# 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()
mpl.figure(figsize=(14, 4))
mpl.subplot(1, 3, 1)
mpl.axis('scaled')
mpl.title('Layer (A/m)')
mpl.pcolor(layer.y, layer.x, layer.props['magnetization'], layer.shape)
mpl.colorbar()
mpl.m2km()
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, solver.predicted(), shape, levels, color='k')
mpl.m2km()
mpl.subplot(1, 3, 3)
mpl.title('Residuals (nT)')
mpl.hist(residuals, bins=10)
mpl.figure()
mpl.axis('scaled')
mpl.title('True (red) | Reduced (black)')
200 * utils.gaussian2d(x, y, 50, 100, x0=80, y0=170))
nodes = (x, y, -1 * height)
relief = mesher.PrismRelief(0, gridder.spacing(area, shape), nodes)
relief.addprop('density', (2670 for i in xrange(relief.size)))
gridarea = (-80, 80, -220, 220)
gridshape = (100, 100)
xp, yp, zp = gridder.regular(gridarea, gridshape, z=-200)
gz = prism.gz(xp, yp, zp, relief)
mpl.figure(figsize=(10, 7))
mpl.subplot(1, 2, 1)
mpl.title("Synthetic topography")
mpl.axis('scaled')
mpl.pcolor(x, y, height, shape)
cb = mpl.colorbar()
cb.set_label("meters")
mpl.square(gridarea, label='Computation grid')
mpl.legend()
mpl.subplot(1, 2, 2)
mpl.title("Topographic effect")
mpl.axis('scaled')
mpl.pcolor(xp, yp, gz, gridshape)
cb = mpl.colorbar()
cb.set_label("mGal")
mpl.show()
myv.figure()
myv.prisms(relief, prop='density')
axes = myv.axes(myv.outline())
# Now I can forward model the layer at the south pole and 500 m above the
# original data. Check against the true solution of the prism
tfpole = prism.tf(x, y, z - 500, model, -90, 0)
tfreduced = sphere.tf(x, y, z - 500, layer, -90, 0)
mpl.figure()
mpl.suptitle('L-curve')
mpl.title("Estimated regularization parameter: %g" % (solver.regul_param_))
solver.plot_lcurve()
mpl.grid()
mpl.figure(figsize=(15, 4))
mpl.subplot(1, 3, 1)
mpl.axis('scaled')
mpl.title('Layer (A/m)')
mpl.pcolor(layer.y, layer.x, layer.props['magnetization'], layer.shape)
mpl.colorbar()
mpl.m2km()
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, solver.predicted(), shape, levels, color='k')
mpl.m2km()
mpl.subplot(1, 3, 3)
mpl.title('Residuals (nT)')
mpl.hist(residuals, bins=10)
mpl.figure(figsize=(10, 4))
mpl.subplot(1, 2, 1)
mpl.axis('scaled')
# 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()
mpl.suptitle('L-curve')
mpl.title("Estimated regularization parameter: %g" % (solver.regul_param_))
solver.plot_lcurve()
mpl.grid()
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.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)')
"""
Gridding: Cut a section from a grid
"""
from fatiando import gridder, utils
from fatiando.vis import mpl
# Generate some synthetic data on a regular grid
x, y = gridder.regular((-10, 10, -10, 10), (100,100))
# Using a 2D Gaussian
z = utils.gaussian2d(x, y, 1, 1)
subarea = [-2, 2, -3, 3]
subx, suby, subscalar = gridder.cut(x, y, [z], subarea)
mpl.figure(figsize=(12, 5))
mpl.subplot(1, 2, 1)
mpl.title("Whole grid")
mpl.axis('scaled')
mpl.pcolor(x, y, z, (100,100))
mpl.square(subarea, 'k', linewidth=2, label='Cut this region')
mpl.legend(loc='lower left')
mpl.subplot(1, 2, 2)
mpl.title("Cut grid")
mpl.axis('scaled')
mpl.pcolor(subx, suby, subscalar[0], (40,60), interp=True)
mpl.show()
200*utils.gaussian2d(x, y, 50, 100, x0=80, y0=170))
nodes = (x, y, -1*height)
relief = mesher.PrismRelief(0, gridder.spacing(area,shape), nodes)
relief.addprop('density', (2670 for i in xrange(relief.size)))
gridarea = (-80, 80, -220, 220)
gridshape = (100, 100)
xp, yp, zp = gridder.regular(gridarea, gridshape, z=-200)
gz = gravmag.prism.gz(xp, yp, zp, relief)
mpl.figure(figsize=(10,7))
mpl.subplot(1, 2, 1)
mpl.title("Synthetic topography")
mpl.axis('scaled')
mpl.pcolor(x, y, height, shape)
cb = mpl.colorbar()
cb.set_label("meters")
mpl.square(gridarea, label='Computation grid')
mpl.legend()
mpl.subplot(1, 2, 2)
mpl.title("Topographic effect")
mpl.axis('scaled')
mpl.pcolor(xp, yp, gz, gridshape)
cb = mpl.colorbar()
cb.set_label("mGal")
mpl.show()
myv.figure()
myv.prisms(relief, prop='density')
axes = myv.axes(myv.outline())
grid = mesher.PointGrid([0, 1000, 0, 2000], 500, (50, 50))
# Add some density to the grid
grid.addprop(
'density', 1000000000 *
utils.gaussian2d(grid.x, grid.y, 100, 500, x0=500, y0=1000, angle=-60))
# and some magnetization
inc, dec = -45, 0
grid.addprop(
'magnetization',
[d / 100. * utils.ang2vec(1, inc, dec) for d in grid.props['density']])
# plot the layer
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.axis('scaled')
mpl.title('Density (mass)')
mpl.pcolor(grid.y, grid.x, grid.props['density'], grid.shape)
mpl.colorbar()
mpl.subplot(2, 1, 2)
mpl.axis('scaled')
mpl.title('Magnetization intensity (dipole moment)')
mpl.pcolor(grid.y, grid.x, utils.vecnorm(grid.props['magnetization']),
grid.shape)
mpl.colorbar()
mpl.show()
# Now do some calculations with the grid
shape = (100, 100)
x, y, z = gridder.regular(grid.area, shape, z=0)
gz = gravmag.sphere.gz(x, y, z, grid)
tf = gravmag.sphere.tf(x, y, z, grid, inc, dec)
mpl.figure()
"""
Gridding: Cut a section from a grid
"""
from fatiando import gridder, utils
from fatiando.vis import mpl
# Generate some synthetic data on a regular grid
x, y = gridder.regular((-10, 10, -10, 10), (100, 100))
# Using a 2D Gaussian
z = utils.gaussian2d(x, y, 1, 1)
subarea = [-2, 2, -3, 3]
subx, suby, subscalar = gridder.cut(x, y, [z], subarea)
mpl.figure(figsize=(12, 5))
mpl.subplot(1, 2, 1)
mpl.title("Whole grid")
mpl.axis('scaled')
mpl.pcolor(x, y, z, (100, 100))
mpl.square(subarea, 'k', linewidth=2, label='Cut this region')
mpl.legend(loc='lower left')
mpl.subplot(1, 2, 2)
mpl.title("Cut grid")
mpl.axis('scaled')
mpl.pcolor(subx, suby, subscalar[0], (40, 60), interp=True)
mpl.show()
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gyz_true, shape, 12)
mpl.colorbar(shrink=0.7)
mpl.contour(yp, xp, gyz, shape, 12, color='k')
mpl.m2km()
mpl.subplot(2, 3, 3)
mpl.title("z deriv (contour) + true (color map)")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gzz_true, shape, 8)
mpl.colorbar(shrink=0.7)
mpl.contour(yp, xp, gzz, shape, levels, color='k')
mpl.m2km()
mpl.subplot(2, 3, 4)
mpl.title("Difference x deriv")
mpl.axis('scaled')
mpl.pcolor(yp, xp, (gxz_true - gxz), shape)
mpl.colorbar(shrink=0.7)
mpl.m2km()
mpl.subplot(2, 3, 5)
mpl.title("Difference y deriv")
mpl.axis('scaled')
mpl.pcolor(yp, xp, (gyz_true - gyz), shape)
mpl.colorbar(shrink=0.7)
mpl.m2km()
mpl.subplot(2, 3, 6)
mpl.title("Difference z deriv")
mpl.axis('scaled')
mpl.pcolor(yp, xp, (gzz_true - gzz), shape)
mpl.colorbar(shrink=0.7)
mpl.m2km()
mpl.show()
from fatiando.vis import mpl
# Generate random points
x, y = gridder.scatter((-2, 2, -2, 2), n=200)
# And calculate a 2D Gaussian on these points
z = utils.gaussian2d(x, y, 1, 1)
# Functions pcolor, contour and contourf take an interp argument
# If it is True, will interpolate the data before plotting using the specified
# grid shape
shape = (100, 100)
mpl.figure()
mpl.subplot(2, 2, 1)
mpl.axis('scaled')
mpl.title("contourf")
mpl.contourf(x, y, z, shape, 50, interp=True)
mpl.subplot(2, 2, 2)
mpl.axis('scaled')
mpl.title("contour")
mpl.contour(x, y, z, shape, 15, interp=True)
mpl.subplot(2, 2, 3)
mpl.axis('scaled')
mpl.title("pcolor")
mpl.pcolor(x, y, z, shape, interp=True)
# You can tell these functions to extrapolate the data to fill in the margins
mpl.subplot(2, 2, 4)
mpl.axis('scaled')
mpl.title("contourf extrapolate")
mpl.contourf(x, y, z, shape, 50, interp=True, extrapolate=True)
mpl.show()
grid = mesher.PointGrid([-7000, 7000, -7000, 7000], 1000, (50, 50))
# Estimate the magnetization intensity
data = [gravmag.eqlayer.TotalField(x, y, z, tf, inc, dec)]
# Need to apply enough damping so that won't try to fit the error as well
intensity, predicted = gravmag.eqlayer.classic(data, grid, damping=0.02)
grid.addprop('magnetization', intensity)
residuals = tf - predicted[0]
print "Residuals:"
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)
""" Vis: Plot a map using the Mercator map projection and pseudo-color """ from fatiando import gridder, utils from fatiando.vis import mpl # Generate some data to plot area = (-20, 40, 20, 80) shape = (100, 100) lon, lat = gridder.regular(area, shape) data = utils.gaussian2d(lon, lat, 10, 20, 10, 60, angle=45) # Now get a basemap to plot with some projection bm = mpl.basemap(area, 'merc') # And now plot everything passing the basemap to the plotting functions mpl.figure(figsize=(5, 8)) mpl.pcolor(lon, lat, data, shape, basemap=bm) mpl.colorbar() bm.drawcoastlines() bm.drawmapboundary() bm.drawcountries() mpl.draw_geolines(area, 10, 10, bm) mpl.show()
grid, (20, 20),
degree=1,
smoothness=10.**-2)
grid.addprop('magnetization', intensity)
# Compute the predicted data and the residuals
predicted = gravmag.sphere.tf(x, y, z, grid, inc, dec)
residuals = tf - predicted
print "Residuals:"
print "mean:", residuals.mean()
print "stddev:", residuals.std()
# Plot the layer and the fit
mpl.figure(figsize=(15, 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.colorbar()
mpl.m2km()
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, shape, levels, color='k')
mpl.m2km()
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 500 m above the
# original data. Check against the true solution of the prism
tfpole = gravmag.prism.tf(x, y, z - 500, model, -90, 0)
layer.addprop('density', solver.estimate_)
residuals = solver[0].residuals()
print("Residuals:")
print("mean:", residuals.mean())
print("stddev:", residuals.std())
# 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)')
# Now I can forward model the layer at the south pole and 500 m above the
# original data. Check against the true solution of the prism
tfpole = prism.tf(x, y, z - 500, model, -90, 0)
tfreduced = sphere.tf(x, y, z - 500, layer, -90, 0)
mpl.figure()
mpl.suptitle('L-curve')
mpl.title("Estimated regularization parameter: %g" % (solver.regul_param_))
solver.plot_lcurve()
mpl.grid()
mpl.figure(figsize=(15, 4))
mpl.subplot(1, 3, 1)
mpl.axis('scaled')
mpl.title('Layer (A/m)')
mpl.pcolor(layer.y, layer.x, layer.props['magnetization'], layer.shape)
mpl.colorbar()
mpl.m2km()
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, solver.predicted(), shape, levels, color='k')
mpl.m2km()
mpl.subplot(1, 3, 3)
mpl.title('Residuals (nT)')
mpl.hist(residuals, bins=10)
mpl.figure(figsize=(10, 4))
mpl.subplot(1, 2, 1)
mpl.axis('scaled')
from fatiando.vis import mpl
grid = mesher.PointGrid([0, 1000, 0, 2000], 500, (50, 50))
# Add some density to the grid
grid.addprop('density', 1000000000*utils.gaussian2d(grid.x, grid.y, 100, 500,
x0=500, y0=1000, angle=-60))
# and some magnetization
inc, dec = -45, 0
grid.addprop('magnetization', [d/100.*utils.ang2vec(1, inc, dec)
for d in grid.props['density']])
# plot the layer
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.axis('scaled')
mpl.title('Density (mass)')
mpl.pcolor(grid.y, grid.x, grid.props['density'], grid.shape)
mpl.colorbar()
mpl.subplot(2, 1, 2)
mpl.axis('scaled')
mpl.title('Magnetization intensity (dipole moment)')
mpl.pcolor(grid.y, grid.x, utils.vecnorm(grid.props['magnetization']),
grid.shape)
mpl.colorbar()
mpl.show()
# Now do some calculations with the grid
shape = (100, 100)
x, y, z = gridder.regular(grid.area, shape, z=0)
gz = gravmag.sphere.gz(x, y, z, grid)
tf = gravmag.sphere.tf(x, y, z, grid, inc, dec)
mpl.figure()
""" Vis: Plot a map using the Mercator map projection and pseudo-color """ from fatiando import gridder, utils from fatiando.vis import mpl # Generate some data to plot area = (-20, 40, 20, 80) shape = (100, 100) lon, lat = gridder.regular(area, shape) data = utils.gaussian2d(lon, lat, 10, 20, 10, 60, angle=45) # Now get a basemap to plot with some projection bm = mpl.basemap(area, 'merc') # And now plot everything passing the basemap to the plotting functions mpl.figure(figsize=(5, 8)) mpl.pcolor(lon, lat, data, shape, basemap=bm) mpl.colorbar() bm.drawcoastlines() bm.drawmapboundary() bm.drawcountries() mpl.draw_geolines(area, 10, 10, bm) mpl.show()