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.

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.

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: Full-decay forward modeling and 1D laterally constrained inversion of Cole-Cole parameters

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. E213-E225 ◽  
Author(s):  
Gianluca Fiandaca ◽  
Esben Auken ◽  
Anders Vest Christiansen ◽  
Aurélie Gazoty
Keyword(s):  
Time Domain ◽  
Mineral Exploration ◽  
Induced Polarization ◽  
Significant Loss ◽  
Step Response ◽  
Model Parameters ◽  
Full Time ◽  
Inversion Algorithm ◽  
Modeling Tools ◽  
Polarization Response

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.

scholarly journals Complex Resistivity Dispersion Characteristics of Water-Bearing Coal Based on Double Cole-Cole Model

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Jian Li ◽  
Dongji Lei ◽  
Chenguang Zhao ◽  
Hui Meng
Keyword(s):  
Experimental Data ◽  
Water Saturation ◽  
Model Parameters ◽  
Frequency Change ◽  
Strongly Correlated ◽  
Complex Resistivity ◽  
Anthracite Coal ◽  
Fundamental Reason ◽  
Conductive Mechanism ◽  
Cole Model

Reservoir fracture evaluation is an important research topic in the coalfield. In recent years, complex resistivity (CR) has been widely used in oil logging and achieved good results, such as permeability evaluation, water saturation (Sw) prediction, and aquifer identification. Therefore, the method has the potential to evaluate coal seam fracture. In the experiment, the real part R and imaginary part X of bituminous and anthracite coal with different Sw were measured by the impedance measuring instrument, then the Double Cole-Cole model was used to fit experimental data and analyze conductive mechanism. The main results are as follows: (1) the dispersion of CR parameters Reρ and Imρ is closely related to the metamorphism degree, frequency, and Sw; (2) induced polarization is the fundamental reason for the variation of coal samples’ complex resistivity parameters with frequency change; and (3) the Double Cole-Cole model agrees well with the experimental data, and the model parameters m1 and τ2 are strongly correlated with Sw. The parameters m1 and τ2 can be used to evaluate the Sw of fractures in coal seams and thus to evaluate the effect of hydraulic fracturing.

On the relationship between iron concentration and induced polarization in marsh soils

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. A1-A5 ◽  
Author(s):  
Nasser Mansoor ◽  
Lee Slater
Keyword(s):  
Surface Area ◽  
Iron Concentration ◽  
Induced Polarization ◽  
Model Parameters ◽  
Soil Geochemistry ◽  
Iron Cycling ◽  
Volume Formula ◽  
Cole Model ◽  
The Relationship ◽  
Fluid Conductivity

Induced polarization (IP) measurements [Formula: see text] were conducted on seventeen clay and peat marsh soils that were subsequently analyzed for heavy metal concentrations, moisture content, organic matter, porosity, specific surface area, and pore fluid conductivity. A Cole-Cole model was fit to each sample and model parameters analyzed in terms of physicochemical properties. We found a linear relation between the normalized chargeability [Formula: see text] and estimated surface area to pore volume [Formula: see text] when iron content (ranging from 0.25% to 1.63% by volume) is accounted for as a polarizable element of the soil. In fact, the dependence of [Formula: see text] on volumetric Fe concentration per unit volume of the bulk soil is described by a linear relationship with a correlation coefficient [Formula: see text] of 0.94. As Fe concentration is a critical biogeochemical parameter, our findings suggest that IP measurements may provide a hitherto unrecognized approach to probing soil geochemistry, iron cycling and anaerobic microbial activity. Furthermore, our results yield insights into physicochemical controls on IP in natural soils.

Spectral induced polarization parameters as determined through time‐domain measurements

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 1993-2003 ◽  
Author(s):  
Ian M. Johnson
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Field Trials ◽  
Induced Polarization ◽  
Polarization Data ◽  
Forward Solution ◽  
Spectral Parameters ◽  
Impedance Model ◽  
Measurement And Analysis ◽  
The Time Domain

A method for the extraction of Cole-Cole spectral parameters from time‐domain induced polarization data is demonstrated. The instrumentation required to effect the measurement and analysis is described. The Cole-Cole impedance model is shown to work equally well in the time domain as in the frequency domain. Field trials show the time‐domain method to generate spectral parameters consistent with those generated by frequency‐domain surveys. This is shown to be possible without significant alteration to field procedures. Cole-Cole time constants of up to 100 s are shown to be resolvable given a transmitted current of a 2 s pulse‐time. The process proves to have added usefulness as the Cole-Cole forward solution proves an excellent basis for quantifying noise in the measured decay.

Hydroelastic Analysis of a 3D Floating Body Considering Uncoupled Flexural and Torsional Vibrations

2018 ◽  
Author(s):  
Debasmit Sengupta ◽  
Ranadev Datta ◽  
Debabrata Sen
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Three Dimensional ◽  
Real Life ◽  
Impulse Response Function ◽  
Floating Body ◽  
Design Stage ◽  
Beam Equation ◽  
Torsional Vibrations ◽  
Wave Induced

A semi analytic three-dimensional time domain method is developed to predict the hydroelastic effect due to wave induced loads on a floating body. The methodology being a semi analytic approach is able to capture real life scenario of bending of a ship like structure on sea taking both flexural and torsional vibrations. A prismatic beam equation with analytically defined modeshapes is taken into consideration to represent the structural response. The elastic deformation is solved using modal superposition technique. The radiation forces for elastic modes are obtained through impulse response function in time domain where frequency domain added mass, damping coefficients and wave exciting forces for the flexible modes are derived from a frequency domain panel method code. The Duhamel integral is employed in order to get the flexural and torsional deflection, velocity. A rectangular barge with zero forward speed is chosen for the analysis. Structural responses, torque, bending moments are calculated to assess the wave induced loads on the floating elastic body. The proposed technique, developed in Fortran, appears to be robust, efficient and computationally less expensive and can be used to predict the wave induced loads on a flexible structure as a first approximation in the initial design stage.

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