def test_confocal_oblate_ellipsoids():
"Confocal bodies with properly scaled suscep produce the same field"
# Reference ellipsoid
a, b, = 400., 1000. # semi-axes
chi = 1.2 # reference susceptibility
ellipsoid = OblateEllipsoid(
0., 0., 1500., a, b, 45., 10., -30., {
'principal susceptibilities': [chi, chi, chi],
'susceptibility angles': [0., 0., 0.]
})
# Intensity of the local-geomagnetic field (in nT)
B0 = 23500.
# Direction parallel to the semi-axis a
_, inc, dec = utils.vec2ang(ellipsoid.transf_matrix.T[0])
# Magnetic moment of the reference ellipsoid
volume = ellipsoid.volume
mag = oblate_ellipsoid.magnetization(ellipsoid, B0, inc, dec, demag=True)
moment = volume * mag
# Confocal ellipsoid
u = 2.0e6
a_confocal = np.sqrt(a * a + u)
b_confocal = np.sqrt(b * b + u)
xc = ellipsoid.x
yc = ellipsoid.y
zc = ellipsoid.z
strike = ellipsoid.strike
dip = ellipsoid.dip
rake = ellipsoid.rake
confocal_ellipsoid = OblateEllipsoid(
xc, yc, zc, a_confocal, b_confocal, strike, dip, rake,
{'susceptibility angles': [0., 0., 0.]})
n11, n22 = oblate_ellipsoid.demag_factors(confocal_ellipsoid)
H0 = B0 / (4 * np.pi * 100)
volume_confocal = confocal_ellipsoid.volume
# Equivalent susceptibility
moment_norm = np.sqrt(np.sum(moment * moment))
chi_confocal = moment_norm / (volume_confocal * H0 - n11 * moment_norm)
confocal_ellipsoid.addprop('principal susceptibilities',
[chi_confocal, chi_confocal, chi_confocal])
# Magnetic moment of the confocal ellipsoid
mag_confocal = oblate_ellipsoid.magnetization(confocal_ellipsoid,
B0,
inc,
dec,
demag=True)
moment_confocal = volume_confocal * mag_confocal
# Total-field anomalies
tf = oblate_ellipsoid.tf(x, y, z, [ellipsoid], B0, inc, dec)
tf_confocal = oblate_ellipsoid.tf(x, y, z, [confocal_ellipsoid], B0, inc,
dec)
# Comparison between the moments and total-field anomalies
assert_almost_equal(moment, moment_confocal, decimal=5)
assert_almost_equal(tf, tf_confocal, decimal=12)
def test_oblate_ellipsoid_principal_susceptibilities_signal():
'principal susceptibilities must be all positive'
e = OblateEllipsoid(x=1, y=2, z=3, small_axis=4, large_axis=6,
strike=10, dip=20, rake=30,
props={'remanent magnetization': [10, 25, 40],
'principal susceptibilities': [0.562, 0.485,
0.9],
'susceptibility angles': [19, -14, 100]})
with raises(AssertionError):
e.susceptibility_tensor
def test_oblate_ellipsoid_susceptibility_tensor_symm():
'susceptibility tensor must be symmetric'
e = OblateEllipsoid(x=1, y=2, z=3,
small_axis=4, large_axis=6,
strike=10, dip=20, rake=30,
props={'remanent magnetization': [10, 25, 40],
'principal susceptibilities': [0.562, 0.485,
0.25],
'susceptibility angles': [-240, 71, -2]})
assert_almost_equal(e.susceptibility_tensor, e.susceptibility_tensor.T,
decimal=15)
def test_oblate_ellipsoid_principal_susceptibilities_fmt():
'principal susceptibilities must be a list containing 3 elements'
e = OblateEllipsoid(x=1, y=2, z=3,
small_axis=4, large_axis=6,
strike=10, dip=20, rake=30,
props={'remanent magnetization': [10, 25, 40],
'principal susceptibilities': [0.562, 0.485],
'susceptibility angles': [90, 0, 0]})
with raises(AssertionError):
e.susceptibility_tensor
def test_oblate_ellipsoid_copy():
'Check the elements of a duplicated ellipsoid'
orig = OblateEllipsoid(1, 2, 3, 4, 6, 10, 20, 30, {
'remanent magnetization': [3, -2, 40],
'susceptibility tensor': [0.562, 0.485, 0.25,
90, 34, 0]})
cp = orig.copy()
assert orig is not cp
assert orig.x == cp.x
assert orig.y == cp.y
assert orig.z == cp.z
assert orig.small_axis == cp.small_axis
assert orig.large_axis == cp.large_axis
assert orig.props == cp.props
cp.x = 4
cp.y = 6
cp.z = 7
cp.props['remanent magnetization'] = [100, -40, -25]
assert orig.x != cp.x
assert orig.y != cp.y
assert orig.z != cp.z
assert orig.props['remanent magnetization'] != \
cp.props['remanent magnetization']
inc = 2
dec = -27
gm = 1000 # geometrical factor
area = [-5. * gm, 5. * gm, -5. * gm, 5. * gm]
x, y, z = gridder.scatter(area, 300, z=0.)
axis_ref = gm # reference semi-axis
# Oblate ellipsoids used for testing
model = [
OblateEllipsoid(x=-3 * gm,
y=-3 * gm,
z=3 * axis_ref,
small_axis=0.6 * axis_ref,
large_axis=axis_ref,
strike=78,
dip=92,
rake=135,
props={
'principal susceptibilities': [0.7, 0.7, 0.7],
'susceptibility angles': [90., 47., 13.]
}),
OblateEllipsoid(x=-gm,
y=-gm,
z=2.4 * axis_ref,
small_axis=0.3 * axis_ref,
large_axis=1.1 * axis_ref,
strike=4,
dip=10,
rake=5,
props={
'principal susceptibilities': [0.2, 0.15, 0.05],