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 = 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()
log.info("Generating synthetic data")
verts = [(10000, 1.), (90000, 1.), (90000, 7000), (10000, 3330)]
model = mesher.Polygon(verts, {'density':-100})
xp = numpy.arange(0., 100000., 1000.)
zp = numpy.zeros_like(xp)
gz = utils.contaminate(gravmag.talwani.gz(xp, zp, [model]), 0.5)
log.info("Preparing for the inversion")
solver = inversion.gradient.levmarq(initial=(9000, 500))
estimate, residuals = gravmag.basin2d.trapezoidal(xp, zp, gz, verts[0:2], -100,
solver)
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.title("Gravity anomaly")
mpl.plot(xp, gz, 'ok', label='Observed')
mpl.plot(xp, gz - residuals, '-r', linewidth=2, label='Predicted')
mpl.legend(loc='lower left', numpoints=1)
mpl.ylabel("mGal")
mpl.xlim(0, 100000)
mpl.subplot(2, 1, 2)
mpl.polygon(estimate, 'o-r', linewidth=2, fill='r', alpha=0.3,
label='Estimated')
mpl.polygon(model, '--k', linewidth=2, label='True')
mpl.legend(loc='lower left', numpoints=1)
mpl.xlabel("X")
mpl.ylabel("Z")
mpl.set_area((0, 100000, 10000, -500))
mpl.show()
import numpy
from fatiando import utils, mesher
from fatiando.gravmag import talwani
from fatiando.vis import mpl
# Notice that the last two number are switched.
# This way, the z axis in the plots points down.
area = (-5000, 5000, 5000, 0)
axes = mpl.figure().gca()
mpl.xlabel("X")
mpl.ylabel("Z")
mpl.axis('scaled')
polygons = [mesher.Polygon(mpl.draw_polygon(area, axes),
{'density': 500})]
xp = numpy.arange(-4500, 4500, 100)
zp = numpy.zeros_like(xp)
gz = talwani.gz(xp, zp, polygons)
mpl.figure()
mpl.axis('scaled')
mpl.subplot(2, 1, 1)
mpl.title(r"Gravity anomaly produced by the model")
mpl.plot(xp, gz, '-k', linewidth=2)
mpl.ylabel("mGal")
mpl.xlim(-5000, 5000)
mpl.subplot(2, 1, 2)
mpl.polygon(polygons[0], 'o-k', linewidth=2, fill='k', alpha=0.5)
mpl.xlabel("X")
mpl.ylabel("Z")
mpl.set_area(area)
mpl.show()
area = bounds[0:4]
xp, yp, zp = gridder.regular(area, shape, z=-1)
noise = 0.1 # 0.1 mGal noise
gz = utils.contaminate(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 = [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 = harvester.sow(locations, mesh)
# Run the inversion
estimate, predicted = harvester.harvest(data, seeds, mesh,
compactness=0.05, threshold=0.0005)
# Put the estimated density values in the mesh
mesh.addprop('density', estimate['density'])
# Plot the adjustment and the result
mpl.figure()
from fatiando import utils, mesher
from fatiando.gravmag import talwani
from fatiando.vis import mpl
# Notice that the last two number are switched.
# This way, the z axis in the plots points down.
area = (-5000, 5000, 5000, 0)
axes = mpl.figure().gca()
mpl.xlabel("X")
mpl.ylabel("Z")
mpl.axis('scaled')
polygons = [mesher.Polygon(mpl.draw_polygon(area, axes),
{'density':500})]
xp = numpy.arange(-4500, 4500, 100)
zp = numpy.zeros_like(xp)
gz = talwani.gz(xp, zp, polygons)
mpl.figure()
mpl.axis('scaled')
mpl.subplot(2,1,1)
mpl.title(r"Gravity anomaly produced by the model")
mpl.plot(xp, gz, '-k', linewidth=2)
mpl.ylabel("mGal")
mpl.xlim(-5000, 5000)
mpl.subplot(2,1,2)
mpl.polygon(polygons[0], 'o-k', linewidth=2, fill='k', alpha=0.5)
mpl.xlabel("X")
mpl.ylabel("Z")
mpl.set_area(area)
mpl.show()
model = mesher.Polygon(verts, {'density': -100})
xp = numpy.arange(0., 100000., 1000.)
zp = numpy.zeros_like(xp)
gz = utils.contaminate(gravmag.talwani.gz(xp, zp, [model]), 1)
solver = inversion.gradient.levmarq(initial=(10000, 1000))
estimate, residuals = gravmag.basin2d.triangular(xp, zp, gz, verts[0:2], -100,
solver)
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.title("Gravity anomaly")
mpl.plot(xp, gz, 'ok', label='Observed')
mpl.plot(xp, gz - residuals, '-r', linewidth=2, label='Predicted')
mpl.legend(loc='lower left')
mpl.ylabel("mGal")
mpl.xlim(0, 100000)
mpl.subplot(2, 1, 2)
mpl.polygon(estimate,
'o-r',
linewidth=2,
fill='r',
alpha=0.3,
label='Estimated')
mpl.polygon(model, '--k', linewidth=2, label='True')
mpl.legend(loc='lower left', numpoints=1)
mpl.xlabel("X")
mpl.ylabel("Z")
mpl.set_area((0, 100000, 10000, -500))
mpl.show()
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,
threshold=0.0005)
# Put the estimated density values in the mesh
depths = (-1e-15*(xs - 50000)**4 + 8000 -
3000*np.exp(-(xs - 70000)**2/(10000**2)))
depths -= depths.min() # Reduce depths to zero
props = {'density': -300}
model = Polygon(np.transpose([xs, depths]), props)
x = np.linspace(0, 100000, 100)
z = -100*np.ones_like(x)
data = utils.contaminate(talwani.gz(x, z, [model]), 0.5, seed=0)
# Make the solver using smoothness regularization and run the inversion
misfit = PolygonalBasinGravity(x, z, data, 50, props, top=0)
regul = Smoothness1D(misfit.nparams)
solver = misfit + 1e-4*regul
# This is a non-linear problem so we need to pick an initial estimate
initial = 3000*np.ones(misfit.nparams)
solver.config('levmarq', initial=initial).fit()
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.plot(x, data, 'ok', label='observed')
mpl.plot(x, solver[0].predicted(), '-r', linewidth=2, label='predicted')
mpl.legend()
ax = mpl.subplot(2, 1, 2)
mpl.polygon(model, fill='gray', alpha=0.5, label='True')
# The estimate_ property of our solver gives us the estimate basin as a polygon
# So we can directly pass it to plotting and forward modeling functions
mpl.polygon(solver.estimate_, style='o-r', label='Estimated')
ax.invert_yaxis()
mpl.legend()
mpl.show()
depths = (-1e-15*(xs - 50000)**4 + 8000 -
3000*np.exp(-(xs - 70000)**2/(10000**2)))
depths -= depths.min() # Reduce depths to zero
props = {'density': -300}
model = Polygon(np.transpose([xs, depths]), props)
x = np.linspace(0, 100000, 100)
z = -100*np.ones_like(x)
data = utils.contaminate(talwani.gz(x, z, [model]), 0.5, seed=0)
# Make the solver and run the inversion
misfit = PolygonalBasinGravity(x, z, data, 50, props, top=0)
regul = Smoothness1D(misfit.nparams)
# Use an L-curve analysis to find the best regularization parameter
lc = LCurve(misfit, regul, [10**i for i in np.arange(-10, -5, 0.5)], jobs=4)
initial = 3000*np.ones(misfit.nparams)
lc.config('levmarq', initial=initial).fit()
mpl.figure()
mpl.subplot(2, 2, 1)
mpl.plot(x, data, 'ok', label='observed')
mpl.plot(x, lc.predicted(), '-r', linewidth=2, label='predicted')
mpl.legend()
ax = mpl.subplot(2, 2, 3)
mpl.polygon(model, fill='gray', alpha=0.5)
mpl.polygon(lc.estimate_, style='o-r')
ax.invert_yaxis()
mpl.subplot(1, 2, 2)
mpl.title('L-curve')
lc.plot_lcurve()
mpl.show()
data = utils.contaminate(talwani.gz(x, z, [model]), 0.5, seed=0)
# Make the solver using smoothness regularization and run the inversion
misfit = PolygonalBasinGravity(x, z, data, 50, props, top=0)
regul = Smoothness1D(misfit.nparams)
solver = misfit + 1e-4*regul
# This is a non-linear problem so we need to pick an initial estimate
initial = 3000*np.ones(misfit.nparams)
solver.config('levmarq', initial=initial).fit()
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.plot(x, data, 'ok', label='Gravity Data')
mpl.plot(x, solver[0].predicted(), '-r', linewidth=2, label='predicted Gravity')
mpl.legend()
ax = mpl.subplot(2, 1, 2)
mpl.polygon(model, fill='gray', alpha=0.5, label='Polygon')
# The estimate_ property of our solver gives us the estimate basin as a polygon
# So we can directly pass it to plotting and forward modeling functions
mpl.polygon(solver.estimate_, style='o-r', label='Inverted')
ax.invert_yaxis()
mpl.legend()
mpl.show()
# columns = ['data','depths']
# values = np.array([data,depths])
# df = pd.DataFrame(data=values.T,columns=columns, index = xs)
# df.to_csv('Fatiando_2DBasin_forGMSYS.csv')
#
