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
def Plot_Onemap(x, y, data, shape, prism_projection, projection_style,
line_width, model, figure_title, label_x, label_y, label_size,
observations, point_style, point_size, unit):
levels = mpl.contourf(y, x, data, shape, 20, interp=True)
cbar = plt.colorbar()
mpl.contour(y, x, data, shape, levels, clabel=False, interp=True)
if observations is True:
plt.plot(y, x, point_style, markersize=point_size)
if unit is not None:
cbar.set_label(unit, fontsize=label_size)
ax = plt.gca()
if prism_projection is True:
for i, sq in enumerate(model):
y1, y2, x1, x2 = sq
xs_project = [x1, x1, x2, x2, x1]
ys_project = [y1, y2, y2, y1, y1]
ax.plot(xs_project,
ys_project,
projection_style,
linewidth=line_width)
if label_x is not None:
ax.set_xlabel(label_x, fontsize=label_size)
if label_y is not None:
ax.set_ylabel(label_y, fontsize=label_size)
if figure_title is not None:
ax.set_title(figure_title, fontsize=label_size)
mpl.m2km()
data = [
polyprism.gxx(xp, yp, zp, model),
polyprism.gxy(xp, yp, zp, model),
polyprism.gxz(xp, yp, zp, model),
polyprism.gyy(xp, yp, zp, model),
polyprism.gyz(xp, yp, zp, model),
polyprism.gzz(xp, yp, zp, model)
]
# and plot it
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
mpl.figure()
mpl.axis('scaled')
mpl.suptitle("Gravity tensor produced by prism model (Eotvos)")
for i in xrange(len(data)):
mpl.subplot(3, 2, i + 1)
mpl.title(titles[i])
mpl.contourf(yp, xp, data[i], 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, 'density')
myv.axes(myv.outline(bounds), ranges=[i * 0.001 for i in bounds])
myv.wall_north(bounds)
myv.wall_bottom(bounds)
myv.show()
"""
GravMag: Generate synthetic gravity data on an irregular grid
"""
from fatiando import mesher, gridder, gravmag
from fatiando.vis import mpl
prisms = [mesher.Prism(-2000, 2000, -2000, 2000, 0, 2000, {'density': 1000})]
xp, yp, zp = gridder.scatter((-5000, 5000, -5000, 5000), n=100, z=-100)
gz = gravmag.prism.gz(xp, yp, zp, prisms)
shape = (100, 100)
mpl.axis('scaled')
mpl.title("gz produced by prism model on an irregular grid (mGal)")
mpl.plot(xp, yp, '.k', label='Grid points')
levels = mpl.contourf(xp, yp, gz, shape, 12, interp=True)
mpl.contour(xp, yp, gz, shape, levels, interp=True)
mpl.legend(loc='lower right', numpoints=1)
mpl.m2km()
mpl.show()
def data(x, y):
return (utils.gaussian2d(x, y, -0.6, -1)
- utils.gaussian2d(x, y, 1.5, 1.5))
z = data(x, y)
shape = (100, 100)
# First, we need to know the real data at the grid points
grdx, grdy = gridder.regular(area, shape)
grdz = data(grdx, grdy)
mpl.figure()
mpl.subplot(2, 2, 1)
mpl.axis('scaled')
mpl.title("True grid data")
mpl.plot(x, y, '.k', label='Data points')
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
# Use the default interpolation (cubic)
grdx, grdy, grdz = gridder.interp(x, y, z, shape)
mpl.subplot(2, 2, 2)
mpl.axis('scaled')
mpl.title("Interpolated using cubic minimum-curvature")
mpl.plot(x, y, '.k', label='Data points')
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
# Use the nearest neighbors interpolation
grdx, grdy, grdz = gridder.interp(x, y, z, shape, algorithm='nn')
lons, lats, heights = gridder.regular(area, shape, z=250000)
# Divide the model into nproc slices and calculate them in parallel
log.info('Calculating...')
def calculate(chunk):
return gravmag.tesseroid.gz(lons, lats, heights, chunk)
def split(model, nproc):
chunksize = len(model)/nproc
for i in xrange(nproc - 1):
yield model[i*chunksize : (i + 1)*chunksize]
yield model[(nproc - 1)*chunksize : ]
start = time.time()
nproc = 8
pool = Pool(processes=nproc)
gz = sum(pool.map(calculate, split(model, nproc)))
pool.close()
print "Time it took: %s" % (utils.sec2hms(time.time() - start))
log.info('Plotting...')
mpl.figure(figsize=(10, 4))
mpl.title('Crust gravity signal at 250km height')
bm = mpl.basemap(area, 'robin')
mpl.contourf(lons, lats, gz, shape, 35, basemap=bm)
cb = mpl.colorbar()
cb.set_label('mGal')
bm.drawcoastlines()
bm.drawmapboundary()
bm.drawparallels(range(-90, 90, 45), labels=[0, 1, 0, 0])
bm.drawmeridians(range(-180, 180, 60), labels=[0, 0, 0, 1])
mpl.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()
baselevel = 10
# Convert from nanoTesla to Tesla because euler and derivatives require things
# in SI
tf = (utils.nt2si(prism.tf(xp, yp, zp, model, inc, dec)) + baselevel)
# 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))
log.info(logger.header())
# Create a synthetic model
model = [Prism(250, 750, 250, 750, 200, 700, {'density':1000})]
# and generate synthetic data from it
shape = (25, 25)
bounds = [0, 1000, 0, 1000, 0, 1000]
area = bounds[0:4]
xp, yp, zp = gridder.regular(area, shape, z=-1)
noise = 0.1 # 0.1 mGal noise
gz = utils.contaminate(gm.prism.gz(xp, yp, zp, model), noise)
# plot the data
mpl.figure()
mpl.title("Synthetic gravity anomaly (mGal)")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gz, shape, 12)
mpl.colorbar()
mpl.xlabel('Horizontal coordinate y (km)')
mpl.ylabel('Horizontal coordinate x (km)')
mpl.m2km()
mpl.show()
# Inversion setup
# Create a mesh
mesh = PrismMesh(bounds, (25, 25, 25))
# Wrap the data so that harvester can use it
data = [gm.harvester.Gz(xp, yp, zp, gz)]
# Make the seed
seeds = gm.harvester.sow([[500, 500, 450, {'density':1000}]], mesh)
# Run the inversioin
estimate, predicted = gm.harvester.harvest(data, seeds, mesh,
"""
Gridding: Load a Surfer ASCII grid file
"""
from fatiando import datasets, gridder
from fatiando.vis import mpl
# Fetching Bouguer anomaly model data (Surfer ASCII grid file)"
# Will download the archive and save it with the default name
archive = datasets.fetch_bouguer_alps_egm()
# Load the GRD file and convert in three numpy-arrays (y, x, bouguer)
y, x, bouguer, shape = gridder.load_surfer(archive, fmt='ascii')
mpl.figure()
mpl.axis('scaled')
mpl.title("Data loaded from a Surfer ASCII grid file")
mpl.contourf(y, x, bouguer, shape, 15)
cb = mpl.colorbar()
cb.set_label('mGal')
mpl.xlabel('y points to East (km)')
mpl.ylabel('x points to North (km)')
mpl.m2km()
mpl.show()
-4000, -3000, -4000, -3000, 0, 2000,
{'magnetization': 2}), # a scalar magnetization means only induced
mesher.Prism(-1000, 1000, -1000, 1000, 0, 2000, {'magnetization': 1}),
# This prism will have magnetization in a different direction
mesher.Prism(2000, 4000, 3000, 4000, 0, 2000,
{'magnetization': utils.ang2vec(3, -10, 45)})
] # induced + remanent
# Create a regular grid at 100m height
shape = (200, 200)
area = bounds[:4]
xp, yp, zp = gridder.regular(area, shape, z=-500)
# Calculate the anomaly for a given regional field
tf = gravmag.prism.tf(xp, yp, zp, prisms, inc, dec)
# Plot
mpl.figure()
mpl.title("Total-field anomaly (nT)")
mpl.axis('scaled')
mpl.contourf(yp, xp, tf, shape, 15)
mpl.colorbar()
mpl.xlabel('East y (km)')
mpl.ylabel('North x (km)')
mpl.m2km()
mpl.show()
# Show the prisms
myv.figure()
myv.prisms(prisms, 'magnetization')
myv.axes(myv.outline(bounds), ranges=[i * 0.001 for i in bounds])
myv.wall_north(bounds)
myv.wall_bottom(bounds)
myv.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()
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()
xp, yp, zp = gridder.regular(area, shape, z=z0)
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')
""" Vis: Plot a map using the Orthographic map projection and filled contours """ from fatiando import gridder, utils from fatiando.vis import mpl # Generate some data to plot area = (-40, 0, 10, -50) shape = (100, 100) lon, lat = gridder.regular(area, shape) data = utils.gaussian2d(lon, lat, 10, 20, -20, -20, angle=-45) # Now get a basemap to plot with some projection bm = mpl.basemap(area, 'ortho') # And now plot everything passing the basemap to the plotting functions mpl.figure() bm.bluemarble() mpl.contourf(lon, lat, data, shape, 12, basemap=bm) mpl.colorbar() mpl.show()
data = [
utils.contaminate(prism.gxx(xp, yp, zp, model), noise),
utils.contaminate(prism.gxy(xp, yp, zp, model), noise),
utils.contaminate(prism.gxz(xp, yp, zp, model), noise),
utils.contaminate(prism.gyy(xp, yp, zp, model), noise),
utils.contaminate(prism.gyz(xp, yp, zp, model), noise),
utils.contaminate(prism.gzz(xp, yp, zp, model), 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, data[i], shape, 10)
mpl.contour(yp, xp, data[i], shape, levels)
mpl.m2km()
mpl.show()
# Get the eigenvectors from the tensor data
eigenvals, eigenvecs = tensor.eigen(data)
# Use the first eigenvector to estimate the center of mass
cm = tensor.center_of_mass(xp, yp, zp, eigenvecs[0])
# Plot the prism and the estimated center of mass
myv.figure()
myv.points([cm], size=200.)
myv.prisms(model, 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)
"""
from fatiando import mesher, gridder, utils, gravmag
from fatiando.vis import mpl
spheres = [mesher.Sphere(0, 0, 2000, 1000, {'density': 1000})]
# Create a set of points at 100m height
area = (-5000, 5000, -5000, 5000)
xp, yp, zp = gridder.scatter(area, 500, z=-100)
# Calculate the anomaly
gz = utils.contaminate(gravmag.sphere.gz(xp, yp, zp, spheres), 0.1)
gzz = utils.contaminate(gravmag.sphere.gzz(xp, yp, zp, spheres), 5.0)
# Plot
shape = (100, 100)
mpl.figure()
mpl.title("gz (mGal)")
mpl.axis('scaled')
mpl.plot(yp * 0.001, xp * 0.001, '.k')
mpl.contourf(yp * 0.001, xp * 0.001, gz, shape, 15, interp=True)
mpl.colorbar()
mpl.xlabel('East y (km)')
mpl.ylabel('North x (km)')
mpl.figure()
mpl.title("gzz (Eotvos)")
mpl.axis('scaled')
mpl.plot(yp * 0.001, xp * 0.001, '.k')
mpl.contourf(yp * 0.001, xp * 0.001, gzz, shape, 15, interp=True)
mpl.colorbar()
mpl.xlabel('East y (km)')
mpl.ylabel('North x (km)')
mpl.show()
utils.gaussian2d(x, y, 1.5, 1.5))
z = data(x, y)
shape = (100, 100)
# First, we need to know the real data at the grid points
grdx, grdy = gridder.regular(area, shape)
grdz = data(grdx, grdy)
mpl.figure()
mpl.subplot(2, 2, 1)
mpl.axis('scaled')
mpl.title("True grid data")
mpl.plot(x, y, '.k', label='Data points')
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
# Use the default interpolation (cubic)
grdx, grdy, grdz = gridder.interp(x, y, z, shape)
mpl.subplot(2, 2, 2)
mpl.axis('scaled')
mpl.title("Interpolated using cubic minimum-curvature")
mpl.plot(x, y, '.k', label='Data points')
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
# Use the nearest neighbors interpolation
grdx, grdy, grdz = gridder.interp(x, y, z, shape, algorithm='nn')
tensor = [utils.contaminate(gravmag.prism.gxx(xp, yp, zp, prisms), noise),
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)]
# Get the eigenvectors from the tensor data
eigenvals, eigenvecs = gravmag.tensor.eigen(tensor)
# 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()
# 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
"""
Gridding: Generate and plot irregular grids (scatter)
"""
from fatiando import gridder, utils
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)
mpl.axis('scaled')
mpl.title("Irregular grid")
mpl.plot(x, y, '.k', label='Grid points')
# Make a filled contour plot and tell the function to automatically interpolate
# the data on a 100x100 grid
mpl.contourf(x, y, z, (100, 100), 50, interp=True)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
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()
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()
mpl.subplot(2, 1, 1)
mpl.axis('scaled')
mpl.title('Gravity anomaly')
mpl.contourf(y, x, gz, shape, 30)
mpl.colorbar()
mpl.subplot(2, 1, 2)
mpl.axis('scaled')
mpl.title('Magnetic total field anomaly')
mpl.contourf(y, x, tf, shape, 30)
mpl.colorbar()
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 gridder, utils
from fatiando.vis import mpl
# Generate some data to plot
area = (-40, 0, 10, -50)
shape = (100, 100)
lon, lat = gridder.regular(area, shape)
data = utils.gaussian2d(lon, lat, 10, 20, -20, -20, angle=-45)
mpl.figure()
# Filled contour plot
mpl.subplot(221)
mpl.title('Filled contours')
mpl.contourf(lon, lat, data, shape, 50)
mpl.colorbar()
# Contour plot
mpl.subplot(222)
mpl.title('Line contours')
mpl.contour(lon, lat, data, shape, 10, color='r', style='dashed')
# Mix contour and contourf
# contour and contourf return a list of the contour values
mpl.subplot(223)
mpl.title('Filled contours + line contours')
levels = mpl.contourf(lon, lat, data, shape, 10)
mpl.colorbar()
# using "levels" tells contour to use the exact same values as contourf
mpl.contour(lon, lat, data, shape, levels)
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()
mesher.Prism(-1000,1000,-1000,1000,0,2000,{'density':-800}),
mesher.Prism(1000,3000,2000,3000,0,1000,{'density':500})]
area = (-5000, 5000, -5000, 5000)
shape = (50, 50)
z0 = -100
xp, yp, zp = gridder.regular(area, shape, z=z0)
gz = utils.contaminate(prism.gz(xp, yp, zp, model), 0.5)
# Now do the upward continuation using the analytical formula
height = 2000
dims = gridder.spacing(area, shape)
gzcont = transform.upcontinue(gz, height, xp, yp, dims)
gztrue = prism.gz(xp, yp, zp - height, model)
mpl.figure(figsize=(14,6))
mpl.subplot(1, 2, 1)
mpl.title("Original")
mpl.axis('scaled')
mpl.contourf(xp, yp, gz, shape, 15)
mpl.contour(xp, yp, gz, shape, 15)
mpl.subplot(1, 2, 2)
mpl.title("Continued + true")
mpl.axis('scaled')
levels = mpl.contour(xp, yp, gzcont, shape, 12, color='b',
label='Continued', style='dashed')
mpl.contour(xp, yp, gztrue, shape, levels, color='r', label='True',
style='solid')
mpl.legend()
mpl.show()
noise = 0.5
gxx = utils.contaminate(gm.prism.gxx(xp, yp, zp, model), noise)
gxy = utils.contaminate(gm.prism.gxy(xp, yp, zp, model), noise)
gxz = utils.contaminate(gm.prism.gxz(xp, yp, zp, model), noise)
gyy = utils.contaminate(gm.prism.gyy(xp, yp, zp, model), noise)
gyz = utils.contaminate(gm.prism.gyz(xp, yp, zp, model), noise)
gzz = utils.contaminate(gm.prism.gzz(xp, yp, zp, model), noise)
tensor = [gxx, gxy, gxz, gyy, gyz, gzz]
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
# plot the data
mpl.figure()
for i in xrange(len(tensor)):
mpl.subplot(2, 3, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, tensor[i], shape, 30)
mpl.colorbar()
mpl.xlabel('y (km)')
mpl.ylabel('x (km)')
mpl.m2km()
mpl.show()
# Inversion setup
# Create a mesh
mesh = PrismMesh(bounds, (30, 30, 30))
# Wrap the data so that harvester can use it
data = [gm.harvester.Gxx(xp, yp, zp, gxx),
gm.harvester.Gxy(xp, yp, zp, gxy),
gm.harvester.Gxz(xp, yp, zp, gxz),
gm.harvester.Gyy(xp, yp, zp, gyy),
gm.harvester.Gyz(xp, yp, zp, gyz),
shape = (50, 50)
lons, lats, heights = gridder.regular(area, shape, z=250000)
start = time.time()
fields = [
gravmag.tesseroid.potential(lons, lats, heights, model),
gravmag.tesseroid.gx(lons, lats, heights, model),
gravmag.tesseroid.gy(lons, lats, heights, model),
gravmag.tesseroid.gz(lons, lats, heights, model),
gravmag.tesseroid.gxx(lons, lats, heights, model),
gravmag.tesseroid.gxy(lons, lats, heights, model),
gravmag.tesseroid.gxz(lons, lats, heights, model),
gravmag.tesseroid.gyy(lons, lats, heights, model),
gravmag.tesseroid.gyz(lons, lats, heights, model),
gravmag.tesseroid.gzz(lons, lats, heights, model)
]
print "Time it took: %s" % (utils.sec2hms(time.time() - start))
titles = [
'potential', 'gx', 'gy', 'gz', 'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz'
]
mpl.figure()
bm = mpl.basemap(area, 'ortho')
for i, field in enumerate(fields):
mpl.subplot(4, 3, i + 3)
mpl.title(titles[i])
mpl.contourf(lons, lats, field, shape, 15, basemap=bm)
bm.drawcoastlines()
mpl.colorbar()
mpl.show()
mesher.Prism(-4000, -3000, -4000, -3000, 0, 2000,
{'magnetization': 2}), # a scalar magnetization means only induced
mesher.Prism(-1000, 1000, -1000, 1000, 0, 2000,
{'magnetization': 1}),
# This prism will have magnetization in a different direction
mesher.Prism(2000, 4000, 3000, 4000, 0, 2000,
{'magnetization': utils.ang2vec(3, -10, 45)})] # induced + remanent
# Create a regular grid at 100m height
shape = (200, 200)
area = bounds[:4]
xp, yp, zp = gridder.regular(area, shape, z=-500)
# Calculate the anomaly for a given regional field
tf = prism.tf(xp, yp, zp, model, inc, dec)
# Plot
mpl.figure()
mpl.title("Total-field anomaly (nT)")
mpl.axis('scaled')
mpl.contourf(yp, xp, tf, shape, 15)
mpl.colorbar()
mpl.xlabel('East y (km)')
mpl.ylabel('North x (km)')
mpl.m2km()
mpl.show()
# Show the prisms
myv.figure()
myv.prisms(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()
xp, yp, zp = gridder.regular(dataarea, shape, z=-500)
tensor = [
gravmag.polyprism.gxx(xp, yp, zp, prisms),
gravmag.polyprism.gxy(xp, yp, zp, prisms),
gravmag.polyprism.gxz(xp, yp, zp, prisms),
gravmag.polyprism.gyy(xp, yp, zp, prisms),
gravmag.polyprism.gyz(xp, yp, zp, prisms),
gravmag.polyprism.gzz(xp, yp, zp, prisms)
]
# Calculate the 3 invariants
invariants = gravmag.tensor.invariants(tensor)
data = tensor + invariants
# and plot it
mpl.figure()
mpl.axis('scaled')
mpl.suptitle("Tensor and invariants produced by prism model (Eotvos)")
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz', 'I1', 'I2', 'I']
for i in xrange(len(data)):
mpl.subplot(3, 3, i + 1)
mpl.title(titles[i])
levels = 20
if i == 8:
levels = numpy.linspace(0, 1, levels)
mpl.contourf(yp, xp, data[i], shape, levels)
mpl.colorbar()
for p in prisms:
mpl.polygon(p, '.-k', xy2ne=True)
mpl.set_area(dataarea)
mpl.m2km()
mpl.show()
xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=-150)
noise = 2
data = [utils.contaminate(prism.gxx(xp, yp, zp, model), noise),
utils.contaminate(prism.gxy(xp, yp, zp, model), noise),
utils.contaminate(prism.gxz(xp, yp, zp, model), noise),
utils.contaminate(prism.gyy(xp, yp, zp, model), noise),
utils.contaminate(prism.gyz(xp, yp, zp, model), noise),
utils.contaminate(prism.gzz(xp, yp, zp, model), 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, data[i], shape, 10)
mpl.contour(yp, xp, data[i], shape, levels)
mpl.m2km()
mpl.show()
# Get the eigenvectors from the tensor data
eigenvals, eigenvecs = tensor.eigen(data)
# Use the first eigenvector to estimate the center of mass
cm = tensor.center_of_mass(xp, yp, zp, eigenvecs[0])
# Plot the prism and the estimated center of mass
myv.figure()
myv.points([cm], size=200.)
myv.prisms(model, 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)
gravmag.prism.gxz(xp, yp, zp, prisms),
gravmag.prism.gyy(xp, yp, zp, prisms),
gravmag.prism.gyz(xp, yp, zp, prisms),
gravmag.prism.gzz(xp, yp, zp, prisms)
]
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(prisms, prop='density')
axes = myv.axes(myv.outline())
myv.wall_bottom(axes.axes.bounds, opacity=0.2)
myv.wall_north(axes.axes.bounds)
# and generate synthetic data from it
shape = (20, 20)
area = bounds[0:4]
xp, yp, zp = gridder.regular(area, shape, z=-1)
noise = 0.1 # 0.1 mGal noise
gz = utils.contaminate(gm.polyprism.gz(xp, yp, zp, model), noise)
# Create a mesh
mesh = PrismMesh(bounds, (25, 50, 50))
# Wrap the data so that harvester can read it
data = [gm.harvester.Gz(xp, yp, zp, gz)]
# Plot the data and pick the location of the seeds
mpl.figure()
mpl.suptitle("Pick the seeds (polygon is the true source)")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gz, shape, 12)
mpl.colorbar()
mpl.polygon(model[0], xy2ne=True)
mpl.xlabel('Horizontal coordinate y (km)')
mpl.ylabel('Horizontal coordinate x (km)')
seedx, seedy = mpl.pick_points(area, mpl.gca(), xy2ne=True).T
# Set the right density and depth
locations = [[x, y, 1500, {'density': 1000}] for x, y in zip(seedx, seedy)]
mpl.show()
# Make the seed and set the compactness regularizing parameter mu
seeds = gm.harvester.sow(locations, mesh)
# Run the inversion
estimate, predicted = gm.harvester.harvest(data,
seeds,
mesh,
compactness=0.05,
xp, yp, zp = gridder.regular(area, shape, z=-500)
data = [
polyprism.gxx(xp, yp, zp, model),
polyprism.gxy(xp, yp, zp, model),
polyprism.gxz(xp, yp, zp, model),
polyprism.gyy(xp, yp, zp, model),
polyprism.gyz(xp, yp, zp, model),
polyprism.gzz(xp, yp, zp, model)]
# and plot it
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
mpl.figure()
mpl.axis('scaled')
mpl.suptitle("Gravity tensor produced by prism model (Eotvos)")
for i in xrange(len(data)):
mpl.subplot(3, 2, i + 1)
mpl.title(titles[i])
mpl.contourf(yp, xp, data[i], 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, 'density')
myv.axes(myv.outline(bounds), ranges=[i * 0.001 for i in bounds])
myv.wall_north(bounds)
myv.wall_bottom(bounds)
myv.show()
"""
GravMag: Generate noise-corrupted gravity gradient tensor data
"""
from fatiando import mesher, gridder, gravmag, utils
from fatiando.vis import mpl
prisms = [mesher.Prism(-1000,1000,-1000,1000,0,2000,{'density':1000})]
shape = (100,100)
xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=-200)
components = [gravmag.prism.gxx, gravmag.prism.gxy, gravmag.prism.gxz,
gravmag.prism.gyy, gravmag.prism.gyz, gravmag.prism.gzz]
print "Calculate the tensor components and contaminate with 5 Eotvos noise"
ftg = [utils.contaminate(comp(xp, yp, zp, prisms), 5.0) for comp in components]
print "Plotting..."
mpl.figure(figsize=(14,6))
mpl.suptitle("Contaminated FTG data")
names = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
for i, data in enumerate(ftg):
mpl.subplot(2,3,i+1)
mpl.title(names[i])
mpl.axis('scaled')
levels = mpl.contourf(xp*0.001, yp*0.001, data, (100,100), 12)
mpl.colorbar()
mpl.contour(xp*0.001, yp*0.001, data, shape, levels, clabel=False)
mpl.show()
"""
GravMag: Forward modeling of the gravity anomaly using spheres (calculate on
random points)
"""
from fatiando import logger, mesher, gridder, utils, gravmag
from fatiando.vis import mpl
log = logger.get()
log.info(logger.header())
log.info(__doc__)
spheres = [mesher.Sphere(0, 0, -2000, 1000, {'density':1000})]
# Create a set of points at 100m height
area = (-5000, 5000, -5000, 5000)
xp, yp, zp = gridder.scatter(area, 500, z=-100)
# Calculate the anomaly
gz = utils.contaminate(gravmag.sphere.gz(xp, yp, zp, spheres), 0.1)
# Plot
shape = (100, 100)
mpl.figure()
mpl.title("gz (mGal)")
mpl.axis('scaled')
mpl.plot(yp*0.001, xp*0.001, '.k')
mpl.contourf(yp*0.001, xp*0.001, gz, shape, 15, interp=True)
mpl.colorbar()
mpl.xlabel('East y (km)')
mpl.ylabel('North x (km)')
mpl.show()
mesh = mesher.PrismMesh(bounds, (20, 40, 40))
seeds = gravmag.harvester.sow([[5000, 5000, 1000, props]], mesh)
# Run the inversion without using weights
data = [gravmag.harvester.Gz(x, y, z, gz)]
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.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
area = (-80, -30, -40, 10)
shape = (50, 50)
lons, lats, heights = gridder.regular(area, shape, z=250000)
start = time.time()
fields = [
gravmag.tesseroid.potential(lons, lats, heights, model),
gravmag.tesseroid.gx(lons, lats, heights, model),
gravmag.tesseroid.gy(lons, lats, heights, model),
gravmag.tesseroid.gz(lons, lats, heights, model),
gravmag.tesseroid.gxx(lons, lats, heights, model),
gravmag.tesseroid.gxy(lons, lats, heights, model),
gravmag.tesseroid.gxz(lons, lats, heights, model),
gravmag.tesseroid.gyy(lons, lats, heights, model),
gravmag.tesseroid.gyz(lons, lats, heights, model),
gravmag.tesseroid.gzz(lons, lats, heights, model)]
print "Time it took: %s" % (utils.sec2hms(time.time() - start))
titles = ['potential', 'gx', 'gy', 'gz',
'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
mpl.figure()
bm = mpl.basemap(area, 'ortho')
for i, field in enumerate(fields):
mpl.subplot(4, 3, i + 3)
mpl.title(titles[i])
mpl.contourf(lons, lats, field, shape, 15, basemap=bm)
bm.drawcoastlines()
mpl.colorbar()
mpl.show()
"""
Gridding: Load a Surfer ASCII grid file
"""
from fatiando import datasets, gridder
from fatiando.vis import mpl
# Fetching Bouguer anomaly model data (Surfer ASCII grid file)"
# Will download the archive and save it with the default name
archive = datasets.fetch_bouguer_alps_egm()
# Load the GRD file and convert in three numpy-arrays (x, y, bouguer)
x, y, bouguer, shape = gridder.load_surfer(archive, fmt='ascii')
mpl.figure()
mpl.axis('scaled')
mpl.title("Data loaded from a Surfer ASCII grid file")
mpl.contourf(y, x, bouguer, shape, 15, cmap=mpl.cm.RdBu_r)
cb = mpl.colorbar()
cb.set_label('mGal')
mpl.xlabel('y points to East (km)')
mpl.ylabel('x points to North (km)')
mpl.m2km()
mpl.show()
from fatiando import mesher, gridder, gravmag
from fatiando.vis import mpl
spheres = [mesher.Sphere(0, 0, 2000, 1000, {'density':1000})]
area = (-5000, 5000, -5000, 5000)
shape = (100, 100)
x, y, z = gridder.regular(area, shape, z=-100)
gz = gravmag.sphere.gz(x, y, z, spheres)
tensor = [gravmag.sphere.gxx(x, y, z, spheres),
gravmag.sphere.gxy(x, y, z, spheres),
gravmag.sphere.gxz(x, y, z, spheres),
gravmag.sphere.gyy(x, y, z, spheres),
gravmag.sphere.gyz(x, y, z, spheres),
gravmag.sphere.gzz(x, y, z, spheres)]
mpl.figure()
mpl.axis('scaled')
mpl.title('gz')
mpl.contourf(y, x, gz, shape, 15)
mpl.colorbar()
mpl.m2km()
mpl.figure()
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
for i, field in enumerate(tensor):
mpl.subplot(2, 3, i + 1)
mpl.axis('scaled')
mpl.title(titles[i])
levels = mpl.contourf(y, x, field, shape, 15)
mpl.colorbar()
mpl.m2km()
mpl.show()
# Generate random points
x, y = gridder.scatter((-2, 2, -2, 2), n=300, seed=1)
# And calculate 2D Gaussians on these points as sample data
def data(x, y):
return (utils.gaussian2d(x, y, -0.6, -1)
- utils.gaussian2d(x, y, 1.5, 1.5))
d = data(x, y)
# Extract a profile along the diagonal
p1, p2 = [-1.5, 0], [1.5, 1.5]
xp, yp, distance, dp = gridder.profile(x, y, d, p1, p2, 100)
dp_true = data(xp, yp)
mpl.figure()
mpl.subplot(2, 1, 2)
mpl.title("Irregular grid")
mpl.plot(xp, yp, '-k', label='Profile', linewidth=2)
mpl.contourf(x, y, d, (100, 100), 50, interp=True)
mpl.colorbar(orientation='horizontal')
mpl.legend(loc='lower right')
mpl.subplot(2, 1, 1)
mpl.title('Profile')
mpl.plot(distance, dp, '.b', label='Extracted')
mpl.plot(distance, dp_true, '-k', label='True')
mpl.xlim(distance.min(), distance.max())
mpl.legend(loc='lower right')
mpl.show()
tesseroid.gy(lons, lats, heights, model),
tesseroid.gz(lons, lats, heights, model),
tesseroid.gxx(lons, lats, heights, model),
tesseroid.gxy(lons, lats, heights, model),
tesseroid.gxz(lons, lats, heights, model),
tesseroid.gyy(lons, lats, heights, model),
tesseroid.gyz(lons, lats, heights, model),
tesseroid.gzz(lons, lats, heights, model)]
print "Time it took: %s" % (utils.sec2hms(time.time() - start))
titles = ['potential', 'gx', 'gy', 'gz',
'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
bm = mpl.basemap(area, 'merc')
mpl.figure()
mpl.title(titles[0])
mpl.contourf(lons, lats, fields[0], shape, 40, basemap=bm)
bm.drawcoastlines()
mpl.colorbar()
mpl.figure()
for i, field in enumerate(fields[1:4]):
mpl.subplot(1, 3, i + 1)
mpl.title(titles[i + 1])
mpl.contourf(lons, lats, field, shape, 40, basemap=bm)
bm.drawcoastlines()
mpl.colorbar()
mpl.figure()
for i, field in enumerate(fields[4:]):
mpl.subplot(2, 3, i + 1)
mpl.title(titles[i + 4])
mpl.contourf(lons, lats, field, shape, 40, basemap=bm)
bm.drawcoastlines()
utils.contaminate(gravmag.prism.gz(x, y, z, model), noisegz),
utils.contaminate(gravmag.prism.gxx(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gxy(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gxz(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gyy(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gyz(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gzz(x, y, z, model), noise)]
with open('data.txt', 'w') as f:
f.write(logger.header(comment='#'))
f.write("# Noise corrupted gz and tensor components:\n")
f.write("# noise = %g Eotvos\n" % (noise))
f.write("# noise = %g mGal\n" % (noisegz))
f.write("# coordinates are in meters\n")
f.write("# gz in mGal and tensor in Eotvos\n")
f.write("# x y z height gz gxx gxy gxz gyy gyz gzz\n")
numpy.savetxt(f, numpy.transpose(data))
# Show it
mpl.figure(figsize=(10, 9))
names = "z height gz gxx gxy gxz gyy gyz gzz".split()
for i, comp in enumerate(data[2:]):
mpl.subplot(3, 3, i + 1)
mpl.axis('scaled')
mpl.title(names[i])
levels = mpl.contourf(y*0.001, x*0.001, comp, shape, 8)
mpl.contour(y*0.001, x*0.001, comp, shape, levels)
if i == 3:
mpl.ylabel('North = x (km)')
if i == 7:
mpl.xlabel('East = y (km)')
mpl.show()
compactness=1., threshold=0.0001)
# Insert the estimated density values into the mesh
mesh.addprop('density', estimate['density'])
# and get only the prisms corresponding to our estimate
density_model = vremove(0, 'density', mesh)
print "Accretions: %d" % (len(density_model) - len(seeds))
# Get the predicted data from the data modules
tensor = (gyy, gyz, gzz)
# plot it
for true, pred in zip(tensor, predicted):
mpl.figure()
mpl.title("True: color | Inversion: contour")
mpl.axis('scaled')
levels = mpl.contourf(y * 0.001, x * 0.001, true, shape, 12)
mpl.colorbar()
mpl.contour(y * 0.001, x * 0.001, pred, shape, levels, color='k')
mpl.xlabel('Horizontal coordinate y (km)')
mpl.ylabel('Horizontal coordinate x (km)')
mpl.show()
# Plot the inversion result
myv.figure()
myv.prisms(model, 'density', style='wireframe')
myv.prisms(density_model, 'density', vmin=0)
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()
(simple example)
"""
from fatiando import gridder, mesher
from fatiando.gravmag import prism, imaging
from fatiando.vis import mpl, myv
# Make some synthetic gravity data from a simple prism model
model = [mesher.Prism(-1000,1000,-2000,2000,2000,4000,{'density':500})]
shape = (25, 25)
xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=-10)
gz = prism.gz(xp, yp, zp, model)
# Plot the data
mpl.figure()
mpl.axis('scaled')
mpl.contourf(yp, xp, gz, shape, 30)
mpl.colorbar()
mpl.xlabel('East (km)')
mpl.ylabel('North (km)')
mpl.m2km()
mpl.show()
mesh = imaging.sandwich(xp, yp, zp, gz, shape, 0, 10000, 25)
# 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)
mpl.points(src, '*y')
initial = mpl.pick_points(area, mpl.gca(), marker='*', color='b')
if len(initial) > 1:
print "Don't be greedy! Pick only one point"
sys.exit()
# Fit using many different solvers
levmarq = [e for e in solver.levmarq(initial=initial[0], iterate=True)]
steepest = [e for e in solver.steepest(initial=initial[0], iterate=True)]
newton = [e for e in solver.newton(initial=initial[0], iterate=True)]
ACO_R = [e for e in solver.acor(bounds=area, maxit=100, iterate=True)]
# Make a map of the objective function
shape = (100, 100)
xs, ys = gridder.regular(area, shape)
obj = [solver.value(numpy.array([x, y])) for x, y in zip(xs, ys)]
mpl.figure()
mpl.title('Epicenter + %d recording stations' % (len(recs)))
mpl.axis('scaled')
mpl.contourf(xs, ys, obj, shape, 60)
mpl.points(recs, '^r')
mpl.points(initial, '*w')
mpl.points(levmarq, '.-k', label="Levemeber-Marquardt")
mpl.points(newton, '.-r', label="Newton")
mpl.points(steepest, '.-m', label="Steepest descent")
mpl.points(ACO_R, '.-c', label="Ant Colony")
mpl.points(src, '*y')
mpl.set_area(area)
mpl.legend(loc='lower right', shadow=True, numpoints=1, prop={'size':12})
mpl.xlabel("X")
mpl.ylabel("Y")
mpl.show()
"""
GravMag: Generate synthetic gravity data on an irregular grid
"""
from fatiando import mesher, gridder, gravmag
from fatiando.vis import mpl
prisms = [mesher.Prism(-2000, 2000, -2000, 2000, 0, 2000, {'density':1000})]
xp, yp, zp = gridder.scatter((-5000, 5000, -5000, 5000), n=100, z=-100)
gz = gravmag.prism.gz(xp, yp, zp, prisms)
shape = (100,100)
mpl.axis('scaled')
mpl.title("gz produced by prism model on an irregular grid (mGal)")
mpl.plot(xp, yp, '.k', label='Grid points')
levels = mpl.contourf(xp, yp, gz, shape, 12, interp=True)
mpl.contour(xp, yp, gz, shape, levels, interp=True)
mpl.legend(loc='lower right', numpoints=1)
mpl.m2km()
mpl.show()
plt.subplot(2, 1, 2)
plt.title("Original data")
plt.plot(xx, yy, '-k', label='Profile', linewidth=2)
scale = np.abs([gz.min(), gz.max()]).max()
plt.tricontourf(xp, yp, gz, 50, cmap='RdBu_r', vmin=-scale, vmax=scale)
plt.colorbar(orientation='horizontal', aspect=50)
plt.legend(loc='lower right')
plt.tight_layout()
plt.show()
#plt.suptitle(strname + '_ztop' + str(za) +'_zbot'+ str(zb), fontsize=15)
#plt.savefig(pathFig+ strname + '_ExempleFig_prof' + str(za) + str(zb) + '.png')
# ------------------------------- Plot the data
plt.figure()
plt.axis('scaled')
mpl.contourf(yp, xp, gz, shape, 30)
plt.colorbar()
plt.xlabel('East (km)')
plt.ylabel('North (km)')
mpl.m2km()
plt.show()
#plt.title(strname +'ztop' + str(za) +'_zbot'+ str(zb) + '_data', fontsize=20)
#plt.savefig(pathFig+strname + '_ExempleFig_z' + str(za) + str(zb) + '_data' + '.png')
#x1, x2, y1, y2, z1, z2 = np.array(model[0].get_bounds())
square([y1, y2, x1, x2])
# %% ------------------------------- derivatives
xderiv = transform.derivx(xp, yp, gz, shape, order=1)
yderiv = transform.derivy(xp, yp, gz, shape)
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()
shape = (100, 100)
xp, yp, zp = gridder.regular(dataarea, shape, z=-500)
data = [
polyprism.gxx(xp, yp, zp, model),
polyprism.gxy(xp, yp, zp, model),
polyprism.gxz(xp, yp, zp, model),
polyprism.gyy(xp, yp, zp, model),
polyprism.gyz(xp, yp, zp, model),
polyprism.gzz(xp, yp, zp, model)]
# Calculate the 3 invariants
invariants = tensor.invariants(data)
data = data + invariants
# and plot it
mpl.figure()
mpl.axis('scaled')
mpl.suptitle("Tensor and invariants produced by prism model (Eotvos)")
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz', 'I1', 'I2', 'I']
for i in xrange(len(data)):
mpl.subplot(3, 3, i + 1)
mpl.title(titles[i])
levels = 20
if i == 8:
levels = numpy.linspace(0, 1, levels)
mpl.contourf(yp, xp, data[i], shape, levels)
mpl.colorbar()
for p in model:
mpl.polygon(p, '.-k', xy2ne=True)
mpl.set_area(dataarea)
mpl.m2km()
mpl.show()
from fatiando.vis import mpl, myv
# Make some synthetic gravity data from a simple prism model
model = [
mesher.Prism(-4000, -1000, -4000, -2000, 2000, 5000, {'density': 800}),
mesher.Prism(-1000, 1000, -1000, 1000, 1000, 6000, {'density': -800}),
mesher.Prism(2000, 4000, 3000, 4000, 0, 4000, {'density': 600})
]
shape = (25, 25)
xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=-10)
gz = utils.contaminate(prism.gz(xp, yp, zp, model), 0.1)
# Plot the data
mpl.figure()
mpl.axis('scaled')
mpl.contourf(yp, xp, gz, shape, 30)
mpl.colorbar()
mpl.xlabel('East (km)')
mpl.ylabel('North (km)')
mpl.m2km()
mpl.show()
# Run the Generalized Inverse
mesh = imaging.geninv(xp, yp, zp, gz, shape, 0, 10000, 25)
# Plot the results
myv.figure()
myv.prisms(model, 'density', style='wireframe')
myv.prisms(mesh, 'density', edges=False, linewidth=5)
axes = myv.axes(myv.outline())
myv.wall_bottom(axes.axes.bounds)
xp, yp, zp = gridder.regular(area, shape, z=-500)
tensor = [
gravmag.polyprism.gxx(xp, yp, zp, prisms),
gravmag.polyprism.gxy(xp, yp, zp, prisms),
gravmag.polyprism.gxz(xp, yp, zp, prisms),
gravmag.polyprism.gyy(xp, yp, zp, prisms),
gravmag.polyprism.gyz(xp, yp, zp, prisms),
gravmag.polyprism.gzz(xp, yp, zp, prisms)]
# and plot it
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
mpl.figure()
mpl.axis('scaled')
mpl.suptitle("Gravity tensor produced by prism model (Eotvos)")
for i in xrange(len(tensor)):
mpl.subplot(3, 2, i + 1)
mpl.title(titles[i])
mpl.contourf(yp, xp, tensor[i], shape, 20)
mpl.colorbar()
for p in prisms:
mpl.polygon(p, '.-k', xy2ne=True)
mpl.set_area(area)
mpl.m2km()
mpl.show()
# Show the prisms
myv.figure()
myv.polyprisms(prisms, 'density')
myv.axes(myv.outline(bounds), ranges=[i*0.001 for i in bounds])
myv.wall_north(bounds)
myv.wall_bottom(bounds)
myv.show()
# Make some synthetic gravity data from a simple prism model
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)
baselevel = 10
# Convert from nanoTesla to Tesla because euler and derivatives require things
# in SI
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)
tensor = [
utils.contaminate(gravmag.prism.gxx(xp, yp, zp, prisms), noise),
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)
from fatiando.vis import mpl
area = [-5000, 5000, -5000, 5000]
model = [Prism(-3000, 3000, -1000, 1000, 0, 1000, {'density': 1000})]
shape = (100, 100)
xp, yp, zp = gridder.regular(area, shape, z=-500)
data = [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)]
# Calculate the 3 invariants
invariants = tensor.invariants(data)
data = data + invariants
# and plot it
mpl.figure()
mpl.axis('scaled')
mpl.suptitle("Tensor and invariants (Eotvos)")
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz', 'I1', 'I2', 'I']
for i in xrange(len(data)):
mpl.subplot(3, 3, i + 1)
mpl.title(titles[i])
levels = 20
if i == 8:
levels = numpy.linspace(0, 1, levels)
mpl.contourf(yp, xp, data[i], shape, levels, cmap=mpl.cm.RdBu_r)
mpl.colorbar()
mpl.m2km()
mpl.show()
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()
mpl.subplot(2, 1, 1)
mpl.axis('scaled')
mpl.title('Gravity anomaly')
mpl.contourf(y, x, gz, shape, 30)
mpl.colorbar()
mpl.subplot(2, 1, 2)
mpl.axis('scaled')
mpl.title('Magnetic total field anomaly')
mpl.contourf(y, x, tf, shape, 30)
mpl.colorbar()
mpl.show()
#-----Drawing-----
#Plot the model
myv.figure()
myv.prisms(lModel, 'density', style='surface')
axes = myv.axes(myv.outline())
myv.wall_bottom(axes.axes.bounds)
myv.wall_north(axes.axes.bounds)
myv.title("Geological Model")
# Plot the forward modelled signal
mpl.figure(figsize=(16, 5))
mpl.subplot(121)
mpl.title("Original signal")
mpl.axis('scaled')
mpl.contourf(aYGridCoords, aXGridCoords, aObservedSignal, tSignalSize,
50) #last arg is number of contours
mpl.colorbar()
mpl.xlabel('East (km)')
mpl.ylabel('North (km)')
mpl.m2km()
mpl.subplot(122)
mpl.title("Forward modelled signal")
mpl.axis('scaled')
mpl.contourf(aYGridCoords, aXGridCoords, aCalcSignal, tSignalSize,
50) #last arg is number of contours
mpl.colorbar()
mpl.xlabel('East (km)')
mpl.ylabel('North (km)')
mpl.m2km()
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()
compactness=1., threshold=0.0001)
# Insert the estimated density values into the mesh
mesh.addprop('density', estimate['density'])
# and get only the prisms corresponding to our estimate
density_model = vremove(0, 'density', mesh)
print "Accretions: %d" % (len(density_model) - len(seeds))
# Get the predicted data from the data modules
tensor = (gyy, gyz, gzz)
# plot it
for true, pred in zip(tensor, predicted):
mpl.figure()
mpl.title("True: color | Inversion: contour")
mpl.axis('scaled')
levels = mpl.contourf(y*0.001, x*0.001, true, shape, 12)
mpl.colorbar()
mpl.contour(y*0.001, x*0.001, pred, shape, levels, color='k')
mpl.xlabel('Horizontal coordinate y (km)')
mpl.ylabel('Horizontal coordinate x (km)')
mpl.show()
# Plot the inversion result
myv.figure()
myv.prisms(model, 'density', style='wireframe')
myv.prisms(density_model, 'density', vmin=0)
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()