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1.
Inversion of 2D spectral induced polarization imaging data   总被引：1，自引：0，他引：1  
Laboratory measurements of various materials suggest that more information can be obtained by measuring the in‐phase and out‐of‐phase potentials at a number of frequencies. One common model used to describe the variation of the electrical properties with frequency is the Cole‐Cole model. Apart from the DC resistivity (ρ) and chargeability (m) parameters used in conventional induced‐polarization (IP) surveys, the Cole‐Cole model has two additional parameters, i.e. the time (τ) and relaxation (c) constants. Much research has been conducted on the use of the additional Cole‐Cole parameters to distinguish between different IP sources. Here, we propose a modified inversion method to recover the Cole‐Cole parameters from a 2D spectral IP (SIP) survey. In this method, an approximate inversion method is initially used to construct a non‐homogeneous starting model for the resistivity and chargeability values. The 2D model consists of a number of rectangular cells with constant resistivity (ρ), chargeability (m), time (τ) and relaxation (c) constant values in each cell. A regularized least‐squares optimization method is then used to recover the time and relaxation constant parameters as well as to refine the chargeability values in the 2D model. We present results from tests carried out with the proposed method for a synthetic data set as well as from a laboratory tank experiment.  相似文献   

2.
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   

3.
Time-Domain Spectral Induced Polarization Based on Pseudo-random Sequence   总被引：2，自引：0，他引：2  
To reduce noise during electrical prospecting, we hereby propose a new method using correlation identification technology and conventional electrical exploration devices. A correlation operation can be carried out with the transmitted pseudo-random sequence and received time signal to suppress the random noise, and the time-domain impulse response and frequency response of the frequency domain of the underground media can be obtained. At the same time, using a dual Cole–Cole model to fit a complex resistivity spectrum, which is close to the frequency response, we can get a variety of induced polarization parameters and electromagnetic parameters of subsurface, which can provide more useful information for the exploration of mineral resources. This time domain prospecting method can effectively improve the efficiency of the spectral induced polarization method. In this article, we have carried out theoretical calculations and a simulation to prove the feasibility of such a method.  相似文献   

4.
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   

5.
The seismic industry is increasingly acquiring broadband data in order to reap the benefits of extra low‐ and high‐frequency contents. At the low end, as the sharp low‐cut decay gets closer to zero frequency, it becomes harder for a well tie to estimate the low‐frequency response correctly. The fundamental difficulty is that well logs are too short to allow accurate estimation of the long‐period content of the data. Three distinctive techniques, namely parametric constant phase, frequency‐domain least squares with multi‐tapering, and Bayesian time domain with broadband priors, are introduced in this paper to provide a robust solution to the wavelet estimation problem for broadband seismic data. Each of these techniques has a different mathematical foundation that would enable one to explore a wide range of solutions that could be used on a case‐by‐case basis depending on the problem at hand. A case study from the North West Shelf Australia is used to analyse the performance of the proposed techniques. Cross‐validation is proposed as a robust quality control measure for evaluating well‐tie applications. It is observed that when the seismic data are carefully processed, then the constant phase approach would likely offer a good solution. The frequency‐domain method does not assume a constant phase. This flexibility makes it prone to over‐fitting when the phase is approximately constant. Broadband priors for the time‐domain least‐squares method are found to perform well in defining low‐frequency side lobes to the wavelet.  相似文献   

6.
This paper addresses the problem of identification of the modal parameters for a structural system using measured non‐stationary response time histories only. A Bayesian time‐domain approach is presented which is based on an approximation of the probability distribution of the response to a non‐stationary stochastic excitation. It allows one to obtain not only the most probable values of the updated modal parameters and stochastic excitation parameters but also their associated uncertainties using only one set of response data. It is found that the updated probability distribution can be well approximated by a Gaussian distribution centred at the most probable values of the parameters. Examples using simulated data are presented to illustrate the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

7.
An important approach for computation of the earths polarizability is achieved by developing a novel method with new parameters called Natural Percent Frequency Effect (NPFE) and Natural Metal Factor (NMF) resulting from telluric logging data taken at different frequencies. The essential advantage of the developed approach relies on using natural electrical currents instead of an artificial electrical source usually needed in the standard frequency domain applied in the induced polarization method. Furthermore, a good qualitative correlation has been found between the new parameters and those of the traditional induced polarization method obtained in time and frequency domains. The new method has been tested in well 32 in the Rouez mine in France, where sulphide mineralization is well known to occur.  相似文献   

8.
The success of modeling groundwater is strongly influenced by the accuracy of the model parameters that are used to characterize the subsurface system. However, the presence of uncertainty and possibly bias in groundwater model source/sink terms may lead to biased estimates of model parameters and model predictions when the standard regression‐based inverse modeling techniques are used. This study first quantifies the levels of bias in groundwater model parameters and predictions due to the presence of errors in irrigation data. Then, a new inverse modeling technique called input uncertainty weighted least‐squares (IUWLS) is presented for unbiased estimation of the parameters when pumping and other source/sink data are uncertain. The approach uses the concept of generalized least‐squares method with the weight of the objective function depending on the level of pumping uncertainty and iteratively adjusted during the parameter optimization process. We have conducted both analytical and numerical experiments, using irrigation pumping data from the Republican River Basin in Nebraska, to evaluate the performance of ordinary least‐squares (OLS) and IUWLS calibration methods under different levels of uncertainty of irrigation data and calibration conditions. The result from the OLS method shows the presence of statistically significant (p < 0.05) bias in estimated parameters and model predictions that persist despite calibrating the models to different calibration data and sample sizes. However, by directly accounting for the irrigation pumping uncertainties during the calibration procedures, the proposed IUWLS is able to minimize the bias effectively without adding significant computational burden to the calibration processes.  相似文献   

9.
Noise suppression or signal‐to‐noise ratio enhancement is often desired for better processing results from a microseismic dataset. In this paper, a polarization–linearity and time–frequency‐thresholding‐based approach is used for denoising waveforms. A polarization–linearity filter is initially applied to preserve the signal intervals and suppress the noise amplitudes. This is followed by time–frequency thresholding for further signal‐to‐noise ratio enhancement in the S transform domain. The parameterisation for both polarization filter and time–frequency thresholding is also discussed. Finally, real microseismic data examples are shown to demonstrate the improvements in processing results when denoised waveforms are considered in the workflow. The results indicate that current denoising approach effectively suppresses the background noise and preserves the vector fidelity of signal waveform. Consequently, the quality of event detection, arrival‐time picking, and hypocenter location improves.  相似文献   

10.
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   

11.
Spectral induced polarization as well as complex electrical measurements are used to estimate, on a non-invasive basis, hydraulic permeability in aquifers. Basic laboratory measurements on a variety of shaly sands, silts and clays showed that the main feature of their conductivity spectra in the frequency range from 10-3 to 103 Hertz is a nearly constant phase angle. Thus, a constant-phase-angle model of electrical conductivity is applied to interpret quantitatively surface and borehole spectral induced polarization measurements. The model allows for the calculation of two independent electrical parameters from only one frequency scan and a simple separation of electrical volume and interface effects. The proposed interpretation algorithm yields the true formation factor, the cation exchange capacity and the surface-area-to-porosity ratio, which corresponds to the inverse hydraulic radius. Using a Kozeny–Carman-like equation, the estimation of hydraulic permeability is possible.  相似文献   

12.
Amplitude variations with offset or incident angle (AVO/AVA) inversion are typically combined with statistical methods, such as Bayesian inference or deterministic inversion. We propose a joint elastic inversion method in the time and frequency domain based on Bayesian inversion theory to improve the resolution of the estimated P- and S-wave velocities and density. We initially construct the objective function using Bayesian inference by combining seismic data in the time and frequency domain. We use Cauchy and Gaussian probability distribution density functions to obtain the prior information for the model parameters and the likelihood function, respectively. We estimate the elastic parameters by solving the initial objective function with added model constraints to improve the inversion robustness. The results of the synthetic data suggest that the frequency spectra of the estimated parameters are wider than those obtained with conventional elastic inversion in the time domain. In addition, the proposed inversion approach offers stronger antinoising compared to the inversion approach in the frequency domain. Furthermore, results from synthetic examples with added Gaussian noise demonstrate the robustness of the proposed approach. From the real data, we infer that more model parameter details can be reproduced with the proposed joint elastic inversion.  相似文献   

13.
The many different existing models describing the spectral behaviour of the resistivity of geological materials at low frequency, combined with the lack of available field data, render the interpretation of complex resistivity (CR) data very difficult. With a recent interest in CR‐measurements for environmental applications and thanks to technological progress, the use of wide‐band frequency equipment seems promising, and it is expected to shed light on the different results among the published solutions to the electromagnetic (EM) coupling problem. We review the theory of EM‐coupling over a homogeneous half‐space with CR‐effects and study some aspects of the complex coupling function. We advocate the use of the CR‐based coupling function in the interpretation process, in order to obtain a better understanding of the physical processes involved in CR‐effects. Application of the model to real field data shows systematic good agreement in two simple cases, even over wide ranges of frequencies. Interpretation with a double Cole–Cole model is applied for comparison, and in spite of good fits to the data, large differences are observed in the interpreted low‐frequency dispersion. We conclude that the use of a second Cole–Cole model to describe EM‐coupling may corrupt the interpretation of the low‐frequency dispersion, even when only the normal range of frequencies (<100 Hz) is considered, and that the use of the actual EM‐coupling expression is essential when the goal is a better understanding of interaction between CR‐effects and EM‐coupling.  相似文献   

14.
The Vincent Thomas Bridge in the Los Angeles metropolitan area, is a critical artery for commercial traffic flow in and out of the Los Angeles Harbor, and is at risk in the seismically active Southern California region, particularly because it straddles the Palos Verdes fault zone. A combination of linear and non‐linear system identification techniques is employed to obtain a complete reduced‐order, multi‐input–multi‐output (MIMO) dynamic model of the Vincent Thomas Bridge based on the dynamic response of the structure to the 1987 Whittier and 1994 Northridge earthquakes. Starting with the available acceleration measurements (which consists of 15 accelerometers on the bridge structure and 10 accelerometers at various locations on its base), an efficient least‐squares‐based time‐domain identification procedure is applied to the data set to develop a reduced‐order, equivalent linear, multi‐degree‐of‐freedom model. Although not the main focus of this study, the linear system identification method is also combined with a non‐parametric identification technique, to generate a reduced‐order non‐linear mathematical model suitable for use in subsequent studies to predict, with good fidelity, the total response of the bridge under arbitrary dynamic environments. Results of this study yield measurements of the equivalent linear modal properties (frequencies, mode shapes and non‐proportional damping) as well as quantitative measures of the extent and nature of non‐linear interaction forces arising from strong ground shaking. It is shown that, for the particular subset of observations used in the identification procedure, the apparent non‐linearities in the system restoring forces are quite significant, and they contribute substantially to the improved fidelity of the model. Also shown is the potential of the identification technique under discussion to detect slight changes in the structure's influence coefficients, which may be indicators of damage and degradation in the structure being monitored. Difficulties associated with accurately estimating damping for lightly damped long‐span structures from their earthquake response are discussed. The technical issues raised in this paper indicate the need for added spatial resolution in sensor instrumentation to obtain identified mathematical models of structural systems with the broadest range of validity. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

15.
Exact representation of unbounded soil contains the single output–single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency‐domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped‐parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least‐squares fitting problem using the hybrid genetic‐simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori. The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil–structure‐interaction examples. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

16.
The induced polarization response of a horizontally multilayered earth with no resistivity contrast can rapidly be calculated on a desk calculator or minicomputer for any electrode array. The formulation is a simple series summation of the products of weighting coefficients and the true induced polarization responses for each of the layers. The coefficients are directly derivable from the corresponding resistivity model. This series approach to IP formulation was originally described by Seigel but has not been treated extensively in the present-day geophysical literature. This method can be applied to either time or frequency domain induced polarization measurements. Once the coefficients are known, apparent induced polarization response can readily be obtained by judicious substitution of known, suspected, or assumed values of the true induced polarization of each layer. Basic formulation is presented for the IP potential coefficients (pole-pole or two array) with no resistivity contrast between the layers. From these coefficients, response of any number of layers for any electrode array can be obtained by suitable differentiation. Some examples of Wenner array for a three-layered earth and dipole-dipole array for a four-layered earth are used to illustrate the application. The results of this technique are valid for many natural situations of modest resistivity contrast. However, they definitely cannot be used if there are highly contrasting resistivity layers present. Such an approach is conceptually simple and is useful for survey planning, checking or setting the “depth-of-penetration”of a given array. For field induced polarization data that fits reasonably well to the no-resistivity-contrast model, this simple approach facilitates quantitative interpretation.  相似文献   

17.
Nowadays, Flood Forecasting and Warning Systems (FFWSs) are known as the most inexpensive and efficient non‐structural measures for flood damage mitigation in the world. Benefit to cost of the FFWSs has been reported to be several times of other flood mitigation measures. Beside these advantages, uncertainty in flood predictions is a subject that may affect FFWS's reliability and the benefits of these systems. Determining the reliability of advanced flood warning systems based on the rainfall–runoff models is a challenge in assessment of the FFWS performance which is the subject of this study. In this paper, a stochastic methodology is proposed to provide the uncertainty band of the rainfall–runoff model and to calculate the probability of acceptable forecasts. The proposed method is based on Monte Carlo simulation and multivariate analysis of the predicted time and discharge error data sets. For this purpose, after the calibration of the rainfall–runoff model, the probability distributions of input calibration parameters and uncertainty band of the model are estimated through the Bayesian inference. Then, data sets of the time and discharge errors are calculated using the Monte Carlo simulation, and the probability of acceptable model forecasts is calculated by multivariate analysis of data using copula functions. The proposed approach was applied for a small watershed in Iran as a case study. The results showed using rainfall–runoff modeling based on real‐time precipitation is not enough to attain high performance for FFWSs in small watersheds, and it seems using weather forecasts as the inputs of rainfall–runoff models is essential to increase lead times and the reliability of FFWSs in small watersheds. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

18.
This paper develops the generalised effective‐medium theory of induced polarisation for rock models with elliptical grains and applies this theory to studying the complex resistivity of typical mineral rocks. We first demonstrate that the developed generalised effective‐medium theory of induced polarisation model can correctly represent the induced polarisation phenomenon in multiphase artificial rock samples manufactured using pyrite and magnetite particles. We have also collected representative rock samples from the Cu–Au deposit in Mongolia and subjected them to mineralogical analysis using Quantitative Evaluation of Minerals by Scanning Electron Microscopy technology. The electrical properties of the same samples were determined using laboratory complex resistivity measurements. As a result, we have established relationships between the mineral composition of the rocks, determined using Quantitative Evaluation of Minerals by Scanning Electron Microscopy analysis, and the parameters of the generalised effective‐medium theory of induced polarisation model defined from the laboratory measurements of the electrical properties of the rocks. These relationships open the possibility for remote estimation of types of mineralisation and for mineral discrimination using spectral induced polarization data.  相似文献   

19.
In comparing the similarity between time, frequency, and phase measurements as used in the induced polarization method of geophysical prospecting, parameters must first be defined and the basis for comparison established. The conditions for mathematical equivalence then follow in a natural sequence. Laboratory measurements are made on a variety of rock samples to indicate the type of comparison and correlation expected from field measurements. Results indicate that frequency domain and phase measurements are equivalent, but two frequency domain measurements are needed to produce the same amount of polarization information as a single phase measurement. Frequency and time domain measurements will be similar but never equivalent due to the basic differences in their respective parameter definitions.  相似文献   

20.
We present a new workflow for imaging damped three‐dimensional elastic wavefields in the Fourier domain. The workflow employs a multiscale imaging approach, in which offset lengths are laddered, where frequency content and damping of the data are changed cyclically. Thus, the inversion process is launched using short‐offset and low‐frequency data to recover the long spatial wavelength of the image at a shallow depth. Increasing frequency and offset length leads to the recovery of the fine‐scale features of the model at greater depths. For the fixed offset, we employ (in the imaging process) a few discrete frequencies with a set of Laplace damping parameters. The forward problem is solved with a finite‐difference frequency‐domain method based on a massively parallel iterative solver. The inversion code is based upon the solution of a least squares optimisation problem and is solved using a nonlinear gradient method. It is fully parallelised for distributed memory computational platforms. Our full‐waveform inversion workflow is applied to the 3D Marmousi‐2 and SEG/EAGE Salt models with long‐offset data. The maximum inverted frequencies are 6 Hz for the Marmousi model and 2 Hz for the SEG/EAGE Salt model. The detailed structures are imaged successfully up to the depth approximately equal to one‐third of the maximum offset length at a resolution consistent with the inverted frequencies.  相似文献   

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