def fwd_grav_fatiando():
"""
GravMag: 3D imaging using the migration method on synthetic gravity data
(more complex model + noisy data)
"""
# Make some synthetic gravity data from a simple prism model
za = 5000
zb = 7000
model = [mesher.Prism(-4000, 0, -4000, -2000, za, zb,
{'density': 1200})] #,
# 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=0)
shape = (25, 25)
xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=0)
#gz = utils.contaminate(prism.gz(xp, yp, zp, model), 0.1)
gz = prism.gz(xp, yp, zp, model)
# 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()
return xp, yp, zp, gz, shape, model
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()
model = [
mesher.Prism(-4000, 0, -4000, -2000, 2000, 5000, {'density': 1200}),
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)
shape = (100, 100)
z0 = -500
x, y, z = gridder.regular(area, shape, z=z0)
tf = utils.contaminate(prism.tf(x, y, z, model, inc, dec), 1, seed=0)
# Reduce to the pole using FFT. Since there is only induced magnetization, the
# magnetization direction (sinc and sdec) is the same as the geomagnetic field
pole = transform.reduce_to_pole(x, y, tf, shape, inc, dec, sinc=inc, sdec=dec)
# Calculate the true value at the pole for comparison
true = prism.tf(x, y, z, model, 90, 0, pmag=utils.ang2vec(10, 90, 0))
fig, axes = mpl.subplots(1, 3, figsize=(14, 4))
for ax in axes:
ax.set_aspect('equal')
mpl.sca(axes[0])
mpl.title("Original total field anomaly")
mpl.contourf(y, x, tf, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(pad=0).set_label('nT')
mpl.m2km()
mpl.sca(axes[1])
mpl.title("True value at pole")
mpl.contourf(y, x, true, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(pad=0).set_label('nT')
mpl.m2km()
mpl.sca(axes[2])
mpl.title("Reduced to the pole")
mpl.contourf(y, x, pole, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(pad=0).set_label('nT')
mpl.m2km()
mpl.tight_layout()
mpl.show()
from fatiando import mesher, gridder, utils
from fatiando.gravmag import prism, transform
from fatiando.vis import mpl
model = [mesher.Prism(-100, 100, -100, 100, 0, 2000, {'magnetization': 10})]
area = (-5000, 5000, -5000, 5000)
shape = (100, 100)
z0 = -500
x, y, z = gridder.regular(area, shape, z=z0)
inc, dec = -30, 0
tf = utils.contaminate(prism.tf(x, y, z, model, inc, dec), 0.001,
percent=True)
# Need to convert gz to SI units so that the result is also in SI
total_grad_amp = transform.tga(x, y, utils.nt2si(tf), shape)
mpl.figure()
mpl.subplot(1, 2, 1)
mpl.title("Original total field anomaly")
mpl.axis('scaled')
mpl.contourf(y, x, tf, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(orientation='horizontal').set_label('nT')
mpl.m2km()
mpl.subplot(1, 2, 2)
mpl.title("Total Gradient Amplitude")
mpl.axis('scaled')
mpl.contourf(y, x, total_grad_amp, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(orientation='horizontal').set_label('nT/m')
mpl.m2km()
mpl.show()
from fatiando import mesher, gridder, utils
from fatiando.gravmag import prism, fourier
from fatiando.vis import mpl
model = [mesher.Prism(-100,100,-100,100,0,2000,{'magnetization':10})]
area = (-5000, 5000, -5000, 5000)
shape = (100, 100)
z0 = -500
xp, yp, zp = gridder.regular(area, shape, z=z0)
inc, dec = -30, 0
tf = utils.contaminate(prism.tf(xp, yp, zp, model, inc, dec), 0.001,
percent=True)
# Need to convert gz to SI units so that the result is also in SI
ansig = fourier.ansig(xp, yp, utils.nt2si(tf), shape)
mpl.figure()
mpl.subplot(1, 2, 1)
mpl.title("Original total field anomaly")
mpl.axis('scaled')
mpl.contourf(yp, xp, tf, shape, 30)
mpl.colorbar(orientation='horizontal')
mpl.m2km()
mpl.subplot(1, 2, 2)
mpl.title("Analytic signal")
mpl.axis('scaled')
mpl.contourf(yp, xp, ansig, shape, 30)
mpl.colorbar(orientation='horizontal')
mpl.m2km()
mpl.show()
gz_true = prism.gz(x, y, z, model)
mpl.figure()
mpl.suptitle('L-curve')
mpl.title("Estimated regularization parameter: %g" % (solver.regul_param_))
solver.plot_lcurve()
mpl.grid()
# Plot the layer and the fit
mpl.figure(figsize=(14, 4))
mpl.suptitle('Observed data (black) | Predicted by layer (red)')
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().set_label(r'Density $kg.m^{-3}$')
mpl.m2km()
mpl.subplot(1, 3, 2)
mpl.axis('scaled')
mpl.title('Fit gz (mGal)')
levels = mpl.contour(y1, x1, gz, shape, 15, color='k', interp=True)
mpl.contour(y1,
x1,
solver.predicted()[0],
shape,
levels,
color='r',
interp=True)
mpl.plot(y1, x1, 'xk', label='Data points')
mpl.legend()
mpl.m2km()
"""
from fatiando import mesher, gridder, utils
from fatiando.gravmag import prism, transform
from fatiando.vis import mpl
model = [mesher.Prism(-100, 100, -100, 100, 0, 2000, {'magnetization': 10})]
area = (-5000, 5000, -5000, 5000)
shape = (100, 100)
z0 = -500
x, y, z = gridder.regular(area, shape, z=z0)
inc, dec = -30, 0
tf = utils.contaminate(prism.tf(x, y, z, model, inc, dec), 0.001, percent=True)
# Need to convert gz to SI units so that the result is also in SI
total_grad_amp = transform.tga(x, y, utils.nt2si(tf), shape)
mpl.figure()
mpl.subplot(1, 2, 1)
mpl.title("Original total field anomaly")
mpl.axis('scaled')
mpl.contourf(y, x, tf, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(orientation='horizontal').set_label('nT')
mpl.m2km()
mpl.subplot(1, 2, 2)
mpl.title("Total Gradient Amplitude")
mpl.axis('scaled')
mpl.contourf(y, x, total_grad_amp, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(orientation='horizontal').set_label('nT/m')
mpl.m2km()
mpl.show()
z0 = -500
x, y, z = gridder.regular(area, shape, z=z0)
tf = utils.contaminate(prism.tf(x, y, z, model, inc, dec),
1, seed=0)
# Reduce to the pole using FFT. Since there is only induced magnetization, the
# magnetization direction (sinc and sdec) is the same as the geomagnetic field
pole = transform.reduce_to_pole(x, y, tf, shape, inc, dec, sinc=inc, sdec=dec)
# Calculate the true value at the pole for comparison
true = prism.tf(x, y, z, model, 90, 0, pmag=utils.ang2vec(10, 90, 0))
fig, axes = mpl.subplots(1, 3, figsize=(14, 4))
for ax in axes:
ax.set_aspect('equal')
mpl.sca(axes[0])
mpl.title("Original total field anomaly")
mpl.contourf(y, x, tf, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(pad=0).set_label('nT')
mpl.m2km()
mpl.sca(axes[1])
mpl.title("True value at pole")
mpl.contourf(y, x, true, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(pad=0).set_label('nT')
mpl.m2km()
mpl.sca(axes[2])
mpl.title("Reduced to the pole")
mpl.contourf(y, x, pole, shape, 30, cmap=mpl.cm.RdBu_r)
mpl.colorbar(pad=0).set_label('nT')
mpl.m2km()
mpl.tight_layout()
mpl.show()
from fatiando import mesher, gridder, utils, gravmag
from fatiando.vis import mpl
prisms = [mesher.Prism(-100, 100, -100, 100, 0, 2000, {'magnetization': 10})]
area = (-5000, 5000, -5000, 5000)
shape = (100, 100)
z0 = -500
xp, yp, zp = gridder.regular(area, shape, z=z0)
inc, dec = -30, 0
tf = utils.contaminate(gravmag.prism.tf(xp, yp, zp, prisms, inc, dec),
0.001,
percent=True)
# Need to convert gz to SI units so that the result is also in SI
ansig = gravmag.fourier.ansig(xp, yp, utils.nt2si(tf), shape)
mpl.figure()
mpl.subplot(1, 2, 1)
mpl.title("Original total field anomaly")
mpl.axis('scaled')
mpl.contourf(yp, xp, tf, shape, 30)
mpl.colorbar(orientation='horizontal')
mpl.m2km()
mpl.subplot(1, 2, 2)
mpl.title("Analytic signal")
mpl.axis('scaled')
mpl.contourf(yp, xp, ansig, shape, 30)
mpl.colorbar(orientation='horizontal')
mpl.m2km()
mpl.show()
gz = utils.contaminate(prism.gz(xp, yp, zp, model), 0.001)
# Need to convert gz to SI units so that the result can be converted to Eotvos
gxz = utils.si2eotvos(transform.derivx(xp, yp, utils.mgal2si(gz), shape))
gyz = utils.si2eotvos(transform.derivy(xp, yp, utils.mgal2si(gz), shape))
gzz = utils.si2eotvos(transform.derivz(xp, yp, utils.mgal2si(gz), shape))
gxz_true = prism.gxz(xp, yp, zp, model)
gyz_true = prism.gyz(xp, yp, zp, model)
gzz_true = prism.gzz(xp, yp, zp, model)
mpl.figure()
mpl.title("Original gravity anomaly")
mpl.axis('scaled')
mpl.contourf(xp, yp, gz, shape, 15)
mpl.colorbar(shrink=0.7)
mpl.m2km()
mpl.figure(figsize=(14, 10))
mpl.subplots_adjust(top=0.95, left=0.05, right=0.95)
mpl.subplot(2, 3, 1)
mpl.title("x deriv (contour) + true (color map)")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gxz_true, shape, 12)
mpl.colorbar(shrink=0.7)
mpl.contour(yp, xp, gxz, shape, 12, color='k')
mpl.m2km()
mpl.subplot(2, 3, 2)
mpl.title("y deriv (contour) + true (color map)")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gyz_true, shape, 12)
gz = utils.contaminate(prism.gz(x, y, z, model), 0.5, seed=0)
height = 1000 # How much higher to go
gzcontf = transform.upcontinue(x, y, gz, shape, height)
# Compute the true value at the new height for comparison
gztrue = prism.gz(x, y, z - height, model)
args = dict(shape=shape, levels=20, cmap=mpl.cm.RdBu_r)
fig, axes = mpl.subplots(1, 3, figsize=(12, 3.5))
axes = axes.ravel()
mpl.sca(axes[0])
mpl.title("Original")
mpl.axis('scaled')
mpl.contourf(x, y, gz, **args)
mpl.colorbar(pad=0).set_label('mGal')
mpl.m2km()
mpl.sca(axes[1])
mpl.title('True higher')
mpl.axis('scaled')
mpl.contourf(y, x, gztrue, **args)
mpl.colorbar(pad=0).set_label('mGal')
mpl.m2km()
mpl.sca(axes[2])
mpl.title("Continued (Fourier)")
mpl.axis('scaled')
mpl.contourf(y, x, gzcontf, **args)
mpl.colorbar(pad=0).set_label('mGal')
mpl.m2km()
mpl.tight_layout()
mpl.show()
gz = utils.contaminate(prism.gz(x, y, z, model), 0.5, seed=0)
height = 1000 # How much higher to go
gzcontf = transform.upcontinue(x, y, gz, shape, height)
# Compute the true value at the new height for comparison
gztrue = prism.gz(x, y, z - height, model)
args = dict(shape=shape, levels=20, cmap=mpl.cm.RdBu_r)
fig, axes = mpl.subplots(1, 3, figsize=(12, 3.5))
axes = axes.ravel()
mpl.sca(axes[0])
mpl.title("Original")
mpl.axis('scaled')
mpl.contourf(x, y, gz, **args)
mpl.colorbar(pad=0).set_label('mGal')
mpl.m2km()
mpl.sca(axes[1])
mpl.title('True higher')
mpl.axis('scaled')
mpl.contourf(y, x, gztrue, **args)
mpl.colorbar(pad=0).set_label('mGal')
mpl.m2km()
mpl.sca(axes[2])
mpl.title("Continued (Fourier)")
mpl.axis('scaled')
mpl.contourf(y, x, gzcontf, **args)
mpl.colorbar(pad=0).set_label('mGal')
mpl.m2km()
mpl.tight_layout()
mpl.show()
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)
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))
gz_true = prism.gz(x, y, z, model)
mpl.figure()
mpl.suptitle('L-curve')
mpl.title("Estimated regularization parameter: %g" % (solver.regul_param_))
solver.plot_lcurve()
mpl.grid()
# Plot the layer and the fit
mpl.figure(figsize=(14, 4))
mpl.suptitle('Observed data (black) | Predicted by layer (red)')
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().set_label(r'Density $kg.m^{-3}$')
mpl.m2km()
mpl.subplot(1, 3, 2)
mpl.axis('scaled')
mpl.title('Fit gz (mGal)')
levels = mpl.contour(y1, x1, gz, shape, 15, color='k', interp=True)
mpl.contour(y1, x1, solver.predicted()[0], shape, levels, color='r',
interp=True)
mpl.plot(y1, x1, 'xk', label='Data points')
mpl.legend()
mpl.m2km()
mpl.subplot(1, 3, 3)
mpl.axis('scaled')
mpl.title('Fit gzz (Eotvos)')
levels = mpl.contour(y2, x2, gzz, shape, 10, color='k', interp=True)
mpl.contour(y2, x2, solver.predicted()[1], shape, levels, color='r',
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()
area = (lon.min(), lon.max(), lat.min(), lat.max())
# First, lets calculate the gravity disturbance (e.g., the free-air anomaly)
# We'll do this using the closed form of the normal gravity for the WGS84
# ellipsoid
gamma = normal_gravity.gamma_closed_form(lat, height)
disturbance = gravity - gamma
# Now we can remove the effect of the Bouguer plate to obtain the Bouguer
# anomaly. We'll use the standard densities of 2.67 g.cm^-3 for crust and 1.04
# g.cm^-3 for water.
bouguer = disturbance - normal_gravity.bouguer_plate(topo)
mpl.figure(figsize=(14, 3.5))
bm = mpl.basemap(area, projection='merc')
mpl.subplot(131)
mpl.title('Gravity (mGal)')
mpl.contourf(lon, lat, gravity, shape, 60, cmap=mpl.cm.Reds, basemap=bm)
mpl.colorbar(pad=0)
mpl.subplot(132)
mpl.title('Gravity disturbance (mGal)')
amp = np.abs(disturbance).max()
mpl.contourf(lon, lat, disturbance, shape, 60, cmap=mpl.cm.RdBu_r, basemap=bm,
vmin=-amp, vmax=amp)
mpl.colorbar(pad=0)
mpl.subplot(133)
mpl.title('Bouguer anomaly (mGal)')
mpl.contourf(lon, lat, bouguer, shape, 60, cmap=mpl.cm.Reds, basemap=bm)
mpl.colorbar(pad=0)
mpl.show()
