def test_pole_reduce():
"gravmag.transform pole reduction matches analytical solution"
# Use remanent magnetization
sinc, sdec = -70, 30
model = [Prism(-100, 100, -500, 500, 0, 100,
{'density': 1000,
'magnetization': utils.ang2vec(5, sinc, sdec)})]
# Use low latitudes to make sure that there are no problems with FFT
# instability.
inc, dec = -60, -15
shape = (50, 50)
x, y, z = gridder.regular([-2000, 2000, -2000, 2000], shape, z=-100)
data = prism.tf(x, y, z, model, inc, dec)
pole = transform.reduce_to_pole(x, y, data, shape, inc, dec, sinc, sdec)
pole_true = prism.tf(x, y, z, model, -90, 0, pmag=utils.ang2vec(5, -90, 0))
npt.assert_allclose(pole, pole_true, atol=10, rtol=0.01)
def test_pole_reduce():
"gravmag.transform pole reduction matches analytical solution"
# Use remanent magnetization
sinc, sdec = -70, 30
model = [
Prism(-100, 100, -500, 500, 0, 100, {
'density': 1000,
'magnetization': utils.ang2vec(5, sinc, sdec)
})
]
# Use low latitudes to make sure that there are no problems with FFT
# instability.
inc, dec = -60, -15
shape = (50, 50)
x, y, z = gridder.regular([-2000, 2000, -2000, 2000], shape, z=-100)
data = prism.tf(x, y, z, model, inc, dec)
pole = transform.reduce_to_pole(x, y, data, shape, inc, dec, sinc, sdec)
pole_true = prism.tf(x, y, z, model, -90, 0, pmag=utils.ang2vec(5, -90, 0))
npt.assert_allclose(pole, pole_true, atol=10, rtol=0.01)
# Direction of the Geomagnetic field
inc, dec = -60, 0
# Make a model with only induced magnetization
model = [
mesher.Prism(-100, 100, -100, 100, 0, 2000,
{'magnetization': utils.ang2vec(10, inc, dec)})
]
area = (-5000, 5000, -5000, 5000)
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')
from fatiando.vis import mpl
# Direction of the Geomagnetic field
inc, dec = -60, 0
# Make a model with only induced magnetization
model = [mesher.Prism(-100, 100, -100, 100, 0, 2000,
{'magnetization': utils.ang2vec(10, inc, dec)})]
area = (-5000, 5000, -5000, 5000)
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')
from fatiando import gridder, utils
# Create some synthetic magnetic data with a total magnetization that is
# different from the geomagnetic field (so there is remanent magnetization or
# some demagnetizing effect)
inc, dec = -60, 23 # Geomagnetic field direction
sinc, sdec = -30, -20 # Source magnetization direction
mag = utils.ang2vec(1, sinc, sdec)
model = [Prism(-1500, 1500, -500, 500, 0, 2000, {'magnetization': mag})]
area = (-7e3, 7e3, -7e3, 7e3)
shape = (100, 100)
x, y, z = gridder.regular(area, shape, z=-300)
data = prism.tf(x, y, z, model, inc, dec)
# Reduce to the pole
data_at_pole = transform.reduce_to_pole(x, y, data, shape, inc, dec, sinc,
sdec)
# Make some plots
plt.figure(figsize=(8, 6))
ax = plt.subplot(1, 2, 1)
ax.set_title('Original data')
ax.set_aspect('equal')
tmp = ax.tricontourf(y/1000, x/1000, data, 30, cmap='RdBu_r')
plt.colorbar(tmp, pad=0.1, aspect=30, orientation='horizontal').set_label('nT')
ax.set_xlabel('y (km)')
ax.set_ylabel('x (km)')
ax.set_xlim(area[2]/1000, area[3]/1000)
ax.set_ylim(area[0]/1000, area[1]/1000)
ax = plt.subplot(1, 2, 2)
from fatiando import gridder, utils
# Create some synthetic magnetic data with a total magnetization that is
# different from the geomagnetic field (so there is remanent magnetization or
# some demagnetizing effect)
inc, dec = -60, 23 # Geomagnetic field direction
sinc, sdec = -30, -20 # Source magnetization direction
mag = utils.ang2vec(1, sinc, sdec)
model = [Prism(-1500, 1500, -500, 500, 0, 2000, {'magnetization': mag})]
area = (-7e3, 7e3, -7e3, 7e3)
shape = (100, 100)
x, y, z = gridder.regular(area, shape, z=-300)
data = prism.tf(x, y, z, model, inc, dec)
# Reduce to the pole
data_at_pole = transform.reduce_to_pole(x, y, data, shape, inc, dec, sinc,
sdec)
# Make some plots
plt.figure(figsize=(8, 6))
ax = plt.subplot(1, 2, 1)
ax.set_title('Original data')
ax.set_aspect('equal')
tmp = ax.tricontourf(y / 1000, x / 1000, data, 30, cmap='RdBu_r')
plt.colorbar(tmp, pad=0.1, aspect=30, orientation='horizontal').set_label('nT')
ax.set_xlabel('y (km)')
ax.set_ylabel('x (km)')
ax.set_xlim(area[2] / 1000, area[3] / 1000)
ax.set_ylim(area[0] / 1000, area[1] / 1000)
ax = plt.subplot(1, 2, 2)