geoana.kernels.rTE_gradient

geoana.kernels.rTE_gradient(frequencies, lamb, sigma, mu, thicknesses)

Compute reflection coefficients for Transverse Electric (TE) mode.

The first layer is considered to be the top most layer. The last layer is considered to have infinite thickness. All physical properties are defined starting from the top most layer.

Parameters:

frequenciesfloat, numpy.ndarray

Frequency (Hz); shape = (n_frequency, ).

lambfloat, numpy.ndarray

Spatial wavenumber (1/m), shape = (n_filter, ).

sigma: complex, numpy.ndarray

Conductivity (S/m), shape = (n_layer, n_frequency).

mu: complex, numpy.ndarray

Magnetic permeability (H/m), shape = (n_layer, n_frequency).

thicknesses: float, numpy.ndarray

Thickness (m) of each layer, shape = (n_layer-1,).

Returns:

rTE_dsigma: complex numpy.ndarray

Reflection coefficients gradient w.r.t. conductivity shape = (n_layer, n_frequency, n_filter)

rTE_dh: complex numpy.ndarray

Reflection coefficients gradient w.r.t. thicknesses shape = (n_layer-1, n_frequency, n_filter)

rTE_dmu: complex numpy.ndarray

Reflection coefficients gradient w.r.t. magnetic permeability shape = (n_layer, n_frequency, n_filter)