def observation_surface(x, y):
'''
Evaluates the function defining the observation
surface at the points with Cartesian coordinates
x and y.
input
x: numpy array - Cartesian coordinates of the points along the x-axis.
y: numpy array - Cartesian coordinates of the points along the y-axis.
output
z: numpy array - observation surface.
'''
assert (x.size == y.size), 'x and y must have the same size'
surface = -550. - 700.*gaussian2d(x, y, 20000., 10000., 12500., 22500., angle=45.)
return surface
"""
Meshing: Generate a topographic model using prisms and calculate its gravity
anomaly
"""
from fatiando import gridder, utils, mesher, gravmag
from fatiando.vis import myv, mpl
area = (-150, 150, -300, 300)
shape = (30, 15)
x, y = gridder.regular(area, shape)
height = (-80*utils.gaussian2d(x, y, 100, 200, x0=-50, y0=-100, angle=-60) +
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()
"""
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()
"""
Vis: Plot contour lines 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)
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()
"""
Extracting a profile from spacial data
========================================
The function :func:`fatiando.gridder.profile` can be used to extract a profile
of data from a map. It interpolates the data onto the profile points so you can
specify the profile in any direction and use irregular point data as input.
"""
import matplotlib.pyplot as plt
import numpy as np
from fatiando import gridder, utils
# Generate random points
x, y = gridder.scatter((-2, 2, -2, 2), n=1000, seed=1)
# And calculate 2D Gaussians on these points as sample data
data = 2 * utils.gaussian2d(x, y, -0.6, -1) - utils.gaussian2d(x, y, 1.5, 1.5)
# Extract a profile between points 1 and 2
p1, p2 = [-1.5, -0.5], [1.5, 1.5]
xp, yp, distance, profile = gridder.profile(x, y, data, p1, p2, 100)
# Plot the profile and the original map data
plt.figure()
plt.subplot(2, 1, 1)
plt.title('Extracted profile points')
plt.plot(distance, profile, '.k')
plt.xlim(distance.min(), distance.max())
plt.grid()
plt.subplot(2, 1, 2)
plt.title("Original data")
plt.plot(xp, yp, '-k', label='Profile', linewidth=2)
"""
Meshing: Generate a topographic model using prisms and calculate its gravity
anomaly
"""
from fatiando import gridder, utils, mesher
from fatiando.gravmag import prism
from fatiando.vis import myv, mpl
area = (-150, 150, -300, 300)
shape = (30, 15)
x, y = gridder.regular(area, shape)
height = (-80 * utils.gaussian2d(x, y, 100, 200, x0=-50, y0=-100, angle=-60) +
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')
Prism(3000, 4000, 1000, 2000, 200, 800, {'density':500}),
Prism(2700, 3200, 3700, 4200, 0, 900, {'density':1500})]
# show it
myv.figure()
myv.prisms(model, '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()
# Generate the data grid
shape = (25, 25)
area = bounds[0:4]
x, y = gridder.regular(area, shape)
# Generate synthetic topography
height = (300*utils.gaussian2d(x, y, 1000, 3000, x0=500, y0=1000, angle=-60)
+ 1000*utils.gaussian2d(x, y, 500, 2000, x0=3000, y0=3000))
# Calculate the data
noise = 1
noisegz = 0.1
z = -height - 150
data = [x, y, z, height,
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='#'))
def data(x, y):
return (utils.gaussian2d(x, y, -0.6, -1)
- utils.gaussian2d(x, y, 1.5, 1.5))
def data(x, y):
return (utils.gaussian2d(x, y, -0.6, -1) -
utils.gaussian2d(x, y, 1.5, 1.5))
""" Vis: Plot a map using the Mercator map projection and pseudo-color """ from fatiando import gridder, utils, vis # 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 = vis.mpl.basemap(area, 'merc') # And now plot everything passing the basemap to the plotting functions vis.mpl.figure(figsize=(5, 8)) vis.mpl.pcolor(lon, lat, data, shape, basemap=bm) vis.mpl.colorbar() bm.drawcoastlines() bm.drawmapboundary() bm.drawcountries() vis.mpl.draw_geolines(area, 10, 10, bm) vis.mpl.show()
"""
Extracting a profile from spacial data
========================================
The function :func:`fatiando.gridder.profile` can be used to extract a profile
of data from a map. It interpolates the data onto the profile points so you can
specify the profile in any direction and use irregular point data as input.
"""
import matplotlib.pyplot as plt
import numpy as np
from fatiando import gridder, utils
# Generate random points
x, y = gridder.scatter((-2, 2, -2, 2), n=1000, seed=1)
# And calculate 2D Gaussians on these points as sample data
data = 2*utils.gaussian2d(x, y, -0.6, -1) - utils.gaussian2d(x, y, 1.5, 1.5)
# Extract a profile between points 1 and 2
p1, p2 = [-1.5, -0.5], [1.5, 1.5]
xp, yp, distance, profile = gridder.profile(x, y, data, p1, p2, 100)
# Plot the profile and the original map data
plt.figure()
plt.subplot(2, 1, 1)
plt.title('Extracted profile points')
plt.plot(distance, profile, '.k')
plt.xlim(distance.min(), distance.max())
plt.grid()
plt.subplot(2, 1, 2)
plt.title("Original data")
plt.plot(xp, yp, '-k', label='Profile', linewidth=2)
"""
Meshing: Making a grid of 3D point sources
"""
from fatiando import mesher, utils, gridder
from fatiando.gravmag import sphere
from fatiando.vis import mpl
grid = mesher.PointGrid([0, 1000, 0, 2000], 500, (50, 50))
# Add some density to the grid
density = 1000000000 * utils.gaussian2d(grid.x, grid.y, 100, 500,
x0=500, y0=1000, angle=-60)
grid.addprop('density', density)
# 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()
myv.figure()
myv.prisms(model, '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()
# Generate the data grid
shape = (25, 25)
area = bounds[0:4]
x, y = gridder.regular(area, shape)
# Generate synthetic topography
height = (
300 * utils.gaussian2d(x, y, 1000, 3000, x0=500, y0=1000, angle=-60) +
1000 * utils.gaussian2d(x, y, 500, 2000, x0=3000, y0=3000))
# Calculate the data
noise = 1
noisegz = 0.1
z = -height - 150
data = [
x, y, z, height,
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)
]
"""
GravMag: Forward modeling of the gravity anomaly using tesseroids in parallel
using ``multiprocessing``
"""
import time
from multiprocessing import Pool
from fatiando import gravmag, gridder, utils
from fatiando.mesher import Tesseroid
from fatiando.vis import mpl, myv
# Make a "crust" model with some thinker crust and variable density
marea = (-70, 70, -70, 70)
mshape = (200, 200)
mlons, mlats = gridder.regular(marea, mshape)
dlon, dlat = gridder.spacing(marea, mshape)
depths = (30000 + 70000 * utils.gaussian2d(mlons, mlats, 10, 10, -20, -20) +
20000 * utils.gaussian2d(mlons, mlats, 5, 5, 20, 20))
densities = (2700 + 500 * utils.gaussian2d(mlons, mlats, 40, 40, -20, -20) +
-300 * utils.gaussian2d(mlons, mlats, 20, 20, 20, 20))
model = [
Tesseroid(lon - 0.5 * dlon,
lon + 0.5 * dlon,
lat - 0.5 * dlat,
lat + 0.5 * dlat,
0,
-depth,
props={'density': density})
for lon, lat, depth, density in zip(mlons, mlats, depths, densities)
]
# Plot the tesseroid model
"""
Meshing: Make and plot a tesseroid mesh with topography
"""
from fatiando import gridder, utils, mesher
from fatiando.vis import myv
w, e = -2, 2
s, n = -2, 2
bounds = (w, e, s, n, 500000, 0)
x, y = gridder.regular((w, e, s, n), (50, 50))
height = (250000 +
-100000 * utils.gaussian2d(x, y, 1, 5, x0=-1, y0=-1, angle=-60) +
250000 * utils.gaussian2d(x, y, 1, 1, x0=0.8, y0=1.7))
mesh = mesher.TesseroidMesh(bounds, (20, 50, 50))
mesh.carvetopo(x, y, height)
scene = myv.figure(zdown=False)
myv.tesseroids(mesh)
myv.earth(opacity=0.3)
myv.continents()
scene.scene.camera.position = [
21592740.078245595, 22628783.944262519, -28903782.916664094
]
scene.scene.camera.focal_point = [
5405474.2152075395, -1711034.715136874, 2155879.3486608281
]
scene.scene.camera.view_angle = 1.6492674416639987
scene.scene.camera.view_up = [
0.91713422625547714, -0.1284658947859818, 0.37730799740742887
"""
Meshing: Make and plot a tesseroid mesh with topography
"""
from fatiando import gridder, utils, mesher
from fatiando.vis import myv
w, e = -2, 2
s, n = -2, 2
bounds = (w, e, s, n, 500000, 0)
x, y = gridder.regular((w, e, s, n), (50, 50))
height = (250000 +
-100000*utils.gaussian2d(x, y, 1, 5, x0=-1, y0=-1, angle=-60) +
250000*utils.gaussian2d(x, y, 1, 1, x0=0.8, y0=1.7))
mesh = mesher.TesseroidMesh(bounds, (20, 50, 50))
mesh.carvetopo(x, y, height)
scene = myv.figure(zdown=False)
myv.tesseroids(mesh)
myv.earth(opacity=0.3)
myv.continents()
scene.scene.camera.position = [21592740.078245595, 22628783.944262519, -28903782.916664094]
scene.scene.camera.focal_point = [5405474.2152075395, -1711034.715136874, 2155879.3486608281]
scene.scene.camera.view_angle = 1.6492674416639987
scene.scene.camera.view_up = [0.91713422625547714, -0.1284658947859818, 0.37730799740742887]
scene.scene.camera.clipping_range = [20169510.286021926, 69721043.718536735]
scene.scene.camera.compute_view_plane_normal()
scene.scene.render()
myv.show()
""" Vis: Plot a map using the Robinson map projection and contours """ from fatiando import gridder, utils from fatiando.vis import mpl # Generate some data to plot area = (-180, 180, -80, 80) shape = (100, 100) lon, lat = gridder.regular(area, shape) data = utils.gaussian2d(lon, lat, 30, 60, 10, 30, angle=-60) # Now get a basemap to plot with some projection bm = mpl.basemap(area, 'robin') # And now plot everything passing the basemap to the plotting functions mpl.figure() mpl.contour(lon, lat, data, shape, 15, basemap=bm) bm.drawcoastlines() bm.drawmapboundary(fill_color='aqua') bm.drawcountries() bm.fillcontinents(color='coral') mpl.draw_geolines((-180, 180, -90, 90), 60, 30, bm) mpl.show()
""" Vis: Plot a map using the Mercator map projection and pseudo-color """ from fatiando import logger, gridder, utils, vis log = logger.get() log.info(logger.header()) log.info(__doc__) # 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 = vis.mpl.basemap(area, 'merc') # And now plot everything passing the basemap to the plotting functions vis.mpl.figure(figsize=(5,8)) vis.mpl.pcolor(lon, lat, data, shape, basemap=bm) vis.mpl.colorbar() bm.drawcoastlines() bm.drawmapboundary() bm.drawcountries() vis.mpl.draw_geolines(area, 10, 10, bm) vis.mpl.show()
""" Vis: Plot a map using the Orthographic map projection and filled contours """ from fatiando import gridder, utils, vis # 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 = vis.mpl.basemap(area, 'ortho') # And now plot everything passing the basemap to the plotting functions vis.mpl.figure() bm.bluemarble() vis.mpl.contourf(lon, lat, data, shape, 12, basemap=bm) vis.mpl.colorbar() vis.mpl.show()
""" Vis: Plot a map using the Robinson map projection and contours """ from fatiando import gridder, utils from fatiando.vis import mpl # Generate some data to plot area = (-180, 180, -80, 80) shape = (100, 100) lon, lat = gridder.regular(area, shape) data = utils.gaussian2d(lon, lat, 30, 60, 10, 30, angle=-60) # Now get a basemap to plot with some projection bm = mpl.basemap(area, 'robin') # And now plot everything passing the basemap to the plotting functions mpl.figure() mpl.contour(lon, lat, data, shape, 15, basemap=bm) bm.drawcoastlines() bm.drawmapboundary(fill_color='aqua') bm.drawcountries() bm.fillcontinents(color='coral') mpl.draw_geolines((-180, 180, -90, 90), 60, 30, bm) mpl.show()
GravMag: Forward modeling of the gravity anomaly using tesseroids in parallel
using ``multiprocessing``
"""
import time
from multiprocessing import Pool
from fatiando import gravmag, gridder, utils
from fatiando.mesher import Tesseroid
from fatiando.vis import mpl, myv
# Make a "crust" model with some thinker crust and variable density
marea = (-70, 70, -70, 70)
mshape = (200, 200)
mlons, mlats = gridder.regular(marea, mshape)
dlon, dlat = gridder.spacing(marea, mshape)
depths = (30000 +
70000*utils.gaussian2d(mlons, mlats, 10, 10, -20, -20) +
20000*utils.gaussian2d(mlons, mlats, 5, 5, 20, 20))
densities = (2700 +
500*utils.gaussian2d(mlons, mlats, 40, 40, -20, -20) +
-300*utils.gaussian2d(mlons, mlats, 20, 20, 20, 20))
model = [
Tesseroid(lon - 0.5*dlon, lon + 0.5*dlon, lat - 0.5*dlat, lat + 0.5*dlat,
0, -depth, props={'density':density})
for lon, lat, depth, density in zip(mlons, mlats, depths, densities)]
# Plot the tesseroid model
myv.figure(zdown=False)
myv.tesseroids(model, 'density')
myv.continents()
myv.earth(opacity=0.7)
myv.show()
"""
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()
"""
Meshing: Making a grid of 3D point sources
"""
from fatiando import mesher, utils, gravmag, gridder
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)
"""
Meshing: Making a grid of 3D point sources
"""
from fatiando import mesher, utils, gravmag, gridder
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()
