conductivity = 3.0 # [W/(m K)]
rad_heat = 1.*10**(-7) # radiogenic head generation [W m^-3]
cond_var = 0.001 # linear coefficient for conductivity [K^-1]
crust_temp = 400. + 273. # temperature at the base of the crust [K]
crust_flux = 17.*10**(-3) # heat flux at the base of the crust [W m^-2]
crust_depth = 35*10**3 # depth of the base of the crust [m]
# Make temperature profiles
depths = numpy.arange(35000., 200000., 1000.)
pylab.figure(figsize=(11,6))
for cond_var in [-10**(-6)*10**i for i in xrange(4)]:
temps = subcrust.synthetic_temp_profile(depths, rad_heat, cond_var,
crust_flux, crust_temp,
conductivity, crust_depth)
pylab.plot(temps - 273., depths*0.001, '-.',
label=r"B=%2.1e $K^{-1}$" % (cond_var), linewidth=3)
temps = subcrust.synthetic_temp_profile(depths, rad_heat, 0,
crust_flux, crust_temp,
conductivity, crust_depth)
pylab.plot(temps - 273., depths*0.001, '-k', label=r"B=0 $K^{-1}$", linewidth=3)
for cond_var in [10**(-6)*10**i for i in xrange(5)]:
temps = subcrust.synthetic_temp_profile(depths, rad_heat, cond_var,
crust_flux, crust_temp,
conductivity, crust_depth)
# Run the inversion
results = subcrust.invert_temp_profile(depths, temps, error,
initial_radheat,
initial_condvar, initial_flux,
ref_temp=crust_temp,
ref_cond=conductivity,
ref_depth=crust_depth,
max_it=10000)
inv_radheat, inv_condvar, inv_flux, cov, adjusted, goals = results
sigma_radheat, sigma_condvar, sigma_flux = numpy.sqrt(numpy.diag(cov))
adjusted = subcrust.synthetic_temp_profile(depths, inv_radheat, inv_condvar,
inv_flux, crust_temp, conductivity,
crust_depth)
residuals = temps - adjusted
print "Inversion results:"
print " A = %.5g +- %.2g" % (inv_radheat, sigma_radheat)
print " B = %.5g +- %.2g" % (inv_condvar, sigma_condvar)
print " qc = %.5g +- %.2g" % (inv_flux, sigma_flux)
# Plot the results
pylab.figure()
pylab.plot(temps - 273., depths*0.001, '.k', label="Data (Russell et al, 2001)")
pylab.ylim(210, 0.001*crust_depth)
pylab.xlabel(r"Temperature [$^\circ$C]")
pylab.ylabel("Depth [km]")
