Transient Hydraulic Tomography Research Articles

Identification of high-permeability and water-rich zones in a fractured karst water source area based on the hydraulic tomography method

Determining the spatial hydraulic parameters of aquifers is of paramount importance for the development and utilization of groundwater in water source areas. However, most methods are unable to accurately characterize the heterogeneity of aquifers because of the influences of complex geology, hydrogeology, structure and insufficient information. Hydraulic tomography (HT) is an effective and robust method for hydraulic parameter inversion to characterize heterogeneity. In this study, a two-dimensional HT model was established to simulate hydraulic parameter fields for a fractured karst aquifer in the Zhangji water source area (Xuzhou city, China). Steady-state hydraulic tomography (SSHT) and transient hydraulic tomography (THT) with different prior information conditions were applied to determine the high-permeability area and water-rich zones, and to infer possible locations of karst conduits and strong runoff paths in the water source area. The results indicate that: (1) THT can better reveal larger-scale heterogeneous characteristics of hydraulic properties compared to SSHT. The hydraulic conductivity distribution estimated by THT correlates well with the geological conditions of the area, especially in identifying water-rich zones formed by faults and other formations. (2) When combined with geological conditions, HT possesses the ability to identify strong runoff paths in fractured karst aquifers. (3) Accurate prior information, which is more relevant to the head response information, is conducive to obtaining more acceptable HT results. (4) THT can simultaneously identify high-permeability and high-storage zones, and the analysis of the overlap of these two regions has the potential to predict underground water reservoirs, which is of the utmost importance for the development and utilization of groundwater resources in water source areas.

Predictive Deep Learning for High‐Dimensional Inverse Modeling of Hydraulic Tomography in Gaussian and Non‐Gaussian Fields

AbstractInverse modeling of hydraulic tomography (HT) is computationally expensive for estimating high‐dimensional hydrogeologic parameter fields. In this work, we develop a novel method called HT‐INV‐NN, which combines dimensionality reduction techniques with a predictive deep learning (DL) model to estimate high‐dimensional Gaussian and non‐Gaussian channel fields. The HT‐INV‐NN model consists of a predictor that directly learns the inverse process from hydraulic head measurements to latent variables of random fields, and a decoder that generates high‐dimensional parameter fields from predicted latent variables. For Gaussian spatially correlated fields, the decoder utilizes principal components derived from spatial covariance, and for non‐Gaussian channel fields, a generative adversarial network (GAN) is trained using generated realizations based on a training image (TI). The predictor is a deep neural network calibrated using the reference data obtained from HT forward simulations, which can be implemented in parallel. HT‐INV‐NN is successfully tested in multiple numerical experiments including steady‐state and transient HT for estimating Gaussian fields in 2D and 3D, as well as binary discontinuous or continuous non‐Gaussian channel fields. The training process is efficient, and the model structure demonstrates robustness for input data with perturbations. The model performance on multiple validation data sets are satisfactory when compared with other numerical and deep learning methods.

Performance of Gradient and Gradient-Free Optimizers in Transient Hydraulic Tomography.

Sub-surface characterization in fractured aquifers is challenging due to the co-existence of contrasting materials namely matrix and fractures. Transient hydraulic tomography (THT) is proved to be an efficient and robust technique to estimate hydraulic (Km, Kf) and storage (Sm, Sf) properties in such complex hydrogeologic settings. However, performance of THT is governed by data quality and optimization technique used in inversion. We assessed the performance of gradient and gradient-free optimizers with THT inversion. Laboratory experiments were performed on a two-dimensional, granite rock (80 cm × 45 cm × 5 cm) with known fracture pattern. Cross-hole pumping experiments were conducted at 10 ports (located on fractures), and time-drawdown responses were monitored at 25 ports (located on matrix and fractures). Pumping ports were ranked based on weighted signal-to-noise ratio (SNR) computed at each observation port. Noise-free, good quality (SNR > 100) datasets were inverted using Levenberg-Marquardt: LM (gradient) and Nelder-Mead: NM (gradient-free) methods. All simulations were performed using a coupled simulation-optimization model. Performance of the two optimizers is evaluated by comparing model predictions with observations made at two validation ports that were not used in simulation. Both LM and NM algorithms have broadly captured the preferential flow paths (fracture network) via K and S tomograms, however LM has outperformed NM during validation ( ). Our results conclude that, while method of optimization has a trivial effect on model predictions, exclusion of low quality (SNR ≤ 100) datasets can significantly improve the model performance.

Comparison of Hydraulic Travel Time and Attenuation Inversions, Thermal Tracer Tomography and Geostatistical Inversion for Aquifer Characterization: A Numerical Study

For the characterization of heterogeneous aquifers, transient hydraulic tomography (THT) was proposed as a promising method to obtain the distribution of hydraulic parameters with satisfying spatial resolution using different approaches. These include hydraulic travel time, attenuation inversions, thermal tracer tomography, and geostatistical inversion with successive linear estimator (SLE). For the same hydrogeological test, different inversion methods tend to use different sub-data sets to obtain different hydraulic parameters. Up to now, however, few studies have focused on revealing the respective characteristics of these inversion methods and attempted to improve the accuracy of aquifer characterization by bridging the shortcomings of the inversion methods. The main objective of this study was to evaluate the utility of multiple inversion techniques on aquifer heterogeneity characterization. A series of warm water injection tests were first simulated in a fluvial aquifer analogue outcrop. The calculated head and temperature datasets from these tests were fully utilized to reveal the aquifer heterogeneity by using all of the four above-mentioned inversion methods. The results show that the thermal tracer tomography, hydraulic travel time, and attenuation tomography characterized the high permeability zones more accurately within the well area, whereas the geological statistical method tended to depict the overall distribution of K values for a larger area. By comparison analysis and combinations of the individual inversion results, the scientific and economic complementarity can be studied and some valuable advice for the choice of different inversion methods can be recommended for future practices.

A new attempt for the detection of potential water-bearing structures in tunnels via hydraulic tomography: The first numerical investigation

Water-bearing geological structures in front of the tunnel and underground engineering are prone to water inrush hazards, which seriously threaten construction safety. This study investigated the potential of hydraulic tomography (HT) in detecting water-bearing structures to prevent groundwater hazards in tunnels. We established two synthetic heterogeneous aquifers with two different water-bearing structures, fractures and cavern zones. A comprehensive HT inversion analysis was performed using hydraulic head records generated by forward hydraulic tests. The results show that 1) sufficient pumping and observation wells can assist in capturing water-bearing structures and hydraulic properties; 2) transient hydraulic tomography (THT) inversion has a better effect than steady-state hydraulic tomography (SSHT) inversion since the temporal variation of head records carries non-redundant characteristics and distribution information of water-bearing structures; 3) inverted hydraulic conductivity and specific storage fields are positively correlated with observed heads at the end and early stages of the pumping test, respectively; 4) taking geological information as a prior can greatly assist in mapping potential water-bearing structures. This study can provide valuable guidance for detecting water-bearing structures in tunnel and underground engineering and formulating effective control schemes for water inrush hazards.

High‐Dimensional Groundwater Flow Inverse Modeling by Upscaled Effective Model on Principal Components

AbstractThe main computational costs of gradient‐based inverse methods for high‐resolution groundwater flow inverse problems include costly forward model simulations and the large number of such simulations required to determine the Jacobian matrix. We develop an upscaling‐based inverse approach, named upscaled principal component inverse approach (UPCIA), which achieves dimensionality reduction and reduces computational cost of forward model simulations by evaluating the Jacobian through upscaled effective models on a coarse‐resolution grid constructed from upscaled principal components. UPCIA integrates downscaling into the inverse problem by estimating principal component coefficients based on the coarse‐resolution forward model, which are then used to generate high‐resolution parameter fields. Various numerical experiments demonstrate the effectiveness and efficiency of UPCIA, including 2‐D/3‐D high‐dimensional steady‐state and transient hydraulic tomography with known storativity to estimate multi‐Gaussian transmissivity or hydraulic conductivity fields. Results show that the hydraulic head is insensitive to small‐scale variability of conductivity, and UPCIA provides high‐quality inversion results similar to inverse methods with high‐resolution forward model simulations and significantly reduces computation time by orders of magnitude. In addition to supporting the characterization of heterogeneity in sufficient detail, UPCIA can also be used to examine whether finer resolution is necessary and possibly to determine an optimal inverse resolution.

Multiscale Hydraulic Conductivity Characterization in a Fractured Granitic Aquifer: The Evaluation of Scale Effect

AbstractWe characterized horizontal hydraulic conductivity (K) of a fractured granitic aquifer using single‐ and cross‐hole hydraulic tests to evaluate “scale effect.” For selected boreholes, K estimates were obtained using single‐hole FLUTe liner and slug tests. Several cross‐hole pumping tests were carried out at various durations. Drawdown responses were first interpreted using analytical well‐test solutions to obtain an effective horizontal conductivity (Keff) assuming a homogeneous and infinite aquifer. The same drawdowns were then numerically inverted using transient hydraulic tomography (THT) to delineate spatial distributions of K and storativity in the area encompassing the boreholes. Papadopulos (1965) and a nonlinear least squares minimization method produced a similar principal Keff direction that is consistent with the dominant fracture strike observed from outcrop and borehole televiewer data. However, principal direction and magnitude of this Keff depend on the pumping test duration and the number of monitoring boreholes used in the interpretation. As a group, K obtained from cross‐hole tests is larger than that obtained from single‐hole tests. However, because cross‐hole tests stressed the aquifer at both interwell and larger scales, Keff obtained from interpreting cross‐hole data is observed to decrease with pumping time, likely due to the dominance of less permeable fractures at larger scale. This lateral reduction of mean K is also revealed by THT as low K zones surrounding the test boreholes. Overall, K is found to increase from single‐hole to the interwell scale and then decrease at larger scale, exhibiting a non‐monotonic scale effect.

The importance of fracture geometry and matrix data on transient hydraulic tomography in fractured rocks: Analyses of synthetic and laboratory rock block experiments

The accurate characterization of hydraulic properties such as hydraulic conductivity (K) and specific storage (Ss) for fractured geologic media as well as imaging of fracture patterns and their connectivity are of paramount importance to robust groundwater flow and transport predictions. Recently, transient hydraulic tomography (THT) has been suggested as a promising approach for imaging the K and Ss distributions of porous and fractured geologic media. This study investigates the importance of geological information on geostatistics-based THT analysis through synthetic and laboratory rock block experiments. Specifically, fracture geometry, connectivity and matrix hydraulic parameters of varying accuracy are utilized as priori information in THT analysis. Comparison of results from model calibration and validation indicates that: 1) THT analysis can capture the overall fracture pattern and their hydraulic properties (K and Ss), but the estimated values are higher within the matrix, where observations are limited when the inversion begins with effective K and Ss; 2) using correct fracture pattern, connectivity and matrix data as prior information can better preserve fracture and matrix hydraulic parameters and their patterns, especially where drawdown data are hard to obtain; and 3) THT analysis starting with homogeneous hydraulic parameter estimates without geologic information is more reliable than the one based on the wrong or incomplete description of geologic features. Overall, results from this study indicate the importance of incorporating accurate geological data in THT analyses when drawdown data are sparse and not available within the matrix. However, existing technology does not allow for the accurate mapping of fracture patterns and their connectivity between boreholes, hence further research is necessary in data fusion of other types of information to improve THT results.

Numerical investigation of hydraulic tomography for mapping karst conduits and its connectivity

Hydraulic tomography (HT) is a well-established approach to successfully describe subsurface hydraulic heterogeneity. This work explored the potential of HT and the simultaneous successive linear estimator algorithm to map the distribution and connectivity of karst conduits and their hydraulic parameters at the engineering scale. Three generalized synthetic karst conduit models, auxiliary conduit, cave and waterfall, were established. A series of pumping tests were conducted at different locations as forward simulations to collect hydraulic head responses. These responses were then used for the HT inversion analysis to estimate hydraulic parameter fields of karst aquifers under steady-state and transient conditions. Our results show that high-density observation wells substantially assist with interpreting the reliable spatial distribution of hydraulic parameters. With the increase in the number of pumping wells in the HT inversion, the estimates of hydraulic conductivity and specific storage became more accurate for the auxiliary conduit model, but for the cave and waterfall models, there was no significant improvement. The hydraulic conductivity (K) tomograms from transient hydraulic tomography (THT) better indicated the heterogeneity of the three karst models than those from steady-state hydraulic tomography (SSHT) because a large number of hydraulic head records were introduced into the THT inversion process. Moreover, when reliable geological data are available, the accuracy of the estimated hydraulic parameter maps can be greatly improved even if only infrequent hydraulic head measurements can be obtained, implying that a priori geological information may be extremely valuable in mapping karst conduit heterogeneity. Finally, the robustness of HT in mapping karst conduits is verified through the simulation of independent cross-hole pumping tests. This study proved that hydraulic tomography utilizing groundwater responses from a series of cross-hole pumping tests is an efficient and cost-effective way and provided a feasible method for accurate identification of hydraulic heterogeneity of karst aquifers.

On the importance of considering specific storage heterogeneity in hydraulic tomography: Laboratory sandbox and synthetic studies

Over the last two decades, various studies on Transient Hydraulic Tomography (THT) have shown that it is an effective approach to characterize subsurface heterogeneity. Typically, high-resolution hydraulic conductivity (K) distributions were recovered, while the spatial variability of specific storage (Ss) was found to be smooth. In some studies, Ss heterogeneity has been intentionally ignored due to the belief that Ss is less variable than K. Therefore, one may question the importance of considering Ss heterogeneity during THT and its impact on the reliability of estimated hydraulic parameters. To investigate these issues, three modeling approaches (i.e., effective parameters, geological, and geostatistics-based) were used to obtain K and Ss estimates of varying spatial resolutions. The reliability of K and Ss estimates were evaluated by comparing their drawdown prediction performances. The values of using different prior K and Ss information for THT analyses were investigated. Our results revealed that: (1) the K distribution estimated from the geostatistics-based steady-state HT analysis accurately predicted the late time drawdowns, while further improvements in transient drawdowns were obtained only after jointly treating the Ss field as heterogeneous; (2) Ss heterogeneity should be considered in addition to K for THT inversions, even when the estimated Ss field is smooth; and (3) using K and Ss estimates from the calibrated geological model as initial mean distributions for the geostatistical inversion approach were helpful in capturing both interlayer and intralayer heterogeneity of K and Ss. These findings suggested that Ss heterogeneity should be properly considered during the implementation of THT.

Potential of Hydraulic Tomography in Identifying Boundary Conditions of Groundwater Basins

AbstractThis study investigates the potential of hydraulic tomography (HT) in identifying the boundary conditions of groundwater basins using numerical experiments. The experiment mimics the scenario of groundwater exploitation reduction in a pilot area of groundwater overexploitation control in the North China Plain. In this study, we propose an approach that integrates the HT concept and readily available groundwater monitoring data to identify the constant head and impermeable boundaries by mapping anomalously high‐ and low‐permeability zones from HT surveys in a large‐scale domain that encompasses the true groundwater basin. The resulting boundaries and conditions were then used in inversion of steady‐state and transient‐state simultaneous pumping tests and HT surveys of heterogeneity within the groundwater basin. The inversion results demonstrated significant advantages of HT surveys over multiple simultaneous pumping tests to identify boundary conditions and heterogeneity in the groundwater basin. Moreover, steady HT inversion outperforms transient HT inversion in capturing the true boundary conditions, leading to the better T estimates from steady HT inversion than those from transient HT inversion. Additionally, the study shows that accurate geological zonation information can significantly improve HT parameter estimations.

Characterization of basin-scale aquifer heterogeneity using transient hydraulic tomography with aquifer responses induced by groundwater exploitation reduction

This study exploits aquifer responses to the reduction of pumping rates at different locations in a synthetic groundwater basin as basin-scale hydraulic tomography (HT) surveys to estimate transmissivity (T) and storage coefficient (S) fields. This experiment mimics the situation of groundwater exploitation reduction in a pilot area of groundwater-overexploitation control in the North China Plain. The results of the study show that taking advantage of the groundwater exploitation reduction as HT surveys is a viable approach for basin-scale parameter estimations. Results also suggest that HT analysis should use accurate mean values of T and S for geological zones as initial guesses for the inversion of parameters. Further, we show that the T and S fields estimated from HT yield accurate predictions of the groundwater flow velocities and breakthrough curves (BTCs). However, the BTCs based on kriged and zonal mean fields are inaccurate. The predicted BTCs using homogeneous fields fail to capture the true trend of solute concentration over time. We advocate that utilizing aquifer responses induced by groundwater exploitation reduction could be a new paradigm for basin-scale aquifer characterization.

Transient hydraulic tomography approach to characterize main flowpaths and their connectivity in fractured media

In sparse fracture systems flow and transport patterns are often dominated by main flowpaths and characterized by a strong complexity induced by the fractures’ surface roughness, hierarchical arrangement in networks, and from the interaction of the fractures with the surrounding rocks. The accurate characterization of the hydraulic properties and connectivity of major fracture zones is essential to model flow, solute and heat transport and fluid pressure propagation in fractured media. In this study, we present a novel deterministic inverse modeling method for imaging the connectivity and spatial variability of transmissivity and storativity of a network of fractures. The method is based on a numerical model that simulates fluid flow in a simple three-dimensional (3-D) discrete fracture network (DFN) with a fixed fracture network structure. The forward model is coupled to an inverse algorithm to match observed pressure transients obtained from sequential hydraulic cross-hole tests. This method has been successfully tested for constant rate injection tests carried out at the Grimsel Test Site (GTS) in Switzerland. Cross-hole injection tests were conducted in a tomographic configuration, with hydraulic responses monitored at four observation intervals at various depths in two different boreholes. A discrete fracture network approach with a simple parametrization is developed to estimate log-transformed transmissivity (T) and storativity (S) values of hydraulically active fractures between boreholes by inverting the pressure transients, under the hypothesis that T and S are independent variables. We identified several permeable fractures and their connectivity without attempting to represent explicitly the true fracture network geometrical properties (length, orientation, dip), focusing instead on the calibration of a simple model capturing the observed pressure main behavior. The identified inter-borehole connectivity structure agrees well with independent information, including additional data from a cross-borehole step rate injection and hydrogeophysical data. Hence, the proposed tomography approach appears to be a promising approach for characterizing the connectivity structure and hydraulic properties of the main flowpaths in sparsely fractured rock.

Transient Hydraulic Tomography Analysis of Fourteen Pumping Tests at a Highly Heterogeneous Multiple Aquifer–Aquitard System

Hydraulic tomography based on geostatistics has proven to be robust in characterizing subsurface heterogeneity in hydraulic conductivity (K) and specific storage (Ss) through the joint inversion of drawdown records from multiple pumping tests. However, the spatially variable estimates can be smooth or even erroneous for areas where pumping/observation data densities are not high. Previous hydraulic tomography surveys conducted at the North Campus Research Site (NCRS) on the University of Waterloo campus in Waterloo, Canada, revealed that the estimated hydraulic parameters were smooth and the known aquitard was erroneously identified as a high K zone. This was likely the consequence of the site being highly heterogeneous, while only utilizing four pumping tests and not having measurable drawdowns in the low K aquitard for inverse modeling. Here, we investigate whether improved K and Ss estimates could be obtained through the inclusion of additional pumping test data by stressing both aquifer and aquitard zones for a sufficiently long period. Specifically, six additional pumping/injection tests were conducted at the site, and a transient hydraulic tomography analysis with 14 tests was completed. Results reveal that there is a significant improvement to the K and Ss tomograms in terms of the visual correspondence with various geologic units, including its connectivity. More importantly, with the availability of additional data, we found that the inverse model now can better capture the high and low K features for nine boreholes when compared with K values obtained from permeameter tests. The estimated K and Ss tomograms are then used for the forward simulation of one additional pumping test not used for model calibration, revealing reasonable predictions. While encouraging results are obtained by including a large number of pumping tests to the transient hydraulic tomography analysis, stratigraphic boundaries are still smoothed, which is a direct consequence of utilizing a geostatistics-based inversion approach that assumes stationarity in statistical properties. To capture such sharp boundaries, incorporation of additional data types, such as geological and geophysical information, may be necessary when data densities are not sufficiently high.

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Transient hydraulic tomography (THT) is a robust method of aquifer characterization to estimate the spatial distributions (or tomograms) of both hydraulic conductivity (K) and specific storage (Ss). However, the highly-parameterized nature of the geostatistical inversion approach renders it computationally intensive for large-scale investigations. In addition, geostatistics-based THT may produce overly smooth tomograms when head data used to constrain the inversion is limited. Therefore, alternative model conceptualizations for THT need to be examined. To investigate this, we simultaneously calibrated different groundwater models with varying parameterizations and zonations using two cases of different pumping and monitoring data densities from a laboratory sandbox. Specifically, one effective parameter model, four geology-based zonation models with varying accuracy and resolution, and five geostatistical models with different prior information are calibrated. Model performance is quantitatively assessed by examining the calibration and validation results. Our study reveals that highly parameterized geostatistical models perform the best among the models compared, while the zonation model with excellent knowledge of stratigraphy also yields comparable results. When few pumping tests with sparse monitoring intervals are available, the incorporation of accurate or simplified geological information into geostatistical models reveals more details in heterogeneity and yields more robust validation results. However, results deteriorate when inaccurate geological information are incorporated. Finally, our study reveals that transient inversions are necessary to obtain reliable K and Ss estimates for making accurate predictions of transient drawdown events.

Three-dimensional imaging of aquifer and aquitard heterogeneity via transient hydraulic tomography at a highly heterogeneous field site

Previous studies have shown that geostatistics-based transient hydraulic tomography (THT) is robust for subsurface heterogeneity characterization through the joint inverse modeling of multiple pumping tests. However, the hydraulic conductivity (K) and specific storage (Ss) estimates can be smooth or even erroneous for areas where pumping/observation densities are low. This renders the imaging of interlayer and intralayer heterogeneity of highly contrasting materials including their unit boundaries difficult. In this study, we further test the performance of THT by utilizing existing and newly collected pumping test data of longer durations that showed drawdown responses in both aquifer and aquitard units at a field site underlain by a highly heterogeneous glaciofluvial deposit. The robust performance of the THT is highlighted through the comparison of different degrees of model parameterization including: (1) the effective parameter approach; (2) the geological zonation approach relying on borehole logs; and (3) the geostatistical inversion approach considering different prior information (with/without geological data). Results reveal that the simultaneous analysis of eight pumping tests with the geostatistical inverse model yields the best results in terms of model calibration and validation. We also find that the joint interpretation of long-term drawdown data from aquifer and aquitard units is necessary in mapping their full heterogeneous patterns including intralayer variabilities. Moreover, as geological data are included as prior information in the geostatistics-based THT analysis, the estimated K values increasingly reflect the vertical distribution patterns of permeameter-estimated K in both aquifer and aquitard units. Finally, the comparison of various THT approaches reveals that differences in the estimated K and Ss tomograms result in significantly different transient drawdown predictions at observation ports.

Training‐Image Based Geostatistical Inversion Using a Spatial Generative Adversarial Neural Network

AbstractProbabilistic inversion within a multiple‐point statistics framework is often computationally prohibitive for high‐dimensional problems. To partly address this, we introduce and evaluate a new training‐image based inversion approach for complex geologic media. Our approach relies on a deep neural network of the generative adversarial network (GAN) type. After training using a training image (TI), our proposed spatial GAN (SGAN) can quickly generate 2‐D and 3‐D unconditional realizations. A key characteristic of our SGAN is that it defines a (very) low‐dimensional parameterization, thereby allowing for efficient probabilistic inversion using state‐of‐the‐art Markov chain Monte Carlo (MCMC) methods. In addition, available direct conditioning data can be incorporated within the inversion. Several 2‐D and 3‐D categorical TIs are first used to analyze the performance of our SGAN for unconditional geostatistical simulation. Training our deep network can take several hours. After training, realizations containing a few millions of pixels/voxels can be produced in a matter of seconds. This makes it especially useful for simulating many thousands of realizations (e.g., for MCMC inversion) as the relative cost of the training per realization diminishes with the considered number of realizations. Synthetic inversion case studies involving 2‐D steady state flow and 3‐D transient hydraulic tomography with and without direct conditioning data are used to illustrate the effectiveness of our proposed SGAN‐based inversion. For the 2‐D case, the inversion rapidly explores the posterior model distribution. For the 3‐D case, the inversion recovers model realizations that fit the data close to the target level and visually resemble the true model well.

Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network

Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media. For inversion purposes, it has the attractive feature that random draws from an uncorrelated standard normal distribution yield model realizations with spatial characteristics that are in agreement with the training set. In comparison with the most commonly used parametric representations in probabilistic inversion, we find that our dimensionality reduction (DR) approach outperforms principle component analysis (PCA), optimization-PCA (OPCA) and discrete cosine transform (DCT) DR techniques for unconditional geostatistical simulation of a channelized prior model. For the considered examples, important compression ratios (200 - 500) are achieved. Given that the construction of our parameterization requires a training set of several tens of thousands of prior model realizations, our DR approach is more suited for probabilistic (or deterministic) inversion than for unconditional (or point-conditioned) geostatistical simulation. Probabilistic inversions of 2D steady-state and 3D transient hydraulic tomography data are used to demonstrate the DR-based inversion. For the 2D case study, the performance is superior compared to current state-of-the-art multiple-point statistics inversion by sequential geostatistical resampling (SGR). Inversion results for the 3D application are also encouraging.

Comparative study of transient hydraulic tomography with varying parameterizations and zonations: Laboratory sandbox investigation

Transient hydraulic tomography (THT) is a robust method of aquifer characterization to estimate the spatial distributions (or tomograms) of both hydraulic conductivity (K) and specific storage (Ss). However, the highly-parameterized nature of the geostatistical inversion approach renders it computationally intensive for large-scale investigations. In addition, geostatistics-based THT may produce overly smooth tomograms when head data used to constrain the inversion is limited. Therefore, alternative model conceptualizations for THT need to be examined. To investigate this, we simultaneously calibrated different groundwater models with varying parameterizations and zonations using two cases of different pumping and monitoring data densities from a laboratory sandbox. Specifically, one effective parameter model, four geology-based zonation models with varying accuracy and resolution, and five geostatistical models with different prior information are calibrated. Model performance is quantitatively assessed by examining the calibration and validation results. Our study reveals that highly parameterized geostatistical models perform the best among the models compared, while the zonation model with excellent knowledge of stratigraphy also yields comparable results. When few pumping tests with sparse monitoring intervals are available, the incorporation of accurate or simplified geological information into geostatistical models reveals more details in heterogeneity and yields more robust validation results. However, results deteriorate when inaccurate geological information are incorporated. Finally, our study reveals that transient inversions are necessary to obtain reliable K and Ss estimates for making accurate predictions of transient drawdown events.

Specific storage and hydraulic conductivity tomography through the joint inversion of hydraulic heads and self-potential data

Transient hydraulic tomography is used to image the heterogeneous hydraulic conductivity and specific storage fields of shallow aquifers using time series of hydraulic head data. Such ill-posed and non-unique inverse problem can be regularized using some spatial geostatistical characteristic of the two fields. In addition to hydraulic heads changes, the flow of water, during pumping tests, generates an electrical field of electrokinetic nature. These electrical field fluctuations can be passively recorded at the ground surface using a network of non-polarizing electrodes connected to a high impedance (> 10MOhm) and sensitive (0.1mV) voltmeter, a method known in geophysics as the self-potential method. We perform a joint inversion of the self-potential and hydraulic head data to image the hydraulic conductivity and specific storage fields. We work on a 3D synthetic confined aquifer and we use the adjoint state method to compute the sensitivities of the hydraulic parameters to the hydraulic head and self-potential data in both steady-state and transient conditions. The inverse problem is solved using the geostatistical quasi-linear algorithm framework of Kitanidis. When the number of piezometers is small, the record of the transient self-potential signals provides useful information to characterize the hydraulic conductivity and specific storage fields. These results show that the self-potential method reveals the heterogeneities of some areas of the aquifer, which could not been captured by the tomography based on the hydraulic heads alone. In our analysis, the improvement on the hydraulic conductivity and specific storage estimations were based on perfect knowledge of electrical resistivity field. This implies that electrical resistivity will need to be jointly inverted with the hydraulic parameters in future studies and the impact of its uncertainty assessed with respect to the final tomograms of the hydraulic parameters.