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Sharp spatially constrained inversion with applications to transient electromagnetic data 总被引：1，自引：0，他引：1 
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下载免费PDF全文 Gianluca Fiandaca Anders Vest Christiansen Casper Kirkegaard Esben Auken 《Geophysical Prospecting》2015,63(1):243-255
Time‐domain electromagnetic data are conveniently inverted by using smoothly varying 1D models with fixed vertical discretization. The vertical smoothness of the obtained models stems from the application of Occam‐type regularization constraints, which are meant to address the ill‐posedness of the problem. An important side effect of such regularization, however, is that horizontal layer boundaries can no longer be accurately reproduced as the model is required to be smooth. This issue can be overcome by inverting for fewer layers with variable thicknesses; nevertheless, to decide on a particular and constant number of layers for the parameterization of a large survey inversion can be equally problematic. Here, we present a focusing regularization technique to obtain the best of both methodologies. The new focusing approach allows for accurate reconstruction of resistivity distributions using a fixed vertical discretization while preserving the capability to reproduce horizontal boundaries. The formulation is flexible and can be coupled with traditional lateral/spatial smoothness constraints in order to resolve interfaces in stratified soils with no additional hypothesis about the number of layers. The method relies on minimizing the number of layers of non‐vanishing resistivity gradient, instead of minimizing the norm of the model variation itself. This approach ensures that the results are consistent with the measured data while favouring, at the same time, the retrieval of horizontal abrupt changes. In addition, the focusing regularization can also be applied in the horizontal direction in order to promote the reconstruction of lateral boundaries such as faults. We present the theoretical framework of our regularization methodology and illustrate its capabilities by means of both synthetic and field data sets. We further demonstrate how the concept has been integrated in our existing spatially constrained inversion formalism and show its application to large‐scale time‐domain electromagnetic data inversions. 相似文献
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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
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Kurt I. Srensen Flemming Effers Esben Auken Louise Pellerin 《Journal of Hydrology》2002,260(1-4):15-29
A field test and analysis method has been developed to estimate the vertical distribution of hydraulic conductivity in shallow unconsolidated aquifers. The field method uses fluid injection ports and pressure transducers in a hollow auger that measure the hydraulic head outside the auger at several distances from the injection point. A constant injection rate is maintained for a duration time sufficient for the system to become steady state. Exploiting the analogy between electrical resistivity in geophysics and hydraulic flow two methods are used to estimate conductivity with depth: a half-space model based on spherical flow from a point injection at each measurement site, and a one-dimensional inversion of an entire dataset.
The injection methodology, conducted in three separate drilling operations, was investigated for repeatability, reproducibility, linearity, and for different injection sources. Repeatability tests, conducted at 10 levels, demonstrated standard deviations of generally less than 10%. Reproducibility tests conducted in three, closely spaced drilling operations generally showed a standard deviation of less than 20%, which is probably due to lateral variations in hydraulic conductivity. Linearity tests, made to determine dependency on flow rates, showed no indication of a flow rate bias. In order to obtain estimates of the hydraulic conductivity by an independent means, a series of measurements were made by injecting water through screens installed at two separate depths in a monitoring pipe near the measurement site. These estimates differed from the corresponding estimates obtained by injection in the hollow auger by a factor of less than 3.5, which can be attributed to variations in geology and the inaccurate estimates of the distance between the measurement and the injection sites at depth. 相似文献
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Buried Quaternary valleys in Denmark are complex structures filled with various deposits consisting primarily of glacio-lacustrine clay, till and meltwater sand, and gravel. The valleys are important geophysical targets, because they often contain significant volumes of groundwater used for public water supply. About 700 km of buried valley structures have been imaged in the western part of Denmark by the transient electromagnetic (TEM) method. The ability to map the valleys depends primarily on valley geometry, infill architecture and the resistivity of the fill sediments as well as the substratum. One-dimensional (1-D) inversion models of the TEM soundings have been used to construct contour maps of 20 m average resistivities and depth to a good conductor, which provide images for geological interpretation. Images of buried valley morphology, fill properties, infill architecture, such as cut-and-fill structures, valley distribution and valley generations, are characterized for case studies from Hornsyld, Holstebro and the Vonsild/Agtrup areas of Denmark. 相似文献
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Dense profile-oriented resistivity data allows for 2D and 3D inversions. However, huge amounts of data make it practically impossible to do full 2D or 3D inversions on a routine basis. Therefore, a number of approximations have been suggested over the years to speed up computations. We suggest using a combination of Broyden's update on the Jacobian matrix with derivatives calculated using a 1D formulation on a parameterized 2D model of locally 1D layered models. The approximations bring down the effective number of 2D forward responses to a minimum, which again gives us the ability to invert very large sections. Broyden's update is not as useful with a parameterized problem as is the case with a smooth minimum structure problem that has been the usual application. 1D derivatives, however, seem to be very effective when initiating a full 2D solution with Broyden's update. We compare the different methods using two different kinds of data on two synthetic models and on two field examples. The most effective and reliable optimization combines 1D derivatives with a full 2D solution and Broyden's update. When using Broyden's update the Jacobian matrix needs to be reset every once in a while. We do this whenever the difference in data residual from the previous iteration is less than 5%. This combined inversion method reduces the computation time approximately a factor of 3 without losing model resolution. 相似文献
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Inversion of band-limited TEM responses 总被引：2，自引：0，他引：2
It is shown that the electromagnetic (EM) spectrum is characterized by strong amplitude-modulated transmitters operating in the target bandwidth of transient electromagnetic (TEM) measurements. As these transmitters cause significant noise in TEM soundings, it is mandatory to band-limit the input signals to improve the signal-to-noise ratio and thereby the depth of exploration. Band-limitation will distort the TEM responses, which leads to erroneous inversion results if the applied low-pass filters are not accounted for in the inversion scheme. We incorporate the low-pass filters in the inversion scheme and test the inversion approach on theoretical and field data. Inversion of band-limited theoretical responses results in recovery of erroneous resistivity models if the filters are not included in the inversion scheme. By contrast, inversion of band-limited theoretical and field data, for which the applied low-pass filters are included in the inversion scheme, leads to recovery of similar resistivity models, independent of the applied cut-off frequencies. 相似文献
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Two different airborne electromagnetic methods were applied in the same area: the frequency-domain helicopter-borne electromagnetic (HEM) system operated by the Federal Institute for Geosciences and Natural Resources, Germany, and the time-domain SkyTEM system of the HydroGeophysics Group at the University of Aarhus, Denmark. For verification of and comparison with the airborne methods, ground-based transient electromagnetics and 2-D resistivity surveying were carried out. The target of investigation was the Cuxhaven valley in Northern Germany, which is a significant local groundwater reservoir. The course of this buried valley was revealed by drillings and the shape was determined by reflection seismics at several cross sections.We applied electrical and electromagnetic methods to investigate the structure of the valley filling consisting of gravel, sand, silt and clay. The HEM survey clearly outlines a shallow conductor at about 20m depth and a deeper conductor below 40m depth inside the valley. This is confirmed by 2-D resistivity surveying and a drilling. The thickness of the deeper conductor, however, is not revealed due to the limited investigation depth of the HEM system. The SkyTEM survey does not resolve the shallow conductor, but it outlines the thickness of the deeper clay layer inside the valley and reveals a conductive layer at about 180m depth outside the valley. The SkyTEM results are very consistent with ground-based transient electromagnetic soundings.Airborne electromagnetic surveying in general has the advantage of fast resistivity mapping with high lateral resolution. The HEM system is cost-efficient and fast, but the more expensive and slower SkyTEM system provides a higher depth of investigation. Ground-based geophysical surveys are often more accurate, but they are definitively slower than airborne surveys. It depends on targets of interest, time, budget, and manpower available by which a method or combination of methods will be chosen. A combination of different methods is useful to obtain a detailed understanding of the subsurface resistivity distribution. 相似文献
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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
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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