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1.
A new method for the 2D inversion of induced polarization (IP) data in the time domain has been developed. The entire IP transients were observed and inverted into 2D Cole-Cole earth models, including resistivity, chargeability, relaxation time and the frequency constant. Firstly, a modified 1D time-domain electromagnetic algorithm was used to calculate the response of a layered polarizable ground. The transient signals were then inverted using the Marquardt method to derive the Cole-Cole parameters of each layer. However, model calculations showed that the EM effects could be neglected for the time range (>1 ms) and for the transmitter–receiver distances (<50 m) used in this study. Therefore, the induction effects were not considered for the solution of the 2D inverse problem and a DC solution was applied. An approximative forward algorithm was introduced in order to calculate the IP transients directly in the time domain and in order to speed up the inverse procedure. The approximation is highly accurate, and this is demonstrated by comparing the approximations with their exact solutions up to 3D. The inverse algorithm presented consists of two steps. The transient voltages of an array data set were inverted separately into a two-dimensional resistivity model for each time channel. The time-dependent resistivity of each cell was then interpreted as the response of a homogeneous half-space. In the 2D inversion algorithm, a 3D DC algorithm was used as a forward operator. The method only requires a standard 2D DC inversion and a homogenous half-space Cole-Cole inversion. The developed algorithm has been successfully applied to synthetic data sets and to a field data set obtained from a waste site situated close to Düren in Germany.  相似文献   

2.
Traditional two-dimensional (2D) complex resistivity forward modeling is based on Poisson’s equation but spectral induced polarization (SIP) data are the coproducts of the induced polarization (IP) and the electromagnetic induction (EMI) effects. This is especially true under high frequencies, where the EMI effect can exceed the IP effect. 2D inversion that only considers the IP effect reduces the reliability of the inversion data. In this paper, we derive differential equations using Maxwell’s equations. With the introduction of the Cole–Cole model, we use the finite-element method to conduct 2D SIP forward modeling that considers the EMI and IP effects simultaneously. The data-space Occam method, in which different constraints to the model smoothness and parametric boundaries are introduced, is then used to simultaneously obtain the four parameters of the Cole—Cole model using multi-array electric field data. This approach not only improves the stability of the inversion but also significantly reduces the solution ambiguity. To improve the computational efficiency, message passing interface programming was used to accelerate the 2D SIP forward modeling and inversion. Synthetic datasets were tested using both serial and parallel algorithms, and the tests suggest that the proposed parallel algorithm is robust and efficient.  相似文献   

3.
从瞬变电磁响应中提取IP信息的研究(英文)   总被引：1，自引：0，他引：1  
在对浙江省某铜矿进行瞬变电磁勘查时,由于感应激发极化效应的影响,造成瞬变电磁晚期测道的数据发生倒转。采用常规的瞬变电磁数据处理方法难以处理,造成晚期测道数据不可用,影响TEM的探测深度及精度。针对这个情况,采用Cole.Cole模型分析了均匀半空问模型中直流电阻率、充电率、时间常数以及频率相关系数对磁性源瞬变电磁响应的影响规律。利用奇异值分解法(The Singular Value Decomposition,简称SVD)对实测TEM数据进行分析及反演,并且从瞬变电磁响应数据中分离出勘探区瞬变电磁测量数据Cole—Cole模型的各参数,将分离出来的参数用于探测结果的辅助解释。经过分析得出充电率和频率相关系数对瞬变电磁响应的影响较大,而直流电阻率和时间常数对其影响较小的结论。通过常规方法和奇异值分解法对实测数据分别进行处理,发现后者视电阻率断面图的异常更加突出,从而较准确的圈定了铜矿体地范围,此结论得到_『钻孔的验证,与实际地质情况吻合较好。  相似文献   

4.
One simulation and two field examples from New Jersey illustrate resolution improvement in geoelectrical soundings applied to groundwater exploration. Layered-earth parameter resolution is derived from data obtained with the commonly used methods of resistivity, induced polarization (IP) and transient electromagnetic (TEM) soundings. Resolution improvement is achieved by simultaneous inversion of two or more data sets and by constraining parameters of the inverse problem. A quantitative analysis showing the contribution of IP data to the resolution of geo-electric sections is presented. Simultaneous inversion of simple IP data with conventional resistivity and resistivity-TEM data sets resulted in improved parameter resolution. IP data improved resolution in three ways: (1) by decoupling correlated layered-earth parameters, (2) by adding information to a geological interpretation about a second physical property, namely chargeability, and (3) by increasing the electrical information available.  相似文献   

5.
Non-linear least-squares inversion operates iteratively by updating the model parameters in each step by a correction vector which is the solution of a set of normal equations. Inversion of geoelectrical data is an ill-posed problem. This and the ensuing suboptimality restrict the initial model to being in the near vicinity of the true model. The problem may be reduced by introducing damping into the system of equations. It is shown that an appropriate choice of the damping parameter obtained adaptively and the use of a conjugate-gradient algorithm to solve the normal equations make the 1D inversion scheme efficient and robust. The scheme uses an optimal damping parameter that is dependent on the noise in the data, in each iterative step. The changes in the damping and relative residual error with iteration number are illustrated. A comparison of its efficacy over the conventional Marquardt and simulated annealing methods, tested on Inman's model, is made. Inversion of induced polarization (IP) sounding is obtained by inverting twice (true and modified) DC apparent resistivity data. The inversion of IP data presented here is generic and can be applied to any of the IP observables, such as chargeability, frequency effect, phase, etc., as long as these observables are explicitly related to the DC apparent resistivity. The scheme is used successfully in inverting noise-free and noisy synthetic data and field data taken from the published literature.  相似文献   

6.
The problem of discrimination between a valid induced polarization (IP) response and electromagnetic (EM) coupling effects is considered and an effective solution is provided. First, a finite dimensional approximation to the Cole‐Cole model is investigated. Using the least‐squares approach, the parameters of the approximate model are obtained. Next, based on the analysis of overvoltage, a finite dimensional structure of the IP model is produced. Using this overvoltage‐based structure, a specific finite dimensional approximation of the Cole‐Cole model is proposed. Summarizing the analysis of the finite dimensional IP model, it is concluded that the proposed IP model, which fits the field data much better than the traditional Cole‐Cole model, is essentially an RC‐circuit. From a circuit‐analysis point of view, it is well known that an electromagnetic effect can be described by an RL‐circuit. The simulation results on experimental data support this conception. According to this observation, a new method to discriminate between a valid IP response and EM coupling effects is proposed as follows: (i) use a special finite dimensional model for IP–EM systems; (ii) obtain the parameters for the model using a least‐squares approach; (iii) separate RC‐type terms and RL‐type terms – the first models the IP behaviour, the latter represents the EM part. Simulation on experimental data shows that the method is very simple and effective.  相似文献   

7.
Induced polarization (IP) is a geophysical method that is potentially sensitive to the presence of cracks in porous rocks and therefore to damage. We performed time‐domain and frequency domain IP measurements at the Tournemire Underground Research Laboratory (URL, Aveyron, France) in areas where different types of cracks are observed. These cracks correspond to both tectonic fractures and new cracks associated with stress release and desiccation resulting from the excavation of a gallery. These measurements were performed both in eastern and northern galleries of the test site. The eastern gallery was excavated in 1996 while the northern gallery was excavated recently in 2008. This gives us the opportunity to study the electrical characteristics of the excavation damaged zone surrounding the galleries with respect to the age of the excavation. Longitudinal profiles were performed along the floor of the galleries with 48 Cu/CuSO4 electrodes separated by a distance of 20 cm. Chargeability and resistivity were inverted using a Gauss‐Newton iterative approach assuming an isotropic heterogeneous clay‐rock material. The resulting IP tomograms show a correlation between high values of chargeability and the presence of calcite‐filled tectonic fractures. X‐ray analysis indicates that the presence of pyrite in these fractures is a potential source of the observed IP signals. The cracks associated with the mechanical damage of the formation exhibit low values of chargeability, on the same order of magnitude than the chargeability of the clay‐rock matrix and are therefore hardly observable. A smaller IP response associated with the presence of these cracks is observed in the older gallery and this observation is qualitatively related to the desaturation process associated with these cracks. In a specific area of one of the galleries, the presence of calcareous nodules is observed to be an important source of anomalous chargeability. This signature seems to be associated with the presence of pyrite.  相似文献   

8.
A sample of Westerly granite was deformed under constant stress conditions: a pore pressure of 5 MPa, a confining pressure of 10 MPa, and an axial load of 170 MPa. Pore volume changes were determined by measuring the volume of pore fluid (0.01M KClaq) injected into the sample. After 6 days of creep, characterized by accelerating volumetric stain, the sample failed along a macroscopic fault. Measurements of complex resistivity over the frequency range 0.001–300 Hz, taken at various times during creep, showed a gradual increase in both conductivity and permittivity. When analysed in terms of standard induced polarization (IP) techniques, the changing complex resistivity resulted in systematic changes in such parameters as percent frequency effect and chargeability. These results suggest that it may be possible to monitor the development of dilatancy in the source region of an impending earthquake through standard IP techniques.  相似文献   

9.
Theoretical model study shows that when an earth model is composed of two (Cole-Cole) polarizable media, its normalized complex resistivity spectrum is approximately a multiplicative combination of the contributions of the two media. This also applies on inversion, but the two dispersions thus obtained are apparent rather than intrinsic dispersions. In models consisting of two media, either a multiplicative or an additive combination of Cole-Cole functions fits the complex apparent resistivity spectrum. On inversion each combination gives similar parameters except for the apparent chargeability of the component with the shorter time constant. However, this can be compensated simply. In this sense the two representations are almost equivalent. We show that the apparent spectrum due to a finite polarizable body is actually a true Cole-Cole dispersion, as is usually assumed in practice. The behavior of a complex apparent resistivity spectrum and its corresponding apparent Cole-Cole dispersion parameters is influenced by the variation of the dilution factor with frequency. Hence when estimating intrinsic parameters from the nomogram, based on constant (frequency-independent) dilution factors, particular care is required to correctly relate apparent parameters to intrinsic parameters.  相似文献   

10.
Electrolytic model tank experiments to study resistivity and time domain induced polarization (IP) response over layered earth models were initiated primarily to facilitate the understanding of field results. Alternate layers of clay and sand (or clay-coated sand) with, in some cases, a surficial layer of water were assembled in the tank and resistivity and IP measurements made for a range of electrode spacings using the Wenner configuration. Graphite and silver-silver chloride electrodes were used as current and potential electrodes respectively. Clay-coated (3% by weight) sand was found to generate stronger polarization than either clay or sand alone. Apparent chargeability ma was observed to be positive for a nonpolarizable surface layer. For a polarizable surface layer, the sign of IP was controlled by the polarizability, the thickness of the second layer, and the spacing of the electrode spreads. The apparent chargeability ma can theoretically change sign from positive to negative and vice versa with a gradual increase in electrode spacing, and such negative IP effects were obtained in a few observations. A simultaneous decrease in IP and an increase in resistivity, which is a qualitative diagnostic feature for the occurrence of clean freshwater sand aquifers, could also be generated in the model tank experiment. Combined resistivity and IP soundings were carried out near Fredericton Junction and Tracy, New Brunswick, Canada. Field curves are presented along with the model curves for qualitative comparison and understanding of IP behaviour over a layered earth. Twenty-five out of twenty-seven soundings show only positive apparent chargeabilities, whereas two show chargeability sign changes (positive/negative/positive). The model study gives reason to believe that surface soils and Quaternary gravel boulder deposits near Fredericton Junction are relatively non-polarizable. As an auxiliary experiment, sand and clay were taken in different proportions by weight and mixed thoroughly with water in a cement mixer. The mixtures were then compressed with a suitable die and plunger under 3.6 Pa pressure to prepare cylindrical samples of height 18 cm and diameter 15.5 cm. IP measurements were done on the flat faces using the Wenner configuration with a= 2 cm. Chargeability was found to be negative for 100 and 90% clay mixtures. It reached a positive maximum for an 80% clay-20% sand mixture and then decreased gradually with increasing sand and decreasing clay content.  相似文献   

11.
Time-domain-induced polarization (IP) laboratory measurements were performed on about 200 fine sediment samples with varying water content. The results permitted an analysis of IP properties of clays, loams, silts, and sands. Particular emphasis has been given to the analysis of the chargeability m as a function of lithotype and the water content. By analyzing decay curves, a new parameter was identified. It is a statistically specific characteristic of the lithotype and is independent of the water content. Therefore, it provides a diagnostic parameter for lithotype identification. In association with the values of chargeability and electrical resistivity, this parameter permits a reliable evaluation of water content and yields useful information about the porosity and permeability of the lithotype.  相似文献   

12.
Electrical induced polarisation surveys are used to detect chargeable materials in the earth. For interpretation of time domain electrical‐induced polarisation data a common procedure is to first invert the direct current data (electric current on time) to recover conductivity and then invert the induced polarisation data (current off‐time) to recover chargeability. This direct current‐induced polarisation inversion procedure assumes that the off time data are free of secondary electromagnetic induction effects. To comply with this, early time data are often discarded or not recorded. For mid‐time data, an electromagnetic decoupling technique, which removes electromagnetic induction in the observations, needs to be implemented. Usually, responses from a half‐space or a layered earth are subtracted. Recent capability in three‐dimensional time domain electromagnetic forward modelling and inversion allows to revisit these procedures. In a Time domain electromagnetic‐induced polarisation survey, a high sampling rate allows early time channels of the electromagnetic data to be recorded. The recovery of chargeability then follows a three‐step workflow: (i) invert early time channel time domain electromagnetic data to recover the three‐dimensional conductivity; (ii) use that conductivity to compute the time domain electromagnetic response at later time channels and subtract this fundamental response from the observations to extract the induced polarisation responses, and (iii) invert the induced polarisation responses to recover a three‐dimensional chargeability. This workflow effectively removes electromagnetic induction effects in the observations and produces better chargeability and conductivity models compared with conventional approaches. In a synthetic example involving a gradient array, we show that the conductivity structure obtained from the early time channel data, which are usually discarded, is superior to that obtained from the steady state direct current voltages. This adds a further reason to collect these electromagnetic data.  相似文献   

13.
It is proposed that the Straightforward Inversion Scheme (SIS) developed by the authors for 1D inversion of resistivity sounding and magneto-telluric sounding data can also be used in similar fashion for time-domain induced polarization sounding data. The necessary formulations based on dynamic dipole theory are presented. It is shown that by using induced polarization potential, measured at the instant when steady state current is switched off, an equation can be developed for apparent ‘chargeability–resistivity’ which is similar to the one for apparent resistivity. The two data sets of apparent resistivity and apparent chargeability–resistivity can be inverted in a combined manner, using SIS for a common uniform thickness layer earth model to estimate the respective subsurface distributions of resistivity and chargeability–resistivity. The quotient of the two profiles will give the sought after chargeability profile. A brief outline of SIS is provided for completeness. Three theoretical models are included to confirm the efficacy of SIS software by inverting only the synthetic resistivity sounding data. Then one synthetic data set based on a geological model and three field data sets (combination of resistivity and IP soundings) from diverse geological and geographical regions are included as validation of the proposal. It is hoped that the proposed scheme would complement the resistivity interpretation with special reference to shaly sand formations.  相似文献   

14.
We present results from the resolution and sensitivity analysis of 1D DC resistivity and IP sounding data using a non-linear inversion. The inversion scheme uses a theoretically correct Metropolis–Gibbs' sampling technique and an approximate method using numerous models sampled by a global optimization algorithm called very fast simulated annealing (VFSA). VFSA has recently been found to be computationally efficient in several geophysical parameter estimation problems. Unlike conventional simulated annealing (SA), in VFSA the perturbations are generated from the model parameters according to a Cauchy-like distribution whose shape changes with each iteration. This results in an algorithm that converges much faster than a standard SA. In the course of finding the optimal solution, VFSA samples several models from the search space. All these models can be used to obtain estimates of uncertainty in the derived solution. This method makes no assumptions about the shape of an a posteriori probability density function in the model space. Here, we carry out a VFSA-based sensitivity analysis with several synthetic and field sounding data sets for resistivity and IP. The resolution capability of the VFSA algorithm as seen from the sensitivity analysis is satisfactory. The interpretation of VES and IP sounding data by VFSA, incorporating resolution, sensitivity and uncertainty of layer parameters, would generally be more useful than the conventional best-fit techniques.  相似文献   

15.
复杂地形、地质条件的大地电磁数据解释容易出现假象,采用三维正演技术模拟地形和地表不均匀体的背景响应,对实测数据阻抗相位不变量进行校正,实现更准确的定性分析;对三维异常体模型的合成数据进行一维、二维多参数反演试算,以确定地形剧变区选择反演技术的最佳方案.合成数据的试反演结果显示一维反演水平切片假异常较多,二维反演能压制测向假异常,但不能压制走向的假异常,水平切片多出现测向条带.使用本文提出的阻抗相位不变量校正法扣除地形、地表背景响应,结合一维、二维反演,能使实际资料解释成果更加可靠.  相似文献   

16.
A method is presented to estimate the elastic parameters and thickness of media that are locally laterally homogeneous using P‐wave and vertically polarized shear‐wave (SV‐wave) data. This method is a ‘layer‐stripping’ technique, and it uses many aspects of common focal point (CFP) technology. For each layer, a focusing operator is computed using a model of the elastic parameters with which a CFP gather can be constructed using the seismic data. Assuming local homogeneity, the resulting differential time shifts (DTSs) represent error in the model due to anisotropy and error in thickness. In the (τ?p) domain, DTSs are traveltimes Δτ that connect error in layer thickness z, vertical slowness q, and ray parameter p. Series expansion is used to linearize Δτ with respect to error in the elastic parameters and thickness, and least‐squares inversion is used to update the model. For stability, joint inversion of P and SV data is employed and, as pure SV data are relatively rare, the use of mode‐converted (PSV) data to represent SV in the joint inversion is proposed. Analytic and synthetic examples are used to demonstrate the utility and practicality of this inversion.  相似文献   

17.
Six thousand three hundred IP measurements made in central and southern Germany have been statistically evaluated. Shapes of IP decay curves obtained in the course of routine prospecting for sulfides were characterized in the following way: three chargeabilities were recorded during the 2 s current-off time. By dividing the last by the first chargeability an “IP decay coefficient’ was calculated and statistically evaluated by means of histograms. When the histograms were compared with the statistics of apparent resistivity and chargeability, no relationship could be detected. Therefore, the histograms of M3/M1 values represent a characteristic property of distinct areas with certain geological features, mineral assemblage and tectonics. Weathering does not alter this geophysical “fingerprint”, which depends solely on geology.  相似文献   

18.
A theoretical model of spectral-induced polarization (IP) of sand is presented. In the proposed model, contacts of sand grains and intergrain solution-filled space are considered as electrical current passages of varying thickness, which differ in values of ion transport number. Ion-selective narrow passages are considered as active zones, large passages as passive. The proposed model describes spectral IP characteristics for the medium where the length of passive zones is much greater than the length of active ones. The model is called short narrow pores (SNP) model. The SNP model predicts a growth of IP time constant with increase of length of ion-selective zone. Both the time domain and frequency domain parameters are described. The parameters of Cole–Cole model corresponding to the SNP model were also found.The behaviour of model parameters is compared with experimental data obtained on natural and sieved sands using time domain technique. The natural sand spectra correspond neither to the simple SNP model nor simple Cole–Cole model with single time constant because the lengths of ion-selective zones vary, reflecting the grain-size distribution.The spectra of sieved sand compared with the theoretical SNP spectra reveal close correspondence between experimental data and theoretical parameters. For four sieved sands, both the theoretical and experimental data show that the time constant of the IP is proportional to the square of the average grain size.  相似文献   

19.
The inversion of induced‐polarization parameters is important in the characterization of the frequency electrical response of porous rocks. A Bayesian approach is developed to invert these parameters assuming the electrical response is described by a Cole–Cole model in the time or frequency domain. We show that the Bayesian approach provides a better analysis of the uncertainty associated with the parameters of the Cole–Cole model compared with more conventional methods based on the minimization of a cost function using the least‐squares criterion. This is due to the strong non‐linearity of the inverse problem and non‐uniqueness of the solution in the time domain. The Bayesian approach consists of propagating the information provided by the measurements through the model and combining this information with a priori knowledge of the data. Our analysis demonstrates that the uncertainty in estimating the Cole–Cole model parameters from induced‐polarization data is much higher for measurements performed in the time domain than in the frequency domain. Our conclusion is that it is very difficult, if not impossible, to retrieve the correct value of the Cole–Cole parameters from time‐domain induced‐polarization data using standard least‐squares methods. In contrast, the Cole–Cole parameters can be more correctly inverted in the frequency domain. These results are also valid for other models describing the induced‐polarization spectral response, such as the Cole–Davidson or power law models.  相似文献   

20.
In this paper it is shown how one may obtain a generalized Ohm's law which relates the induced polarization electric field to the steady-state current density through the introduction of a fictitious resistivity defined as the product of the chargeability and the resistivity of a given medium. The potential generated by the induced polarization is calculated at any point in a layered earth by the same procedure as used for calculating the potential due to a point source of direct current. On the basis of the definition of the apparent chargeability ma, the expressions of ma for different stratigraphie situations are obtained, provided the IP measurements are carried out on surface with an appropriate AMNB array. These expressions may be used to plot master curves for IP vertical soundings. Finally some field experiments over sedimentary formations and the quantitative interpretation procedure are reported.  相似文献   

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