Probabilistic modeling of aquifer heterogeneity using reliability methods

A probabilistic model of groundwater contaminant transport is presented. The model is based on coupling first- and second-order reliability methods (FORM and SORM) with a two-dimensional finite element solution of groundwater transport equations. Uncertainty in aquifer media is considered by modeling hydraulic conductivity as a spatial random field with a prescribed correlation structure. FORM and SORM provide the probability that a contaminant exceeds a target level at a well, termed the probability of failure. Sensitivity of the probability of failure to basic variabilities in grid block conductivity is also obtained, at no additional computational effort. The effect of the choice of the predetermined target level at the observation well is provided, along with its effect on the relevant sensitivity information. Considerable saving in computational time was achieved by superimposing a coarse random variables mesh on a finer numerical mesh. The presence of regions of lower conductivity on the probabilistic event is analyzed, and the regions in which conductivity most affects the results are identified.     

Effect of heterogeneity on radionuclide retardation in the alluvial aquifer near Yucca Mountain, Nevada

The U.S. Department of Energy is currently studying Yucca Mountain, Nevada, as a potential site for a geological high-level waste repository. In the current conceptual models of radionuclide transport at Yucca Mountain, part of the transport path to pumping locations would be through an alluvial aquifer. Interactions with minerals in the alluvium are expected to retard the downstream migration of radionuclides, thereby delaying arrival times and reducing ground water concentrations. We evaluate the effectiveness of the alluvial aquifer as a transport barrier using the stochastic Lagrangian framework. A transport model is developed to account for physical and chemical heterogeneities and rate-limited mass transfer between mobile and immobile zones. The latter process is caused by small-scale heterogeneity and is thought to control the macroscopic-scale retardation in some field experiments. A geostatistical model for the spatially varying sorption parameters is developed from a site-specific database created from hydrochemical measurements and a calibrated modeling approach (Turner and Pabalan 1999). Transport of neptunium is considered as an example. The results are sensitive to the rate of transfer between mobile and immobile zones, and to spatial variability in the hydraulic conductivity. Chemical heterogeneity has only a small effect, as does correlation between hydraulic conductivity and the neptunium distribution coefficient. These results illustrate how general sensitivities can be explored with modest effort within the Lagrangian framework. Such studies complement and guide the application of more detailed numerical simulations.     

Influence of aquifer heterogeneity and return flow on pumping test data interpretation

Analytical solutions of drawdown in unconfined aquifers are widely applied for determining the specific yield, S_y, and the horizontal and the vertical hydraulic conductivity K_r and K_z, respectively. In many previous studies, estimates of S_y and K_z were observed to be highly variable and physically unrealistic. This has been attributed to the conceptualization of flow above the declining water table and aquifer heterogeneity in the applied models. We present the analysis of time-drawdown data from a pumping test instrumented with depth-differentiated observation piezometers arranged in clusters. Applying homogeneous anisotropic aquifer models in combination with nonlinear least squares parameter identification techniques, the data were analyzed in different groups: analysis of data from individual piezometer clusters and simultaneous analysis of the entire data set from all piezometer clusters (global analysis). From the cluster analyses, estimates of S_y and K_z exhibit large variances and depart from a priori estimates inferred from the hydrostratigraphy. Parameter estimates from the global analysis do not fall within the parameter bounds (minimum and maximum values) defined by the cluster analyses. While heterogeneity appears to be the important reason for large parameter variances, we discuss the influence of rarely considered aquifer return flow on drawdown and the inconsistent results from the cluster and global analyses. We corroborate our findings with data on hydraulic gradients, slug test data, and results from the application of a more realistic numerical flow model.     

Modeling multiscale heterogeneity and aquifer interconnectivity

A number of methods involving indicator geostatistics were combined in a methodology for characterizing and modeling multiscale heterogeneity. The methodology circumvents sources of bias common in data from borehole logs. We applied this methodology to the complex heterogeneity within a regional system of buried valley aquifers, which occurs in the western glaciated plains of North America and includes the Spiritwood Aquifer. The region is conceptualized as having a hierarchical organization with three facies assemblage types (large-scale heterogeneity) and two facies types within each assemblage (small-scale heterogeneity). We statistically characterized the sedimentary architecture at both scales, formulated indicator correlation models from those characterizations, and used the models to simulate the architecture in a multiscale realization. We focused on the interconnectivity of units creating higher-permeability pathways. Higher-permeability pathways span the realization even though the proportion of higher-permeability facies is less than the percolation threshold. Thus, geologic structures as represented in the indicator correlation models create interconnectivity above that which would occur if the higher-permeability facies were randomly placed. This amount of interconnection among higher-permeability facies within the multiscale realization is consistent with that suggested in prior hydraulic and geochemical studies of the regional system.     

Estimating aquifer channel recharge using optical data interpretation

Recharge through intermittent and ephemeral stream channels is believed to be a primary aquifer recharge process in arid and semiarid environments. The intermittent nature of precipitation and flow events in these channels, and their often remote locations, makes direct flow and loss measurements difficult and expensive. Airborne and satellite optical images were interpreted to evaluate aquifer recharge due to stream losses on the Frio River in south-central Texas. Losses in the Frio River are believed to be a major contributor of recharge to the Edwards Aquifer. The results of this work indicate that interpretation of readily available remote sensing optical images can offer important insights into the spatial distribution of aquifer recharge from losing streams. In cases where upstream gauging data are available, simple visual analysis of the length of the flowing reach downstream from the gauging station can be used to estimate channel losses. In the case of the Frio River, the rate of channel loss estimated from the length of the flowing reach at low flows was about half of the loss rate calculated from in-stream gain-loss measurements. Analysis based on water-surface width and channel slope indicated that losses were mainly in a reach downstream of the mapped recharge zone. The analysis based on water-surface width, however, did not indicate that this method could yield accurate estimates of actual flow in pool and riffle streams, such as the Frio River and similar rivers draining the Edwards Plateau.     

Three-dimensional imaging of subsurface structures using resistivity data

We have developed a three-dimensional inverse scheme for carrying out DC resistivity surveys, incorporating complicated topography as well as arbitrary electrode arrays. The algorithm is based on the finite-element approximation to the forward problem, so that the effect of topographic variation on the resistivity data is effectively evaluated and incorporated in the inversion. Furthermore, we have enhanced the resolving power of the inversion using the active constraint balancing method. Numerical verifications show that a correct earth image can be derived even when complicated topographic variation exists. By inverting the real field data acquired at a site for an underground sewage disposal plant, we obtained a reasonable image of the subsurface structures, which correlates well with the surface geology and drill log data.     

Inversion of DC resistivity data using neural networks

The inversion of geoelectrical resistivity data is a difficult task due to its non-linear nature. In this work, the neural network (NN) approach is studied to solve both 1D and 2D resistivity inverse problems. The efficiency of a widespread, supervised training network, the back-propagation technique and its applicability to the resistivity problem, is investigated. Several NN paradigms have been tried on a basis of trial-and-error for two types of data set. In the 1D problem, the batch back-propagation paradigm was efficient while another paradigm, called resilient propagation, was used in the 2D problem. The network was trained with synthetic examples and tested on another set of synthetic data as well as on the field data. The neural network gave a result highly correlated with that of conventional serial algorithms. It proved to be a fast, accurate and objective method for depth and resistivity estimation of both 1D and 2D DC resistivity data. The main advantage of using NN for resistivity inversion is that once the network has been trained it can perform the inversion of any vertical electrical sounding data set very rapidly.     

Over-exploitation of an alluvial aquifer in Gujarat,India

Abstract

Over-exploitation of an alluvial aquifer in India has occurred since tubewells were drilled into deeper aquifers. Field information concerning-the fall in both the water table and the piezometric heads in the deeper aquifers has been examined and a numerical model has been developed to represent a heavily exploited area. Predictions using the model suggest that the annual declines in the water table and the piezometric heads are accelerating as the water table moves into a zone having a lower specific yield. Careful monitoring of the movement of the water table is proposed.     

用相位感应测井数据反演地层电阻率和介电常数

基于相位感应测井的两个接收线圈获取的总场相位差和幅度比曲线,在二维轴对称非均匀介质中同时反演地层电阻率和介电常数. 通过相位差和幅度比测井曲线提取地层纵向边界位置的初始值,利用测井响应方程和变分原理建立反演方程,然后采用共轭梯度(CG)法进行求解. 对多层地层的电阻率、介电常数和纵向边界位置进行整体反演,模拟计算结果表明了方法的可行性.     

Statistical analyses and modeling approaches to hydrodynamic characteristics in alluvial aquifer

This study is aimed at quantifying the difference in aquifer's response to recharge between some different locations in a fan aquifer and a delta aquifer for a preliminary study of revealing mechanisms of water transport in alluvial aquifer. The aquifer's response to recharge is statistically quantified with the two viewpoints: (1) timing and volume of recharge and (2) time length of aquifer's holding water. For the first point, a statistical model that links precipitation and groundwater level is introduced, and its parameters are identified using correlation analysis. Our results show that the recharge rate at the toe is higher than that at the apex and at the delta. For the second point, the concept of ‘memory effect’ of aquifer is adopted and quantified using the autocorrelation and spectral analyses. Our results show that the memory effect is longer at the toe of fan than at the apex, and thus, a temporary increase of water level has about five times as long‐term influence on subsequent water levels at the toe of the fan as at the apex. This study demonstrates that the statistical analyses and modeling of hydrological data are useful for characterizing aquifer's hydrodynamics. Copyright © 2012 John Wiley & Sons, Ltd.     

Spectral bandwidth enhancement of GPR profiling data using multiple-frequency compositing

The amplitude spectrum of ground penetrating radar (GPR) reflection data acquired with a particular antenna set is normally concentrated over a spectral bandwidth of a single octave, limiting the resolving power of the GPR wavelet. Where variously-sized GPR targets are located at numerous depths in the ground, it is often necessary to acquire several profiles of GPR data using antennas of different nominal frequencies. The most complete understanding of the subsurface is obtained when those frequency-limited radargrams are jointly interpreted, since each frequency yields a particular response to subsurface reflectivity. The application of deconvolution to GPR data could improve image quality, but is often hindered by limited spectral bandwidth.We present multiple-frequency compositing as a means of combining data from several frequency-limited datasets and improving the spectral bandwidth of the GPR profile. A multiple-frequency composite is built by summing together a number of spatially-coincident radargrams, each acquired with antennae of different centre frequency. The goal of the compositing process is therefore to produce a composite radargram with balanced contributions from frequency-limited radargrams and obtain a composite wavelet that has properties approximating a delta function (i.e. short in duration and having a broad, uniform spectral bandwidth).A synthetic investigation of the compositing process was performed using Berlage wavelets as proxies for GPR source pulses. This investigation suggests that a balanced, broad bandwidth, effective source pulse is obtained by a compositing process that equalises the spectral maxima of frequency-limited wavelets prior to summation into the composite. The compositing of real GPR data was examined using a set of 225, 450 and 900 MHz GPR common offset profiles acquired at a site on the Waterloo Moraine in Ontario, Canada. The most successful compositing strategy involved derivation of scaling factors from a time-variant least squares analysis of the amplitude spectra of each frequency-limited dataset. Contributions to the composite from each nominal acquisition frequency are clear, and the trace averaged amplitude spectrum of the corresponding composite is broadened uniformly over a bandwidth approaching two-octaves. Improvements to wavelet resolution are clear when a composite radargram is treated with a spiking deconvolution algorithm. Such improvement suggests that multiple-frequency compositing is a useful imaging tool, and a promising foundation for improving deconvolution of GPR data.     

Estimation of the 3D correlation structure of an alluvial aquifer from surface-based multi-frequency ground-penetrating radar reflection data

Knowledge about the stochastic nature of heterogeneity in subsurface hydraulic properties is critical for aquifer characterization and the corresponding prediction of groundwater flow and contaminant transport. Whereas the vertical correlation structure of the heterogeneity is often well constrained by borehole information, the lateral correlation structure is generally unknown because the spacing between boreholes is too large to allow for its meaningful inference. There is, however, evidence to suggest that information on the lateral correlation structure may be extracted from the correlation statistics of the subsurface reflectivity structure imaged by surface-based ground-penetrating radar measurements. To date, case studies involving this approach have been limited to 2D profiles acquired at a single antenna centre frequency in areas with limited complementary information. As a result, the practical reliability of this methodology has been difficult to assess. Here, we extend previous work to 3D and consider reflection ground-penetrating radar data acquired using two antenna centre frequencies at the extensively explored and well-constrained Boise Hydrogeophysical Research Site. We find that the results obtained using the two ground-penetrating radar frequencies are consistent with each other, as well as with information from a number of other studies at the Boise Hydrogeophysical Research Site. In addition, contrary to previous 2D work, our results indicate that the surface-based reflection ground-penetrating radar data are not only sensitive to the aspect ratio of the underlying heterogeneity, but also, albeit to a lesser extent, to the so-called Hurst number, which is a key parameter characterizing the local variability of the fine-scale structure.     

Truncated plurigaussian simulations to characterize aquifer heterogeneity

Integrating geological concepts, such as relative positions and proportions of the different lithofacies, is of highest importance in order to render realistic geological patterns. The truncated plurigaussian simulation method provides a way of using both local and conceptual geological information to infer the distributions of the facies and then those of hydraulic parameters. The method ( Le Loc'h and Galli 1994 ) is based on the idea of truncating at least two underlying multi-Gaussian simulations in order to create maps of categorical variable. In this article, we show how this technique can be used to assess contaminant migration in highly heterogeneous media. We illustrate its application on the biggest contaminated site of Switzerland. It consists of a contaminant plume located in the lower fresh water Molasse on the western Swiss Plateau. The highly heterogeneous character of this formation calls for efficient stochastic methods in order to characterize transport processes.     

Relationships between water flow rate and geophysical measurements in an alluvial aquifer

Our study focuses on the potential usefulness of surface geophysical data to constrain the water content within an alluvial aquifer. On a study area where two wells have been drilled, we have performed several geophysical measurements, including ground penetrating radar, DC resistivity prospecting, seismic refraction survey and magnetic resonance soundings. From these data, we estimated several parameters, namely, the water height in the deposits, the effective porosity, the water content, the permeability, and the transmissivity of alluvial deposits. These physical parameters allow us to characterize the alluvial deposits in order to constrain the estimation of the potential water flow. The lithology and water flow rate known from the wells enabled us to compare geophysical results obtained in a high water flow rate zone to those in a low water flow rate zone. Correlation has been found between the water flow rate observed in both wells and the geophysical data obtained in the vicinity of these wells.     

Increasing waveform inversion efficiency of GPR data using compression during reconstruction

We propose a method to avoid large amounts of data storage and reading during the reconstruction of a forward–backward time-stepping (FBTS) method for ground-penetrating radar (GPR) data using compression and decompression. The reconstruction example shows that the reconstruction result is acceptable if the compression ratio is less than 90%.     

Localization of saturated karst aquifer with magnetic resonance sounding and resistivity imagery

To answer one of the main questions of hydrogeologists implementing boreholes or working on pollution questions in a karst environment--i.e., where is the ground water?--numerous tools including geophysics are used. However, the contribution of geophysics differs from one method to the other. The magnetic resonance sounding (MRS) method has the advantage of direct detection of ground water over other geophysical methods. Eight MRSs were implemented over a known karst conduit explored and mapped by speleologists to estimate the MRS ability to localize ground water. Two direct current resistivity imageries (DC-2D imagery) were also implemented to check their capability to map a known cave. We found that the MRS is a useful tool to locate ground water in karst as soon as the quantity of water is enough to be detected. The threshold quantity is a function of depth and it was estimated by forward modeling to propose a support graph to hydrogeologists. The measured MRS's signals could be used to calculate transmissivity and permeability estimators. These estimators were used to map and to draw a cross section of the case study site, which underline accurately the known karst conduit location and depth. We also found that the DC-2D imagery could underline the karst structures: It was able to detect the known cave through its associated faults. We prepared a computer simulation to check the depth of such a cave to induce resistivity anomaly which could be measured in similar conditions.     

Characterization of a coastal aquifer basin using gravity and resistivity methods: a case study from Aqaba in Jordan

The southern basin of Aqaba forms coastal aquifer and comprises an area of about 90 km². Alluviums and Pleistocene deposits fill the basin bounded by Precambrian Granite Basement to the east and north. Hydrogeophysical investigations were carried out to investigate its groundwater potentials and characteristics. Direct modeling on Bouger and residual gravity revealed some local subsurface faults that form subbasins and sub-grabens in the body of the basin, each one of them is bounded by two to three faults. The spatial distribution of groundwater was found to be affected by the presence of the sub-basins and grabens. Geoelectrical layers have been vertically digitized and put in a four variable space-lattice, 2D slices of the different depths and 3D visualizations have been produced. The extents of seawater intrusion and zones of water qualities were delineated. The geoelectric inferred some local subsurface faults that were found in spatial correlation with those inferred from the gravity. A good combination was made between gravity and resistivity methods to confirm the 3D distribution of groundwater in the basin.     

Estimation of actual evapotranspiration from an alluvial aquifer of the Kouris catchment (Cyprus) using continuous streamflow records

The Kouris catchment is located in the south of the Troodos massif in Cyprus. The hydrology is driven by a Mediterranean climate, a mountainous topography, and a complex distribution of hydrogeological properties resulting from complex geology. To quantify the regional water balance further, a simple method using continuous streamflow records in the River Limnatis (Kouris catchment) was applied to calculate the actual evapotranspiration rate in the dry seasons. It was found that daily cycles of streamflow, recorded by automatic pressure logger, were caused by direct evaporation from the groundwater table and by transpiration of riparian forest. The daily amounts of ‘missing’ streamflow were calculated for the period 30 October–4 November 2001 and were extrapolated to the entire dry season and to the whole Kouris catchment. The actual evapotranspiration rate from the alluvial aquifer of the region is 2·4 ± 0·5 Mm³ for April–September 2001. The validity of the assumptions and the uncertainties in the estimates used in the method are discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

Transient heterogeneity in an aquifer undergoing bioremediation of hydrocarbons

Localized, transient heterogeneity was studied in a sand aquifer undergoing benzene, toluene, ethylbenzene, and xylene bioremediation using a novel array of multilevel, in situ point velocity probes (PVPs). The experiment was conducted within a sheet-pile alleyway to maintain a constant average flow direction through time. The PVPs measured changes in groundwater velocity direction and magnitude at the centimeter scale, making them ideal to monitor small-scale changes in hydraulic conductivity (K). Velocities were shown to vary nonuniformly by up to a factor of 3 when a source of oxygen was established down-gradient of the petroleum spill. In spite of these local variations, the average groundwater velocity within the 7 m × 20 m sheet-piled test area only varied within ± 25%. The nonuniform nature of the velocity variations across the gate indicated that the changes were not due solely to seasonal hydraulic gradient fluctuations. At the conclusion of the experiment, microbial biomass levels in the aquifer sediments was approximately 1 order of magnitude higher in the oxygen-amended portion of the aquifer than at the edge of the plume or in locations up-gradient of the source. These data suggest that the transient velocities resulted, at least in part, from enhanced biological activity that caused transient heterogeneities in the porous medium.     

1D inversion of DC resistivity data using a quality-based truncated SVD

Many DC resistivity inversion schemes use a combination of standard iterative least-squares and truncated singular value decomposition (SVD) to optimize the solution to the inverse problem. However, until quite recently, the truncation was done arbitrarily or by a trial-and-error procedure, due to the lack of workable guidance criteria for discarding small singular values. In this paper we present an inversion scheme which adopts a truncation criterion based on the optimization of the total model variance. This consists of two terms: (i) the term associated with the variance of statistically significant principal components, i.e. the standard model estimate variance, and (ii) the term associated with statistically insignificant principal components of the solution, i.e. the variance of the bias term. As an initial model for the start of iterations, we use a multilayered homogeneous half-space whose layer thicknesses increase logarithmically with depth to take into account the decrease of the resolution of the DC resistivity technique with depth. The present inversion scheme has been tested on synthetic and field data. The results of the tests show that the procedure works well and the convergence process is stable even in the most complicated cases. The fact that the truncation level in the SVD is determined intrinsically in the course of inversion proves to be a major advantage over other inversion schemes where it is set by the user.