempMax - 23, '(a)', fontsize=14)
ax2.text(1225, xiMax - 0.12, '(b)', fontsize=14)
ax3.text(1225, jMax - .2e-7, '(c)', fontsize=14)
ax4.text(1225, denMax - 20, '(d)', fontsize=14)
plt.tight_layout()
if saveOn == 1:
if not os.path.exists('figures/profiles'):
os.makedirs('figures/profiles')
saveName = foldername + "_" + filename + saveTag
plt.savefig('figures/profiles/' + saveName + '.pdf',
format='pdf',
dpi=200)
plt.show()
def plot_seismic_dark(layer_thickness,
thermal_conductivity,
icb_heatflux,
csb_heatflux,
saveOn,
figAspect=0.75):
w, h = plt.figaspect(figAspect)
fig, ax = plt.subplots(1, 1, figsize=(1.25 * w, 1.25 * h))
n = layer_thickness.size*thermal_conductivity.size \
*icb_heatflux.size*csb_heatflux.size
if n != 1:
fig_label = [r'high $Le$', r'low $Le$']
start = 0.2
stop = 0.5
cm_subsection = np.linspace(start, stop, n)
colors = [cm.gray_r(x) for x in cm_subsection]
# Load data
k = 0
for w, x, y, z in [(w, x, y, z) for w in layer_thickness
for x in icb_heatflux for y in csb_heatflux
for z in thermal_conductivity]:
foldername, filename = get_outputDir(w, x, y, z)
inputDir = "results/{}/{}/".format(foldername, filename)
try:
inputs, outputs, profiles = readdata(inputDir)
except:
print('{} does not exist'.format(inputDir))
return
# Calculate bulk modulus from PREM
bulk_modulus = premvp(profiles.r)**2 * premdensity(profiles.r)
# Calculate vp using slurry density and PREM bulk modulus
vp_slurry = np.sqrt(bulk_modulus / profiles.density)
# Calculate FVW P wave speed (Ohtaki et al. 2015, fig 11a)
x = profiles.r / earth_radius
vp_fvw = 3.3 * x[0] - 3.3 * x + 10.33
max_diff = np.max((vp_fvw - vp_slurry * 1e-3) / vp_fvw * 100)
print('Maximum difference with Ohtaki et al. (2015) is {:.2f}%'.format(
max_diff))
max_diff = np.max(
(premvp(profiles.r) - vp_slurry) / premvp(profiles.r) * 100)
print('Maximum difference with PREM is {:.2f}%'.format(max_diff))
print('Density on slurry side of ICB is {:.2f}'.format(
profiles.density[0]))
density_jump = profiles.density[0] - profiles.density.iloc[-1]
print('Density jump is {:.2f}'.format(density_jump))
rho_bod = density_solidFe - profiles.density[0]
print('Delta rho bod is {:.2f}'.format(rho_bod))
rho_mod = rho_bod + density_jump
print('Delta rho mod is {:.2f}'.format(rho_mod))
# Plot P wave speed
if n == 1:
ax.plot(profiles.r * 1e-3,
vp_slurry * 1e-3,
color='darkgrey',
lw=2,
label='slurry') #(km/s)
ax.vlines(profiles.r[0] * 1e-3,
vp_slurry[0] * 1e-3,
10.4,
color='darkgrey',
lw=2)
else:
ax.plot(profiles.r * 1e-3,
vp_slurry * 1e-3,
color=colors[k],
lw=2,
label=fig_label[k]) #(km/s)
ax.vlines(profiles.r[0] * 1e-3,
vp_slurry[0] * 1e-3,
10.4,
color=colors[k],
lw=2)
# Check density
# ax1.plot(profiles.r*1e-3,premdensity(profiles.r),'k--')
# ax1.plot(profiles.r*1e-3,profiles.density)
k += 1
# Look up AK135
radius_ak135 = ak135radius()
vp_ak135 = ak135vp(radius_ak135)
ax.plot(profiles.r * 1e-3,
vp_fvw,
color='blue',
lw=2,
ls=':',
label='Ohtaki et al. (2015)')
ax.vlines(profiles.r[0] * 1e-3,
vp_fvw[0],
10.4,
color='blue',
lw=2,
ls=':')
ax.plot(profiles.r * 1e-3,
premvp(profiles.r) * 1e-3,
color='white',
ls='--',
label='PREM')
ax.vlines(profiles.r[0] * 1e-3,
premvp(profiles.r[0]) * 1e-3,
10.4,
'white',
linestyle='--')
ax.plot(radius_ak135 * 1e-3, vp_ak135 * 1e-3, 'white', label='ak135')
ax.vlines(radius_ak135[0] * 1e-3, vp_ak135[0] * 1e-3, 10.4, 'white')
ax.legend(fontsize=11.5)
ax.set(xlabel="Radius (km)")
ax.set(ylabel="P wave speed (km/s)")
ax.set_xlim([1200, profiles.r.iloc[-1] * 1e-3])
ax.set_ylim([10.1, 10.4])
plt.yticks(np.arange(10.1, 10.41, 0.1))
if saveOn == 1:
saveDir = 'figures/seismic/'
if not os.path.exists(saveDir + foldername):
os.makedirs(saveDir + foldername)
fig.savefig(saveDir + foldername + "/" + filename + "_dark.pdf",
format='pdf',
dpi=200,
bbox_inches='tight')
fig.savefig(saveDir + foldername + "/" + filename + "_dark.png",
format='png',
dpi=200,
bbox_inches='tight')
print('Figure saved as {}'.format(saveDir + foldername + "/" +
filename + ".pdf"))
plt.show()
return profiles.r, vp_slurry, profiles.density
def plot_profile(inputDir):
# Read data
try:
# print(inputDir)
inputs, outputs, profiles = readdata(inputDir)
except:
print('Folder does not exist')
# print('State = {}'.format(outputs.state.iloc[0]))
# Plots
csb_radius = pd.to_numeric(profiles.r.iloc[-1])
radius = (profiles.r) * 1e-3
w, h = plt.figaspect(0.75) * 2
# Temperature
fig1 = plt.figure
fig1, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2,
2,
sharex=True,
figsize=(w, h))
ax1.plot(radius, profiles.temp)
ax1.set(ylabel="Temperature (K)")
# Oxygen
(mass_conc_O, acore) = getcsbmassoxygen(inputs.oxygen_bulk)
acore = float(acore)
ax2.plot(radius, profiles.oxygen * acore / aO * 100)
ax2.set(ylabel="Oxygen (mol.%)")
ax3.plot(radius, profiles.solidflux)
ax3.set(xlabel="Radius (km)",
ylabel="Solid flux ($\mathrm{kg m^{-2} s^{-1}}$)")
# Density
ax4.plot(radius, profiles.density)
ax4.set(xlabel="Radius (km)", ylabel="Density ($\mathrm{kg m^{-3}}$)")
# Liquidus
radius_liquidus = np.linspace(icb_radius, csb_radius)
temp_liquidus = liquidus(radius_liquidus)
ax1.plot(radius_liquidus * 1e-3,
temp_liquidus,
'k--',
label='Liquidus (Davies et al. 2015)')
ax1.legend()
# Seismology
radius_prem = np.linspace(icb_radius, csb_radius)
density_prem = premdensity(radius_prem)
ax4.plot(radius_prem * 1e-3, density_prem, 'k--')
ax4.set(xlabel="Radius (km)", ylabel="Density ($\mathrm{kg m^{-3}}$)")
ax1.set(ylabel="Temperature (K)")
ax2.set(ylabel="Oxygen (mol.%)")
ax3.set(xlabel="Radius (km)",
ylabel="Solid flux ($\mathrm{kg m^{-2} s^{-1}}$)")
ax1.set_xlim([radius.iloc[0], radius.iloc[-1]])
plt.tight_layout()
plt.show()
def plot_sedimentation(sed_con,
saveOn,
mol_conc_oxygen_bulk=8,
figAspect=0.75):
nSed = sed_con.size
colors = plt.cm.gnuplot_r(np.linspace(0.4, 1, nSed))
w, h = plt.figaspect(figAspect)
fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(w, 2 * h))
# Format function for scientific notation in legend
my_fun = mticker.ScalarFormatter(useOffset=False, useMathText=True)
for i in range(nSed):
filename = 'sensitivity/sed_{:.0f}'.format(np.log10(
sed_con[i])).replace('.', '_')
with open(filename, 'rb') as f:
(radius, temp, xi, solidFlux, density) = pickle.load(f)
# FIX:
# ax1.plot(radius*1e-3,density,label=r'$k_\phi =$ {} $\mathrm{{kgm^{{-3}}s}}$'.format(my_fun.format_data(sed_con[i])),
# color=colors[i])
ax1.plot(radius * 1e-3,
density,
label=r'$k_\phi = {} \mathrm{{kgm^{{-3}}s}}$'.format(
my_fun.format_data(sed_con[i])).replace('{',
'{{').replace(
'}', '}}'),
color=colors[i])
ax1.plot(radius * 1e-3, density, color=colors[i])
Kphi = getKphi(sed_con[i], radius, mol_conc_oxygen_bulk)
phi = getphi(Kphi, solidFlux)
ax2.plot(radius * 1e-3, phi, color=colors[i])
# PREM
density_prem = premdensity(radius)
ax1.plot(radius * 1e-3, density_prem, 'k--', label='PREM')
ax1.set(ylabel="Density ($\mathrm{kg m^{-3}}$)") #,yscale="log")
ax2.set(xlabel="Radius (km)", ylabel="Solid fraction", yscale='log')
ax2.axhline(0.6, color='k', linestyle='--') # rheological transition
# labels = ['$k_\phi =${} $\mathrm{{kgm^{{-3}}s}}$'.format(my_fun.format_data(sed_con[i])),
# '1','2','3','4']
fig.legend(loc='center right', bbox_to_anchor=(1.4, 0.5), fontsize=11.5)
ax1.set_xlim([radius[0] * 1e-3, radius[-1] * 1e-3])
ax2.set_ylim([1e-4, 1])
ax1.set_title('(a)', x=0.95, y=1, fontsize=14)
ax2.set_title('(b)', x=0.95, y=1, fontsize=14)
if saveOn == 1:
saveDir = 'figures/sensitivity/'
if not os.path.exists(saveDir):
os.makedirs(saveDir)
fig.savefig(saveDir + "sedimentation.pdf",
format='pdf',
dpi=200,
bbox_inches='tight')
fig.savefig(saveDir + "sedimentation.png",
format='png',
dpi=200,
bbox_inches='tight')
print('Figure saved as {}'.format(saveDir + "sedimentation.pdf"))
plt.show()
