In [ ]:
from geoscilabs.dcip.CondUtils import ColeColePelton, vizColeCole
from geoscilabs.dcip.FreqtoTime import transFilt
import matplotlib
from ipywidgets import interact, FloatText, FloatSlider, ToggleButtons
In [ ]:
matplotlib.rcParams['font.size'] = 16

# Purpose¶

Using a simple Cole-Cole model, we parameterize complex resistivity with four parameters: resistivity at zero frequency ($\rho_0$), chargeability($\eta$), time constant ($\tau$), and frequency dependence ($c$). Based upon those parameters, we understand how resistivity and conductivity changes when medium is chargeable both in frequency domain and time domain.

# Set up¶

Pelton's Cole-Cole model for resistivity and conductivity can be written as

$$\rho(\omega) = \rho_0 \Big[1 - \eta \Big(1-\frac{1}{1+(\imath\omega\tau)^c}\Big) \Big]$$

and

$$\sigma(\omega) = \sigma_{\infty}\Big(1-\frac{\eta}{1+(1-\eta)(\imath\omega\tau)^c} \Big)$$

respectively.

# Cole-Cole app¶

## Parameters¶

• $\sigma_1$: Conductivity of the first layer (S/m)

• $\sigma_2$: Conductivity of the first layer (S/m)

• $f$ (Hz): Frequency (Hz)

• Type:

• Reflection: Transmission power as a function of incident angle
• Transmission: Transmission power as a function of incident angle
• Angle: relationship between $\theta_i$ and $\theta_t$
In [ ]:
interact(vizColeCole, eta=FloatSlider(min=0.1, max=0.5, step=0.05, value=0.4),
tau=FloatText(value=0.1),
c=FloatSlider(min=0.1, max=1., step=0.1, value=0.5),
sigres = ToggleButtons(options=['sigma','resis']),
t1=FloatText(value=800),
t2=FloatText(value=1400),
);
In [ ]: