misfit = srtomo.SRTomo(tts, srcs, recs, mesh)
regularization = Smoothness2D(mesh.shape)
# Will use the l-curve criterion to find the best regularization parameter
tomo = LCurve(misfit, regularization,
[10 ** i for i in np.arange(0, 10, 1)], jobs=8).fit()
mesh.addprop('vp', tomo.estimate_)
# Plot the L-curve annd print the regularization parameter estimated
mpl.figure()
mpl.title('L-curve: triangle marks the best solution')
tomo.plot_lcurve()
print "Estimated regularization parameter: %g" % (tomo.regul_param_)
# Calculate and print the standard deviation of the residuals
# Should be close to the data error if the inversion was able to fit the data
residuals = tomo.residuals()
print "Assumed error: %g" % (error)
print "Standard deviation of residuals: %g" % (np.std(residuals))
mpl.figure(figsize=(14, 5))
mpl.subplot(1, 2, 1)
mpl.axis('scaled')
mpl.title('Vp model')
mpl.squaremesh(model, prop='vp', cmap=mpl.cm.seismic)
cb = mpl.colorbar()
cb.set_label('Velocity')
mpl.points(src_loc, '*y', label="Sources")
mpl.points(rec_loc, '^r', label="Receivers")
mpl.legend(loc='lower left', shadow=True, numpoints=1, prop={'size': 10})
mpl.m2km()
mpl.subplot(1, 2, 2)
regularization = Smoothness2D(mesh.shape)
# Will use the l-curve criterion to find the best regularization parameter
tomo = LCurve(misfit,
regularization, [10**i for i in np.arange(0, 10, 1)],
jobs=8).fit()
mesh.addprop('vp', tomo.estimate_)
# Plot the L-curve annd print the regularization parameter estimated
mpl.figure()
mpl.title('L-curve: triangle marks the best solution')
tomo.plot_lcurve()
print "Estimated regularization parameter: %g" % (tomo.regul_param_)
# Calculate and print the standard deviation of the residuals
# Should be close to the data error if the inversion was able to fit the data
residuals = tomo.residuals()
print "Assumed error: %g" % (error)
print "Standard deviation of residuals: %g" % (np.std(residuals))
mpl.figure(figsize=(14, 5))
mpl.subplot(1, 2, 1)
mpl.axis('scaled')
mpl.title('Vp model')
mpl.squaremesh(model, prop='vp', cmap=mpl.cm.seismic)
cb = mpl.colorbar()
cb.set_label('Velocity')
mpl.points(src_loc, '*y', label="Sources")
mpl.points(rec_loc, '^r', label="Receivers")
mpl.legend(loc='lower left', shadow=True, numpoints=1, prop={'size': 10})
mpl.m2km()
mpl.subplot(1, 2, 2)
# Make synthetic data
inc, dec = -60, 23
props = {'magnetization': 10}
model = [mesher.Prism(-500, 500, -1000, 1000, 500, 4000, props)]
shape = (25, 25)
x, y, z = gridder.regular([-5000, 5000, -5000, 5000], shape, z=0)
tf = utils.contaminate(prism.tf(x, y, z, model, inc, dec), 5, seed=0)
# Setup the layer
layer = mesher.PointGrid([-7000, 7000, -7000, 7000], 700, (50, 50))
# Estimate the magnetization intensity
# Need to apply regularization so that won't try to fit the error as well
misfit = EQLTotalField(x, y, z, tf, inc, dec, layer)
regul = Damping(layer.size)
# Use an L-curve analysis to find the best regularization parameter
solver = LCurve(misfit, regul, [10 ** i for i in range(-30, -15)]).fit()
residuals = solver.residuals()
layer.addprop('magnetization', solver.estimate_)
print "Residuals:"
print "mean:", residuals.mean()
print "stddev:", residuals.std()
# Now I can forward model the layer at the south pole and check against the
# true solution of the prism
tfpole = prism.tf(x, y, z, model, -90, 0)
tfreduced = sphere.tf(x, y, z, layer, -90, 0)
mpl.figure()
mpl.suptitle('L-curve')
mpl.title("Estimated regularization parameter: %g" % (solver.regul_param_))
solver.plot_lcurve()
mpl.grid()
