def hz_kernel_vertical_magnetic_dipole(
self, lamda, f, n_layer, sig, chi, depth, h, z,
flag, output_type='response'
):
"""
Kernel for vertical magnetic component (Hz) due to
vertical magnetic diopole (VMD) source in (kx,ky) domain
"""
u0 = lamda
coefficient_wavenumber = 1/(4*np.pi)*lamda**3/u0
n_frequency = self.survey.n_frequency
n_layer = self.survey.n_layer
n_filter = self.n_filter
if output_type == 'sensitivity_sigma':
drTE = np.zeros([n_layer, n_frequency, n_filter], dtype=np.complex128, order='F')
rte_fortran.rte_sensitivity(f, lamda, sig, chi, depth, self.survey.half_switch, drTE, n_layer, n_frequency, n_filter)
kernel = drTE * np.exp(-u0*(z+h)) * coefficient_wavenumber
else:
rTE = np.empty([n_frequency, n_filter], dtype=np.complex128, order='F')
rte_fortran.rte_forward(f, lamda, sig, chi, depth, self.survey.half_switch, rTE, n_layer, n_frequency, n_filter)
kernel = rTE * np.exp(-u0*(z+h)) * coefficient_wavenumber
if output_type == 'sensitivity_height':
kernel *= -2*u0
return kernel
def hz_kernel_vertical_magnetic_dipole(
self, lamda, f, n_layer, sig, chi, depth, h, z,
flag, output_type='response'
):
"""
Kernel for vertical magnetic component (Hz) due to
vertical magnetic diopole (VMD) source in (kx,ky) domain
"""
u0 = lamda
coefficient_wavenumber = 1/(4*np.pi)*lamda**3/u0
n_frequency = self.survey.n_frequency
n_layer = self.survey.n_layer
n_filter = self.n_filter
if output_type == 'sensitivity_sigma':
drTE = np.zeros(
[n_layer, n_frequency, n_filter],
dtype=np.complex128, order='F'
)
if rte_fortran is None:
drTE = rTEfunjac(
n_layer, f, lamda, sig, chi, depth, self.survey.half_switch
)
else:
rte_fortran.rte_sensitivity(
f, lamda, sig, chi, depth, self.survey.half_switch, drTE,
n_layer, n_frequency, n_filter
)
kernel = drTE * np.exp(-u0*(z+h)) * coefficient_wavenumber
else:
rTE = np.empty(
[n_frequency, n_filter], dtype=np.complex128, order='F'
)
if rte_fortran is None:
rTE = rTEfunfwd(
n_layer, f, lamda, sig, chi, depth,
self.survey.half_switch
)
else:
rte_fortran.rte_forward(
f, lamda, sig, chi, depth, self.survey.half_switch,
rTE, n_layer, n_frequency, n_filter
)
kernel = rTE * np.exp(-u0*(z+h)) * coefficient_wavenumber
if output_type == 'sensitivity_height':
kernel *= -2*u0
return kernel
def hz_kernel_circular_loop(
self, lamda, f, n_layer, sig, chi, depth, h, z, I, a,
flag, output_type='response'
):
"""
Kernel for vertical magnetic component (Hz) at the center
due to circular loop source in (kx,ky) domain
.. math::
H_z = \\frac{Ia}{2} \int_0^{\infty} [e^{-u_0|z+h|} +
\\r_{TE}e^{u_0|z-h|}]
\\frac{\lambda^2}{u_0} J_1(\lambda a)] d \lambda
"""
n_frequency = self.survey.n_frequency
n_layer = self.survey.n_layer
n_filter = self.n_filter
w = 2*np.pi*f
u0 = lamda
radius = np.empty([n_frequency, n_filter], order='F')
radius[:, :] = np.tile(a.reshape([-1, 1]), (1, n_filter))
coefficient_wavenumber = I*radius*0.5*lamda**2/u0
if output_type == 'sensitivity_sigma':
drTE = np.zeros([n_layer, n_frequency, n_filter], dtype=np.complex128, order='F')
rte_fortran.rte_sensitivity(f, lamda, sig, chi, depth, self.survey.half_switch, drTE, n_layer, n_frequency, n_filter)
kernel = drTE * np.exp(-u0*(z+h)) * coefficient_wavenumber
else:
rTE = np.empty([n_frequency, n_filter], dtype=np.complex128, order='F')
rte_fortran.rte_forward(f, lamda, sig, chi, depth, self.survey.half_switch, rTE, n_layer, n_frequency, n_filter)
if flag == 'secondary':
kernel = rTE * np.exp(-u0*(z+h)) * coefficient_wavenumber
else:
kernel = rTE * (
np.exp(-u0*(z+h)) + np.exp(u0*(z-h))
) * coefficient_wavenumber
if output_type == 'sensitivity_height':
kernel *= -2*u0
return kernel
def hz_kernel_circular_loop(
self, lamda, f, n_layer, sig, chi, depth, h, z, I, a,
flag, output_type='response'
):
"""
Kernel for vertical magnetic component (Hz) at the center
due to circular loop source in (kx,ky) domain
.. math::
H_z = \\frac{Ia}{2} \int_0^{\infty} [e^{-u_0|z+h|} +
\\r_{TE}e^{u_0|z-h|}]
\\frac{\lambda^2}{u_0} J_1(\lambda a)] d \lambda
"""
n_frequency = self.survey.n_frequency
n_layer = self.survey.n_layer
n_filter = self.n_filter
w = 2*np.pi*f
u0 = lamda
radius = np.empty([n_frequency, n_filter], order='F')
radius[:, :] = np.tile(a.reshape([-1, 1]), (1, n_filter))
coefficient_wavenumber = I*radius*0.5*lamda**2/u0
if output_type == 'sensitivity_sigma':
drTE = np.empty(
[n_layer, n_frequency, n_filter],
dtype=np.complex128, order='F'
)
if rte_fortran is None:
drTE[:, :] = rTEfunjac(
n_layer, f, lamda, sig, chi, depth,
self.survey.half_switch
)
else:
rte_fortran.rte_sensitivity(
f, lamda, sig, chi, depth, self.survey.half_switch,
drTE, n_layer, n_frequency, n_filter
)
kernel = drTE * np.exp(-u0*(z+h)) * coefficient_wavenumber
else:
rTE = np.empty(
[n_frequency, n_filter], dtype=np.complex128, order='F'
)
if rte_fortran is None:
rTE[:, :] = rTEfunfwd(
n_layer, f, lamda, sig, chi, depth, self.survey.half_switch
)
else:
rte_fortran.rte_forward(
f, lamda, sig, chi, depth, self.survey.half_switch,
rTE, n_layer, n_frequency, n_filter
)
if flag == 'secondary':
kernel = rTE * np.exp(-u0*(z+h)) * coefficient_wavenumber
else:
kernel = rTE * (
np.exp(-u0*(z+h)) + np.exp(u0*(z-h))
) * coefficient_wavenumber
if output_type == 'sensitivity_height':
kernel *= -2*u0
return kernel