共查询到20条相似文献，搜索用时 812 毫秒
1.
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
2.
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
3.
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
4.
We propose a Bayesian fusion approach to integrate multiple geophysical datasets with different coverage and sensitivity. The fusion strategy is based on the capability of various geophysical methods to provide enough resolution to identify either subsurface material parameters or subsurface structure, or both. We focus on electrical resistivity as the target material parameter and electrical resistivity tomography (ERT), electromagnetic induction (EMI), and ground penetrating radar (GPR) as the set of geophysical methods. However, extending the approach to different sets of geophysical parameters and methods is straightforward. Different geophysical datasets are entered into a trans-dimensional Markov chain Monte Carlo (McMC) search-based joint inversion algorithm. The trans-dimensional property of the McMC algorithm allows dynamic parameterisation of the model space, which in turn helps to avoid bias of the post-inversion results towards a particular model. Given that we are attempting to develop an approach that has practical potential, we discretize the subsurface into an array of one-dimensional earth-models. Accordingly, the ERT data that are collected by using two-dimensional acquisition geometry are re-casted to a set of equivalent vertical electric soundings. Different data are inverted either individually or jointly to estimate one-dimensional subsurface models at discrete locations. We use Shannon's information measure to quantify the information obtained from the inversion of different combinations of geophysical datasets. Information from multiple methods is brought together via introducing joint likelihood function and/or constraining the prior information. A Bayesian maximum entropy approach is used for spatial fusion of spatially dispersed estimated one-dimensional models and mapping of the target parameter. We illustrate the approach with a synthetic dataset and then apply it to a field dataset. We show that the proposed fusion strategy is successful not only in enhancing the subsurface information but also as a survey design tool to identify the appropriate combination of the geophysical tools and show whether application of an individual method for further investigation of a specific site is beneficial. 相似文献
5.
Irfan Akca 《Acta Geophysica》2016,64(2):443-462
ELRIS2D is an open source code written in MATLAB for the two-dimensional inversion of direct current resistivity (DCR) and time domain induced polarization (IP) data. The user interface of the program is designed for functionality and ease of use. All available settings of the program can be reached from the main window. The subsurface is discre-tized using a hybrid mesh generated by the combination of structured and unstructured meshes, which reduces the computational cost of the whole inversion procedure. The inversion routine is based on the smoothness constrained least squares method. In order to verify the program, responses of two test models and field data sets were inverted. The models inverted from the synthetic data sets are consistent with the original test models in both DC resistivity and IP cases. A field data set acquired in an archaeological site is also used for the verification of outcomes of the program in comparison with the excavation results. 相似文献
6.
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
7.
Laust B. Pedersen Lena Persson Mehrdad Bastani Sören Byström 《Journal of Applied Geophysics》2009,67(3):250-258
Airborne VLF data are routinely collected by The Geological Survey of Sweden (SGU) as part of its bedrock mapping programme. In this paper we demonstrate that the novel Tensor VLF technique developed at Uppsala University and SGU can provide useful qualitative and quantitative information about the electrical conductivity distribution in the upper few hundred meters. Single transmitter scalar VLF maps emphasize those conductive structures that have dominant strikes in the direction of the transmitter. The tensor tipper (essentially the vertical magnetic field from currents along the strike direction) calculated from multiple transmitters is dependent only upon the underlying conductivity structure. Transformation of the tipper into the peaker (the horizontal divergence) has proven to enhance the lateral resolution while the transformation to the apparent resistivity can be used to discriminate different rock types. Two case histories from the application of VLF data are presented in this study. Two dimensional structures can be quantitatively modelled by modern inversion methods developed originally for deep electromagnetic MT soundings. Direct inversion of the real and imaginary parts of the tipper provides more quantitative information about the subsurface resistivity distribution. 相似文献
8.
地电体对频率域电磁波激发源的响应为电磁感应和激电效应的综合响应.传统CSAMT法进行数据正反演时认为大地介质电阻率是与频率无关的实数,而实际上因为激电效应,地下可极化体的电阻率是一个与频率相关的复数.为推进二者总体响应研究,并扩展激电法的应用范围,同时提高电磁法勘探的精度,本文基于Dias模型,以复电阻率代替不考虑地电体极化效应的直流电阻率,对CSAMT场源一维层状模型进行了正演模拟,为提取CSAMT信号中所含激电信息提供理论基础.结果表明,考虑激电参数后,视电阻率及相位响应曲线出现明显异常（包括远场、过渡场、近场）;极化前后振幅比值异常峰值、相位差值异常峰值可直观体现激电异常;异常峰值与极化层层厚、埋深以及电阻率变化有连续的对应关系.认为从频率域电磁法信号中提取激电信息有乐观的前景. 相似文献
9.
Bernhard Siemon Esben Auken Anders Vest Christiansen 《Journal of Applied Geophysics》2009,67(3):259-268
Helicopter-borne frequency-domain electromagnetic (HEM) surveys are used for fast high-resolution, three-dimensional resistivity mapping. Standard interpretation tools are often based on layered earth inversion procedures which, in general, explain the HEM data sufficiently. As a HEM system is moved while measuring, noise on the data is a common problem. Generally, noisy data will be smoothed prior to inversion using appropriate low-pass filters and consequently information may be lost.For the first time the laterally constrained inversion (LCI) technique has been applied to HEM data combined with the automatic generation of dynamic starting models. The latter is important because it takes the penetration depth of the electromagnetic fields, which can heavily vary in survey areas with different geological settings, into account. The LCI technique, which has been applied to diverse airborne and ground geophysical data sets, has proven to be able to improve the HEM inversion results of layered earth structures. Although single-site 1-D inversion is generally faster and — in case of strong lateral resistivity variations — more flexible, LCI produces resistivity — depth sections which are nearly identical to those derived from noise-free data.The LCI results are compared with standard single-site Marquardt–Levenberg inversion procedures on the basis of synthetic data as well as field data. The model chosen for the generation of synthetic data represents a layered earth structure having an inhomogeneous top layer in order to study the influence of shallow resistivity variations on the resolution of deep horizontal conductors in one-dimensional inversion results. The field data example comprises a wide resistivity range in a sedimentary as well as hard-rock environment.If a sufficient resistivity contrast between air and subsurface exists, the LCI technique is also very useful in correcting for incorrect system altitude measurements by using the altitude as a constrained inversion parameter. 相似文献
10.
Daan Herckenrath Nick Odlum Vanessa Nenna Rosemary Knight Esben Auken Peter Bauer‐Gottwein 《Ground water》2013,51(3):385-397
Salt water intrusion models are commonly used to support groundwater resource management in coastal aquifers. Concentration data used for model calibration are often sparse and limited in spatial extent. With airborne and ground‐based electromagnetic surveys, electrical resistivity models can be obtained to provide high‐resolution three‐dimensional models of subsurface resistivity variations that can be related to geology and salt concentrations on a regional scale. Several previous studies have calibrated salt water intrusion models with geophysical data, but are typically limited to the use of the inverted electrical resistivity models without considering the measured geophysical data directly. This induces a number of errors related to inconsistent scales between the geophysical and hydrologic models and the applied regularization constraints in the geophysical inversion. To overcome these errors, we perform a coupled hydrogeophysical inversion (CHI) in which we use a salt water intrusion model to interpret the geophysical data and guide the geophysical inversion. We refer to this methodology as a Coupled Hydrogeophysical Inversion‐State (CHI‐S), in which simulated salt concentrations are transformed to an electrical resistivity model, after which a geophysical forward response is calculated and compared with the measured geophysical data. This approach was applied for a field site in Santa Cruz County, California, where a time‐domain electromagnetic (TDEM) dataset was collected. For this location, a simple two‐dimensional cross‐sectional salt water intrusion model was developed, for which we estimated five uniform aquifer properties, incorporating the porosity that was also part of the employed petrophysical relationship. In addition, one geophysical parameter was estimated. The six parameters could be resolved well by fitting more than 300 apparent resistivities that were comprised by the TDEM dataset. Except for three sounding locations, all the TDEM data could be fitted close to a root‐mean‐square error of 1. Possible explanations for the poor fit of these soundings are the assumption of spatial uniformity, fixed boundary conditions and the neglecting of 3D effects in the groundwater model and the TDEM forward responses. 相似文献
11.
12.
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
13.
E. SZARANIEC 《Geophysical Prospecting》1982,30(6):850-854
Seismic dynamic deconvolution is the mathematical basis on which a degree of unification in different prospecting methods is possible, relative to the parameter identification in horizontally stratified media. There is a basic structure which has some immediate applications to the inversion of resistivity data and possibly to other problems. For resistivity soundings there exists a key equation which is parallel to the energy conservation law in the theory of synthetic seismograms. 相似文献
14.
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
15.
HANS A. MEINARDUS 《Geophysical Prospecting》1970,18(3):415-433
The digital computer technique described for interpreting resistivity soundings over a horizontally stratified earth requires two steps. First, the kernel function is evaluated numerically from the inverse Hankel transform of the observed apparent resistivity curve. Special attention is given to the inversion of resistivity data recorded over a section with a resistant basement. The second step consists in the least-squares estimation of layer resistivities and thicknesses from the kernel function. For the case of S or T-equivalent beds only one layer-parameter can be obtained, either the longitudinal conductance, or the transverse resistance respectively. Two examples given in the paper show that a wide tolerance is permitted for Choosing the starting values of the layering parameters in the successive approximation procedure. Another important feature for practical applications is good convergence of the iterations. The method is probably best suited for interpreting profiles of electrical soundings with the purpose of mapping approximately horizontal interfaces at depth. 相似文献
16.
D. PATELLA 《Geophysical Prospecting》1979,27(3):628-639
This paper deals with a new method of quantitative interpretation of induced polarization soundings in the frequency-domain. From the general expression of the apparent frequency-effect for soundings carried out on a multi-layered earth the application of Hankel's inversion theorem allows to introduce a new function, called here the “frequency-effect transform”. The new interpretation method consists of two steps: 1) the inversion of field data to obtain the frequency-effect transform graph and 2) the analysis of this graph to derive the layering parameters. The first step is performed by means of a slightly revised version of a simple numerical procedure, previously suggested by the author for the inversion of d.c. resistivity sounding data. The second step is carried out by a complete curve-matching procedure, applied directly on the transform graph. This implies suitable master curves, whose preparation doesn't meet all the mathematical difficulties which are present when preparing master curves of the apparent frequency-effect function. 相似文献
17.
Airborne electromagnetic (AEM) surveys are currently being flown over populated areas and applied to detailed problems using high flight line densities. Interpretation information is supplied through a model of the subsurface resistivity distribution. Theoretical and survey data are used here to study the character and reliability of such models. Although the survey data were obtained using a fixed-wing system, the corresponding associations with helicopter, towed-bird systems are discussed. Both Fraser half-space and 1D inversion techniques are considered in relation to their ability to distinguish geological, cultural and environmental influences on the survey data. Fraser half-space modelling provides the dual interpretation parameters of apparent resistivity and apparent depth at each operational frequency. The apparent resistivity was found to be a remarkably stable parameter and appears robust to the presence of a variety of at-surface cultural features. Such features provide both incorrect altitude data and multidimensional influences. Their influences are observed most strongly in the joint estimate of apparent depth and this accounts for the stability of the apparent resistivity. Positive apparent depths, in the example data, result from underestimated altitude measurements. It is demonstrated that increasingly negative apparent depths are associated with increasing misfits between a 1D model and the data. Centroid depth calculations, which are a transform of the Fraser half-space parameters, provide an example of the detection of non-1D influences on data obtained above a populated area. 1D inversion of both theoretical and survey data is examined. The simplest use of the 1D inversion method is in providing an estimate of a half-space resistivity. This can be undertaken prior to multilayer inversion as an initial assessment. Underestimated altitude measurements also enter the problem and, in keeping with the Fraser pseudo-layer concept, an at-surface highly resistive layer of variable thickness can be usefully introduced as a constrained parameter. It is clearly difficult to ascribe levels of significance to a ‘measure’ of misfit contained in a negative apparent depth with the dimensions of metres. The reliability of 1D models is better assessed using a formal misfit parameter. With the misfit parameter in place, the example data suggest that the 1D inversion methods provide reliable apparent resistivity values with a higher resolution than the equivalent information from the Fraser half-space estimates. 相似文献
18.
Piecewise 1D laterally constrained inversion of resistivity data 总被引：1，自引：0，他引：1
Esben Auken ers V. Christiansen Bo H. Jacobsen Nikolaj Foged Kurt I. Sørensen 《Geophysical Prospecting》2005,53(4):497-506
In a sedimentary environment, layered models are often capable of representing the actual geology more accurately than smooth minimum structure models. Furthermore, interval thicknesses and resistivities are often the parameters to which non‐geophysicist experts can relate and base decisions on when using them in waste site remediation, groundwater modelling and physical planning. We present a laterally constrained inversion scheme for continuous resistivity data based on a layered earth model (1D). All 1D data sets and models are inverted as one system, producing layered sections with lateral smooth transitions. The models are regularized through laterally equal constraints that tie interface depths and resistivities of adjacent layers. Prior information, e.g. originating from electric logs, migrates through the lateral constraints to the adjacent models, making resolution of equivalences possible to some extent. Information from areas with well‐resolved parameters will migrate through the constraints in a similar way to help resolve the poorly constrained parameters. The estimated model is complemented by a full sensitivity analysis of the model parameters, supporting quantitative evaluation of the inversion result. Examples from synthetic 2D models show that the model recognition of a sublayered 2D wedge model is improved using the laterally constrained inversion approach when compared with a section of combined 1D models and when compared with a 2D minimum structure inversion. Case histories with data from two different continuous DC systems support the conclusions drawn from the synthetic example. 相似文献
19.
Inversion of resistivity in Magnetic Resonance Sounding 总被引：3，自引：0，他引：3
Magnetic Resonance Sounding (MRS, or Surface Nuclear Magnetic Resonance - SNMR) is used for groundwater exploration and aquifer characterization. Since this is an electromagnetic method, the excitation magnetic field depends on the resistivity of the subsurface. Therefore, the resistivity has to be taken into account in the inversion: either as a priori information or as an inversion parameter during the inversion process, as introduced in the presented paper. Studies with synthetic data show that water content and resistivity can be resolved for a low resistive aquifer even using only the amplitude of the MRS signal. However, the inversion result can be significantly improved using amplitude and phase of the MRS signal. The successful implementation of the inversion for field data shows that the resistivities derived from MRS are comparable to those from conventional geoelectric methods such as DC resistivity and transient electromagnetic. By having information about both the resistivity and the water content, MRS inversions give information about the quality of the water in the aquifer. This is of utmost interest in hydrogeological studies as this specific information cannot be determined solely by geoelectric measurements, due to the nonunique dependence of resistivity on water content and salinity. 相似文献
20.
M. Poddar 《Pure and Applied Geophysics》1996,147(3):551-566
There is growing interest in the use of transient electromagnetic (TEM) sounding for shallow geotechnical, environmental and groundwater investigations. Two commonly used transmitterreceiver configurations for TEM sounding are 1) loop-loop or its variation, in-loop configuration and 2) wire-loop configuration. The less common configuration of a horizontal electric dipole (HED) transmitter and receiver is treated in this study and called wire-wire configuration.Two important problems of shallow investigation in hard and soft rocks respectively are, defining 1) a fractured/fissured zone of medium resistivity, sandwiched between an overlying surface weathered rock of low resistivity and an underlying fresh compact rock of high resistivity and 2) a body of resistive sand buried in conductive clay. Lateral change in the middle layer resistivity is modeled by including a 3-D body of anomalous resistivity. The effect of perturbing the resistivity of the 3-D inclusion and the host middle layer for the wire-wire configuration is compared with that of the commonly used loop-loop configuration. The wire-wire configuration is found more sensitive to the model perturbations than the loop-loop configuration.1-D inversion of synthetic 1-D data sets for the wire-wire configuration finds resolution and estimation errors to be less than 10 percent for all the model parameters. For 3-D models, 1-D inversion results give a resolution error of 10 percent or less for the depth to, resistivity and thickness of, the 3-D inclusion. The estimate is within 10 percent of the true value for the first parameter but 40 percent for the other two. Resolution as well as estimation of the basement resistivity is always very poor.Using the wire-wire configuration, it is theoretically possible to define a buried resistive layer and any lateral change in its resistivity, subject to the above limitations of 1-D inversion. However, the basement resistivity cannot be estimated with reasonable accuracy in the presence of a lateral inhomogeneity in the overlying layer. 相似文献