# The Shin (2015) model¶

## Introduction¶

The model proposed by Shin (2015) is an equivalent circuit that aims to reproduce SIP data This model predicts that the complex resistivity spectra $$\rho^*$$ of a polarizable rock sample can be described by

\begin{equation} \rho^* = \sum_{i=1}^2 \frac{\rho_i}{(i\omega)^{n_i} \rho_iQ_i + 1} \end{equation}

where $$\omega$$ is the measurement angular frequencies ($$\omega=2\pi f$$) and $$i$$ is the imaginary unit.

Here, $$\rho^*$$ depends on 3 pairs of parameters:

• $$\rho_i \in [0, \infty)$$, the resistivity of the resistance element in Shin’s circuit.
• $$Q_i \in [0, \infty)$$, the capacitance of the CPE.
• $$n_i \in [0, 1]$$, the exponent of the CPE impedance (0 = resistor, 0.5 = warburg, 1.0 = capacitance).

In this tutorial we will perform batch inversion of all SIP data files provided with BISIP with the Shin (2015) and double Cole-Cole models, and we will compare their respective relaxation time ($$\tau$$) parameters.

## Exploring the parameter space¶

First import the required packages.

:

import numpy as np
from bisip import PeltonColeCole
from bisip import Shin2015
from bisip import DataFiles

np.random.seed(42)

:

# Load the data file paths
data_files = DataFiles()

results = {'Shin': {},
'Pelton': {},
}

nsteps = 1000
for fname, fpath in data_files.items():

if fname == 'SIP-K389175':
model = Shin2015(fpath, nsteps=nsteps)
model.fit()
results['Shin'][fname] = model

#             model = PeltonColeCole(fpath, nsteps=nsteps, n_modes=2)
#             model.fit()
#             results['Pelton'][fname] = model


100%|██████████| 1000/1000 [00:01<00:00, 724.53it/s]

:

fig = results['Shin']['SIP-K389175'].plot_traces()

:

fig = results['Shin']['SIP-K389175'].plot_fit(discard=500)

:

import matplotlib.pyplot as plt
freq = np.logspace(-2, 100, 10000)
w = 2*np.pi*freq
theta = np.array([8.16E02, 3.12E03, np.log(1.80E-14), np.log(2.25E-06), 0.3098, 0.4584])

Z = model.forward(theta, w)
plt.plot(*Z)

:

[<matplotlib.lines.Line2D at 0x12336b978>]


### Conclusions¶

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