• Geophysics and Geophysical Exploration
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• v.24 no.4
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• pp.171-179
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• 2021

We outline a process for estimating Cole-Cole parameters from time-domain induced polarization (IP) data. The IP transients are all inverted to 2D Cole-Cole earth models that include resistivity, chargeability, relaxation time, and the frequency exponent. Our inversion algorithm consists of two stages. We first convert the measured voltage decay curves into time series of current-on time apparent resistivity to circumvent the negative chargeability problem. As a first step, a 4D inversion recovers the resistivity model at each time channel that increases monotonically with time. The desired intrinsic Cole-Cole parameters are then recovered by inverting the resistivity time series of each inversion block. In the second step, the Cole-Cole parameters can be estimated readily by setting the initial model close to the true value through a grid search method. Finally, through inversion procedures applied to synthetic data sets, we demonstrate that our algorithm can image the Cole-Cole earth models effectively.

• Geophysics and Geophysical Exploration
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• v.24 no.4
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• pp.158-163
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• 2021

The frequency-domain induced polarization (IP) response based on Cole-Cole model is expressed as a simple equation in close form. However, it is difficult to compute the time-domain IP response based on Cole-Cole model or any other relaxation model because it cannot be written in closed form. In this study, using numerical experiments, we compared three numerical methods for calculating the time-domain IP response of the Cole-Cole model asymptotically: series expansion, digital linear filtering and Fourier transform. The series expansion method is inadequately accurate for certain time values and converges very slowly. A digital linear filter specially designed to calculate the time-domain IP response does not present the desired accuracy, especially at later times. The Fourier transform method can overcome the abovementioned problems and present the time-domain IP response with adequate accuracy for all time values, even though more computing time is required.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.7 s.110
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• pp.684-693
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• 2006

In this paper, the SA (Specific Absorption) distribution in a human head, exposed to wideband pulse EMF, has been analyzed by taking into account the dispersion characteristics of biological tissues. The dispersive properties of biological tissues are characterized by the 4th Cole-Cole model. Currently, there is no dispersive FDTD algorithm to implement the 4th Cole-Cole model accurately. Thus, in this paper the FDTD methods with the dispersive algorithm for the 1st-order Cole-Cole model and the 3rd-order Debye model were used for SA analysis. The validity of each model has been investigated first, and then the effects of dispersion on SA distribution have been studied.

• Geophysics and Geophysical Exploration
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• v.24 no.4
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• pp.164-170
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• 2021

Frequency-domain and time-domain induced polarization methods can provide spectral information about subsurface media. Analysis of spectral characteristics has been studied mainly in the frequency-domain, however, time-domain induced polarization research has recently become popular. In this study, assuming a homogeneous half-space model, an inversion method was developed to extract Cole-Cole parameters from the measured secondary potential or electrical resistivity. Since the Cole-Cole parameters of chargeability, time constant, and frequency index are not independent of each other, various problems, such as slow convergence rate, initial model problem, local minimum problem, and divergence, frequently occur when conventional nonlinear inversion is applied. In this study, we developed an effective inversion method using the initial model close to the true model by introducing a grid search method. Finally, the validity of the developed inversion method was verified using inversion experiments.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2009.11a
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• pp.171-171
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• 2009

We have investigated dielectric properties depending on temperature and voltage in organic light-emitting diodes using N,N'-diphenyl-N,N'-bis(3-methylphenyl)-(1,1'-biphenyl)-4,4'-di-amine (TPD) as an hole transport. We analyzed the Cole-Cole plot of TPD. When the voltage is over 3 V, we found that a radius of Cole-Cole plot and $\beta$ increase as the temperature increases to 65 $^{\circ}C$, However, as the over the 65 $^{\circ}C$, those values decrease. Also, when the voltage is below 3 V, a radius of cole-cole plot and $\beta$ increase with the increased temperature.

• Korean Journal of Soil Science and Fertilizer
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• v.16 no.1
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• pp.1-6
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• 1983

The results of COLE(Coefficient of Linear Extensibility) measurement on various paddy soils in Korea are summarized as follows; 1. The COLE values of paddy soil in Korea varied from 0.024 to 0.094 in the surface soil while in the sub-surface soils those were ranging from 0.022 to 0.115. The poorer the relative drainage and the finer the texture caused, the greater the COLE values. 2. The matured clayey soils on fluvio-marine plains and local alluvium derived from the Tertiary materials have COLE values more than 0.09 which is demonstrated that the necessity of COLE measurement throughout profiles so that could be considered the characteristic in the characteristic of those soils. 3. The clay content has the highest positive correlation (r=0.81~0.76) values. The content of organic matter, water content at 1/3 bar, Atterberg limits, water stable aggregate etc. also have significant positive correlation with COLE values while the context of sand and silt show negative correlation. 4. Although the COLE values measured on horizontal linear bases were slightly greater than those measured on volume bases practicability was for granted. For more accurate measurement of COLE, it is reasonable to have the average values of COLE calculated from the horizontal and vertical bases.

• Geophysics and Geophysical Exploration
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• v.17 no.4
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• pp.242-246
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• 2014

Spectral induced polarization (SIP) is a useful technique, which uses electrochemical properties, for exploration of metallic sulfide minerals. Equivalent circuit analysis is commonly conducted to calculate IP parameters from SIP data. An equivalent circuit model, which indicates the SIP response of rock, has a non-uniqueness problem. For this reason, it is very important to select the proper model for accurate analysis. Thus, this study focused on suggesting a new model, which suitable for the analysis of an anomalous SIP response, such as ore. A suitability of the new model was verified by comparing it with the existing Dias model and Cole-Cole models. Analysis errors were represented as a normalized root mean square error (NRMSE). The analysis result using the Dias model was the NRMSE of 10.50% and was the NRMSE using the Cole-Cole model of 17.03%. Howerver, because the NRMSE of the new model is 0.87%, it is considered that the new model is more useful for analyzing the anomalous SIP data than other models.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2005.07a
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• pp.481-482
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• 2005

유기발광소자의 발광층의 전압에 따른 임피던스의 변화를 살펴보았다. 임피던스는 전압의 변화에 따른 의존성을 보이며, 그에 따른 임피던스와 Cole-Cole 반원의 변화를 전기전도기구와 비교하여 살펴보았다. 소자의 구조는 ITO/$Alq_3$/Al의 구조로 발광층의 두께는 60 nm로 열증착하여 실험하였다. 실험에서 전기전도기구의 Ohmic 영역, SCLC 영역, 부성저항영역, TCLC 영역에서 각각 임피던스를 측정하였고, 전압의 증가에 따라 임피던스의 크기가 감소하고, 위상각은 0V에서 용량성을 보이다가 발광영역에서 저항성을 나타내는 것을 알 수 있었다. 또한 전압에 따른 Cole-Cole 반원을 살며보면 전압이 증가할수록 반원의 크기가 감소하는 것을 알 수 있으며, 이를 통해 간단한 등가회로를 예측할 수 있었다.

• Geophysics and Geophysical Exploration
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• v.25 no.3
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• pp.99-108
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• 2022

Among induced polarization (IP) methods, spectral IP (SIP) uses alternating current as a transmission source to measure amplitudes and phase of complex electrical resistivity at each source frequency, which disperse with respect to source frequencies. The frequency dependence, which can be explained by a relaxation model such as Cole-Cole model or equivalent models, is analyzed to estimate SIP parameters from dispersion curves of complex resistivity employing multi-objective optimization (MOO). The estimation uses a generic algorithm to optimize two objective functions minimizing data misfits of amplitude and phase based on Cole-Cole model, which is most widely used to explain IP relaxation effects. The MOO-based estimation properly recovered Cole-Cole model parameters for synthetic examples but hardly fitted for the real laboratory measures ones, which have relatively smaller values of phases (less than about 10 mrad). Discrepancies between scales for data misfits of amplitude and phase, used as parameters of MOO method, and it is in necessity to employ other methods such as machine learning, which can deal with the discrepancies, to estimate SIP parameters from dispersion curves of complex resistivity.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.383-389
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• 2003

Clay minerals show a distinct induced-polarization phenomenon, which is one of the most important factors for predicting groundwater flow and contaminant transport. This paper presents a step-by-step process to estimate Cole-Cole parameters from spectral induced-polarization (IP) data measured on the surface of three-dimensional earth. First, the inversion of low-frequency resistivity survey data is made to identify the dc resistivity ${\rho}_dc$ of a volume having IP effects. The other parameters, chargeability m, time constant $\tau$, and frequency dependence c, are sought for the polarizable volume. Next, using multi-frequency data, c can be obtained as high or low asymptotes of the slope of log phase vs. log frequency. Further, for low m, intrinsic $\tau$ is approximated by apparent one, ${\tau}_a$, which is derived from the relation ${{\omega}{\tau}}_a$=1 at an angular frequency $\omega$, where the imaginary component of spectral IP data has an extreme value. Finally, to obtain intrinsic m a two-step linearized procedure has been derived. For a body of given $\tau$ and c, forward modeling with a progression of m values yields a plot of observed vs. intrinsic imaginary components for a frequency. Since this plot is essentially linear, to extract the intrinsic imaginary component is quite simple with an observed value. Using the plot of intrinsic imaginary component vs. m, intrinsic m is determined. We present a synthetic example to illustrate that the Cole-Cole parameters can be recovered from spectral IP data.