print e
# Plot the fit and the normalized histogram of the residuals
mpl.figure(figsize=(14, 5))
mpl.subplot(1, 2, 1)
mpl.title("Total Field Anomaly (nT)", fontsize=14)
mpl.axis('scaled')
nlevels = mpl.contour(y, x, tf, (50, 50), 15, interp=True, color='r',
label='Observed', linewidth=2.0)
mpl.contour(y, x, solver.predicted(), (50, 50), nlevels, interp=True,
color='b', label='Predicted', style='dashed', linewidth=2.0)
mpl.legend(loc='upper left', shadow=True, prop={'size': 13})
mpl.xlabel('East y (m)', fontsize=14)
mpl.ylabel('North x (m)', fontsize=14)
mpl.subplot(1, 2, 2)
residuals_mean = numpy.mean(solver.residuals())
residuals_std = numpy.std(solver.residuals())
# Each residual is subtracted from the mean and the resulting
# difference is divided by the standard deviation
s = (solver.residuals() - residuals_mean) / residuals_std
mpl.hist(s, bins=21, range=None, normed=True, weights=None,
cumulative=False, bottom=None, histtype='bar', align='mid',
orientation='vertical', rwidth=None, log=False,
color=None, label=None)
mpl.xlim(-4, 4)
mpl.title("mean = %.3f std = %.3f" % (residuals_mean, residuals_std),
fontsize=14)
mpl.ylabel("P(z)", fontsize=14)
mpl.xlabel("z", fontsize=14)
mpl.show()
# 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)
mpl.axis('scaled')
mpl.title('Tomography result')
mpl.squaremesh(mesh, prop='vp', vmin=4000, vmax=10000, cmap=mpl.cm.seismic)
cb = mpl.colorbar()
cb.set_label('Velocity')
mpl.m2km()
mpl.figure()
mpl.grid()
mpl.title('Residuals (data with %.4f s error)' % (error))
mpl.hist(residuals, color='gray', bins=10)
mpl.xlabel("seconds")
mpl.show()
# 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)
mpl.axis('scaled')
mpl.title('Tomography result')
mpl.squaremesh(mesh, prop='vp', vmin=4000, vmax=10000,
cmap=mpl.cm.seismic)
cb = mpl.colorbar()
cb.set_label('Velocity')
mpl.m2km()
mpl.figure()
mpl.grid()
mpl.title('Residuals (data with %.4f s error)' % (error))
mpl.hist(residuals, color='gray', bins=10)
mpl.xlabel("seconds")
mpl.show()
mpl.subplot(2, 3, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, tensor[i], shape, 12)
mpl.colorbar()
mpl.contour(yp, xp, predicted[i], shape, levels, color='k')
mpl.xlabel('y (km)')
mpl.ylabel('x (km)')
mpl.m2km()
mpl.figure()
mpl.suptitle("Residuals")
for i in xrange(len(tensor)):
residuals = tensor[i] - predicted[i]
mpl.subplot(2, 3, i + 1)
mpl.title(titles[i] + ': stddev=%g' % (residuals.std()))
mpl.hist(residuals, bins=10, color='gray')
mpl.xlabel('Residuals (Eotvos)')
mpl.show()
# Plot the result
myv.figure()
myv.prisms(model, 'density', style='wireframe')
myv.prisms(seeds, 'density')
myv.axes(myv.outline(bounds), ranges=[i*0.001 for i in bounds], fmt='%.1f',
nlabels=6)
myv.wall_bottom(bounds)
myv.wall_north(bounds)
myv.figure()
myv.prisms(model, 'density', style='wireframe')
myv.prisms(vremove(0, 'density', mesh), 'density')
myv.axes(myv.outline(bounds), ranges=[i*0.001 for i in bounds], fmt='%.1f',
nlabels=6)
# Now I can forward model the layer at a greater height and check against the
# true solution of the prism
gz_true = prism.gz(x, y, z - 500, model)
gz_up = sphere.gz(x, y, z - 500, layer)
mpl.figure(figsize=(14, 4))
mpl.subplot(1, 3, 1)
mpl.axis('scaled')
mpl.title('Layer (kg.m^-3)')
mpl.pcolor(layer.y, layer.x, layer.props['density'], layer.shape)
mpl.colorbar()
mpl.m2km()
mpl.subplot(1, 3, 2)
mpl.axis('scaled')
mpl.title('Fit (mGal)')
levels = mpl.contour(y, x, gz, shape, 15, color='r')
mpl.contour(y, x, solver[0].predicted(), shape, levels, color='k')
mpl.m2km()
mpl.subplot(1, 3, 3)
mpl.title('Residuals (mGal)')
mpl.hist(residuals, bins=10)
mpl.figure()
mpl.axis('scaled')
mpl.title('True (red) | Layer (black)')
levels = mpl.contour(y, x, gz_true, shape, 12, color='r')
mpl.contour(y, x, gz_up, shape, levels, color='k')
mpl.m2km()
mpl.show()
# Put the estimated density values in the mesh
mesh.addprop('density', estimate['density'])
# Plot the adjustment
mpl.figure()
mpl.title("True: color | Inversion: contour")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gz, shape, 12)
mpl.colorbar()
mpl.contour(yp, xp, predicted[0], shape, levels, color='k')
mpl.xlabel('Horizontal coordinate y (km)')
mpl.ylabel('Horizontal coordinate x (km)')
mpl.m2km()
residuals = gz - predicted[0]
mpl.figure()
mpl.title('Residuals: mean=%g stddev=%g' % (residuals.mean(), residuals.std()))
mpl.hist(residuals, bins=10)
mpl.xlabel('Residuals (mGal)')
mpl.ylabel('# of')
mpl.show()
# Plot the result
myv.figure()
myv.prisms(model, 'density', style='wireframe')
myv.prisms(vremove(0, 'density', mesh), 'density')
myv.axes(myv.outline(bounds), ranges=[i*0.001 for i in bounds], fmt='%.1f',
nlabels=6)
myv.wall_bottom(bounds)
myv.wall_north(bounds)
myv.show()
mpl.subplot(2, 3, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, tensor[i], shape, 12)
mpl.colorbar()
mpl.contour(yp, xp, predicted[i], shape, levels, color='k')
mpl.xlabel('y (km)')
mpl.ylabel('x (km)')
mpl.m2km()
mpl.figure()
mpl.suptitle("Residuals")
for i in xrange(len(tensor)):
residuals = tensor[i] - predicted[i]
mpl.subplot(2, 3, i + 1)
mpl.title(titles[i] + ': stddev=%g' % (residuals.std()))
mpl.hist(residuals, bins=10, color='gray')
mpl.xlabel('Residuals (Eotvos)')
mpl.show()
# Plot the result
myv.figure()
myv.prisms(model, 'density', style='wireframe')
myv.prisms(seeds, 'density')
myv.axes(myv.outline(bounds),
ranges=[i * 0.001 for i in bounds],
fmt='%.1f',
nlabels=6)
myv.wall_bottom(bounds)
myv.wall_north(bounds)
myv.figure()
myv.prisms(model, 'density', style='wireframe')
myv.prisms(vremove(0, 'density', mesh), 'density')
print "mean:", residuals.mean()
print "stddev:", residuals.std()
# Plot the layer and the fit
mpl.figure(figsize=(14,4))
mpl.subplot(1, 3, 1)
mpl.axis('scaled')
mpl.title('Layer (A/m)')
mpl.pcolor(grid.y, grid.x, grid.props['magnetization'], grid.shape)
mpl.subplot(1, 3, 2)
mpl.axis('scaled')
mpl.title('Fit (nT)')
levels = mpl.contour(y, x, tf, shape, 15, color='r')
mpl.contour(y, x, predicted[0], shape, levels, color='k')
mpl.subplot(1, 3, 3)
mpl.title('Residuals (nT)')
mpl.hist(residuals, bins=10)
mpl.show()
# Now I can forward model the layer at the south pole and check against the
# true solution of the prism
tfpole = gravmag.prism.tf(x, y, z, model, -90, 0)
tfreduced = gravmag.sphere.tf(x, y, z, grid, -90, 0)
mpl.figure(figsize=(14,4))
mpl.subplot(1, 2, 1)
mpl.axis('scaled')
mpl.title('True (red) | Reduced (black)')
levels = mpl.contour(y, x, tfpole, shape, 12, color='r')
mpl.contour(y, x, tfreduced, shape, levels, color='k')
mpl.subplot(1, 2, 2)
mpl.title('True - reduced (nT)')
mpl.hist(tfpole - tfreduced, bins=10)
mpl.show()
linewidth=2.0)
mpl.legend(loc='upper left', shadow=True, prop={'size': 13})
mpl.xlabel('East y (m)', fontsize=14)
mpl.ylabel('North x (m)', fontsize=14)
mpl.subplot(1, 2, 2)
residuals_mean = numpy.mean(solver.residuals())
residuals_std = numpy.std(solver.residuals())
# Each residual is subtracted from the mean and the resulting
# difference is divided by the standard deviation
s = (solver.residuals() - residuals_mean) / residuals_std
mpl.hist(s,
bins=21,
range=None,
normed=True,
weights=None,
cumulative=False,
bottom=None,
histtype='bar',
align='mid',
orientation='vertical',
rwidth=None,
log=False,
color=None,
label=None)
mpl.xlim(-4, 4)
mpl.title("mean = %.3f std = %.3f" % (residuals_mean, residuals_std),
fontsize=14)
mpl.ylabel("P(z)", fontsize=14)
mpl.xlabel("z", fontsize=14)
mpl.show()
