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

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. E47-E54 ◽  
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.

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 Evaluation of induced polarization measurements using a new inversion method

2021 ◽  
Author(s):  
Tamás Fancsik ◽  
Endre Turai ◽  
Norbert Péter Szabó ◽  
Judit Somogyiné Molnár ◽  
Tünde Edit Dobróka ◽  
...  
Keyword(s):  
Objective Function ◽  
Series Expansion ◽  
Least Squares Method ◽  
Delta Function ◽  
Induced Polarization ◽  
General Definition ◽  
Inversion Method ◽  
Model Parameters ◽  
Ore Minerals ◽  
Inversion Procedure

AbstractIn this paper, a new inversion method is proposed to process laboratory-measured induced polarization (IP) data. In the new procedure, the concept of the series expansion-based inversion is combined with a more general definition of the objective function. The time constant spectrum of the IP effect is assumed a line spectrum approximated by a series of Dirac’s delta function resulting in a square-integrable forward problem formula. This gives the applicability of the generalized objective function. The expansion coefficients as unknowns represent the model parameters of the inversion procedure. We use the new inversion procedure on an apparent polarizability dataset measured on a rock sample originated from the Recsk ore complex, northeast Hungary. The inversion results was compared to those of three additional laboratory datasets, which were measured on samples rich in ore minerals collected from the same area. The results are compared to those given by the traditional series expansion-based least squares method. It is shown that the newly proposed method gives more accurate and stable parameter estimation.

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.

scholarly journals Seismic AVO statistical inversion incorporating poroelasticity

2020 ◽  
Vol 17 (5) ◽  
pp. 1237-1258
Author(s):  
Kun Li ◽  
Xing-Yao Yin ◽  
Zhao-Yun Zong ◽  
Hai-Kun Lin
Keyword(s):  
Monte Carlo Algorithm ◽  
Inversion Method ◽  
Probability Density Distribution ◽  
Simultaneous Estimation ◽  
Model Parameters ◽  
Reflection Coefficients ◽  
Rock Matrix ◽  
Critical Porosity ◽  
Avo Inversion ◽  
Rock Porosity

Abstract Seismic amplitude variation with offset (AVO) inversion is an important approach for quantitative prediction of rock elasticity, lithology and fluid properties. With Biot–Gassmann’s poroelasticity, an improved statistical AVO inversion approach is proposed. To distinguish the influence of rock porosity and pore fluid modulus on AVO reflection coefficients, the AVO equation of reflection coefficients parameterized by porosity, rock-matrix moduli, density and fluid modulus is initially derived from Gassmann equation and critical porosity model. From the analysis of the influences of model parameters on the proposed AVO equation, rock porosity has the greatest influences, followed by rock-matrix moduli and density, and fluid modulus has the least influences among these model parameters. Furthermore, a statistical AVO stepwise inversion method is implemented to the simultaneous estimation of rock porosity, rock-matrix modulus, density and fluid modulus. Besides, the Laplace probability model and differential evolution, Markov chain Monte Carlo algorithm is utilized for the stochastic simulation within Bayesian framework. Models and field data examples demonstrate that the simultaneous optimizations of multiple Markov chains can achieve the efficient simulation of the posterior probability density distribution of model parameters, which is helpful for the uncertainty analysis of the inversion and sets a theoretical fundament for reservoir characterization and fluid discrimination.

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

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. E31-E50 ◽  
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.

Mapping reservoirs based on resistivity and induced polarization derived from continuous 3D magnetotelluric profiling: Case study from Qaidam basin, China

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. B25-B33 ◽  
Author(s):  
Zhanxiang He ◽  
Zuzhi Hu ◽  
Weifeng Luo ◽  
Caifu Wang
Keyword(s):  
Qaidam Basin ◽  
Geophysical Methods ◽  
Noise Removal ◽  
Induced Polarization ◽  
High Resistivity ◽  
Inversion Method ◽  
Gas Reservoirs ◽  
To Come ◽  
Gas Bearing

In Sanfu, Qaidam basin, China, traditional geophysical methods have failed to find subtle hydrocarbon reservoirs. In an attempt to predict and delineate gas reservoirs, we used a type of magnetotelluric (MT) profiling called 3D continuous electromagnetic profiling (CEMP). Electric logs indicate that gas-bearing formations have high resistivity relative to nongas-bearing formations. Obvious resistivity anomalies derived from MT sounding curves are interpreted to come from gas-bearing formations; we observed no such anomalous resistivity away from gas-bearing reservoirs. For CEMP, five electric components were recorded at each station; the inline electric components of all stations were measured using dipoles placed end to end. Becausethe survey area was quite wide, we divided it into three rectangular blocks for data processing and inversion. After noise removal and static corrections, the data from each block were inverted with a 3D nonlinear conjugate-gradient inversion method to obtain the spatial distribution of resistivity. Using this resistivity, we created a 2D model, which we inverted to determine the induced polarization (IP) parameters. We found that a high-resistivity anomaly and high IP anomaly are two key indicators when predicting and delineating the location of gas-bearing reservoirs. In our case study, a known gas-bearing formation had a high-resistivity anomaly and a high IP anomaly. We identified two similar anomalous regions outside the known gas-bearing formations. As a result, two new prospects were determined as targets worth drilling.

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.

Decoupling induced polarization effect from time domain electromagnetic data in a Bayesian framework

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. A59-A63 ◽  
Author(s):  
Hai Li ◽  
Guoqiang Xue ◽  
Yiming He
Keyword(s):  
Time Domain ◽  
Computational Cost ◽  
Bayesian Framework ◽  
Induced Polarization ◽  
Linear Perturbation ◽  
Model Parameters ◽  
Bayesian Sampling ◽  
3D Space ◽  
Time Domain Electromagnetic ◽  
Induced Polarization Effect

We have developed a scheme for decoupling the induced polarization (IP) effect from time-domain electromagnetic (TDEM) data. This scheme is achieved by simultaneously sampling the resistivity and pseudochargeability in a Bayesian framework. The TDEM and IP responses are simulated separately with the sampled model parameters and then are stacked to fit the IP-affected TDEM data. Thus, the influence of the IP phenomenon is eliminated in the process of recovering the resistivity. To reduce the computational cost brought by the Bayesian sampling, we use a 2D parametrization instead of sampling the full 3D space and we use a linear perturbation approximation for calculating the IP response. The linearized inversion results are used as the initial model, and a multiple proposed points algorithm is used to accelerate the sampling. We validate the proposed method with synthetic and field examples showing that it restores accurate estimates of electrical structures from the TDEM data that are significantly affected by the IP phenomenon. Our method could advance the application of the TDEM method to the scenario in which the IP may affect the TDEM data and mask the underlying geologic targets.

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