def run(title):
if title == 'Migration':
result = gravmag.imaging.migrate(xp, yp, zp, gz, bounds[-2], bounds[-1],
meshshape, power=0.5)
elif title == 'Generalized Inverse':
result = gravmag.imaging.geninv(xp, yp, zp, gz, meshshape[1:],
bounds[-2], bounds[-1], meshshape[0])
elif title == 'Sandwich':
result = gravmag.imaging.sandwich(xp, yp, zp, gz, meshshape[1:],
bounds[-2], bounds[-1], meshshape[0], power=0.5)
# Plot the results
myv.figure()
myv.polyprisms(prisms, 'density', style='wireframe', linewidth=2)
myv.prisms(result, 'density', edges=False)
axes = myv.axes(myv.outline(), ranges=[b*0.001 for b in bounds],
fmt='%.0f')
myv.wall_bottom(axes.axes.bounds)
myv.wall_north(axes.axes.bounds)
myv.title(title)
myv.show()
mesher.Prism(-1000, 1000, -1000, 1000, 1000, 7000, {'density': -800}),
mesher.Prism(2000, 4000, 3000, 4000, 0, 2000, {'density': 600})
]
# Calculate on a scatter of points to show that migration doesn't need gridded
# data
xp, yp, zp = gridder.scatter((-6000, 6000, -6000, 6000), 1000, z=-10)
gz = utils.contaminate(prism.gz(xp, yp, zp, model), 0.1)
# Plot the data
shape = (50, 50)
mpl.figure()
mpl.axis('scaled')
mpl.contourf(yp, xp, gz, shape, 30, interp=True)
mpl.colorbar()
mpl.plot(yp, xp, '.k')
mpl.xlabel('East (km)')
mpl.ylabel('North (km)')
mpl.m2km()
mpl.show()
mesh = imaging.migrate(xp, yp, zp, gz, 0, 10000, (30, 30, 30), power=0.8)
# Plot the results
myv.figure()
myv.prisms(model, 'density', style='wireframe', linewidth=2)
myv.prisms(mesh, 'density', edges=False)
axes = myv.axes(myv.outline())
myv.wall_bottom(axes.axes.bounds)
myv.wall_north(axes.axes.bounds)
myv.show()
area = bounds[:4]
axis = mpl.figure().gca()
mpl.axis('scaled')
model = [
mesher.PolygonalPrism(
mpl.draw_polygon(area, axis, xy2ne=True),
# Use only induced magnetization
0, 2000, {'magnetization': 2})]
# Calculate the effect
shape = (100, 100)
xp, yp, zp = gridder.regular(area, shape, z=-500)
tf = polyprism.tf(xp, yp, zp, model, inc, dec)
# and plot it
mpl.figure()
mpl.axis('scaled')
mpl.title("Total field anomalyproduced by prism model (nT)")
mpl.contourf(yp, xp, tf, shape, 20)
mpl.colorbar()
for p in model:
mpl.polygon(p, '.-k', xy2ne=True)
mpl.set_area(area)
mpl.m2km()
mpl.show()
# Show the prisms
myv.figure()
myv.polyprisms(model, 'magnetization')
myv.axes(myv.outline(bounds), ranges=[i * 0.001 for i in bounds])
myv.wall_north(bounds)
myv.wall_bottom(bounds)
myv.show()
"""
Vis: Exaggerate the vertical dimension of 3D plots
"""
from fatiando.mesher import Prism, PolygonalPrism
from fatiando.vis import myv
prism = Prism(0, 1000, 0, 1000, 0, 10)
poly = PolygonalPrism([[-2000, -2000], [-1000, -1000], [-2000, -1000]], 0, 10)
bounds = (-3000, 3000, -3000, 3000, 0, 20)
myv.figure()
myv.prisms([prism])
myv.polyprisms([poly])
myv.axes(myv.outline(bounds))
myv.wall_north(bounds)
myv.wall_bottom(bounds)
myv.title('No exaggeration')
scale = (1, 1, 50) # Exaggerate 50x the z axis
myv.figure()
myv.prisms([prism], scale=scale)
myv.polyprisms([poly], scale=scale)
myv.axes(myv.outline(bounds, scale=scale), ranges=bounds)
myv.wall_north(bounds, scale=scale)
myv.wall_bottom(bounds, scale=scale)
myv.title('50x exaggeration')
myv.show()
"""
Meshing: Make and plot a 3D prism mesh with topography
"""
from fatiando import gridder, utils, mesher
from fatiando.vis import myv
x1, x2 = -100, 100
y1, y2 = -200, 200
bounds = (x1, x2, y1, y2, -200, 0)
x, y = gridder.regular((x1, x2, y1, y2), (50,50))
height = (100 +
-50*utils.gaussian2d(x, y, 100, 200, x0=-50, y0=-100, angle=-60) +
100*utils.gaussian2d(x, y, 50, 100, x0=80, y0=170))
mesh = mesher.PrismMesh(bounds, (20,40,20))
mesh.carvetopo(x, y, height)
myv.figure()
myv.prisms(mesh)
myv.axes(myv.outline(bounds), fmt='%.0f')
myv.wall_north(bounds)
myv.show()
fields = [prism.potential(xp, yp, zp, model),
prism.gx(xp, yp, zp, model),
prism.gy(xp, yp, zp, model),
prism.gz(xp, yp, zp, model),
prism.gxx(xp, yp, zp, model),
prism.gxy(xp, yp, zp, model),
prism.gxz(xp, yp, zp, model),
prism.gyy(xp, yp, zp, model),
prism.gyz(xp, yp, zp, model),
prism.gzz(xp, yp, zp, model)]
titles = ['potential', 'gx', 'gy', 'gz',
'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
mpl.figure(figsize=(8, 9))
mpl.subplots_adjust(left=0.03, right=0.95, bottom=0.05, top=0.92, hspace=0.3)
mpl.suptitle("Potential fields produced by a 3 prism model")
for i, field in enumerate(fields):
mpl.subplot(4, 3, i + 3)
mpl.axis('scaled')
mpl.title(titles[i])
levels = mpl.contourf(yp*0.001, xp*0.001, field, shape, 15)
cb = mpl.colorbar()
mpl.contour(yp*0.001, xp*0.001, field, shape, levels, clabel=False, linewidth=0.1)
mpl.show()
myv.figure()
myv.prisms(model, prop='density')
axes = myv.axes(myv.outline())
myv.wall_bottom(axes.axes.bounds, opacity=0.2)
myv.wall_north(axes.axes.bounds)
myv.show()
""" Meshing: Make and plot a 3D prism mesh """ from fatiando import mesher from fatiando.vis import myv mesh = mesher.PrismMesh(bounds=(-2, 2, -3, 3, 0, 1), shape=(4,4,4)) myv.figure() plot = myv.prisms(mesh) axes = myv.axes(plot) myv.show()
levels = mpl.contourf(yp, xp, tensor[i], shape, 10)
mpl.contour(yp, xp, tensor[i], shape, levels)
mpl.m2km()
mpl.show()
# Pick the centers of the expanding windows
# The number of final solutions will be the number of points picked
mpl.figure()
mpl.suptitle('Pick the centers of the expanding windows')
mpl.axis('scaled')
mpl.contourf(yp, xp, tensor[-1], shape, 50)
mpl.colorbar()
centers = mpl.pick_points(area, mpl.gca(), xy2ne=True)
cms = []
for center in centers:
# Use the first eigenvector to estimate the center of mass
cm, sigma = gravmag.tensor.center_of_mass(xp, yp, zp, eigenvecs[0],
windows=100, wcenter=center)
cms.append(cm)
print "Sigma = %g" % (sigma)
# Plot the prism and the estimated center of mass
# It won't work well because we're using only a single window
myv.figure()
myv.points(cms, size=200.)
myv.prisms(prisms, prop='density', opacity=0.5)
axes = myv.axes(myv.outline(extent=[-5000, 5000, -5000, 5000, 0, 5000]))
myv.wall_bottom(axes.axes.bounds, opacity=0.2)
myv.wall_north(axes.axes.bounds)
myv.show()
"""
Meshing: Make a 3D prism mesh with depth-varying density
"""
from fatiando import gridder, mesher
from fatiando.vis import myv
shape = (10, 20, 10)
nz, ny, nx = shape
mesh = mesher.PrismMesh((0, 100, 0, 200, 0, 50), shape)
def fill(i):
k = i / (nx * ny)
return k
mesh.addprop('density', [fill(i) for i in xrange(mesh.size)])
myv.figure()
myv.prisms(mesh, prop='density')
myv.axes(myv.outline(), fmt='%.0f')
myv.show()
tf = (utils.nt2si(gravmag.prism.tf(xp, yp, zp, model, inc, dec)) + baselevel)
# Calculate the derivatives using FFT
xderiv = gravmag.fourier.derivx(xp, yp, tf, shape)
yderiv = gravmag.fourier.derivy(xp, yp, tf, shape)
zderiv = gravmag.fourier.derivz(xp, yp, tf, shape)
mpl.figure()
titles = ['Total field', 'x derivative', 'y derivative', 'z derivative']
for i, f in enumerate([tf, xderiv, yderiv, zderiv]):
mpl.subplot(2, 2, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
mpl.contourf(yp, xp, f, shape, 50)
mpl.colorbar()
mpl.m2km()
mpl.show()
# Run the euler deconvolution on a single window
# Structural index is 3
results = gravmag.euler.classic(xp, yp, zp, tf, xderiv, yderiv, zderiv, 3)
print "Base level used: %g" % (baselevel)
print "Estimated base level: %g" % (results['baselevel'])
myv.figure()
myv.points([results['point']], size=300.)
myv.prisms(model, 'magnetization', opacity=0.5)
axes = myv.axes(myv.outline(extent=bounds))
myv.wall_bottom(axes.axes.bounds, opacity=0.2)
myv.wall_north(axes.axes.bounds)
myv.show()
mesh.addprop('density', estimate['density'])
bodies = mesher.vremove(0, 'density', mesh)
mpl.figure()
mpl.axis('scaled')
mpl.title('No weights: Observed (color) vs Predicted (black)')
levels = mpl.contourf(y, x, gz, shape, 17)
mpl.colorbar()
mpl.contour(y, x, predicted[0], shape, levels, color='k')
mpl.m2km()
mpl.xlabel('East (km)')
mpl.ylabel('North (km)')
myv.figure()
plot = myv.prisms(model, 'density', style='wireframe', linewidth=4)
plot.actor.mapper.scalar_visibility = False
myv.prisms(bodies, 'density')
myv.axes(myv.outline(bounds))
myv.wall_north(bounds)
myv.wall_bottom(bounds)
myv.title('No weights')
# Run the inversion again with weights
weights = gravmag.harvester.weights(x, y, seeds, [2000], decay=6)
data = [gravmag.harvester.Gz(x, y, z, gz, weights=weights)]
estimate, predicted = gravmag.harvester.harvest(data,
seeds,
mesh,
compactness=1.5,
threshold=0.001)
mesh.addprop('density', estimate['density'])
bodies = mesher.vremove(0, 'density', mesh)
mpl.figure()
mpl.show()
# Pick the centers of the expanding windows
# The number of final solutions will be the number of points picked
mpl.figure()
mpl.suptitle('Pick the centers of the expanding windows')
mpl.axis('scaled')
mpl.contourf(yp, xp, tf, shape, 50)
mpl.colorbar()
centers = mpl.pick_points(area, mpl.gca(), xy2ne=True)
# Run the euler deconvolution on an expanding window
# Structural index is 3
index = 3
results = []
for center in centers:
results.append(
gravmag.euler.expanding_window(xp, yp, zp, tf, xderiv, yderiv, zderiv,
index, gravmag.euler.classic, center, 500, 5000))
print "Base level used: %g" % (baselevel)
print "Estimated base level: %g" % (results[-1]['baselevel'])
print "Estimated source location: %s" % (str(results[-1]['point']))
myv.figure()
myv.points([r['point'] for r in results], size=300.)
myv.prisms(model, opacity=0.5)
axes = myv.axes(myv.outline(bounds), ranges=[b*0.001 for b in bounds])
myv.wall_bottom(bounds)
myv.wall_north(bounds)
myv.show()
"""
Meshing: Filter prisms from a 3D prism mesh based on their physical properties
"""
from fatiando import gridder, mesher
from fatiando.vis import myv
shape = (5, 20, 10)
bounds = (0, 100, 0, 200, 0, 50)
mesh = mesher.PrismMesh(bounds, shape)
# Fill the even prisms with 1 and odd with -1
def fill(i):
if i%2 == 0:
return 1
return -1
mesh.addprop('density', [fill(i) for i in xrange(mesh.size)])
# Separate even and odd prisms
odd = mesher.vfilter(-1, 0, 'density', mesh)
even = mesher.vfilter(0, 1, 'density', mesh)
myv.figure()
myv.prisms(odd, prop='density', vmin=-1, vmax=1)
myv.prisms(even, prop='density', style='wireframe', vmin=-1, vmax=1)
myv.axes(myv.outline(bounds))
myv.show()
mpl.figure()
titles = ['Gravity anomaly', 'x derivative', 'y derivative', 'z derivative']
for i, f in enumerate([gz, xderiv, yderiv, zderiv]):
mpl.subplot(2, 2, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
mpl.contourf(yp, xp, f, shape, 50)
mpl.colorbar()
mpl.m2km()
mpl.show()
# Run the euler deconvolution on moving windows to produce a set of solutions
euler = Classic(xp, yp, zp, gz, xderiv, yderiv, zderiv, 2)
solver = MovingWindow(euler, windows=(10, 10), size=(2000, 2000)).fit()
mpl.figure()
mpl.axis('scaled')
mpl.title('Moving window centers')
mpl.contourf(yp, xp, gz, shape, 50)
mpl.points(solver.window_centers)
mpl.show()
myv.figure()
myv.points(solver.estimate_, size=100.)
myv.prisms(model, opacity=0.5)
axes = myv.axes(myv.outline(bounds), ranges=[b * 0.001 for b in bounds])
myv.wall_bottom(bounds)
myv.wall_north(bounds)
myv.title('Euler solutions')
myv.show()
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)
myv.wall_bottom(bounds)
myv.wall_north(bounds)
myv.show()
from fatiando.vis import myv
mesh = PrismMesh(bounds=(0, 100, 0, 200, 0, 150), shape=(5, 6, 7))
# We'll give each prism a density value corresponding to it's index on the
# mesh. Notice that meshes take lists/arrays as their property values
mesh.addprop('density', list(range(mesh.size)))
# You can iterate over meshes like lists of elements
for p in mesh:
print(p.props['density'], end=' ')
scene = myv.figure(size=(600, 600))
# Because you can iterate over a mesh, you can pass it anywhere a list of
# prisms is accepted
plot = myv.prisms(mesh, prop='density')
# The code below enables and configures the color bar. This will be automated
# on a function in the future (write to the mailing list if you'd like to help
# out!)
plot.module_manager.scalar_lut_manager.show_scalar_bar = True
plot.module_manager.scalar_lut_manager.lut_mode = 'Greens'
plot.module_manager.scalar_lut_manager.reverse_lut = True
plot.module_manager.scalar_lut_manager.label_text_property.color = (0, 0, 0)
plot.module_manager.scalar_lut_manager.title_text_property.color = (0, 0, 0)
plot.module_manager.scalar_lut_manager.scalar_bar_representation.position = \
[0.9, 0.4]
plot.module_manager.scalar_lut_manager.scalar_bar_representation.position2 = \
[0.1, 0.6]
myv.axes(myv.outline(), fmt='%.1f')
myv.show()
utils.contaminate(gravmag.prism.gxy(xp, yp, zp, prisms), noise),
utils.contaminate(gravmag.prism.gxz(xp, yp, zp, prisms), noise),
utils.contaminate(gravmag.prism.gyy(xp, yp, zp, prisms), noise),
utils.contaminate(gravmag.prism.gyz(xp, yp, zp, prisms), noise),
utils.contaminate(gravmag.prism.gzz(xp, yp, zp, prisms), noise)
]
# Plot the data
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
mpl.figure()
for i, title in enumerate(titles):
mpl.subplot(3, 2, i + 1)
mpl.title(title)
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, tensor[i], shape, 10)
mpl.contour(yp, xp, tensor[i], shape, levels)
mpl.m2km()
mpl.show()
# Get the eigenvectors from the tensor data
eigenvals, eigenvecs = gravmag.tensor.eigen(tensor)
# Use the first eigenvector to estimate the center of mass
cm, sigma = gravmag.tensor.center_of_mass(xp, yp, zp, eigenvecs[0])
print "Sigma = %g" % (sigma)
# Plot the prism and the estimated center of mass
myv.figure()
myv.points([cm], size=300.)
myv.prisms(prisms, prop='density', opacity=0.5)
axes = myv.axes(myv.outline(extent=[-5000, 5000, -5000, 5000, 0, 5000]))
myv.wall_bottom(axes.axes.bounds, opacity=0.2)
myv.wall_north(axes.axes.bounds)
myv.show()
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)
myv.wall_bottom(bounds)
myv.wall_north(bounds)
myv.show()
""" Meshing: Make and plot a 3D prism mesh """ from fatiando import mesher from fatiando.vis import myv mesh = mesher.PrismMesh(bounds=(-2, 2, -3, 3, 0, 1), shape=(4, 4, 4)) myv.figure() plot = myv.prisms(mesh) axes = myv.axes(plot) myv.show()
# Calculate the derivatives using FFT
xderiv = fourier.derivx(xp, yp, tf, shape)
yderiv = fourier.derivy(xp, yp, tf, shape)
zderiv = fourier.derivz(xp, yp, tf, shape)
mpl.figure()
titles = ['Total field', 'x derivative', 'y derivative', 'z derivative']
for i, f in enumerate([tf, xderiv, yderiv, zderiv]):
mpl.subplot(2, 2, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
mpl.contourf(yp, xp, f, shape, 50)
mpl.colorbar()
mpl.m2km()
mpl.show()
# Run the Euler deconvolution on the whole dataset
euler = Classic(xp, yp, zp, tf, xderiv, yderiv, zderiv, 3).fit()
print "Base level used: %g" % (baselevel)
print "Estimated:"
print " Base level: %g" % (euler.baselevel_)
print " Source location: %s" % (str(euler.estimate_))
myv.figure()
myv.points([euler.estimate_], size=100.)
myv.prisms(model, 'magnetization', opacity=0.5)
axes = myv.axes(myv.outline(extent=bounds))
myv.wall_bottom(axes.axes.bounds, opacity=0.2)
myv.wall_north(axes.axes.bounds)
myv.show()
area = bounds[:4]
axis = mpl.figure().gca()
mpl.axis('scaled')
model = [
mesher.PolygonalPrism(
mpl.draw_polygon(area, axis, xy2ne=True),
# Use only induced magnetization
0, 2000, {'magnetization':2})]
# Calculate the effect
shape = (100, 100)
xp, yp, zp = gridder.regular(area, shape, z=-500)
tf = polyprism.tf(xp, yp, zp, model, inc, dec)
# and plot it
mpl.figure()
mpl.axis('scaled')
mpl.title("Total field anomalyproduced by prism model (nT)")
mpl.contourf(yp, xp, tf, shape, 20)
mpl.colorbar()
for p in model:
mpl.polygon(p, '.-k', xy2ne=True)
mpl.set_area(area)
mpl.m2km()
mpl.show()
# Show the prisms
myv.figure()
myv.polyprisms(model, 'magnetization')
myv.axes(myv.outline(bounds), ranges=[i*0.001 for i in bounds])
myv.wall_north(bounds)
myv.wall_bottom(bounds)
myv.show()
"""
Meshing: Make and plot a 3D prism mesh with topography
"""
from fatiando import gridder, utils, mesher
from fatiando.vis import myv
x1, x2 = -100, 100
y1, y2 = -200, 200
bounds = (x1, x2, y1, y2, -200, 0)
x, y = gridder.regular((x1, x2, y1, y2), (50, 50))
height = (100 +
-50 * utils.gaussian2d(x, y, 100, 200, x0=-50, y0=-100, angle=-60) +
100 * utils.gaussian2d(x, y, 50, 100, x0=80, y0=170))
mesh = mesher.PrismMesh(bounds, (20, 40, 20))
mesh.carvetopo(x, y, height)
myv.figure()
myv.prisms(mesh)
myv.axes(myv.outline(bounds), fmt='%.0f')
myv.wall_north(bounds)
myv.show()