• 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.

• 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.

• 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.

• 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.

• 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.

• Journal of electromagnetic engineering and science
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• v.10 no.4
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• pp.231-236
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• 2010

This study proposes a temperature compensation method of the complex permittivities of biological tissues and organs. The method is based on the temperature dependence of the Debye model of water, which has been thoroughly investigated. This method was applied to measured data at room temperature for whole blood, kidney cortex, bile, liver, and heart muscle. It is shown that our method can compensate for the Cole-Cole model using measured data at 20 $^{\circ}C$, given the Cole-Cole model based on measured data at 35 $^{\circ}C$, with a root-mean-squared deviation of 3~11 % and 2~6 % for the real and imaginary parts of the complex permittivities, respectively, among the measured tissues.

• The Journal of the Korea institute of electronic communication sciences
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• v.16 no.4
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• pp.763-770
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• 2021

In this paper, in order to exclude the influence of BAN(Body Area Network) signals operating in the ISM band, the design and optimization process of an on-body microstrip patch antenna operating at 4.567 GHz is presented. The antenna for the monitoring of the lower legs with cancellous osteoporosis is designed to be lightweight and compact with improved return loss and bandwidth. The structure around the applied lower leg consisted of a five-layer dielectric plane. Taking into account losses, the complex dielectric constant of each layer is calculated using multi Cole-Cole model parameters, whereas a unipolar model is used for normal or osteoporotic cancellous bones. The return loss of the coaxial feed antenna on the phantom is -67.26 dB at 4.567 GHz, and in the case of osteoporosis, at the same frequency the return loss difference is 35.88 dB, and the resonance frequency difference is about 7 MHz.

• Coupled systems mechanics
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• v.3 no.1
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• pp.89-110
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• 2014

In this work we provide the theoretical formulation, discrete approximation and solution algorithm for instability problems combing geometric instability at large displacements and material instability due to softening under combined thermo-mechanical extreme loads. While the proposed approach and its implementation are sufficiently general to apply to vast majority of structural mechanics models, more detailed developments are provided for truss-bar model. Several numerical simulations are presented in order to illustrate a very satisfying performance of the proposed methodology.

• Geophysics and Geophysical Exploration
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• v.10 no.1
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• pp.60-68
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• 2007

Conventional analysis of spectral induced polarization (SIP) data consists of measuring impedances over a range of frequencies, followed by spectral analysis to estimate spectral parameters. For the quantitative and accurate estimation of subsurface SIP parameter distribution, however, a sophisticated and stable inversion technique is required. In this study, we have developed a two-step inversion approach to obtain the two-dimensional distribution of SIP parameters. In the first inversion step, all the SIP data measured over a range of frequencies are simultaneously inverted, adopting cross regularisation of model complex resistivities at each frequency. The cross regularisation makes it possible to enhance the noise characteristics of the inversion by imposing a strong assumption, that complex resistivities should show similar characteristics over a range of frequencies. In numerical experiments, we could verify that our inversion approach successfully reduced inversion artefacts. As a second step, we have also developed an inversion algorithm to obtain SIP parameters based on the Cole-Cole model, in which frequency-dependent complex resistivities from the first step are inverted to obtain a two-dimensional distribution of SIP parameters. In numerical tests, the SIP parameter images showed a fairly good match with the exact model, which suggests that SIP imaging can provide a very useful subsurface image to complement resistivity.