3D numerical modeling of induced-polarization electromagnetic response based on the finite-difference time-domain method

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. E385-E398 ◽  
Author(s):  
Yanju Ji ◽  
Yanqi Wu ◽  
Shanshan Guan ◽  
Xuejiao Zhao
Keyword(s):  
Frequency Dependence ◽  
Impulse Response ◽  
Time Constant ◽  
Time Domain ◽  
Characteristic Time ◽  
Induced Polarization ◽  
Order System ◽  
Ohm’S Law ◽  
Ohm's Law ◽  
Cole Model

Induced-polarization (IP) effects have a significant influence on transient electromagnetic (TEM) data, which commonly manifest a reversed sign. Polarization media usually have a very high economic value. To study the IP effects, a new method for modeling the time-domain electromagnetic signals of 3D dispersive materials is developed. Due to the fractional time derivatives, two main difficulties are needed to be conquered: the derivation of Cole-Cole model impulse response function and the discrete recursion of convolution in Ohm’s law. We use a frequency-domain rational approximation method and the linear programming technique to transfer the fractional order system into an integer order system. This method enables us to achieve a relatively simple and high-precision solution of the Cole-Cole model impulse response. A discrete recursion method for Ohm’s law convolution is proposed to realize an efficient numerical simulation of 3D polarization media by eliminating the prohibitive computing demands. Comparisons with published methods demonstrate the accuracy and efficiency of our algorithm. The characteristic time constant and chargeability have monotonic influences on the IP effects, whereas the frequency dependence indicates a nonmonotonic influence on the IP effects. The negative response is more significant when the frequency dependence is in the midrange. For a 3D low-resistivity chargeable body, a larger size reduces the decay rate of the induced field, which contributes to the obscuration of the polarization field. The middle-sized chargeable body can be detected under certain conditions: high chargeability, millisecond characteristic time constant, and middle frequency dependence. Small-sized chargeable bodies cannot be recognized at all by using the current forward-modeling method and instrument, which highlights the significance of precision improvement.

An examination of the relationship between time‐domain integral chargeability and the Cole‐Cole impedance model

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1249-1252 ◽  
Author(s):  
Kenneth Duckworth ◽  
H. Thomas Calvert
Keyword(s):  
Electrical Properties ◽  
Frequency Dependence ◽  
Time Constant ◽  
Time Domain ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Impedance Model ◽  
Domain Integral ◽  
The Relationship

The Cole‐Cole impedance model developed in Pelton et al. (1978) for describing the induced polarization (IP) phenomenon has proven to be useful for characterizing the electrical properties of rocks. The model characterizes the impedance Z(ω) of a rock using only four parameters as follows [Formula: see text] where [Formula: see text] is the DC resistivity, m is the dimensionless chargeability, τ is the time constant, c is the frequency dependence, and [Formula: see text] [Formula: see text]

The quantitative advantages of using B-field sensors in time-domain EM measurement for mineral exploration and unexploded ordnance search

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. WB137-WB148 ◽  
Author(s):  
Michael W. Asten ◽  
Andrew C. Duncan
Keyword(s):  
Impulse Response ◽  
Time Constant ◽  
Exponential Decay ◽  
Time Domain ◽  
Step Response ◽  
Late Time ◽  
Additional Parameter ◽  
Unexploded Ordnance ◽  
Response Measurement ◽  
Response Systems

The use of simple models for decay of conductive targets under conductive overburden and for the decay of magnetically permeable conductive steel objects allows quantitative consideration of the advantages of the use of magnetic-field detectors in time-domain electromagnetic (TEM) measurements, or more generally, the advantage of step response over impulse response TEM systems. We identified eight advantages of the step response versus impulse-response systems. The first two advantages relate to the inductive limit (early time) decay behavior, in which a target response amplitude is largely dependent on geometrical rather than conductivity parameters. Five further advantages occur when measuring response of a target in a conductive host or under conductive overburden; the maximum target-to-overburden response occurs 25%–30% earlier in time, the earliest target detection time occurs a factor 2–4 earlier, and the amplitude advantage of target-to-overburden response is a factor in the range of 1–10 for the step versus impulse-response systems, respectively. These advantages agree quantitatively with field observations on a chalcopyrite orebody under conductive cover. We used a model response for a conductive permeable sphere to derive mathematically consistent approximations for the power-law and exponential decay behaviors for step and impulse responses of metal objects, from which the onset of late-time exponential decay of EM responses of unexploded ordnance occurs about a factor of two earlier in time for the step response. This earlier-time transition together with the higher signal-to-noise ratio available from the step-response measurement makes measurement of the fundamental time-constant of unexploded ordnance (UXO) possible for medium and large UXO where the time constant is in the range of tens of milliseconds. This time-constant thus becomes accessible as an additional parameter for UXO characterization and discrimination.

The Cole‐Cole model in time domain induced polarization

Geophysics ◽  
1981 ◽  
Vol 46 (6) ◽  
pp. 932-933 ◽  
Author(s):  
T. Lee
Keyword(s):  
Equivalent Circuit ◽  
Time Domain ◽  
Induced Polarization ◽  
Relaxation Model ◽  
Trivial Case ◽  
Alternative Expression ◽  
Transient Voltage ◽  
Transient Voltages ◽  
Cole Model ◽  
The Given

Recently Pelton et al. (1978) used a Cole‐Cole relaxation model to simulate the transient voltages that are observed during an induced‐polarization survey. These authors took the impedance of the equivalent circuit Z(ω) to be [Formula: see text]They then gave the expression for the transient voltage [Formula: see text] as [Formula: see text]In equation (2), [Formula: see text] was misprinted as [Formula: see text]. In these equations, [Formula: see text] and [Formula: see text], [Formula: see text] and τ are constants to be determined for the given model. [Formula: see text] is the height of the step current that will flow in the transmitter. A disadvantage of equation (2) is that it is only slowly convergent for large t/τ. Pelton et al. (1978) used a τ which ranged from [Formula: see text] to [Formula: see text]. The purpose of this note is to provide an alternative expression for [Formula: see text] that is valid only at the later stages but which does not have this disadvantage. The trivial case of c = 1.0 is ignored.

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

Geophysics ◽  
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.

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

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. B49-B61 ◽  
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.

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

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.

Inversions of time-domain spectral induced polarization data using stretched exponential

2019 ◽  
Vol 219 (3) ◽  
pp. 1851-1865
Author(s):  
Seogi Kang ◽  
Douglas W Oldenburg
Keyword(s):  
Time Constant ◽  
Time Domain ◽  
Induced Polarization ◽  
Small Time ◽  
Mineral Deposit ◽  
The Body ◽  
Stretched Exponential ◽  
Simultaneous Inversion ◽  
Spectral Induced Polarization ◽  
Alteration Halo

SUMMARY We provide a two-stage approach to extract spectral induced polarization (SIP) information from time-domain IP data. In the first stage we invert dc data to recover the background conductivity. In the second, we solve a linear inverse problem and invert all time channels simultaneously to recover the IP parameters. The IP decay curves are represented by a stretched exponential (SE) rather than the traditional Cole–Cole model, and we find that defining the parameters in terms of their logarithmic values is advantageous. To demonstrate the capability of our simultaneous SIP inversion we use synthetic data simulating a porphyry mineral deposit. The challenge is to image a mineral body that is hosted within an alteration halo having the same chargeability but a different time constant. For a 2-D problem, we were able to distinguish the body using our simultaneous inversion but we were not successful in using a sequential (or conventional) SIP inversion approach. For the 3-D problem we recovered 3-D distributions of the SIP parameters and used those to construct a 3-D rock model having four rock units. Three chargeable units were distinguished. The compact mineralization zone, having a large time constant, was distinguished from the circular alteration halo that had a small time constant. Finally, to promote the use of the SIP technique, and to have further development of SIP inversion, all examples presented in this paper are available in our open source resources (https://github.com/simpeg-research/kang-2018-spectral-inducedpolarization).

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