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B field fix for magnetic prism #61

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Jun 22, 2023
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137 changes: 35 additions & 102 deletions geoana/em/fdem/wholespace.py
Original file line number Diff line number Diff line change
@@ -543,31 +543,15 @@ def vector_potential(self, xyz):
>>> ax2.set_title('Imag component {} Hz'.format(frequency[f_ind]))

"""
# r = self.distance(xyz)
# f = (
# (1j * self.omega * self.mu * self.moment) / (4 * np.pi * r) *
# np.exp(-1j * self.wavenumber * r)
# )
# f = np.kron(np.ones(1, 3), np.atleast_2d(f).T)
# return self.dot_orientation(f)

n_freq = len(self.frequency)
n_loc = np.shape(xyz)[0]

r = self.distance(xyz)
xyz = check_xyz_dim(xyz)
r = np.linalg.norm(xyz, axis=-1)
k = self.wavenumber

tile_r = np.tile(r.reshape((1, n_loc)), (n_freq, 1))
tile_w = np.tile(self.omega.reshape((n_freq, 1)), (1, n_loc))

a = (1j * tile_w * self.mu * self.moment) * (
1 / (4*np.pi*tile_r) * np.exp(-1j*np.outer(k, r))
)

v = self.orientation.reshape(1, 1, 3)
a = a.reshape((n_freq, n_loc, 1))

return np.kron(v, a).squeeze()
omega = self.omega
for i in range(r.ndim):
k = k[..., None]
omega = omega[..., None]
f = 1j * omega * self.mu * self.moment / (4 * np.pi * r) * np.exp(-1j * k * r)
return (f[..., None] * self.orientation).squeeze()

def electric_field(self, xyz):
r"""Electric field for the harmonic magnetic dipole at a set of gridded locations.
@@ -650,42 +634,22 @@ def electric_field(self, xyz):
>>> ax2.set_title('Imag component {} Hz'.format(frequency[f_ind]))

"""
# dxyz = self.vector_distance(xyz)
# r = repeat_scalar(self.distance(xyz))
# kr = self.wavenumber*r
# ikr = 1j * kr

# front_term = (
# (1j * self.omega * self.mu * self.moment) / (4. * np.pi * r**2) *
# (ikr + 1) * np.exp(-ikr)
# )
# return front_term * self.cross_orientation(dxyz) / r

n_freq = len(self.frequency)
n_loc = np.shape(xyz)[0]

xyz = check_xyz_dim(xyz)
dxyz = xyz - self.location
r = np.linalg.norm(dxyz, axis=-1)
k = self.wavenumber
r = self.distance(xyz)

# (n_freq, n_loc)
tile_r = np.tile(r.reshape((1, n_loc)), (n_freq, 1))
tile_w = np.tile(self.omega.reshape((n_freq, 1)), (1, n_loc))
kr = np.outer(k, r)
omega = self.omega
for i in range(r.ndim):
k = k[..., None]
omega = omega[..., None]
kr = k * r
ikr = 1j * kr

first_term = (
(1j * tile_w * self.mu * self.moment) *
(1 / (4 * np.pi * tile_r**2) * (ikr + 1) * np.exp(-ikr))
).reshape((n_freq, n_loc, 1))
first_term = np.tile(first_term, (1, 1, 3))

r = repeat_scalar(r)
dxyz = self.vector_distance(xyz)

second_term = (self.cross_orientation(dxyz) / r).reshape((1, n_loc, 3))
second_term = np.tile(second_term, (n_freq, 1, 1))

return (first_term * second_term).squeeze()
front_term = (
(1j * omega * self.mu * self.moment) / (4. * np.pi * r**2) *
(ikr + 1) * np.exp(-ikr)
) / r
return (front_term[..., None] * np.cross(dxyz, self.orientation)).squeeze()

def current_density(self, xyz):
r"""Current density for the harmonic magnetic dipole at a set of gridded locations.
@@ -852,53 +816,22 @@ def magnetic_field(self, xyz):
>>> ax2.set_title('Imag component {} Hz'.format(frequency[f_ind]))

"""
# dxyz = self.vector_distance(xyz)
# r = repeat_scalar(self.distance(xyz))
# kr = self.wavenumber*r
# ikr = 1j*kr

# front_term = self.moment / (4. * np.pi * r**3) * np.exp(-ikr)
# symmetric_term = (
# repeat_scalar(self.dot_orientation(dxyz)) * dxyz *
# (-kr**2 + 3*ikr + 3) / r**2
# )
# oriented_term = (
# (kr**2 - ikr - 1) *
# np.kron(self.orientation, np.ones((dxyz.shape[0], 1)))
# )

# return front_term * (symmetric_term + oriented_term)

n_freq = len(self.frequency)
n_loc = np.shape(xyz)[0]

xyz = check_xyz_dim(xyz)
dxyz = xyz - self.location
r = np.linalg.norm(dxyz, axis=-1)
k = self.wavenumber
r = self.distance(xyz)
dxyz = self.vector_distance(xyz)

# (n_freq, n_loc)
kr = np.outer(k, r)
for i in range(r.ndim):
k = k[..., None]
kr = k * r
ikr = 1j * kr
tile_r = np.outer(np.ones(n_freq), r)

front_term = self.moment * (
1 / (4 * np.pi * tile_r**3) * np.exp(-ikr)
).reshape((n_freq, n_loc, 1))
front_term = np.tile(front_term, (1, 1, 3))

temp_1 = repeat_scalar(self.dot_orientation(dxyz)) * dxyz
temp_1 = np.tile(temp_1.reshape((1, n_loc, 3)), (n_freq, 1, 1))
temp_2 = (-kr**2 + 3*ikr + 3) / tile_r**2
temp_2 = np.tile(temp_2.reshape((n_freq, n_loc, 1)), (1, 1, 3))
symmetric_term = temp_1 * temp_2

temp_1 = (kr**2 - ikr - 1)
temp_1 = np.tile(temp_1.reshape((n_freq, n_loc, 1)), (1, 1, 3))
temp_2 = np.kron(self.orientation, np.ones((dxyz.shape[0], 1)))
temp_2 = np.tile(temp_2.reshape((1, n_loc, 3)), (n_freq, 1, 1))
oriented_term = temp_1 * temp_2

return (front_term * (symmetric_term + oriented_term)).squeeze()

front_term = self.moment / (4. * np.pi * r**3) * np.exp(-ikr)

symmetric_term = (dxyz @ self.orientation)[None, ...]*((-kr**2 + 3*ikr + 3) / r**2)

oriented_term = (kr**2 - ikr - 1)[..., None] * self.orientation

return (front_term[..., None] * (symmetric_term[..., None] * dxyz + oriented_term)).squeeze()

def magnetic_flux_density(self, xyz):
r"""Magnetic flux density for the harmonic magnetic dipole at a set of gridded locations.
10 changes: 9 additions & 1 deletion geoana/em/static/freespace.py
Original file line number Diff line number Diff line change
@@ -322,7 +322,15 @@ def magnetic_flux_density(self, xyz):
(..., 3) numpy.ndarray
Magnetic flux density or prism at location xyz in units :math:`T`.
"""
return mu_0 * self.magnetic_field(xyz)
xyz = check_xyz_dim(xyz)
H = self.magnetic_field(xyz)
is_inside = (
np.all(xyz >= self.min_location, axis=-1)
& np.all(xyz <= self.max_location, axis=-1)
)
H[is_inside] = H[is_inside] + self.magnetization

return mu_0 * H

def magnetic_field_gradient(self, xyz):
"""