Time-domain-induced polarization: Full-decay forward modeling and 1D laterally constrained inversion of Cole-Cole parameters

Time-domain-induced polarization has significantly broadened its field of reference during the last decade, from mineral exploration to environmental geophysics, e.g., for clay and peat identification and landfill characterization. Though, insufficient modeling tools have hitherto limited the use of time-domain-induced polarization for wider purposes. For these reasons, a new forward code and inversion algorithm have been developed using the full-time decay of the induced polarization response, together with an accurate description of the transmitter waveform and of the receiver transfer function, to reconstruct the distribution of the Cole-Cole parameters of the earth. The accurate modeling of the transmitter waveform had a strong influence on the forward response, and we showed that the difference between a solution using a step response and a solution using the accurate modeling often is above 100%. Furthermore, the presence of low-pass filters in time-domain-induced polarization instruments affects the early times of the acquired decays (typically up to 100 ms) and has to be modeled in the forward response to avoid significant loss of resolution. The developed forward code has been implemented in a 1D laterally constrained inversion algorithm that extracts the spectral content of the induced polarization phenomenon in terms of the Cole-Cole parameters. Synthetic examples and field examples from Denmark showed a significant improvement in the resolution of the parameters that control the induced polarization response when compared to traditional integral chargeability inversion. The quality of the inversion results has been assessed by a complete uncertainty analysis of the model parameters; furthermore, borehole information confirm the outcomes of the field interpretations. With this new accurate code in situ time-domain-induced polarization measurements give access to new applications in environmental and hydrogeophysical investigations, e.g., accurate landfill delineation or on the relation between Cole-Cole and hydraulic parameters.

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Spread Spectrum Time Domain Reflectometry and Steepest Descent Inversion Spread Spectrum Time Domain Reflectometry and Steepest Descent Inversion

Applied Computational Electromagnetics Society ◽

10.47037/2020.aces.j.360211 ◽

2021 ◽

Vol 36 (2) ◽

pp. 190-198

Author(s):

Samuel Kingston ◽

Hunter Ellis ◽

Mashad Saleh ◽

Evan Benoit ◽

Ayobami Edun ◽

...

Keyword(s):

Time Domain ◽

Spread Spectrum ◽

Complex Impedance ◽

Time Domain Reflectometry ◽

Steepest Descent ◽

Model Parameters ◽

Inversion Algorithm ◽

Parametric Function ◽

Descent Algorithm ◽

Steepest Descent Algorithm

In this paper, we present a method for estimating complex impedances using reflectometry and a modified steepest descent inversion algorithm. We simulate spread spectrum time domain reflectometry (SSTDR), which can measure complex impedances on energized systems for an experimental setup with resistive and capacitive loads. A parametric function, which includes both a misfit function and stabilizer function, is created. The misfit function is a least squares estimate of how close the model data matches observed data. The stabilizer function prevents the steepest descent algorithm from becoming unstable and diverging. Steepest descent iteratively identifies the model parameters that minimize the parametric function. We validate the algorithm by correctly identifying the model parameters (capacitance and resistance) associated with simulated SSTDR data, with added 3 dB white Gaussian noise. With the stabilizer function, the steepest descent algorithm estimates of the model parameters are bounded within a specified range. The errors for capacitance (220pF to 820pF) and resistance (50 Ω to 270 Ω) are < 10%, corresponding to a complex impedance magnitude |R +1/jωC| of 53 Ω to 510 Ω.

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Resolution of well-known resistivity equivalences by inclusion of time-domain induced polarization data

Geophysics ◽

10.1190/geo2017-0009.1 ◽

2018 ◽

Vol 83 (1) ◽

pp. E47-E54 ◽

Cited By ~ 4

Author(s):

Line Meldgaard Madsen ◽

Gianluca Fiandaca ◽

Anders Vest Christiansen ◽

Esben Auken

Keyword(s):

Time Domain ◽

Equivalence Problem ◽

Induced Polarization ◽

Monte Carlo Algorithm ◽

High Resistivity ◽

Inversion Method ◽

Model Parameters ◽

Clay Layer ◽

Equivalent Models ◽

Equivalence Problems

The principle of equivalence is known to cause nonuniqueness in interpretations of direct current (DC) resistivity data. Low- or high-resistivity equivalences arise when a thin geologic layer with a low/high resistivity is embedded in a relative high-/low-resistivity background formation causing strong resistivity-thickness correlations. The equivalences often make it impossible to resolve embedded layers. We found that the equivalence problem could be significantly reduced by combining the DC data with full-decay time-domain induced polarization (IP) measurements. We applied a 1D Markov chain Monte Carlo algorithm to invert synthetic DC data of models with low- and high-resistivity equivalences. By applying this inversion method, it is possible to study the space of equivalent models that have an acceptable fit to the observed data, and to make a full sensitivity analysis of the model parameters. Then, we include a contrast in chargeability into the model, modeled in terms of spectral Cole-Cole IP parameters, and invert the DC and IP data in combination. The results show that the addition of IP data largely resolves the DC equivalences. Furthermore, we present a field example in which DC and IP data were measured on a sand formation with an embedded clay layer known from a borehole drilling. Inversion results show that the DC data alone do not resolve the clay layer due to equivalence problems, but by adding the IP data to the inversion, the layer is resolved.

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Application of electric polarization to contaminant detection in soils

Canadian Geotechnical Journal ◽

10.1139/t89-067 ◽

1989 ◽

Vol 26 (4) ◽

pp. 536-550 ◽

Cited By ~ 6

Author(s):

Raymond N. Yong ◽

Edward J. Hoppe

Keyword(s):

Contaminant Transport ◽

Time Domain ◽

Mineral Exploration ◽

Electric Polarization ◽

Induced Polarization ◽

Time Domain Reflectometry ◽

Dielectric Measurements ◽

Polarization Method ◽

Contaminant Detection ◽

Nonpolar Liquids

Preliminary experiments indicate the feasibility of constructing for field use a contaminant-detection instrumentation based on dielectric measurements. This study applies the technique of time-domain reflectometry to assess characteristic "signatures" of some selected contaminants and soil–contaminant mixtures. The results imply that a proper differentiation between various signatures can be attained, allowing an assessment in regard to soil–contaminant status. The proposed technique is similar in principle to the induced-polarization method applied in mineral exploration. Key words: electric polarization, contaminant transport, dielectrics, induced polarization, nonpolar liquids, time-domain reflectometry, relaxation, contaminant–soil interaction.

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Time-domain induced polarization forward modeling and an apparent spectral parameter solution based on the Weibull growth model

Geophysics ◽

10.1190/geo2018-0693.1 ◽

2020 ◽

Vol 85 (5) ◽

pp. D145-D155

Author(s):

Qingxin Meng ◽

Xiangyun Hu ◽

Heping Pan ◽

Huolin Ma ◽

Miao Luo

Keyword(s):

Growth Model ◽

Time Domain ◽

Forward Modeling ◽

Induced Polarization ◽

Forward Model ◽

Model Parameters ◽

Time Varying ◽

Basic Algorithm ◽

Cole Model ◽

Physical Principles

The application of the Cole-Cole model within time-domain induced polarization (TDIP) forward field modeling shows that the model parameters can characterize time-varying states of the TDIP field and support observed data analysis. The Cole-Cole model contains real and imaginary parts, and it requires a frequency-to-time conversion for TDIP forward modeling. However, the TDIP field is usually expressed by a real number, and its intuitive time-varying states field intensity increases with charging time. Therefore, the forward model should be constructed in a simpler form. We have aimed to develop a forward model using mathematical functions not based on physical principles. The Weibull (WB) growth model, which is primarily used to describe the time-varying curve features in regression analysis, is introduced into the basic algorithm of the TDIP forward model. Subsequently, a forward expression of the TDIP effect is established. Based on the time-varying shape and scale parameters, this expression describes the time-varying rate and relaxation states of the TDIP fields. Furthermore, based on the extensively used conjugate gradient optimization, an apparent WB parameter scheme is initiated to calculate the spectral parameters that represent the relaxation and time-varying rate obtained from the multi-time-channel TDIP data. Finally, this scheme is applied to interpret the different simulated and actual TDIP data. The results demonstrate that the WB growth model can be used for the TDIP forward model without involving physical principles, the model parameters without specific physical significance can be used to represent the time-varying states of TDIP fields, and apparent WB parameters can be used to discern different TDIP observed data. The setting of the TDIP forward model and model parameters can actually be more flexible and diverse, so as to obtain simpler forward expressions and ensure a highly efficient inverse solution.

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

Geophysics ◽

10.1190/geo2016-0096.1 ◽

2017 ◽

Vol 82 (2) ◽

pp. E31-E50 ◽

Cited By ~ 9

Author(s):

Andrea Viezzoli ◽

Vladislav Kaminski ◽

Gianluca Fiandaca

Keyword(s):

Time Domain ◽

A Priori ◽

Induced Polarization ◽

Earth Model ◽

Model Parameters ◽

Model Approximation ◽

Generic Models ◽

Time Domain Electromagnetic ◽

Airborne Electromagnetic ◽

Priori Information

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.

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

Geophysics ◽

10.1190/geo2016-0103.1 ◽

2017 ◽

Vol 82 (2) ◽

pp. B49-B61 ◽

Cited By ~ 15

Author(s):

Vladislav Kaminski ◽

Andrea Viezzoli

Keyword(s):

Time Domain ◽

Signal To Noise Ratio ◽

Mineral Exploration ◽

Induced Polarization ◽

Electromagnetic Transients ◽

Additional Information ◽

Time Domain Electromagnetic ◽

Airborne Electromagnetic ◽

Cole Model ◽

Inversion Techniques

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.

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Time Domain and Frequency Domain Induced Polarization Modeling for Three-dimensional Anisotropic Medium

Journal of Environmental and Engineering Geophysics ◽

10.2113/jeeg22.4.435 ◽

2017 ◽

Vol 22 (4) ◽

pp. 435-439

Author(s):

Weiqiang Liu ◽

Pinrong Lin ◽

Qingtian Lü ◽

Rujun Chen ◽

Hongzhu Cai ◽

...

Keyword(s):

Frequency Domain ◽

Half Space ◽

Anisotropic Medium ◽

Time Domain ◽

Three Dimensional ◽

Induced Polarization ◽

Model Parameters ◽

Complex Resistivity ◽

Cole Model ◽

Synthetic Models

Time domain induced polarization (TDIP) and frequency domain induced polarization (FDIP) synthetic models, incorporating three-dimensional (3D) anisotropic medium, were tested. In TDIP modeling, both resistivity and chargeability of the medium were anisotropic, and the apparent chargeability values were calculated by carrying out two resistivity forward calculations using resistivity with and without an IP effect. We analyzed the TDIP response of a 3D isotropic cube model embedded in the anisotropic subsurface half-space. In FDIP modeling, the complex resistivity of the medium at various frequencies was anisotropic. The complex resistivity was determined by a Cole-Cole model with anisotropic model parameters. We then analyzed the FDIP response of a 3D anisotropic cube model embedded in an isotropic subsurface half-space. Both of the TDIP and FDIP simulation results suggest that IP responses acquired in two orthogonal directions on the surface are different when the same arrays are used and acquisition in orthogonal directions helps resolve the presence of anisotropy. The anisotropy should be taken into account in practice for TDIP and FDIP exploration.

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The effect of local distortions on time‐domain electromagnetic measurements

Geophysics ◽

10.1190/1.1649378 ◽

2004 ◽

Vol 69 (1) ◽

pp. 87-96 ◽

Cited By ~ 19

Author(s):

Andreas Hördt ◽

Carsten Scholl

Keyword(s):

Magnetic Field ◽

Electric Field ◽

Time Domain ◽

Step Response ◽

Model Parameters ◽

Difficult Case ◽

Storage Site ◽

Transient Electromagnetic ◽

Electromagnetic Measurements ◽

Distortion Tensor

Based on the time‐domain integral equation, we derive expressions for the effect of an anomalous body close to the receiver or close to the transmitter on transient electromagnetic measurements. Similar to magnetotellurics, the distortion of electric fields at late times can be described by a constant distortion tensor relating the secondary electric field to the primary field components that would be obtained in the absence of the body. The distortion of a single electric field transient is a static shift only for particular configurations over a layered half‐space. In the general case, the perturbation is time dependent because the direction of the total electric field vector varies with time. The theory nicely explains spatial variations in electric field transients measured during a high‐redundancy long‐offset transient electromagnetics (LOTEM) survey over an underground gas storage site. An inversion example with synthetic data illustrates how distortion can be corrected. The elements of the distortion tensor are determined simultaneously with the model parameters. Ambiguity is reduced by a regularization of the distortion parameters. In the example, the background model is recovered well, even for the difficult case where only one transmitter is used. The distortion of the magnetic field time derivatives caused by bodies close to the receiver is proportional to the time derivative of the primary electric step response. The distortion is generally not limited to early times and cannot be neglected in general. Transmitter overprint effects resulting in static shifts of vertical magnetic field time derivatives may also be understood from the theory.

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Influence of Clay on Time Domain Induced Polarization

Indonesian Journal of Science and Technology ◽

10.17509/ijost.v3i1.10794 ◽

2018 ◽

Vol 3 (1) ◽

pp. 1

Author(s):

Yatini Yatini

Keyword(s):

Time Domain ◽

Physical Modeling ◽

Mineral Exploration ◽

Total Content ◽

Spherical Model ◽

Induced Polarization ◽

Soil Medium ◽

Spherical Target ◽

Target Value ◽

Modeling Data

The main problem in mineral exploration is how to determine the existence of deposits at subsurface based on resistivity and chargeability parameters. Clay almost exists in rocks. Here, this study was to understand the influence of clay on time domain induced polarization. To clarify the clay parameters, field physical modeling was conducted. The results showed physical modeling data of 20-cm diameter spherical target with a total content of 28.3% of iron did not show any significant response. The high content of clays on the medium used in field physical modeling seems to be the main reason for the change in sample. In the case of the subsurface spherical model that is near to the soil medium, the presence of clay leads to the medium resistivity value to be identical to the target value. As a consequence, the resistivity response can not be identified clearly. The chargeability between the medium and the target remains small but the chargeability response remains constant.

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