• 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.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.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.

• 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.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.

• Clinical and Experimental Otorhinolaryngology
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• v.11 no.4
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• pp.301-308
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• 2018

Objectives. The age-based Cole formula has been employed for the estimation of endotracheal tube (ETT) size due to its ease of use, but may not appropriately consider growth rates among children. Child growth is assessed by calculating the body surface area (BSA). The association between the outer diameter of an appropriate uncuffed-endotracheal-tube (ETT-OD) and the BSA values of patients at 24-96 months of age was our primary outcome. Methods. Cole formula, BSA, age, height, weight and ultrasound measurement of subglottic-transverse-diameter were evaluated for correlations with correct uncuffed ETT-OD. The Cole formula, BSA, and ultrasound measurements were analyzed for estimation rates in all patients and age subgroups. The maximum allowed error for the estimation of ETT-OD was ${\leq}0.3mm$. Patients' tracheas were intubated with tubes chosen by Cole formula and correct ETT-OD values were determined using leak test. ETT exchange rates were recorded. Results. One-hundred twenty-seven patients were analyzed for the determination of estimation rates. Thirteen patients aged ${\geq}72months$ were intubated with cuffed ETT-OD of 8.4 mm and were accepted to need uncuffed ETT-OD >8.4 mm in order to be included in estimation rates, but excluded from correlations for size analysis. One-hundred fourteen patients were analyzed for correlations between correct ETT-OD (determined by the leak test) and outcome parameters. Cole formula, ultrasonography, and BSA had similar correct estimation rates. All three parameters had higher underestimation rates as age increased. Conclusion. The Cole formula, BSA, and ultrasonography had similar estimation rates in patients aged ${\geq}24$ to ${\leq}96months$. BSA had a correct estimation rate of 40.2% and may not be reliable in clinical practice to predict uncuffed-ETT-size.

• 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.

• Journal of Sensor Science and Technology
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• v.26 no.1
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• pp.15-23
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• 2017

In this study, bioelectrical impedance analysis, which has been used to assess an alteration in intracellular fluid (ICF) of the body, was applied to detect intravenous infiltration. The experimental results are described as follows. Firstly, when infiltration occurred, the resistance gradually decreased with time and frequency i.e., the resistance decreased with increasing time, proportional to the amount of infiltrated intravenous (IV) solution. At each frequency, the resistance gradually decreased with time, indicating the IV solution (also blood) accumulated in the extracellular fluid (ECF) (including interstitial fluid). Secondly, the resistance ratio started to increase at infiltration, showing the highest value after 1.4 min of infiltration, and gradually decreased thereafter. Thirdly, the impedance ($Z_C$) of cell membrane decreased significantly (especially at 50 kHz) during infiltration and gradually decreased thereafter. Fourthly, Cole-Cole plot indicated that the positions of (R, $X_C$) shifted toward left owing to infiltration, reflecting the IV solution accumulated in the ECF. The resistance ($R_0$) at zero frequency decreased continuously over time, indicating that it is a vital impedance parameter capable of detecting early infiltration during IV infusion. Finally, the mechanism of the current flowing through the ECF, cell membrane, and ICF in the subcutaneous tissues was analyzed as a function of time before and after infiltration, using an equivalent circuit model of the human cell. In conclusion, it was confirmed that the infiltration could be detected early using these impedance parameters during the infusion of IV solution.

• The Journal of the Korea institute of electronic communication sciences
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• v.18 no.4
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• pp.587-594
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• 2023

In this paper, we present the design and optimization process of an on-body microstrip patch antenna with a paired T-type defect for monitoring fracture recovery of human legs. This antenna is designed to be light, thin and compact despite the improvement of return loss and bandwidth performance by adjusting the size of the T-type defect. The structure around the applied human leg is structured as a 5-layer dielectric plane, and the complex dielectric constant of each layer is calculated using the 4-pole Cole-Cole model parameters. In a normal case without bone fracture, the return loss of the on-body antenna is -66.71dB at 4.0196GHz, and the return loss difference ΔS₁₁ is 37.95dB when the gallus layer have a length of 10.0mm, width of 1.0mme, and height of 2.0mm. A 3'rd degree polynomial is presented to predict the height of the gallus layer for the change in return loss, and the polynomial has a very high prediction suitability as RSS = 1.4751, R² = 0.9988246, P-value = 0.0001841.