共查询到20条相似文献，搜索用时 500 毫秒
1.
Ahmad Neyamadpour W. A. T. Wan Abdullah Samsudin Taib 《Studia Geophysica et Geodaetica》2010,54(2):299-311
The objective of this paper is to investigate the applicability of four-electrode arrays in 3D electrical resistivity imaging
survey. A 3D resistivity imaging survey was carried out along fourteen parallel lines using dipole-dipole, Wenner-Schlumberger,
and Wenner arrays with 2 m minimum electrode spacings. Roll-along measurements using a line spacing of 1 m were carried out
covering a grid of 20 × 14 electrodes. The 3D least squares algorithm, based on the robust inversion method, was used in the
inversion of the 3D apparent resistivity data sets. The results show that the 3D electrical resistivity imaging survey using
the Wenner-Schlumberger and the dipole-dipole arrays, or the Wenner and the dipole-dipole arrays, in combination with an appropriate
3D inversion method, can be highly useful when the site conditions do not allow using the pole-pole or pole-dipole arrays. 相似文献
2.
Numerical simulations are used to compare the resolution and efficiency of 2D resistivity imaging surveys for 10 electrode arrays. The arrays analysed include pole‐pole (PP), pole‐dipole (PD), half‐Wenner (HW), Wenner‐α (WN), Schlumberger (SC), dipole‐dipole (DD), Wenner‐β (WB), γ‐array (GM), multiple or moving gradient array (GD) and midpoint‐potential‐referred measurement (MPR) arrays. Five synthetic geological models, simulating a buried channel, a narrow conductive dike, a narrow resistive dike, dipping blocks and covered waste ponds, were used to examine the surveying efficiency (anomaly effects, signal‐to‐noise ratios) and the imaging capabilities of these arrays. The responses to variations in the data density and noise sensitivities of these electrode configurations were also investigated using robust (L1‐norm) inversion and smoothness‐constrained least‐squares (L2‐norm) inversion for the five synthetic models. The results show the following. (i) GM and WN are less contaminated by noise than the other electrode arrays. (ii) The relative anomaly effects for the different arrays vary with the geological models. However, the relatively high anomaly effects of PP, GM and WB surveys do not always give a high‐resolution image. PD, DD and GD can yield better resolution images than GM, PP, WN and WB, although they are more susceptible to noise contamination. SC is also a strong candidate but is expected to give more edge effects. (iii) The imaging quality of these arrays is relatively robust with respect to reductions in the data density of a multi‐electrode layout within the tested ranges. (iv) The robust inversion generally gives better imaging results than the L2‐norm inversion, especially with noisy data, except for the dipping block structure presented here. (v) GD and MPR are well suited to multichannel surveying and GD may produce images that are comparable to those obtained with DD and PD. Accordingly, the GD, PD, DD and SC arrays are strongly recommended for 2D resistivity imaging, where the final choice will be determined by the expected geology, the purpose of the survey and logistical considerations. 相似文献
3.
In this paper we analyze the onsite characterization of a geosynthetic clay liner (GCL) that serves to ensure the impermeability of a landfill cap by DC electrical methods. The imaging of the GCL geoelectrical properties is a challenging problem because it is a very thin (between 4 and 7 mm thick) and resistive layer (from 100,000 to 2,000,000 Ω·m) depending on meteorological conditions and aging. We compare results obtained using electrical resistivity tomography (ERT) using two different kinds of arrays (dipole–dipole DD and Wenner–Schlumberger) on an experimental site with engineered defects. To confirm these results and to find the real onsite GCL resistivity we have performed sampling of the posterior distribution of this parameter using vertical electrical sounding (VES) inversions. Different VES methods were extracted from ERT with DD array and converted into a Schlumberger array.As a main conclusion the dipole–dipole array provides a better resistivity resolution of the defects than the Wenner–Schlumberger array. On ERT images, the defect detection seems to be impossible if the GCL has very high resistivity, as it happened when it was put in place. Taking into account the equivalence rules, the inversions are in both cases (ERT and VES) compatible. The GCL resistivity estimated from PSO (particle swarm optimization) varies from 3.0 105 to 1.106 Ω·m depending on saturation conditions during the twenty first months of its placing. Then, the resistivity dropped to 4.104–9.104 Ω·m, indicating a probable chemical damage of the GCL due to aging. Finally the fact that the VES inversions are solved via PSO sampling allows for the detection of a very thin and resistive layer and opens the possibility of performing micro VES surveys along the landfill to detect possible GCL defects. 相似文献
4.
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
5.
Out‐of‐plane effects in 2D borehole‐to‐surface resistivity tomography and applications in mineral exploration 
下载免费PDF全文
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
6.
Abstract A resistivity survey in Wenner arrangement has been conducted in the water-table aquifer in the eastern part of the Coastal Area of Belgium. Bore holes have been drilled to test the geoelectrical data and also to collect water samples. The chemical characteristics and the distribution of different water types explain the hydrochemistry of the water-table aquifer. The fresh-/brackish-water boundary as determined by the resistivity survey has been expressed in terms of total dissolved-solids content. 相似文献
7.
Wm. MANSFIELD ADAMS 《Geophysical Prospecting》1970,18(Z1):728-737
In order to locate relatively optimum sites for drilling exploratory holes for fresh water, an electrical resistivity survey was conducted along the new Mahukona-Kawaihae Road on the west flank of the Kohala Mountain. Two resistivity soundings made at the same stations, using the Schlumberger electrode configuration, determined an a spacing of 275 feet for horizontal profiling with the Wenner array. The correlation coefficient of the elevation to profile data was 0.41. A procedure for removing elevation effect from observed apparent resistivity was developed. Based on the reduced resistivity profile, four relatively optimum sites for additional exploration, such as by drilling, are specified. There is no specific interpretation of the data that can definitely indicate the occurrence of large underground reservoirs of fresh water anywhere along the profile. This is because the interpretation of horizontal profiling data is essentially relative and not absolute. 相似文献
8.
TSVI MEIDAV 《Geophysical Prospecting》1970,18(4):550-563
A number of electrical resistivity arrays are available to the exploration geophysicist in the conduct of vertical or horizontal profiling. The advantage of using central-type arrays which produce large potential drops, such as the Wenner or the Schlumberger, must be weighed against the ease of acentral arrays such as the polar and equatorial arrays. A series of nomograms has been designed to provide a means of rapid calculation of the potential drop to be obtained by any of the various central and acentral arrays, as a function of apparent resistivity, electrode spacings and available transmitter power. The same nomograms may also be used for approximate computation of the apparent resistivities in routine surveys. However, the accuracy of resistivity calculation is directly related to the accuracy of drawing lines between the scales and hence is rather limited in reduced-size nomograms in this paper. 相似文献
9.
Electrical imaging provides important subsurface information for the construction of hypervelocity impact models. We here provide an overview and evaluation of the current electrical imaging methods used in impact cratering studies. Although apparent resistivity models are commonly used in the geoelectrical imaging of impact structures, the reliability of these models has not hitherto been determined. In order to assess these imaging approaches in impact cratering, we investigate for the first time the discrepancies between the apparent resistivity and true resistivity models of an impact structure. To this end, we present (1) a new true resistivity model of the Araguainha impact structure in central Brazil by applying L2-norm inversion to previously published data, (2) apparent resistivity model of the impact structure, and (3) models obtained from different stages of the iterative tomographic inversions. Our results show that changes in vertical resistivity gradient are significantly better defined in the true resistivity models than in the apparent resistivity model. On the basis of these results, we outline a new approach that true resistivity models can be effectively assessed by applying both L1- and L2-norm inversion schemes together with the monitoring of intermediate models from iterative inversion. The results of our study highlight the importance of tomographic inversion of resistivity data in impact cratering studies, and they provide a data modeling framework and foundation for cost-effective subsurface imaging of impact structures in the future. 相似文献
10.
There have been major improvements in instrumentation, field survey design and data inversion techniques for the geoelectrical method over the past 25 years. Multi-electrode and multi-channel systems have made it possible to conduct large 2-D, 3-D and even 4-D surveys efficiently to resolve complex geological structures that were not possible with traditional 1-D surveys. Continued developments in computer technology, as well as fast data inversion techniques and software, have made it possible to carry out the interpretation on commonly available microcomputers. Multi-dimensional geoelectrical surveys are now widely used in environmental, engineering, hydrological and mining applications. 3-D surveys play an increasingly important role in very complex areas where 2-D models suffer from artifacts due to off-line structures. Large areas on land and water can be surveyed rapidly with computerized dynamic towed resistivity acquisition systems. The use of existing metallic wells as long electrodes has improved the detection of targets in areas where they are masked by subsurface infrastructure. A number of PC controlled monitoring systems are also available to measure and detect temporal changes in the subsurface. There have been significant advancements in techniques to automatically generate optimized electrodes array configurations that have better resolution and depth of investigation than traditional arrays. Other areas of active development include the translation of electrical values into geological parameters such as clay and moisture content, new types of sensors, estimation of fluid or ground movement from time-lapse images and joint inversion techniques. In this paper, we investigate the recent developments in geoelectrical imaging and provide a brief look into the future of where the science may be heading. 相似文献
11.
The paper focuses on defining the performance and limits of ERI in the detection and sedimentary characterization of near-bottom thin layers. The analysis of the resolution of floating and submerged cables, and the effect of the accuracy of a priori information (resistivity and thickness) in the data inversion, is based on theory, models and actual data. Theoretical models show that the actual reconstruction of the near water-bottom sediments, in terms of geometry and resistivity, can be obtained only with the submerged cable, however, the data, unlike that acquired with the floating cable, require a priori information on water resistivity and thickness for the data inversion. Theoretical forward models based on wrong a priori water thickness and resistivity information influence the inverted model in different ways, depending on the under- and over-estimation of water resistivity and thickness, and the resistivity contrast of the water–solid layer; however a water–solid resistivity contrast of less than 2 and within 10% of error in water resistivity has no effect. Overestimating water resistivity depicts a ground similar to the actual ground in terms of resistivity, more so than the underestimation of water resistivity. Moreover, the data inversion is less influenced by water parameter error in the case of low resistivity contrast in the water–solid layer, than it is for high resistivity contrast. Wenner and Schlumberger arrays give comparable results, while a dipole–dipole array seems to be more sensitive to the accuracy of apparent resistivity measurements and a priori information on water.The theoretical considerations were validated by actual data acquired with a submerged cable on the Tiber River. The study has shown that if highly accurate measurements are made of water thickness and resistivity, then electrical resistivity imaging from the submerged cable can be used in addition to, or even to substitute, seismic data for the reconstruction of the features and sedimentary characterization of near-bed sediments where seismic data fail to give a suitable resolution. 相似文献
12.
Youcef Meheni Roger Guérin Yves Benderitter Alain Tabbagh 《Journal of Applied Geophysics》1996,34(4):255-269
Resistivity prospecting is the main tool used to investigate the shallow structure of the ground. A series of new techniques for determining the 2-D and 3-D geometry of the ground is now finding increasing use, but the light and simple Wenner prospecting technique remains a practical and efficient tool for rapidly mapping lateral variations in resistivity. When the resistivity changes are smooth, 1-D modelling can be used to interpret the data, and the criteria governing this approximation can be defined from synthetic data generated by a 3-D slab-model. For a Wenner array, two quadripole configurations can be used, Normal and Dipole-Dipole. For these two configurations the width of the transition zone, the apparent anisotropy effect and the precision of the resistivity values recovered from 1-D inversion differ. However the simultaneous inversion of both sets of data gives better results than for either configuration by itself. Two examples illustrate that in geological contexts where the thickness of the weathered zone causes the changes in the apparent resistivity value, this parameter can be recovered from 1-D inversion. 相似文献
13.
The surface resistivity method has been used to study a few exposed coal seams located in the northwestern part of the Raniganj Coalfield (belonging to the Damodar Valley Gondwana basin), India. Different electrode configurations, viz., Wenner, two-electrode and half-Schlumberger, have been used with different electrode spacings in horizontal profiling. The vertical distribution of resistivity has been studied using Schlumberger configuration at different locations along the profile. Laboratory studies of resistivity (at partial to full water saturation conditions) and porosity of different coal, shaly sandstone and sandstone samples of the survey area had already been carried out before the field survey. The results indicated the presence of a good resistivity contrast between the coal seams and the surrounding formations. The field results did not bear this out: the resistivity responses of the coal formations on the profiles and sounding curves are not as clear as one would expect for such high contents. The Wenner profiles show a broad resistivity anomaly over the coal seams. Two-electrode profiles are less noisy than Wenner profiles. Sharp peaks have been observed over the coal seams. The half-Schlumberger configuration seems the best: all the coal seams and their edges can be accurately outlined on the resistivity curves. Borehole data close to the profile have been used for correlating the field results. There is good agreement with vertical electrical soundings. 相似文献
14.
2D电阻率成像技术近年来被广泛应用于工程、水文、环境和矿产等领域,在实际应用中它具有多种的装置类型,不同的装置类型对特定的地质情况有不同的应用效果.本文通过采用Wenner、Wenner-Schlumberger和dipole-dipole三种排列装置在一个水平和一个垂直模型上正演模拟和块反演,揭示了不同的排列装置在水平结构和垂直结构的异常响应,并对高阻体和低阻体进行了模拟.结果显示当采用Wenner,Wenner-Schlumberger和dipole-dipole数据采集技术时,不同的模型结构异常响应有明显的不同,三种排列类型对地下低阻体的分辨能力均高于高阻体,Wenner装置和dipole-dipole装置分别对水平层状结构和垂直结构有较好的分辨力,wenner-Schlumberger装置对水平层状结构有好的分辨力,对垂直结构有中等的分辨能力. 相似文献
15.
电阻率层析成像是一种广泛应用在水文、考古和地质等浅地表勘探领域的地球物理方法。为了增强电阻率层析成像的分辨率、应对复杂的地质问题,本文提出基于雅可比矩阵的不同电极阵列直流电阻率数据的加权联合反演算法,并以温纳和偶极-偶极电极阵列数据为例,在理论模型和古墓探测的野外实例中测试该算法的有效性。结果表明,加权联合反演结果的横向和纵向分辨率都优于单一电极阵列的反演结果,并在实例中缓解“U形”电极阵列的固有缺陷、减少反演模糊性、更好地约束墓室宽度的反演结果。 相似文献
16.
M. E. Sholpo 《Izvestiya Physics of the Solid Earth》2013,49(1):113-119
The sensitivity of transversal apparent resistivity to the changes in the electrical resistivity of elements of a two-dimensional (2D) geoelectrical structure is studied by numerical modeling. This sensitivity is found to have a series of specific features, due to which the monitoring of transversal apparent resistivity can serve as a helpful addition to the monitoring of longitudinal apparent resistivity to trace the dynamics of subsurface and shallow crustal elements of the medium. It is shown that the method previously suggested for the inversion of relative changes in apparent resistivity into relative changes in electrical resistivities of the elements of the geoelectrical structure is applicable to the transversal electrical resistivity. 相似文献
17.
Henri Robain Marc Descloitres Michel Ritz Quantin Yene Atangana 《Journal of Applied Geophysics》1996,34(4):237-253
Resistivity investigations were carried out on an elementary watershed in SW Cameroon, firstly to assess the applicability of direct-current (DC) resistivity methods to solve various pedological problems in intertropical regions, and subsequently to determine the relationships between electrical resistivities and pedological properties of lateritic soil systems. The survey included measurements in pits with a small Wenner fixed-spacing array (SWA), vertical electrical soundings (VES) and vertical electrical “quick soundings” (VEQS) both using the Schlumberger configuration. The VES data were interpreted using a conventional multilayer inversion program to obtain best-fit models. Constraints to the interpretation of these data were provided by SWA and pedological information from existing observation pits. The results of the interpretation reveal five distinct geoelectrical layers overlying a resistive bedrock. The first is a thin organo-mineral upper layer with low resistivities in the range 250–450 Ωm. The second layer corresponds to micro-aggregated clayey materials and is more resistive (1300–1800 Ωm). The third represents the main part of ferruginous materials and is even more resistive (2000–4500 Ωm). The fourth corresponds to unsaturated saprolite and the last to saturated saprolite (ground water) with resistivities ranging from 800 to 1500 Ωm and from 150 to 250 Ωm, respectively. Estimates of soil volumes for the entire study area were obtained from VEQS interpretations. Most of the soil cover corresponds to saprolite (74%, being saturated by ground water), while topsoil and ferruginous materials represent 14 and 12%, respectively. Finally, geophysical results based upon 1-D inversion provide a satisfactory approximation of the various lateritic components' 3-D geometry over the watershed. The study provides original quantitative results concerning the behaviour of intertropical soil systems as well as some geomorphological keys for soil mapping at a regional scale. 相似文献
18.
Albert Casas Pietro L. Cosentino Gianluca Fiandaca Mahjoub Himi Josep M. Macias Raffaele Martorana Andreu Muñoz Lluís Rivero Roger Sala Imma Teixell 《Surveys in Geophysics》2018,39(6):1107-1124
An integrated geophysical survey has been conducted at the Tarragona’s Cathedral (Catalonia, NE Spain) with the aim to confirm the potential occurrence of archaeological remains of the Roman Temple dedicated to the Emperor Augustus. Many hypotheses have been proposed about its possible location, the last ones regarding the inner part of the Cathedral, which is one of the most renowned temples of Spain (twelfth century) evolving from Romanesque to Gothic styles. A geophysical project including electrical resistivity tomography (ERT) and ground probing radar (GPR) was planned over 1 year considering the administrative and logistic difficulties of such a project inside a cathedral of religious veneration. Finally, both ERT and GPR have been conducted during a week of intensive overnight surveys that provided detailed information on subsurface existing structures. The ERT method has been applied using different techniques and arrays, ranging from standard Wenner–Schlumberger 2D sections to full 3D electrical imaging with the advanced Maximum Yield Grid array. Electrical resistivity data were recorded extensively, making available many thousands of apparent resistivity data to obtain a complete 3D image after a full inversion. In conclusion, some significant buried structures have been revealed providing conclusive information for archaeologists. GPR results provided additional information about shallowest structures. The geophysical results were clear enough to persuade religious authorities and archaeologists to conduct selected excavations in the most promising areas that confirmed the interpretation of geophysical data. In conclusion, the significant buried structures revealed by geophysical methods under the cathedral were confirmed by archaeological digging as the basement of the impressive Roman Temple that headed the Provincial Forum of Tarraco, seat of the Concilium of Hispania Citerior Province. 相似文献
19.
The effectiveness of the electrical resistivity method has been studied using various configurations with different spacings over the Southern Boundary Fault in the northwestern part, and across a dolerite dyke named “Salma dyke” in the central part, of the Raniganj Coalfield, India. It has been observed that the delineation of the fault and the dyke was made possible under differential tropical weathering conditions. Geoelectric sections across the fault and the dyke have been prepared on the basis of Schlumberger sounding results. In profiling, Wenner, two-electrode, half-Schlumberger and part of Al-Chalabi's configurations were applied over the Southern Boundary Fault. Across the dyke, alpha-, beta-, and gamma-Wenner, Schlumberger, half-Schlumberger and two-electrode configurations were employed. Azi-muthal two-electrode sounding was also studied over the fault. The interpretation of the results of apparent resistivity profiles across the Southern Boundary Fault suggests that the Wenner and two-electrode configurations possess certain diagnostic features which help in mapping a single lithological contact, provided sufficient resistivity contrast exists. Although Schlumberger configuration seems to be quite suitable, other configurations may also be usefully employed over the dyke. 相似文献
20.
Said Attia al Hagrey 《Pure and Applied Geophysics》2012,169(7):1283-1292
Modern optimization approaches for electrode configurations can significantly improve the resolution of 2.5D resistivity imaging surveys. This study presents a brief review of the 2.5D optimization approach, particularly for borehole–borehole surveys with applications for mapping virtual CO2 plumes sequestrated in deep saline reservoir formations. The applied algorithm searches for arrays that maximize the spatial resolution of the survey among the comprehensive dataset of best possible spatial resolution (i.e. least temporal resolution). A main goal of this study is to increase the temporal resolution of ERT borehole–borehole surveys by selecting optimized electrode configurations in order to minimise the required data acquisition time while sustaining a high spatial resolution. The optimized dataset starts with a base set and is iteratively increased based on the model resolution matrix (R ) until the required number of data points is achieved. Among four different optimization methods, the compare R (CR) method of the best resolution is applied to directly calculate R for each new array added to the optimized dataset. Small optimized datasets generated by this technique are only <5% of their comprehensive sets but of an average resolution ratio (R r) of >0.95 (i.e. almost the same resolution). With increasing the size of the optimized dataset (during its generation), the algorithm progressively enhances R r values in the central interwell region (of low sensitivities and low resolution) far higher than in the near borehole region (of high sensitivities). Also the inverted tomogram reliability increases by increasing the optimized data size. Briefly, the optimized arrays improve the resolution in the interwell region which is commonly low in borehole–borehole ERT studies. The inverted output model is evaluated quantitatively using the model difference relative to the input model. The results reflect the common smearing effects and artefacts of varying degrees that overpredict volumes, underpredict magnitudes and blur boundaries of the target anomalies. This input model is a synthetic resistivity model that was used to generate synthetic (forward solution) data used during the inversion. Applications on synthetic CO2 models show that the mapping resolution for optimized datasets is better than that for other highly resolving arrays of the same number of data points. Problems of smeared boundaries and thin layers are less visible in the optimized array than in the other highly resolving arrays. 相似文献