simpeg.electromagnetics.time_domain.Simulation1DLayered.compute_complex_sigma

Simulation1DLayered.compute_complex_sigma(frequencies)

Computes the complex conductivity matrix using Pelton’s Cole-Cole model:

Parameters:

frequencies(n_frequencies,) array

Array with frequencies.

Important

For IP cases (non-null chargeability), computations assume conductivity/frequency at infinite frequency were passed (see notes below).

Returns:

out(n_layers, n_frequencies) array

A 2D array of complex conductivities for all layers.

Notes

Complex conductivity is obtained following (Pelton, 1978):

\[\sigma (\omega ) = \sigma_{\infty} \Bigg ( 1 - \frac{\eta}{1 + (1-\eta ) (i\omega \tau)^c} \Bigg )\]

where \(\eta\), \(\tau\) and \(c\) are the model chargeability (V/V), relaxation time (s) and frequency exponent (-)

This formulation relies on the conductivity at infinite frequency \(\sigma_{\infty}\) which lightly differs from Pelton’s — based on the conductivity at 0 frequency \(\sigma_0\):

\[\sigma_0 = ( 1 - \eta ) \sigma_{\infty}\]