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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.
The reliability of inversion of apparent resistivity pseudosection data to determine accurately the true resistivity distribution over 2D structures has been investigated, using a common inversion scheme based on a smoothness‐constrained non‐linear least‐squares optimization, for the Wenner array. This involved calculation of synthetic apparent resistivity pseudosection data, which were then inverted and the model estimated from the inversion was compared with the original 2D model. The models examined include (i) horizontal layering, (ii) a vertical fault, (iii) a low‐resistivity fill within a high‐resistivity basement, and (iv) an upfaulted basement block beneath a conductive overburden. Over vertical structures, the resistivity models obtained from inversion are usually much sharper than the measured data. However, the inverted resistivities can be smaller than the lowest, or greater than the highest, true model resistivity. The substantial reduction generally recorded in the data misfit during the least‐squares inversion of 2D apparent resistivity data is not always accompanied by any noticeable reduction in the model misfit. Conversely, the model misfit may, for all practical purposes, remain invariant for successive iterations. It can also increase with the iteration number, especially where the resistivity contrast at the bedrock interface exceeds a factor of about 10; in such instances, the optimum model estimated from inversion is attained at a very low iteration number. The largest model misfit is encountered in the zone adjacent to a contact where there is a large change in the resistivity contrast. It is concluded that smooth inversion can provide only an approximate guide to the true geometry and true formation resistivity. 相似文献
3.
A 3D model of collected time-domain induced polarization (IP) and electrical resistivity tomography (ERT) data is compiled by geostatistical methods as well as studying spatial correlation among the database. Mesgaran copper deposit, located in Birjand eastern Iran, was chosen to compile and verify the model, leading to five parallel surveyed IP and ERT profiles with dipole–dipole arrays. The collected data were inverted, and then 2D models of IP and ER were prepared; also 3D inversion was done. Afterward, the 3D model has been built by geostatistical methods. Correspondingly, the anomalies threshold was detected by fractal methods and the estimation variance and Kriging efficiency were calculated to validate the modeling. The mineralization zones were determined according to the classified anomalies and those with the lowest error. Results indicated a high correlation between anomalies identified from the model and mineralization. The results made it possible to construct 3D models from surveyed 2D data with acceptable error level. 相似文献
4.
Out‐of‐plane effects in 2D borehole‐to‐surface resistivity tomography and applications in mineral exploration 
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下载免费PDF全文 In this paper, we discuss the effects of anomalous out‐of‐plane bodies in two‐dimensional (2D) borehole‐to‐surface electrical resistivity tomography with numerical resistivity modelling and synthetic inversion tests. The results of the two groups of synthetic resistivity model tests illustrate that anomalous bodies out of the plane of interest have an effect on two‐dimensional inversion and that the degree of influence of out‐of‐plane body on inverted images varies. The different influences are derived from two cases. One case is different resistivity models with the same electrode array, and the other case is the same resistivity model with different electrode arrays. Qualitative interpretation based on the inversion tests shows that we cannot find a reasonable electrode array to determine the best inverse solution and reveal the subsurface resistivity distribution for all types of geoelectrical models. Because of the three‐dimensional effect arising from neighbouring anomalous bodies, the qualitative interpretation of inverted images from the two‐dimensional inversion of electrical resistivity tomography data without prior information can be misleading. Two‐dimensional inversion with drilling data can decrease the three‐dimensional effect. We employed two‐ and three‐dimensional borehole‐to‐surface electrical resistivity tomography methods with a pole–pole array and a bipole–bipole array for mineral exploration at Abag Banner and Hexigten Banner in Inner Mongolia, China. Different inverse schemes were carried out for different cases. The subsurface resistivity distribution obtained from the two‐dimensional inversion of the field electrical resistivity tomography data with sufficient prior information, such as drilling data and other non‐electrical data, can better describe the actual geological situation. When there is not enough prior information to carry out constrained two‐dimensional inversion, the three‐dimensional electrical resistivity tomography survey is the better choice. 相似文献
5.
Use of VFSA for resolution, sensitivity and uncertainty analysis in 1D DC resistivity and IP inversion 总被引：1，自引：0，他引：1
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
6.
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
7.
EXAMPLES OF RESOLUTION IMPROVEMENT IN GEOELECTRICAL SOUNDINGS APPLIED TO GROUNDWATER INVESTIGATIONS1
STEWART K. SANDBERG 《Geophysical Prospecting》1993,41(2):207-227
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
8.
Global optimization with very fast simulated annealing (VFSA) in association with joint inversion is performed for 1D earth structures. The inherent problems of equivalence and suppression in electromagnetic (EM) and direct current (DC) resistivity methods are studied. Synthetic phase data from multifrequency sounding using a horizontal coplanar coil system and synthetic apparent resistivity data from Schlumberger DC resistivity measurements are inverted individually and jointly over different types of layered earth structures. Noisy data are also inverted. The study reveals that global optimization of individual data sets cannot solve inherent equivalence or suppression problems. Joint inversion of EM and DC measurements can overcome the problem of equivalence very well. However, a suppression problem cannot be solved even after combination of data sets. This study reveals that the K-type earth structure is easiest to resolve while the A-type is the most difficult. We also conclude that the equivalence associated with a thin resistive layer can be resolved better than that for a thin conducting layer. 相似文献
9.
地表起伏地形在野外矿产资源勘察中不可避免,其对直流电阻率法勘探影响巨大.近年来,电阻率三维正演取得诸多进展,特别是应用非结构网格我们能够进行任意复杂地形和几何模型的电阻率三维数值模拟,但面向实际应用的起伏地形下电阻率三维反演依然困难.本文基于非结构化四面体网格,并考虑到应用GPS/GNSS时,区域地球物理调查中可非规则布设测网的实际特点,实现了任意地形(平坦或起伏)条件下、任意布设的偶极-偶极视电阻率数据的不完全Gauss-Newton三维反演.合成数据的反演结果表明了方法的有效性,可应用于复杂野外环境下的三维电法勘探. 相似文献
10.
Interpretation of a single geophysical data set is not sufficient to get complete subsurface information. Cooperative or joint inversion of geophysical data sets is the preferred method for most case studies. In the present study, we present the results of the cooperative inversion approach of direct current resistivity and gravity data. The algorithm uses fuzzy c-means clustering to determine the petrophysical relationship between density and resistivity to obtain the similarity. Synthetic data set has demonstrated that the cooperative inversion approach can produce more reliable and better resistivity and density models of the subsurface as compared to those obtained through individual inversions. To utilize the presented cooperative inversion algorithm, the number of geologic units (number of clusters) in the study region must be known a priori. As a field study, the cooperative inversion approach was used to identify the extension of uranium-bearing target rock around the Beldih open cast mine. We noted the inconsistencies in both resistivity and density models obtained from the individual inversions. However, the presented cooperative inversion approach was able to produce similar resistivity and density models while maintaining the same error level of the respective individual inversions. We have considered four geologic units in the presented cooperative inversion as a field case study. We have also compared our cooperative results with drilled borehole and found to be a reliable tool to differentiate between the target rocks (kaolinite and quartz–magnetite–apatite rocks) and the ultramafic rock (host rock quartzite/alkaline granite). However, this study is subject to certain limitations such as the inability to differentiate between closely spaced kaolinite and quartz–magnetite–apatite rocks. 相似文献
11.
为了克服时间域航空电磁数据单点反演结果中常见的电阻率或层厚度横向突变造成数据难以解释的问题,通过引入双向约束实现航空电磁拟三维空间约束反演.除考虑沿测线方向相邻测点之间的横向约束外,同时还考虑了垂直测线方向测点在空间上的相互约束.为此,首先设计拟三维模型中固定层厚和可变层厚两种空间约束反演方案,然后通过在目标函数中引入沿测线和垂直测线方向上的模型参数约束矩阵,并使用L-BFGS算法使目标函数最小化,获得最优拟三维模型空间反演解.基于理论模型和实测数据反演,对单点反演与两种空间约束反演方案的有效性进行比较,证明本文空间约束反演算法对于噪声的压制效果好,反演的界面连续光滑,同时内存需求和反演时间少,是一种快速有效的反演策略. 相似文献
12.
One of the ways to improve the information content of a set of field data is that of combining the interpretation of disparate
data sets. Electromagnetic and direct current resistivity methods suffer from inherent equivalence problem. Application of
joint inversion for these measurements can overcome the problem of equivalence very well. In the present work, synthetic data
from vertical electrical sounding (VES) and horizontal coplanar low-frequency induction sounding (EMHD) are inverted individually
and jointly over different types of 1D earth structures. Global optimization with Monte Carlo Multistart algorithm was used
in the calculations. The results obtained from the inversions of synthetic data indicate that the joint inversion significantly
improves the solution reducing the ambiguity of the models. 相似文献
13.
Radio-magnetotelluric(RMT)是以无线电发射机为信号源的一种地球物理勘探方法,近年来被广泛应用于数米至数十米内的近地表工程和环境地球物理勘探.目前,各类电磁资料的反演均是以寻求满足目标拟合差的地下介质电阻率分布为目的.然而,对于勘探频率为10~300kHz的RMT数据,由介电常数所引起的波动场在总场中的比例可达20%以上,在这种情况下,忽略介电常数,仅通过电阻率参数的反演来进行数据拟合势必降低反演资料解释的准确性.为解决这一问题,本文研究了基于电阻率-介电常数的双参数同步反演算法.构建了一个全新的双参数目标函数,并推导了双参数反演迭代方程组;通过灵敏度分析,研究了电阻率和介电常数对正演响应的影响,并据此提出相对电导率的概念,统一了反演参数的灵敏度;通过理论模型分析了参考频率、双参数正则化因子对反演结果的影响,并给出了一般性的参数优选方案.此外,为了能够灵活处理复杂地形,本文采用非结构的正反演双网格进行模型离散,并通过局部加密技术保证反演的速度和精度.最后,对一带地形的理论模型分别进行了单参数和双参数反演,结果表明单参数反演无法正确反映出地电信息,而双参数反演能够准确得到异常的分布,验证了本文所开发的双参数反演程序的有效性. 相似文献
14.
In order to interpret field data from small-loop electromagnetic (EM) instruments with fixed source–receiver separation, 1D inversion method is commonly used due to its efficiency with regard to computation costs. This application of 1D inversion is based on the assumption that small-offset broadband EM signals are insensitive to lateral resistivity variation. However, this assumption can be false when isolated conductive bodies such as man-made objects are embedded in the earth. Thus, we need to clarify the applicability of the 1D inversion method for small-loop EM data. In order to systematically analyze this conventional inversion approach, we developed a 2D EM inversion algorithm and verified this algorithm with a synthetic EM data set. 1D and 2D inversions were applied to synthetic and field EM data sets. The comparison of these inversion results shows that the resistivity distribution of the subsurface constructed by the 1D inversion approach can be distorted when the earth contains man-made objects, because they induce drastic variation of the resistivity distribution. By analyzing the integrated sensitivity of the small-loop EM method, we found that this pitfall of 1D inversion may be caused by the considerable sensitivity of the small-loop EM responses to lateral resistivity variation. However, the application of our 2D inversion algorithm to synthetic and field EM data sets demonstrate that the pitfall of 1D inversion due to man-made objects can be successfully alleviated. Thus, 2D EM inversion is strongly recommended for detecting conductive isolated bodies, such as man-made objects, whereas this approach may not always be essential for interpreting the EM field data. 相似文献
15.
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
16.
Indrajit G Roy 《Geophysical Prospecting》1999,47(4):527-550
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
17.
Clay-rich till plains cover much of the UK. Such sites are attractive locations for landfills, since clay aquitards lower the risk of landfill leachate entering groundwater. However, such tills often contain sand and gravel bodies that can act as leachate flow routes. Such bodies may not be detected by conventional site investigation techniques such as drilling boreholes and trial pitting. A method of guided inversion, where a priori data are used to construct structural reference models for use in inverting electrical resistivity tomography data, was proposed as a tool to improve the detection of sand and gravel bodies within clay-rich till sequences.
Following a successful 2D guided inversion synthetic modelling study, a field study was undertaken. Wenner 2D electrical resistivity tomography lines, resistivity cone penetrometry bores and electromagnetic induction ground resistivity data were collected over a site on the East Yorkshire coast, England, where sand and gravel lenses were known to exist from cliff exposures. A number of equally valid geoelectrical models were constructed using the electromagnetic and resistivity cone data. These were used as structural reference models in the inversion of the resistivity tomography data. Blind inversion using an homogenous reference model was also carried out for comparison.
It was shown for the first time that the best solution model produced by 2D inversion of one data set with a range of structural reference models could be determined by using the l2 model misfit between the solution models and associated reference models (reference misfit) as a proxy for the l 2 misfit between the solution models and the synthetic model or 'best-guess' geoelectrical model (true misfit). The 2D methodology developed here is applicable in clay-rich till plains containing sand and gravel bodies throughout the UK. 相似文献
Following a successful 2D guided inversion synthetic modelling study, a field study was undertaken. Wenner 2D electrical resistivity tomography lines, resistivity cone penetrometry bores and electromagnetic induction ground resistivity data were collected over a site on the East Yorkshire coast, England, where sand and gravel lenses were known to exist from cliff exposures. A number of equally valid geoelectrical models were constructed using the electromagnetic and resistivity cone data. These were used as structural reference models in the inversion of the resistivity tomography data. Blind inversion using an homogenous reference model was also carried out for comparison.
It was shown for the first time that the best solution model produced by 2D inversion of one data set with a range of structural reference models could be determined by using the l
18.
We present a new, fast and versatile method, the lateral parameter correlation method, of invoking lateral smoothness in model sections of one-dimensional (1D) models. Modern, continuous electrical and electromagnetic methods are capable of recording very large data sets and except for a few cases, standard inversion methodology still relies on 1D models. In environments where the lateral rate of change of resistivity is small, 1D inversion can be justified but model sections of concatenated 1D models do not necessarily display the expected lateral smoothness.
The lateral parameter correlation method has three steps. First, all sounding data are inverted individually. Next, a laterally smooth version of each model parameter, one at a time, is found by solving a simple constrained inversion problem. Identity is postulated between the uncorrelated and correlated parameters and the equations are solved including a model covariance matrix. As a last step, all sounding data are inverted again to produce models that better fit the data, now subject to constraints by including the correlated parameter values as a priori values. Because the method separates the inversion from the correlation it is much faster than methods where the inversion and correlation are solved simultaneously, typically with a factor of 200–500.
Theoretical examples show that the method produces laterally smooth model sections where the main influence comes from the well-determined parameters in such a way that problems with equivalence and poor resolution are alleviated. A field example is presented, demonstrating the improved resolution obtained with the lateral parameter correlation method. The method is very flexible and is capable of coupling models from inversion of different data types and information from boreholes. 相似文献
The lateral parameter correlation method has three steps. First, all sounding data are inverted individually. Next, a laterally smooth version of each model parameter, one at a time, is found by solving a simple constrained inversion problem. Identity is postulated between the uncorrelated and correlated parameters and the equations are solved including a model covariance matrix. As a last step, all sounding data are inverted again to produce models that better fit the data, now subject to constraints by including the correlated parameter values as a priori values. Because the method separates the inversion from the correlation it is much faster than methods where the inversion and correlation are solved simultaneously, typically with a factor of 200–500.
Theoretical examples show that the method produces laterally smooth model sections where the main influence comes from the well-determined parameters in such a way that problems with equivalence and poor resolution are alleviated. A field example is presented, demonstrating the improved resolution obtained with the lateral parameter correlation method. The method is very flexible and is capable of coupling models from inversion of different data types and information from boreholes. 相似文献
19.
电阻率法和背景噪声法是通过获得地下介质的电阻率和速度参数的分布来探究地球内部物质分布的非均匀性特征,联合反演可以有效地发挥两种方法的优势,减小反演多解性.本文采用有限内存拟牛顿（L-BFGS）算法实现了电阻率法和背景噪声法的单方法三维反演,然后基于电阻率和速度模型结构耦合约束,采用交替迭代方式实现了电阻率法和背景噪声法的三维联合反演.通过设计规则体组合模型和不规则体组合模型进行理论模型合成数据三维反演试算,结果表明：联合反演可以获得同时满足数据拟合差和结构更为相似的速度-电阻率模型;联合反演可以压制背景噪声单方法反演出现的假异常,获得更精细的速度结构;联合反演获得的电阻率模型对倾斜异常体、高阻覆层下方异常体、圈闭的高/低阻体等边界信息有明显的提升,有效克服电阻率法单方法反演的局限,提高深部电阻率的分辨率. 相似文献
20.
The increased application of airborne electromagnetic surveys to hydrogeological studies is driving a demand for data that can consistently be inverted for accurate subsurface resistivity structure from the near surface to depths of several hundred metres. We present an evaluation of three commercial airborne electromagnetic systems over two test blocks in western Nebraska, USA. The selected test blocks are representative of shallow and deep alluvial aquifer systems with low groundwater salinity and an electrically conductive base of aquifer. The aquifer units show significant lithologic heterogeneity and include both modern and ancient river systems. We compared the various data sets to one another and inverted resistivity models to borehole lithology and to ground geophysical models. We find distinct differences among the airborne electromagnetic systems as regards the spatial resolution of models, the depth of investigation, and the ability to recover near‐surface resistivity variations. We further identify systematic biases in some data sets, which we attribute to incomplete or inexact calibration or compensation procedures. 相似文献