ax = figure.add_subplot(3, 3, reorder[i] + 1)
# plt.subplots_adjust(left=0, bottom=None, right=0, top=None,
# wspace=None, hspace=None)
plt.subplots_adjust(wspace=0, hspace=0.2)
plt.plot(seis_p / 1.e9,
seis_vs / 1.e3,
linestyle="-",
color='k',
linewidth=2.0,
label='PREM')
plt.plot(seis_p / 1.e9,
base_vs / 1.e3,
color=colors.color(3),
dashes=dashstyle2,
linewidth=1.5,
markersize=6,
markerfacecolor='None',
label='pv')
plt.plot(seis_p / 1.e9,
vsmin / 1.e3,
color=colors.color(3),
linestyle="-",
linewidth=.5,
markersize=6,
markerfacecolor='None',
label='min')
plt.plot(seis_p / 1.e9,
# speed up computation for the automatic tests:
if "RUNNING_TESTS" in globals():
xx = np.linspace(0.0, 1.0, 10)
errs = np.array([material_error(x) for x in xx])
yy_vs = errs[:, 0]
yy_vphi = errs[:, 1]
vs_average_prem = sum(seis_vs) / len(seis_vs)
vphi_average_prem = sum(seis_vphi) / len(seis_vphi)
print(vs_average_prem, vphi_average_prem)
yy_vs /= vs_average_prem
yy_vphi /= vphi_average_prem
yy_sum = (yy_vs + yy_vphi) # we scale by a factor so it fits in the plot
# plt.figure(dpi=100,figsize=figsize)
plt.subplot(2, 2, 1)
plt.plot(xx * 100, yy_vs, "-", color=colors.color(1),
label=("$V_s$ error"), linewidth=1.5, dashes=dashstyle2)
plt.plot(xx * 100, yy_vphi, "-", color=colors.color(3),
label=("$V_\phi$ error"), linewidth=1.5)
# plt.plot (xx*100,yy_vs+yy_vphi,"g--",label=("sum"),linewidth=1.5)
plt.plot(xx * 100, yy_sum, "-", color=colors.color(4),
label=("weighted sum"), linewidth=1.5, dashes=dashstyle3)
ymin = 1e-2
ymax = 1e2
plt.ylim([ymin, ymax])
print(xx[np.argmin(yy_vs)], xx[np.argmin(yy_vphi)], xx[np.argmin(yy_sum)])
B = np.around(xx[np.argmin(yy_vs)], decimals=3)
A = np.around(xx[np.argmin(yy_vphi)], decimals=3)
uncertain = np.ones(len)
uncertain[i] += spread[i] * x
_, vs, vphi, _ = eval(uncertain)
vsmin = np.minimum(vs,vsmin)
vsmax = np.maximum(vs,vsmax)
vphimin = np.minimum(vphi,vphimin)
vphimax = np.maximum(vphi,vphimax)
ax = figure.add_subplot(3,3,reorder[i]+1)
#plt.subplots_adjust(left=0, bottom=None, right=0, top=None, wspace=None, hspace=None)
plt.subplots_adjust(wspace=0, hspace=0.2)
plt.plot(seis_p/1.e9,seis_vs/1.e3,linestyle="-",color='k',linewidth=2.0,label='PREM')
plt.plot(seis_p/1.e9,base_vs/1.e3,color=colors.color(3),dashes=dashstyle2,linewidth=1.5, markersize=6,markerfacecolor='None',label='pv')
plt.plot(seis_p/1.e9,vsmin/1.e3,color=colors.color(3),linestyle="-",linewidth=.5, markersize=6,markerfacecolor='None',label='min')
plt.plot(seis_p/1.e9,vsmax/1.e3,color=colors.color(3),linestyle="-",linewidth=.5, markersize=6,markerfacecolor='None',label='max')
plt.fill_between(seis_p/1.e9,vsmax/1.e3, vsmin/1.e3, facecolor='#ffbbbb', lw=0, label='asdf',interpolate=False)
plt.title('Vs %s +/- %d\\%% '%(names[i], spread[i]*100) )
plt.ylim([6.2,7.6])
if (reorder[i]%3==0):
plt.ylabel('Wave speed (km/s)')
else:
ax.yaxis.set_ticklabels([])
if (reorder[i]>5):
((0.834 * mat_vs_1 + 0.166 * mat_vs_2) +
np.ones_like(mat_vs_1) / (0.834 / mat_vs_1 + 0.166 / mat_vs_2))
mat_vs_4_wr = 0.5 * \
((0.92 * mat_vs_1 + 0.08 * mat_vs_2) +
np.ones_like(mat_vs_1) / (0.92 / mat_vs_1 + 0.08 / mat_vs_2))
plt.subplot(1, 2, 2)
plt.ylim(5.2, 7.4)
plt.xlim(25, 135)
# fig1 = mpimg.imread('input_figures/murakami_book_chapter.png')
# plt.imshow(fig1, extent=[25,135,5.0,7.6], aspect='auto')
plt.plot(
seis_p / 1.e9, seis_vs / 1.e3, color='k', linestyle='-', marker='None',
markerfacecolor='w', markersize=4, label='PREM', linewidth=3.0, mew=1.5)
plt.plot(
seis_p / 1.e9, mat_vs_1 / 1.e3, color=colors.color(3), marker='v', markerfacecolor=colors.color(3),
markersize=4, markeredgecolor=colors.color(3), markevery=2, linewidth=1.5, label='perovskite')
plt.plot(
seis_p / 1.e9, mat_vs_2 / 1.e3, color=colors.color(1), linestyle='-',
linewidth=1.5, marker='^', markerfacecolor=colors.color(1), markersize=4,
markeredgecolor=colors.color(1), markevery=2, label='periclase')
plt.plot(
seis_p / 1.e9, mat_vs_4_wr / 1.e3, color=colors.color(4), dashes=dashstyle3,
linewidth=1.5, marker='o', markerfacecolor=colors.color(4), markersize=4,
markeredgecolor=colors.color(4), markevery=2, label='92\% pv')
plt.plot(
seis_p / 1.e9, mat_vs_3_wr / 1.e3, color='g', linestyle='-', dashes=dashstyle2,
linewidth=1.5, marker='o', markerfacecolor='w', markersize=4, markeredgecolor='g', markevery=2, label='83\% pv')
plt.legend(loc='lower right', prop={'size': 12})
plt.title("Phase average on velocities")
uncertain = np.ones(len)
uncertain[i] += spread[i] * x
_, vs, vphi, _ = eval(uncertain)
vsmin = np.minimum(vs, vsmin)
vsmax = np.maximum(vs, vsmax)
vphimin = np.minimum(vphi, vphimin)
vphimax = np.maximum(vphi, vphimax)
ax = figure.add_subplot(3, 3, order_idx + 1)
plt.subplots_adjust(wspace=0, hspace=0.2)
ax.plot(seis_p / 1.e9, seis_vs / 1.e3, linestyle="-",
color='k', linewidth=2.0, label='PREM')
ax.plot(
seis_p / 1.e9, base_vs / 1.e3, color=colors.color(3), dashes=dashstyle2,
linewidth=1.5, markersize=6, markerfacecolor='None', label='$V_S$')
ax.plot(
seis_p / 1.e9, vsmin / 1.e3, color=colors.color(3), linestyle="-",
linewidth=.5, markersize=6, markerfacecolor='None')
ax.plot(
seis_p / 1.e9, vsmax / 1.e3, color=colors.color(3), linestyle="-",
linewidth=.5, markersize=6, markerfacecolor='None')
ax.fill_between(seis_p / 1.e9, vsmax / 1.e3, vsmin / 1.e3,
facecolor='#ffbbbb', lw=0, interpolate=False)
if (reorder[i] % 3 == 0):
ax.set_ylabel('Wave speed (km/s)')
else:
errs = np.array([material_error(x) for x in xx])
yy_vs = errs[:, 0]
yy_vphi = errs[:, 1]
vs_average_prem = sum(seis_vs) / len(seis_vs)
vphi_average_prem = sum(seis_vphi) / len(seis_vphi)
print(vs_average_prem, vphi_average_prem)
yy_vs /= vs_average_prem
yy_vphi /= vphi_average_prem
yy_sum = (yy_vs + yy_vphi) # we scale by a factor so it fits in the plot
# plt.figure(dpi=100,figsize=figsize)
plt.subplot(2, 2, 1)
plt.plot(xx * 100,
yy_vs,
"-",
color=colors.color(1),
label=("$V_s$ error"),
linewidth=1.5,
dashes=dashstyle2)
plt.plot(xx * 100,
yy_vphi,
"-",
color=colors.color(3),
label=("$V_\phi$ error"),
linewidth=1.5)
# plt.plot (xx*100,yy_vs+yy_vphi,"g--",label=("sum"),linewidth=1.5)
plt.plot(xx * 100,
yy_sum,
"-",
color=colors.color(4),
label=("weighted sum"),
# Lower bound for Hashin-Shtrikman averaging
rock.set_averaging_scheme(burnman.averaging_schemes.HashinShtrikmanLower())
rho_hsl, vp_hsl, vs_hsl, vphi_hsl, K_hsl, G_hsl = \
rock.evaluate(
['rho', 'v_p', 'v_s', 'v_phi', 'K_S', 'G'], pressures, temperatures)
# linear fit
vs_lin = vs_pv * amount_perovskite + vs_fp * (1.0 - amount_perovskite)
# PLOTTING
# plot vs
ax = figure.add_subplot(1, 1, 1)
ax.plot(pressures / 1.e9,
vs_v / 1.e3,
color=colors.color(0),
linewidth=2,
linestyle='-',
marker='^',
markersize=4,
label='Voigt')
ax.plot(pressures / 1.e9,
vs_r / 1.e3,
color=colors.color(5),
linewidth=2,
linestyle='-',
marker='v',
markersize=4,
label='Reuss')
ax.plot(pressures / 1.e9,
vs_vrh / 1.e3,
model_vs_2nd_order_incorrect = calc_shear_velocities(
sol[0], sol[1], mg_perovskite_test, pressures)
# now do third-order fit
mg_perovskite_test.set_method("bm3")
func = lambda x: error(x, mg_perovskite_test, obs_pressures, obs_vs)
sol = opt.fmin(func, guess)
print("3rd order fit: G = ", sol[0] / 1.e9, "GPa\tG' = ", sol[1])
model_vs_3rd_order_correct = calc_shear_velocities(
sol[0], sol[1], mg_perovskite_test, pressures)
mg_perovskite_test.set_method("bm2")
model_vs_3rd_order_incorrect = calc_shear_velocities(
sol[0], sol[1], mg_perovskite_test, pressures)
plt.plot(
pressures / 1.e9, model_vs_2nd_order_correct / 1000., color=colors.color(3), linestyle='-',
marker='x', markevery=7, linewidth=1.5, label="Correct 2nd order extrapolation")
plt.plot(
pressures / 1.e9, model_vs_2nd_order_incorrect / 1000., color=colors.color(3), linestyle='--',
marker='x', markevery=7, linewidth=1.5, label="2nd order fit, 3rd order extrapolation")
plt.plot(
pressures / 1.e9, model_vs_3rd_order_correct / 1000., color=colors.color(1),
linestyle='-', linewidth=1.5, label="Correct 3rd order extrapolation")
plt.plot(
pressures / 1.e9, model_vs_3rd_order_incorrect / 1000., color=colors.color(1),
linestyle='--', linewidth=1.5, label="3rd order fit, 2nd order extrapolation")
plt.scatter(obs_pressures / 1.e9, obs_vs /
1000., zorder=1000, marker='o', c='w')
plt.ylim([6.7, 8])
plt.xlim([25., 135.])
if "RUNNING_TESTS" not in globals():
# Lower bound for Hashin-Shtrikman averaging
rock.set_averaging_scheme(burnman.averaging_schemes.HashinShtrikmanLower())
rho_hsl, vp_hsl, vs_hsl, vphi_hsl, K_hsl, G_hsl = \
rock.evaluate(
['rho', 'v_p', 'v_s', 'v_phi', 'K_S', 'G'], pressures, temperatures)
# linear fit
vs_lin = vs_pv * amount_perovskite + vs_fp * (1.0 - amount_perovskite)
# PLOTTING
# plot vs
ax = figure.add_subplot(1, 1, 1)
plt.plot(
pressures / 1.e9, vs_v / 1.e3, color=colors.color(0), linewidth=2, linestyle='-', marker='^',
markersize=4, label='Voigt')
plt.plot(
pressures / 1.e9, vs_r / 1.e3, color=colors.color(5), linewidth=2, linestyle='-', marker='v',
markersize=4, label='Reuss')
plt.plot(
pressures / 1.e9, vs_vrh / 1.e3, color=colors.color(1), linestyle='-', marker='*',
markersize=6, label='Voigt-Reuss-Hill')
plt.fill_between(pressures / 1.e9, vs_hsu / 1.e3, vs_hsl / 1.e3,
facecolor='red', lw=0, label='asdf', interpolate=False)
# plt.plot(pressures/1.e9,vs_hsu/1.e3,color='r',linestyle='-',\
# markersize=4,label='Hashin-Shtrikman')
# plt.plot(pressures/1.e9,vs_hsl/1.e3,color='r',linestyle='-',marker='x',\
# markersize=4)
plt.plot(
sol = opt.fmin(func, guess)
print("2nd order fit: G = ", sol[0]/1.e9, "GPa\tG' = ", sol[1])
model_vs_2nd_order_correct = calc_shear_velocities(sol[0], sol[1], mg_perovskite_test, pressures)
mg_perovskite_test.set_method("bm3")
model_vs_2nd_order_incorrect = calc_shear_velocities(sol[0], sol[1], mg_perovskite_test, pressures)
#now do third-order fit
mg_perovskite_test.set_method("bm3")
func = lambda x : error( x, mg_perovskite_test, obs_pressures, obs_vs)
sol = opt.fmin(func, guess)
print("3rd order fit: G = ", sol[0]/1.e9, "GPa\tG' = ", sol[1])
model_vs_3rd_order_correct = calc_shear_velocities(sol[0], sol[1], mg_perovskite_test, pressures)
mg_perovskite_test.set_method("bm2")
model_vs_3rd_order_incorrect = calc_shear_velocities(sol[0], sol[1], mg_perovskite_test, pressures)
plt.plot(pressures/1.e9,model_vs_2nd_order_correct/1000.,color=colors.color(3), linestyle='-', marker='x',markevery=7,linewidth=1.5, label = "Correct 2nd order extrapolation")
plt.plot(pressures/1.e9,model_vs_2nd_order_incorrect/1000.,color=colors.color(3), linestyle='--', marker='x',markevery=7, linewidth=1.5, label = "2nd order fit, 3rd order extrapolation")
plt.plot(pressures/1.e9,model_vs_3rd_order_correct/1000.,color=colors.color(1), linestyle='-', linewidth=1.5, label = "Correct 3rd order extrapolation")
plt.plot(pressures/1.e9,model_vs_3rd_order_incorrect/1000.,color=colors.color(1), linestyle='--', linewidth=1.5, label = "3rd order fit, 2nd order extrapolation")
plt.scatter(obs_pressures/1.e9, obs_vs/1000., zorder=1000, marker='o',c='w')
plt.ylim([6.7, 8])
plt.xlim([25., 135.])
if "RUNNING_TESTS" not in globals():
plt.ylabel(r'Shear velocity ${V}_{\mathlarger{\mathlarger{\mathlarger{s}}}}$ (km/s)')
plt.xlabel("Pressure (GPa)")
plt.legend(loc = "lower right",prop=prop)
if "RUNNING_TESTS" not in globals():
plt.savefig("example_fit_data.pdf", bbox_inches='tight')
plt.show()