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1.
Streambed hydraulic conductivity (K) and vertical K (K v) are key controls on groundwater and surface water exchange and biogeochemical fluxes through the hyporheic zone, but drivers of transient hydraulic properties in different fluvial environments are poorly understood. This study combines hydrogeology, geophysics, and sedimentology to reveal mechanisms of K and K v transience in the upper 0.5 m of a sandy streambed during low discharge. Hydraulic tests (44 slug tests, 130 falling-head permeameter tests) and 130 grain-size analyses were repeated three times over 8 weeks on a 1,200 m2 grid spanning: (a) a channel with continuously flowing water and mobile bed load; (b) an adjacent mid-channel bar that was stationary and infrequently submerged. Aerial photographs and ground-penetrating radar show scour and complete reworking of fluvial sediments in the channel. Bar sediments below the water table remained immobile, but infrequent flows of moderate discharge reworked the uppermost few centimetres of the bar top. Despite differences in sediment mobility and stream flow characteristics across environments, K and K v exhibited order-of-magnitude differences in spatial heterogeneity and temporal variability in both the channel and bar. Mean K and K v values in the channel were comparatively stable over time. In the immobile bar, mean K declined 20% and K v declined 26% after increased discharge temporarily inundated the bar. Grain-size distributions were steady across both environments over time, but repeat geophysical surveys of the bar show a decrease in electrical conductivity, likely from porosity reduction. These findings suggest that sediment dynamics and stream flow characteristics in different streambed environments are important drivers of K transience during low discharge conditions. Specifically, pore clogging can be an important mechanism of transience over short durations (weeks to months) in immobile sediments subject to infrequent flows and minor reworking.  相似文献   

2.
Remediation of subsurface contamination requires an understanding of the contaminant (history, source location, plume extent and concentration, etc.), and, knowledge of the spatial distribution of hydraulic conductivity (K) that governs groundwater flow and solute transport. Many methods exist for characterizing K heterogeneity, but most if not all methods require the collection of a large number of small‐scale data and its interpolation. In this study, we conduct a hydraulic tomography survey at a highly heterogeneous glaciofluvial deposit at the North Campus Research Site (NCRS) located at the University of Waterloo, Waterloo, Ontario, Canada to sequentially interpret four pumping tests using the steady‐state form of the Sequential Successive Linear Estimator (SSLE) ( Yeh and Liu 2000 ). The resulting three‐dimensional (3D) K distribution (or K‐tomogram) is compared against: ( 1 ) K distributions obtained through the inverse modeling of individual pumping tests using SSLE, and ( 2 ) effective hydraulic conductivity (Keff) estimates obtained by automatically calibrating a groundwater flow model while treating the medium to be homogeneous. Such a Keff is often used for designing remediation operations, and thus is used as the basis for comparison with the K‐tomogram. Our results clearly show that hydraulic tomography is superior to the inversions of single pumping tests or Keff estimates. This is particularly significant for contaminated sites where an accurate representation of the flow field is critical for simulating contaminant transport and injection of chemical and biological agents used for active remediation of contaminant source zones and plumes.  相似文献   

3.
Streambed horizontal hydraulic conductivity (Kh) has a substantial role in controlling exchanges between stream water and groundwater. We propose a new approach for determining Kh of the shallow streambed sediments. Undisturbed sediment samples were collected using tubes that were horizontally driven into streambeds. The sediment columns were analysed using a permeameter test (PT) on site. This new test approach minimizes uncertainties due to vertical flow in the vicinity of test tube and stream stage fluctuations in the computation of the Kh values. Ninety‐eight PTs using the new approach were conducted at eight sites in four tributaries of the Platte River, east‐central Nebraska, USA. The Kh values were compared with the nondirectional hydraulic conductivity values (Kg) determined from 12 empirical grain‐size analysis methods. The grain‐size analysis methods used the same sediment samples as Kh tests. Only two methods, the Terzaghi and Shepherd methods, yielded Kg values close to the Kh values. Although the Sauerbrei method produced a value relatively closer to Kh than other nine grain‐size analysis methods, the values from this method were not as reliable as the methods of Terzaghi and Shepherd due to the inconsistent fluctuation of the average estimates at each of the test sites. The Zunker, Zamarin, Hazen, Beyer, and Kozeny methods overestimated Kh, while the Slichter, US Bureau of Reclamation (USBR), Harleman, and Alyamani and Sen methods underestimated Kh. Any of these specific grain‐size methods might yield good estimates of streambed Kh at some sites, but give poor estimates at other sites, indicating that the relationship between Kg and Kh is significantly site dependent in our study. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

4.
Over the past several decades, different groundwater modeling approaches of various complexities and data use have been developed. A recently developed approach for mapping hydraulic conductivity (K) and specific storage (Ss) heterogeneity is hydraulic tomography, the performance of which has not been compared to other more “traditional” methods that have been utilized over the past several decades. In this study, we compare seven methods of modeling heterogeneity which are (1) kriging, (2) effective parameter models, (3) transition probability/Markov Chain geostatistics models, (4) geological models, (5) stochastic inverse models conditioned to local K data, (6) hydraulic tomography, and (7) hydraulic tomography conditioned to local K data using data collected in five boreholes at a field site on the University of Waterloo (UW) campus, in Waterloo, Ontario, Canada. The performance of each heterogeneity model is first assessed during model calibration. In particular, the correspondence between simulated and observed drawdowns is assessed using the mean absolute error norm, (L1), mean square error norm (L2), and correlation coefficient (R) as well as through scatterplots. We also assess the various models on their ability to predict drawdown data not used in the calibration effort from nine pumping tests. Results reveal that hydraulic tomography is best able to reproduce these tests in terms of the smallest discrepancy and highest correlation between simulated and observed drawdowns. However, conditioning of hydraulic tomography results with permeameter K data caused a slight deterioration in accuracy of drawdown predictions which suggests that data integration may need to be conducted carefully.  相似文献   

5.
In granite aquifers, fractures can provide both storage volume and conduits for groundwater. Characterization of fracture hydraulic conductivity (K) in such aquifers is important for predicting flow rate and calibrating models. Nuclear magnetic resonance (NMR) well logging is a method to quickly obtain near-borehole hydraulic conductivity (i.e., KNMR) at high-vertical resolution. On the other hand, FLUTe flexible liner technology can produce a K profile at comparable resolution but requires a fluid driving force between borehole and formation. For three boreholes completed in a fractured granite, we jointly interpreted logging NMR data and FLUTe K estimates to calibrate an empirical equation for translating borehole NMR data to K estimates. For over 90% of the depth intervals investigated from these boreholes, the estimated KNMR are within one order of magnitude of KFLUTe. The empirical parameters obtained from calibrating the NMR data suggest that “intermediate diffusion” and/or “slow diffusion” during the NMR relaxation time may occur in the flowing fractures when hydraulic aperture are sufficiently large. For each borehole, “intermediate diffusion” dominates the relaxation time, therefore assuming “fast diffusion” in the interpretation of NMR data from fractured rock may lead to inaccurate KNMR estimates. We also compare calibrations using inexpensive slug tests that suggest reliable KNMR estimates for fractured rock may be achieved using limited calibration against borehole hydraulic measurements.  相似文献   

6.
Streambed hydraulic conductivity is one of the main factors controlling variability in surface water‐groundwater interactions, but only few studies aim at quantifying its spatial and temporal variability in different stream morphologies. Streambed horizontal hydraulic conductivities (Kh) were therefore determined from in‐stream slug tests, vertical hydraulic conductivities (Kv) were calculated with in‐stream permeameter tests and hydraulic heads were measured to obtain vertical head gradients at eight transects, each comprising five test locations, in a groundwater‐dominated stream. Seasonal small‐scale measurements were taken in December 2011 and August 2012, both in a straight stream channel with homogeneous elevation and downstream of a channel meander with heterogeneous elevation. All streambed attributes showed large spatial variability. Kh values were the highest at the depositional inner bend of the stream, whereas high Kv values were observed at the erosional outer bend and near the middle of the channel. Calculated Kv values were related to the thickness of the organic streambed sediment layer and also showed higher temporal variability than Kh because of sedimentation and scouring processes affecting the upper layers of the streambed. Test locations at the channel bend showed a more heterogeneous distribution of streambed properties than test locations in the straight channel, whereas within the channel bend, higher spatial variability in streambed attributes was observed across the stream than along the stream channel. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

7.
Hydraulic conductivity (K) and specific storage (S(s)) are required parameters when designing transient groundwater flow models. The purpose of this study was to evaluate the ability of commonly used hydrogeologic characterization approaches to accurately delineate the distribution of hydraulic properties in a highly heterogeneous glaciofluvial deposit. The metric used to compare the various approaches was the prediction of drawdown responses from three separate pumping tests. The study was conducted at a field site, where a 15 m × 15 m area was instrumented with four 18-m deep Continuous Multichannel Tubing (CMT) wells. Each CMT well contained seven 17 cm × 1.9 cm monitoring ports equally spaced every 2 m down each CMT system. An 18-m deep pumping well with eight separate 1-m long screens spaced every 2 m was also placed in the center of the square pattern. In each of these boreholes, cores were collected and characterized using the Unified Soil Classification System, grain size analysis, and permeameter tests. To date, 471 K estimates have been obtained through permeameter analyses and 270 K estimates from empirical relationships. Geostatistical analysis of the small-scale K data yielded strongly heterogeneous K fields in three-dimensions. Additional K estimates were obtained through slug tests in 28 ports of the four CMT wells. Several pumping tests were conducted using the multiscreen and CMT wells to obtain larger scale estimates of both K and S(s). The various K and S(s) estimates were then quantitatively evaluated by simulating transient drawdown data from three pumping tests using a 3D forward numerical model constructed using HydroGeoSphere (Therrien et al. 2005). Results showed that, while drawdown predictions generally improved as more complexity was introduced into the model, the ability to make accurate drawdown predictions at all CMT ports was inconsistent.  相似文献   

8.
The hydraulic profiling tool (HPT) is widely used to generate profiles of relative permeability vs. depth. In this work, prior numerical modeling results are used to develop a relationship between probe advance rate V (cm/s), probe diameter D (cm), water injection rate Q (mL/min), corrected pressure Pc (psi), and hydraulic conductivity K (feet/d) ((1)) where E is an empirically derived hydraulic efficiency factor. The relationship is validated by 23 HPT profiles that, after averaging K vertically, were similar to slug test results in adjoining monitoring wells. The best fit value of E for these profiles was 2.02. This equation provides a physically based approach for generating hydraulic conductivity profiles with HPT tooling.  相似文献   

9.
Fractured rocks have presented formidable challenges for accurately predicting groundwater flow and contaminant transport. This is mainly due to our difficulty in mapping the fracture‐rock matrix system, their hydraulic properties and connectivity at resolutions that are meaningful for groundwater modeling. Over the last several decades, considerable effort has gone into creating maps of subsurface heterogeneity in hydraulic conductivity (K) and specific storage (Ss) of fractured rocks. Developed methods include kriging, stochastic simulation, stochastic inverse modeling, and hydraulic tomography. In this article, I review the evolution of various heterogeneity mapping approaches and contend that hydraulic tomography, a recently developed aquifer characterization technique for unconsolidated deposits, is also a promising approach in yielding robust maps (or tomograms) of K and Ss heterogeneity for fractured rocks. While hydraulic tomography has recently been shown to be a robust technique, the resolution of the K and Ss tomograms mainly depends on the density of pumping and monitoring locations and the quality of data. The resolution will be improved through the development of new devices for higher density monitoring of pressure responses at discrete intervals in boreholes and potentially through the integration of other data from single‐hole tests, borehole flowmeter profiling, and tracer tests. Other data from temperature and geophysical surveys as well as geological investigations may improve the accuracy of the maps, but more research is needed. Technological advances will undoubtedly lead to more accurate maps. However, more effort should go into evaluating these maps so that one can gain more confidence in their reliability.  相似文献   

10.
Saturated hydraulic conductivity (K) is one of the most important parameters determining groundwater flow and contaminant transport in both unsaturated and saturated porous media. Although several well‐established laboratory methods exist for determining K, in situ measurements of this parameter remain very complex and scale dependent. Often, the limited accessibility of subsurface sediments for sampling means an additional impediment to our ability to quantify subsurface K heterogeneity. One potential solution is the use of outcrops as analogues for subsurface sediments. This paper investigates the use of air permeameter measurements on outcrops of unconsolidated sediments to quantify K and its spatial heterogeneity on a broad range of sediment types. The Neogene aquifer in northern Belgium is used as a case study for this purpose. To characterize the variability in K, 511 small‐scale air permeability measurements were performed on outcrop sediments representative over five of the aquifer's lithostratigraphic units. From these measurements, outcrop‐scale equivalent K tensors were calculated using numerical upscaling techniques. Validation of the air permeameter‐based K values by comparison with laboratory constant head K measurements reveals a correlation of 0.93. Overall, the results indicate that hand‐held air permeameters are very efficient and accurate tools to characterize saturated K, as well as its small‐scale variability and anisotropy on a broad range of unconsolidated sediments. The studied outcrops further provided a qualitative understanding of aquifer hydrostratigraphy and quantitative estimates about K variability at the centimetre‐scale to metre‐scale. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

11.
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12.
We present transient streaming potential data collected during falling‐head permeameter tests performed on samples of two sands with different physical and chemical properties. The objective of the work is to estimate hydraulic conductivity (K) and the electrokinetic coupling coefficient (Cl) of the sand samples. A semi‐empirical model based on the falling‐head permeameter flow model and electrokinetic coupling is used to analyze the streaming potential data and to estimate K and Cl. The values of K estimated from head data are used to validate the streaming potential method. Estimates of K from streaming potential data closely match those obtained from the associated head data, with less than 10% deviation. The electrokinetic coupling coefficient was estimated from streaming potential vs. (1) time and (2) head data for both sands. The results indicate that, within limits of experimental error, the values of Cl estimated by the two methods are essentially the same. The results of this work demonstrate that a temporal record of the streaming potential response in falling‐head permeameter tests can be used to estimate both K and Cl. They further indicate the potential for using transient streaming potential data as a proxy for hydraulic head in hydrogeology applications.  相似文献   

13.
This study presents an extension of the concept of “quasi-saturation” to a quasi-saturated layer, defined as the uppermost dynamic portion of the saturated zone subject to water table fluctuations. Entrapped air here may cause substantial reductions in the hydraulic conductivity (K) and fillable pore water. Air entrapment is caused by a rising water table, usually as a result of groundwater recharge. The most significant effects of entrapped air are recharge overestimation based on methods that use specific yield (Sy), such as the water table fluctuation method (WTF), and reductions in K values. These effects impact estimation of fluid flow velocities and contaminant migration rates in groundwater. In order to quantify actual groundwater recharge rates and the effects of entrapped air, numerical simulations with the FEFLOW (Version 7.0) groundwater flow model were carried out using a quasi-saturated layer for a pilot area in Rio Claro, Brazil. The calculated recharge rate represented 16% of the average precipitation over an 8-year period, approximately half of estimates using the WTF method. Air entrapment amounted to a fillable porosity of 0.07, significant lower that the value of 0.17 obtained experimentally for Sy. Numerical results showed that the entrapped air volume in the quasi-saturated layer can be very significant (0.58 of the air fraction) and hence can significantly affect estimates of groundwater recharge and groundwater flow rates near the water table.  相似文献   

14.
E. Rosa  M. Larocque 《水文研究》2008,22(12):1866-1875
Flow dynamics within a peatland are governed by hydraulic parameters such as hydraulic conductivity, dispersivity and specific yield, as well as by anisotropy and heterogeneity. The aim of this study is to investigate hydraulic parameters variability in peat through the use of different field and laboratory methods. An experimental site located in the Lanoraie peatland complex (southern Quebec, Canada) was used to test the different approaches. Slug and bail tests were performed in piezometer standpipes to investigate catotelm hydraulic conductivity. Combined Darcy tests and tracer experiments were conducted on cubic samples using the modified cube method (MCM) to assess catotelm hydraulic conductivity, anisotropy and dispersivity. A new laboratory method is proposed for assessing acrotelm hydraulic conductivity and gravity drainage using a laboratory experimental tank. Most of slug tests' recovery curves were characteristic of compressible media, and important variability was observed depending on the initial head difference. The Darcy experiments on cubic samples provided reproducible results, and anisotropy (Kh > Kv) was observed for most of samples. All tracer experiments displayed asymmetrical breakthrough curves, suggesting the presence of retardation and/or dual porosity. Hydraulic conductivity estimates performed using the experimental tank showed K variations over a factor of 44 within the upper 40 cm of the acrotelm. The results demonstrate that the intrinsic variability associated with the different field and laboratory methods is small compared with the spatial variability of hydraulic parameters. It is suggested that a comprehensive assessment of peat hydrological properties can be obtained through the combined use of complementary field and laboratory investigations. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

15.
The characterization of heterogeneity in hydraulic conductivity (K) is a major challenge for subsurface remediation projects. There are a number of field studies that compare the K estimates obtained using various techniques, but to our knowledge, no field‐based studies exists that compare the performance of estimated K heterogeneity fields or the associated characterization costs. In this paper, we compare the costs of characterizing the three‐dimensional K heterogeneity and its uncertainty estimates of a glaciofluvial aquifer‐aquitard sequence at a 15 m × 15 m × 18 m field site situated on the University of Waterloo campus. We compare geostatistical analysis of high resolution permeameter K data obtained from repacked core samples in five boreholes and hydraulic tomography analysis of four pumping tests consisting of up to 41 monitoring points per test. Aside from the comparison of costs, we also assess the performance of each method by predicting several pumping tests. Our analysis reveals that hydraulic tomography is somewhat more costly than the geostatistical analysis of high resolution permeameter K data due to the higher capital costs associated with the method. However, the equipment may be reused at other sites; hence these costs may be recovered over the life of the equipment. More significantly, hydraulic tomography is able to capture the most important features of the aquifer‐aquitard sequence leading to more accurate predictions of independent pumping tests. This suggests that more robust remediation systems may be designed if site characterization is performed with hydraulic tomography.  相似文献   

16.
The estimation of recharge through groundwater model calibration is hampered by the nonuniqueness of recharge and aquifer parameter values. It has been shown recently that the estimability of spatially distributed recharge through calibration of steady‐state models for practical situations (i.e., real‐world, field‐scale aquifer settings) is limited by the need for excessive amounts of hydraulic‐parameter and groundwater‐level data. However, the extent to which temporal recharge variability can be informed through transient model calibration, which involves larger water‐level datasets, but requires the additional consideration of storage parameters, is presently unknown for practical situations. In this study, time‐varying recharge estimates, inferred through calibration of a field‐scale highly parameterized groundwater model, are systematically investigated subject to changes in (1) the degree to which hydraulic parameters including hydraulic conductivity (K) and specific yield (Sy) are constrained, (2) the number of water‐level calibration targets, and (3) the temporal resolution (up to monthly time steps) at which recharge is estimated. The analysis involves the use of a synthetic reality (a reference model) based on a groundwater model of Uley South Basin, South Australia. Identifiability statistics are used to evaluate the ability of recharge and hydraulic parameters to be estimated uniquely. Results show that reasonable estimates of monthly recharge (<30% recharge root‐mean‐squared error) require a considerable amount of transient water‐level data, and that the spatial distribution of K is known. Joint estimation of recharge, Sy and K, however, precludes reasonable inference of recharge and hydraulic parameter values. We conclude that the estimation of temporal recharge variability through calibration may be impractical for real‐world settings.  相似文献   

17.
Although widely used in wetland hydrological studies, hydraulic conductivity (K) estimates from piezometer slug tests are often of questionable validity. Frequently, this is because insufficient attention is paid to the details of the test procedure. Further, in a potentially heterogeneous and anisotropic medium such as peat, the use of slug tests is prone to error. In this paper we address some of the methodological issues surrounding piezometer slug tests in peat. We compare slug test data with laboratory determinations of vertical and horizontal K obtained using a new method. Piezometers were installed at three depths in a floodplain fen peat in Norfolk, UK. Slug tests were initiated by both slug insertion and slug withdrawal, and repeat tests were conducted to examine the robustness of our K estimates. Most of the tests displayed departures from the log‐linear model of Hvorslev, the form of departure being consistent with compressible soil behaviour. The results suggest that insertion tests gave similar results to those initiated by withdrawal. Repeat testing showed that withdrawal data, in particular, gave highly reproducible normalized responses that were independent of the initial head. Values for K estimated using the slug tests were in the range 1 × 10−4 to 1·6 × 10−3 cm s−1, which is towards the upper end of the range reported for peats generally. Laboratory tests yielded similar values of K to those obtained from the slug tests. Although the laboratory tests showed that the peat was anisotropic, the K values generated by slug testing proved relatively good estimates of both vertical and horizontal K. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

18.
This study evaluated the spatial variability of streambed vertical hydraulic conductivity (Kv) in different stream morphologies in the Frenchman Creek Watershed, Western Nebraska, using different variogram models. Streambed Kv values were determined in situ using permeameter tests at 10 sites in Frenchman, Stinking Water and Spring Creeks during the dry season at baseflow conditions. Measurements were taken both in straight and meandering stream channels during a 5 day period at similar flow conditions. Each test site comprised of at least three transects and each transect comprised of at least three Kv measurements. Linear, Gaussian, exponential and spherical variogram models were used with Kriging gridding method for the 10 sites. As a goodness-of-fit statistic for the variogram models, cross-validation results showed differences in the median absolute deviation and the standard deviation of the cross-validation residuals. Results show that using the geometric means of the 10 sites for gridding performs better than using either all the Kv values from the 93 permeameter tests or 10 Kv values from the middle transects and centre permeameters. Incorporating both the spatial variability and the uncertainty involved in the measurement at a reach segment can yield more accurate grid results that can be useful in calibrating Kv at watershed or sub-watershed scales in distributed hydrological models.  相似文献   

19.
River confluences and their associated tributaries are key morphodynamic nodes that play important roles in controlling hydraulic geometry and hyporheic water exchange in fluvial networks. However, the existing knowledge regarding hyporheic water exchange associated with river confluence morphology is relatively scarce. On January 14 and 15, 2016, the general hydraulic and morphological characteristics of the confluent meander bend (CMB) between the Juehe River and the Haohe River in the southern region of Xi'an City, Shaanxi Province, China, were investigated. The patterns and magnitudes of vertical hyporheic water exchange (VHWE) were estimated based on a one‐dimensional heat steady‐state model, whereas the sediment vertical hydraulic conductivity (Kv) was calculated via in situ permeameter tests. The results demonstrated that 6 hydrodynamic zones and their extensions were observed at the CMB during the test period. These zones were likely controlled by the obtuse junction angle and low momentum flux ratio, influencing the sediment grain size distribution of the CMB. The VHWE patterns at the test site during the test period mostly showed upwelling flow dominated by regional groundwater discharging into the river. The occurrence of longitudinal downwelling and upwelling patterns along the meander bend at the CMB was likely subjected to the comprehensive influences of the local sinuosity of the meander bend and regional groundwater discharge and finally formed regional and local flow paths. Additionally, in dominated upwelling areas, the change in VHWE magnitudes was nearly consistent with that in Kv values, and higher values of both variables generally occurred in erosional zones near the thalweg paths of the CMB, which were mostly made up of sand and gravel. This was potentially caused by the erosional and depositional processes subjected to confluence morphology. Furthermore, lower Kv values observed in downwelling areas at the CMB were attributed to sediment clogging caused by local downwelling flow. The confluence morphology and sediment Kv are thus likely the driving factors that cause local variations in the VHWE of fluvial systems.  相似文献   

20.
The vertical hydraulic conductivity (Kv), elastic (Sske), and inelastic (Sskv) skeletal specific storage of aquitards are three of the most critical parameters in land subsidence investigations. Two new analytic methods are proposed to estimate the three parameters. The first analytic method is based on a new concept of delay time ratio for estimating Kv and Sske of an aquitard subject to long‐term stable, cyclic hydraulic head changes at boundaries. The second analytic method estimates the Sskv of the aquitard subject to linearly declining hydraulic heads at boundaries. Both methods are based on analytical solutions for flow within the aquitard, and they are jointly employed to obtain the three parameter estimates. This joint analytic method is applied to estimate the Kv, Sske, and Sskv of a 34.54‐m thick aquitard for which the deformation progress has been recorded by an extensometer located in Shanghai, China. The estimated results are then calibrated by PEST (Doherty 2005), a parameter estimation code coupled with a one‐dimensional aquitard‐drainage model. The Kv and Sske estimated by the joint analytic method are quite close to those estimated via inverse modeling and performed much better in simulating elastic deformation than the estimates obtained from the stress‐strain diagram method of Ye and Xue (2005). The newly proposed joint analytic method is an effective tool that provides reasonable initial values for calibrating land subsidence models.  相似文献   

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