Cole-Cole Parameters Research Articles

A Weighting Inversion Method of Spectrum Induced Polarization

The inversion results of complex resistivity method are four Cole-Cole model parameters. Among the four parameters, the frequency dependence and the time constant are more difficult to invert. It is necessary to study an algorithm that can invert the four Cole-Cole model parameters at the same time. In this paper, the least squares and OCCAM inversion algorithms are used to invert four Cole-Cole model parameters. In other words, two model constraints are added to the objective function. When inverting different Cole-Cole model parameters, the real and imaginary parts of the data are weighted to adjust the proportion of real part and imaginary part of data in inversion. Firstly, the formula of the algorithm is deduced. Then the theoretical models are designed for inversion trial calculation. In the inversion process, the inversion converges steadily by adjusting the Lagrange factor, and the inversion effect is improved by adjusting the weighting coefficients of real part and imaginary part. This method can get better inversion results by adjusting the proportion of the real and imaginary parts of the data in the inversion. The model trial results show that the weighting inversion algorithm significantly improves the results of the inversion of the four Cole-Cole parameters.

A thorough synthetic study on IP effects in AEM data from different systems

IP effects in AEM data are subject of current research around the world, due to the recent recognition of their significance for exploration and general (hydro)geological mapping. There have been success stories and it is now practical to model AIP on thousands of line kms of AEM data. However there still is a need to study more accurately the boundaries of the effect and of its relevance, beyond common past acceptance. In this paper we present a systematic, extended analysis of AIP effect in different AEM (TEM) systems’ data, , based on synthetic modelling of different pseudo geologies. Its goal is to provide a clear overview of possible AIP effects in the data space, without imposing simplistic assumptions (e.g., fixing some parameters to arbitrary values or limited boundaries). We produce 1D forward responses with dispersive resistivity for hundreds of thousands of combinations of Cole-Cole model parameters and AEM system transfer functions. The results are analyzed using various metrics (e.g., sum of negative voltages, exponential fitting) that capture different AIP signatures in the transients. Experiments include half spaces, 2 and 3 layer models, combined with different waveforms, Rx types (dB/dt and B), Tx-Rx geometries, flying heights, transients’ binning, base frequencies. The results, presented as 4D hyperspaces, each with 104transients obtained from the combinations of 4 x 10 different Cole-Cole parameters, allow a clear assessment of the AIP effects over a wide range of geophysical situations. Some of the main observations are: AIP effects are increased most often by the presence of a resistive bedrock, often using slow turn-off of the waveform, are generally better observed recording the B field instead of its derivative, and in any most cases lowering base frequencies to 12.5 Hz. In general, they are more pervasive than previously thought and should be carefully considered in virtually any AEM survey. If present, they can often be sensitive to model parameters down to depth.

Cell concentrations and metabolites enhance the SIP response to biofilm matrix components

We investigated the relative effect of different bacterial biofilm components to influence spectral induced polarization (SIP) signals and Cole-Cole model parameters (i.e. normalized chargeability (S m−1) and relaxation time (τ)) in order to reduce the ambiguity associated with interpretation of SIP signatures in biostimulated environments. SIP measurements were collected over a frequency range, (i.e. 0.1 Hz–1 kHz) from experimental columns containing Pseudomonas aeruginosa PAO1 (non-mucoid bacterial strain) cell suspensions alone and cell suspensions mixed with different molecules associated with P. aeruginosa biofilm matrix (alginate, DNA and phenazine). Results from SIP measurements of cell density investigations suggest an increase in phase (~ 200%), imaginary conductivity (σ″ S m−1), and normalized chargeability (S m−1) values as cell densities increase (1.50–5.55 × 109 CFUml−1), yet no significant change in the real conductivity (σ′ S m−1) or relaxation time was observed. The addition of alginate resulted in a suppression of phase (φ mrads), imaginary conductivity (σ″ S m−1), and normalized chargeability (S m−1) response. However, a mixture of cells and alginate increased all parameters but with no significant changes in real conductivity (σ′ S m−1) or relaxation time. Similar trend was observed in the DNA treatments; increasing concentrations of DNA reduced the imaginary conductivity (σ″ S m−1), phase (φ mrads), and normalized chargeability (S m−1) response. In contrast, the addition of phenazine, a secondary metabolite of P. aeruginosa, resulted in a significant increase in both imaginary conductivity (σ″ S m−1), phase (φ mrads), and normalized chargeability (S m−1) values especially at larger concentrations (>50 mM). Our work suggests that cell density and metabolites are significant factors increasing the polarization response in biofilms and advances the interpretation of electrical signals associated with biofilms in the subsurface.

Induced polarization response of porous media with metallic particles — Part 8: Influence of temperature and salinity

We have investigated the influence of temperature and salinity upon the spectral induced polarization of 10 samples including rocks with their mineralization (galena, chalcopyrite) plus sand mixed with semiconductors such as magnetite grains, graphite, and pyrite cubes of two different sizes. Measurements are made in a temperature-controlled bath with a high-precision impedance meter and using NaCl solutions. We cover the temperature range 5°C−50°C and the frequency range [Formula: see text] to 45 kHz. For one large pyrite cube, we also investigated six salinities from 0.1 to [Formula: see text] (at 25°C, NaCl) and three salinities for graphite. The spectra are fitted with a Cole-Cole complex parametric conductivity model for which we provide a physical meaning to the four Cole-Cole parameters. As expected, the Cole-Cole exponent and the chargeability are independent of the temperature and salinity. The instantaneous and steady state (direct current [DC]) conductivities depend on the salinity and temperature. This temperature dependence can be fitted with an Arrhenius law (combining the Stokes-Einstein and Vogel-Fulcher-Tammann equations) with an activation energy in the range of [Formula: see text]. This activation energy is the same as for the bulk pore-water conductivity demonstrating the control by the background electrolyte of these quantities, as expected. The instantaneous and DC conductivities depend on the salinity in a predictable way. The Cole-Cole relaxation time decreases with the temperature and decreases with the salinity. This behavior can be modeled with an Arrhenius law with an apparent activation energy of [Formula: see text]. A finite-element model is used further to analyze the mechanisms of polarization, and it can reproduce the temperature and salinity dependencies observed in the laboratory.

Experimental Study of Spectral Induced Polarization Response Based on Laboratory Measurement

The spectral induced polarization (SIP) method can provide apparent complex resistivity based on measurements of multi frequency. SIP method also can provide more detail information about physical properties of rocks and minerals because SIP can give spectral parameters or Cole-Cole parameters such as, changeability (m), time constant (τ) and frequency dependence (c). An Experimental study in laboratory has been conducted to knowing the SIP response of some test sample. The measurement system is built with digital oscilloscope Pico ADC-100 as device for sampling the input and output voltage. Amplifier is used to doubled up the signal and input differential. The range frequency of measurement is 10−2 Hz - 103 Hz. Porouspot Cu − CuSO4 is used to minimize the polarization at potential electrode. A Matlab listings is used to calculate the response of impedance and phase. The result from calibration that used the parallel circuit RC indicate that the measurement system was good. SIP response of porous model indicate that the response form an asymptotic resistivity, and the peak of phase is in the range frequency where the dispersion happen. The result also indicate that resistivity of small grain size model is larger than the big grain size model. Result from sample of mineralized rocks did not indicate a perfect SIP response, it is influenced by the contact between mineral and water was minimum.

Sensitivity of galvanic and inductive Induced Polarization methods to the Cole-Cole parameters

The Induced Polarization (IP) method is recognized as a valuable geophysical tool for resource exploration and environmental studies. In many of these studies, the Cole-Cole relaxation expression has been used to describe how subsurface resistivity depends on the frequency of the fields. In this study, we estimate the resolution of the Cole-Cole parameters of simple models measured by three geophysical methods. We compare the Spectral IP (SIP), the time-domain or Transient IP (TIP), and the in-loop Transient Electromagnetic (TEM) methods. In the first two, a current is injected directly into the ground (galvanic), while in the last one, the current is created by electromagnetic induction. The sensitivities and parameter uncertainties are estimated with a Singular Value Decomposition of the sensitivity matrix for a series of homogeneous and two-layered models. In general, the SIP method gives the best parameter resolutions, followed by those of the TIP and TEM methods. Of the four Cole-Cole parameters, generally the time constant is the least well resolved. The parameters are better resolved when the time constant is less than 10 s. When the polarizable medium is buried under a non-polarizable layer, the uncertainties of the TEM method show an important increase.

Extraction of Cole-Cole model parameters through low-frequency measurements

A novel in-direct method for extracting the four parameters of the single dispersion Cole-Cole model is introduced in this Letter. Compared with the corresponding already introduced methods, the main offered advantage is the relaxed unity-gain bandwidth requirement of the employed active element. This is originated from the fact that only measurements from dc to the cutoff frequency of the realized filter function are required. Experimental results using apples are provided and their comparison with those obtained using a LCR tester confirm the accuracy of the proposed method.

Predicting the cation exchange capacity of reservoir rocks from complex dielectric permittivity measurements

Dimensional analysis was performed to understand the physics of ionic dispersion in reservoir rocks and to identify the factors influencing the cation exchange capacity (CEC) of these rocks. Dimensional analysis revealed the existence of a general relation independent of the unit system between two dimensionless groups denoted as the cationic dispersion number [Formula: see text] and the conductivity number [Formula: see text]. The former group [Formula: see text] stands for the ratio of the CEC to the electrical double-layer dispersion. The latter group [Formula: see text] represents the ratio of the low-frequency ionic conductivity to the high-frequency electronic polarization. Complex dielectric permittivity measurements on 121 water-saturated sandstone and carbonate rock samples were used to validate the dimensionless groups. In retrospect, dimensional analysis was useful in identifying variables influencing the CEC of hydrocarbon rocks. In particular, these variables consist of rock porosity [Formula: see text], specific surface area, and five other parameters of the Cole-Cole function, which describes the frequency dependence of the complex permittivity of rock samples in the range 10–1300 MHz. The Cole-Cole function parameters are [Formula: see text], which is a characteristic relaxation time; [Formula: see text] is the so-called spread parameter; [Formula: see text] is the real DC conductivity of water-saturated rocks; and [Formula: see text] and [Formula: see text], which are the real numbers representing the static and the high-frequency dielectric permittivities of the water-saturated rock, respectively. A general regression neural network (GRNN) model was developed to predict the CEC of shaly sandstones and carbonate rocks as a function of the variables identified by the dimensional analysis as essential in predicting the CEC. The CEC prediction capability of the GRNN model has been tested with a blind data set, and it has been compared with the CEC prediction capability using a nonlinear regression model developed in this study and using a linear regression model available in the literature. The GRNN model outperformed both of these empirical models. With the GRNN model, it is possible to obtain reliable quantitative estimates of the CEC of shaly sandstone and carbonate rocks using nondestructive frequency-dependent dielectric permittivity measurements that are rapid, economic, and accurate. In return, accurate and fast estimates of the CEC are useful in many petroleum engineering applications. They can be used to identify clay types and can also be used to quantify the volume of hydrocarbon in shaly sands using well-log resistivity data. The results of this study represent a major advantage for formation evaluation, wellbore stability analysis, and designing stimulation jobs.

Variations of petrophysical properties and spectral induced polarization in response to drainage and imbibition: a study on a correlated random tube network

We implement a procedure to simulate the drainage and imbibition in random, two-dimensional, square networks. We compute the resistivity index, the relative permeability, and the characteristic lengths of a correlated network at various saturation states, under the assumption that the surface conductivity can be neglected. These parameters exhibit a hysteretic behaviour. Then, we calculate the Spectral Induced Polarization (SIP) response of the medium, under the assumption that the electrical impedance of each tube follows a local Warburg conductivity model, with identical DC conductivity and chargeability for all the tubes. We evidence that the shape of the SIP spectra depends on the saturation state. The analysis of the evolution of the macroscopic Cole-Cole parameters of the spectra in function of the saturation also behaves hysteretically, except for the Cole-Cole exponent. We also observe a power-law relationship between the macroscopic DC conductivity and time constant and the relative permeability. We also show that the frequency peak of the phase spectra is directly related to the characteristic length and to the relative permeability, underlining the potential interest of SIP measurements for the estimation of the permeability of unsaturated media.

Influence of Bi2O3 on the physical and electrical properties of some Boro-Iron glasses

The rapid quenching method was used to prepare some of Bismuth Boro-Iron glasses doped with a constant amount of iron ions. The melting temperature adjusted to be about 1000±50°C. The obtained glasses were characterized by X-ray diffraction (XRD), FTIR and Mossbauer Effect (ME) spectra. Both of XRD and ME showed that all samples of x<15 had formed pure glass phases, while the sample of x=15 exhibited crystalline phase embedded in an amorphous structure. DC activation energy was observed to increase as Bi content increase. Cole-Cole parameters referred to a distribution of the relaxation time. The refractive index as the Bi ion was increased.

Inversion of airborne geophysics over the DO-27/DO-18 kimberlites — Part 3: Induced polarization

The geologically distinct DO-27 and DO-18 kimberlites, often called the Tli Kwi Cho (TKC) kimberlites, have been used as a testbed for airborne geophysical methods applied to kimberlite exploration. This paper focuses on extracting chargeability information from time-domain electromagnetic (TEM) data. Three different TEM surveys, having similar coincident-loop geometry, have been carried out over TKC. Each records negative transients over the main kimberlite units and this is a signature of induced polarization (IP) effects. By applying a TEM-IP inversion workflow to a versatile time domain EM (VTEM) data set we decouple the EM and IP responses in the observations and then recover 3D pseudo-chargeability models at multiple times. A subsequent analysis is used to recover Cole-Cole parameters. Our models demonstrate that both DO-18 and DO-27 pipes are chargeable, but they have different Cole-Cole time constants: 110 and 1160 μs, respectively. At DO-27, we also distinguish between two adjacent kimberlite units based on their respective Cole-Cole time constants. Our chargeability models are combined with the density, magnetic susceptibility and conductivity models to build a 3D petrophysical model of TKC using only information obtained from airborne geophysics. Comparison of this final petrophysical model to a 3D geological model derived from the extensive drilling program demonstrates that we can characterize the three main kimberlite units at TKC: HK, VK, and PK in three dimensions by using airborne geophysics.

Evaluation of water content in honey using microwave transmission line technique

The microwave transmission line technique is presented as an effective method for the evaluation of honey for the first time. The electrical permittivity is an intrinsic parameter of a material that can be used as an index of added water content. For the permittivity calculation, it is found that the combination of the characteristic matrix method and Tischer’s model can offer the highest accuracy. A genetic algorithm is introduced to provide an initial approximate permittivity value and acquire the Cole-Cole parameters of the honeys examined. The accuracy provided by the methodology used in this study is superior to that offered by a commercially available probe. Operating at room temperature and a frequency range of 6–8 GHz, the measurements demonstrate that the permittivity of honey increases with increased added water. A relationship between the added water content and the permittivity of honey-water mixture is established, which could be a powerful tool for detecting honey adulteration.

Inductive induced polarization effect in heliborne time-domain electromagnetic data for uranium exploration, northern part of Cuddapah Basin, India

The Peddagattu, Lambapur, Chitrial and Koppunuru uranium deposits along the northern margins of the Cuddapah Basin are confined to the middle Proterozoic unconformity interface between Archean basement granites and the overlying resistive quartzites. Negative transients observed in the coincident loop heliborne time-domain electromagnetic (HTEM) data over these deposits (occurring in outliers) are believed to be due to thick polarizable conductive zones occurring along the unconformity. Similar negative HTEM responses are recorded over the Gorukunta Tanda outlier. A ground spectral induced polarization (SIP) survey conducted over the outlier and ground geologic observations indicated an altered basement/regolith with thickness up to 5 m below 20–30 m thick quartzite. Interpretation of Cole-Cole parameters computed from the SIP data indicated a change in the dispersion. These Cole-Cole parameters were used in modeling negative HTEM data assuming a polarizable plate placed in a layered earth at a depth of approximately 50 m using the CSIRO LeroiAir program. A negative [Formula: see text] response in the late channels indicated that the negatives can be explained in terms of inductive induced polarization effects. Modeling of HTEM [Formula: see text] data for the profile through the Lambapur uranium deposit and the Gorukunta Tanda reveals the presence of a polarizable lithologic unit at a depth of approximately 40 m. This unit is interpreted as an argillic alteration of basement, with the presence of clay and/or disseminated sulfides as evidenced from the core extracted from the boreholes at depths below the highly resistive quartzite. Uranium mineralization is closely associated with altered basement and sulfides along the unconformity where the distinct negative electromagnetic (EM) signature is recorded. Furthermore, there exists a good correlation between the uranium mineralization grade and the thickness versus the averaged late-channel negative HTEM response over the known deposits. The negative EM response helped in locating the new target areas for uranium exploration.

Modeling induced polarization effects in helicopter time-domain electromagnetic data: Field case studies

Induced polarization (IP) effects are becoming more evident in time-domain helicopter airborne electromagnetic (AEM) data thanks to advances in instrumentation, mainly due to improvements in the signal-to-noise ratio and hence better data quality. Although the IP effects are often manifested as negative receiver voltage values, which are easy to detect, in some cases, IP effects can distort recovered transients in other ways so they may be less obvious and require careful data analysis and processing. These effects represent a challenge for modeling and inversion of the AEM data. For proper modeling of electromagnetic transients, the chargeability of the subsurface and other parameters describing the dispersion also need to be taken into consideration. We use the Cole-Cole model to characterize the dispersion and for modeling of the IP effects in field AEM data, collected by different airborne systems over different geologies and exploration targets, including examples from diamond, gold, and base metal exploration. We determined how multiparametric inversion techniques can simultaneously recover all four Cole-Cole parameters, including resistivity [Formula: see text], chargeability [Formula: see text], relaxation time [Formula: see text], and frequency parameter [Formula: see text]. The results obtained are in good agreement with the ancillary information available. Interpretation of the IP effects in AEM data is therefore seen by the authors as providing corrected electrical resistivity distributions, as well as additional information that could assist in mineral exploration.

Modeling induced polarization effects in helicopter time domain electromagnetic data: Synthetic case studies

We have developed a synthetic multiparametric modeling and inversion exercise undertaken to study the robustness of inverting airborne time-domain electromagnetic (TDEM) data to extract Cole-Cole parameters. The following issues were addressed: nonuniqueness, ill posedness, dependency on manual processing and the effect of constraints, and a priori information. We have used a 1D layered earth model approximation and lateral constraints. Synthetic simulations were performed for several models and the corresponding Cole-Cole parameters. The possibility to recover these models by means of laterally constrained multiparametric inversion was evaluated, including recovery of chargeability distributions from shallow and deep targets based on analysis of induced polarization (IP) effects, simulated in airborne TDEM data. Different scenarios were studied, including chargeable targets associated with the conductive and resistive environments. In particular, four generic models were considered for the exercise: a sulfide model, a kimberlite model, and two generic models focusing on the depth of investigation. Our study indicated that, in cases when relaxation time ([Formula: see text]) values are in the range to which the airborne electromagnetic is most sensitive (e.g., approximately 1 ms), it is possible to recover deep chargeable targets (to depths more than 130 m) in association with high electrical conductivity and in resistive environments. Furthermore, it was found that the recovery of a deep conductor, masked by a shallower chargeable target, became possible only when full Cole-Cole modeling was used in the inversion. Lateral constraints improved the recoverability of model parameters. Finally, modeling IP effects increased the accuracy of recovered electrical resistivity models.

1D Cole-Cole inversion of TEM transients influenced by induced polarization

Effects of induced polarization (IP) can have an impact on time-domain electromagnetic measurements (TEM) and may lead to sign reversals in the recorded transients. To study these IP effects on TEM data, a new 1D inversion algorithm was developed for both, the central-loop and the separate-loop TEM configurations using the Cole-Cole relaxation model. 1D forward calculations for a homogeneous half-space were conducted with the aim of analyzing the impacts of the Cole-Cole parameters on TEM transients with respect to possible sign reversals. The forward modelings showed that the variation of different parameters have comparable effects on the TEM transients. This leads to an increasing number of equivalent models as a result of inversion calculations. Subsequently, 1D inversions of synthetic data were performed to study the potentials and limitations of the algorithm regarding the resolution of the Cole-Cole parameters. In order to achieve optimal inversion results, it was essential to error-weight the data points in the direct vicinity of sign reversals. The obtained findings were eventually adopted on the inversion of real field data which contained considerable IP signatures such as sign reversals. One field data set was recorded at the Nakyn kimberlite field in Western Yakutiya, Russia, in the central-loop configuration. Another field data set originates from a waste site in Cologne, Germany, and was measured utilizing the separate-loop configuration.

Dielectric variations of potato induced by irreversible electroporation under different pulses based on the cole-cole model

To investigate dielectric property variations induced by electric pulses, equivalent doses of conventional irreversible electroporation (IRE) and high-frequency IRE were used to treat potato slices. The dielectric property of the potatoes were measured before and after treatment in the frequency band of 0.1 Hz-10 MHz, and then the Cole-Cole model was used to fit the experimental data in the frequency band of 1 kHz-10 MHz to explain the β dispersion mechanism. The Cole-Cole model parameters showed that under an equivalent dose, the conventional IRE pulses were more efficient than the high-frequency IRE pulses for electroporation. After treatment with conventional IRE pulses, the DC conductivity greatly increased at time 0 after the pulses and showed little recovery over time. The electroporation effect of the high-frequency IRE pulses improved with increasing pulse duration. This study presents a potential new method for evaluating the effects of IRE during and immediately after the treatment process.

Airborne IP detects only fine-grained minerals when compared to conventional IP

Using a thin-sheet model, it is possible to predict Cole-Cole parameters of polarizable materials in the near-surface from airborne EM data. With the high frequency of AEM systems, typically more than 100 times higher than ground IP systems, most conventional IP targets will often not show an AIP response. Very fine-grained minerals, around 0.1 mm in average dimension, are however good sources for AIP responses. In 6 examples from Tasmania and NSW comparing AIP with ground IP, 5 have AIP responses that are not coincident with ground responses, but may detect finer grained minerals in the periphery of the alteration system associated with a mineral deposit.

Fitting superparamagnetic and distributed Cole-Cole parameters to airborne electromagnetic data: A case history from Quebec

Our aim was to confirm the ability of polarizable and superparamagnetic (SPM) thin sheets in the near surface to improve the model fit of airborne electromagnetic data. Our method was to fit induced polarization (IP) effects with Cole-Cole complex conductivity and fit SPM effects with Chikazumi complex permeability. Surficial conductors were assumed to be the source of the conductivity and IP effects. In this case history from Lac Brûlé, Quebec over an anorthosite intrusion, small to large IP effects were found to be essential to fit most of the observed data. In some areas, it was also possible to separate SPM effects from IP effects in the data. Most IP effects in this unusually polarizable area were adequately fit with a distributed decay characterized with a frequency dependence of [Formula: see text], but some required a sharper response characterized by [Formula: see text]. In general, fitted IP time constants were anticorrelated with fitted frequency dependence, with short time constants fitted to the larger [Formula: see text] values and vice versa. SPM effects were detected in a small but significant fraction of the data, and appear to be spatially related to static magnetic anomalies. The SPM in this case is presumably related to fine-grained rock magnetism, rather than the more common case of weathering products.

Ultrasound monitoring of the cure kinetics of an epoxy resin: Identification, frequency and temperature dependence

In this paper the monitoring of ultrasonic parameters of a thermosetting resin during an isothermal curing process is described. The ultrasonic properties are studied within the context of the monitoring of composite plate production by resin transfer molding (RTM). These ultrasonic characteristics can be related directly to cure kinetic models. An ultrasonic method, based on the measurement of the elastic constant and associated mechanical loss has been developed to identify the variations of the phase transformation. To study the reaction kinetics, the time dependence of the elastic coefficient is modeled using a Weibull distribution. The approximate time derivative form of this Weibull model makes it possible to find the relationship between ultrasonic parameters and the chemical Kamal model. The ultrasonic monitoring of a cooling process was also performed to study the temperature sensitivity after curing. Thanks to experimental measurements of the ultrasonic velocity and attenuation, the power law coefficient variations and their temperature sensitivity can be examined. The resulting viscoelastic Cole-Cole parameters were estimated and a frequency-temperature (f, T) model was proposed.