Yoram Rubin

A comparison of seven geostatistically based inverse approaches to estimate transmissivities for modeling advective transport by groundwater flow

This paper describes the first major attempt to compare seven different inverse approaches for identifying aquifer transmissivity. The ultimate objective was to determine which of several geostatistical inverse techniques is better suited for making probabilistic forecasts of the potential transport of solutes in an aquifer where spatial variability and uncertainty in hydrogeologic properties are significant. Seven geostatistical methods (fast Fourier transform (FF), fractal simulation (FS), linearized cokriging (LC), linearized semianalytical )LS), maximum likelihood (ML), pilot point (PP), and sequential self-calibration (SS)) were compared on four synthetic data sets. Each data set had specific features meeting (or not) classical assumptions about stationarity, amenability to a geostatistical description, etc. The comparison of the outcome of the methods is based on the prediction of travel times and travel paths taken by conservative solutes migrating in the aquifer for a distance of 5 km. Four of the methods, LS, ML, PP, and SS, were identified as being approximately equivalent for the specific problems considered. The magnitude of the variance of the transmissivity fields, which went as high as 10 times the generally accepted range for linearized approaches, was not a problem for the linearized methods when applied to stationary fields; that is, their inverse solutions and travel time predictions were as accurate as those of the nonlinear methods. Nonstationarity of the “true” transmissivity field, or the presence of “anomalies” such as high-permeability fracture zones was, however, more of a problem for the linearized methods. The importance of the proper selection of the semivariogram of the log10 (T) field (or the ability of the method to optimize this variogram iteratively) was found to have a significant impact on the accuracy and precision of the travel time predictions. Use of additional transient information from pumping tests did not result in major changes in the outcome. While the methods differ in their underlying theory, and the codes developed to implement the theories were limited to varying degrees, the most important factor for achieving a successful solution was the time and experience devoted by the user of the method.

Hydrogeological characterization of the south oyster bacterial transport site using geophysical data

A multidisciplinary research team has conducted a field-scale bacterial transport study within an uncontaminated sandy Pleistocene aquifer near Oyster, Virginia. The overall goal of the project was to evaluate the importance of heterogeneities in controlling the field-scale transport of bacteria that are injected into the ground for remediation purposes. Geochemical, hydrological, geological, and geophysical data were collected to characterize the site prior to conducting chemical and bacterial injection experiments. In this paper we focus on results of a hydrogeological characterization effort using geophysical data collected across a range of spatial scales. The geophysical data employed include surface ground-penetrating radar, radar cross-hole tomography, seismic cross-hole tomography, cone penetrometer, and borehole electromagnetic flowmeter. These data were used to interpret the subregional and local stratigraphy, to provide high-resolution hydraulic conductivity estimates, and to provide information about the log conductivity spatial correlation function. The information from geophysical data was used to guide and assist the field operations and to constrain the numerical bacterial transport model. Although more field work of this nature is necessary to validate the usefulness and cost-effectiveness of including geophysical data in the characterization effort, qualitative and quantitative comparisons between tomographically obtained flow and transport parameter estimates with hydraulic well bore and bromide breakthrough measurements suggest that geophysical data can provide valuable, high-resolution information. This information, traditionally only partially obtainable by performing extensive and intrusive well bore sampling, may help to reduce the ambiguity associated with hydrogeological heterogeneity that is often encountered when interpreting field-scale bacterial transport data.

Linear equilibrium adsorbing solute transport in physically and chemically heterogeneous porous formations. 1. Analytical solutions

A first-order analytical solution for the transport of reactive solutes in physically and chemically heterogeneous porous media is derived and discussed. The solution relies on the assumption of chemical activity described by the local linear equilibrium assumption postulating the existence of a (spatially variable) retardation factor. Retardation factors and log permeabilities modeling heterogeneities are described statistically by random space functions with assigned correlation structure. Correlated as well as uncorrelated physical and chemical heterogeneities are studied. The analytical expressions derived reduce to Dagans classic solution for the case of nonreactive solute transport and obey asymptotic limits already known from the literature.

Estimating the hydraulic conductivity at the south oyster site from geophysical tomographic data using Bayesian Techniques based on the normal linear regression model

This study explores the use of ground penetrating radar (GPR) tomographic velocity, GPR tomographic attenuation, and seismic tomographic velocity for hydraulic conductivity estimation at the South Oyster Site, using a Bayesian framework. Since site- specific relations between hydraulic conductivity and geophysical properties are often nonlinear and subject to a large degree of uncertainty such as at this site, we developed a normal linear regression model that allows exploring these relationships systematically. Although the log-conductivity displays a small variation (s 2 5 0.30) and the geophysical data vary over only a small range, results indicate that the geophysical data improve the estimates of the hydraulic conductivity. The improvement is the most significant where prior information is limited. Among the geophysical data, GPR and seismic velocity are more useful than GPR attenuation.

Flow and Transport in Bimodal Heterogeneous Formations

A spatial correlation model is presented for the case of a spatially distributed, bimodal attribute. This model can be used for modeling the hydraulic conductivity in sand-shale or sand-clay formations or in fractured rocks, where the conductivities of the fractured and nonfractured rocks display dramatically different spatial structures. In the proposed model each of the modes is defined by a different multivariate probability density function and correlation scale. A length scale other than the one specified for each mode is used to characterize the relative distribution of the modes in space. Effective conductivity and transport parameters are then defined and analyzed. In developing the transport parameters our goal is to see the effects of the different scales and the different modes on transport. Unlike the case of a unimodal distribution, the macrodispersion is not a linear function of the total variance of the population, and the relative contributions of the variabilities of the different modes are determined by the ratios between the various length scales. We found that the effects of the large-scale variability on longitudinal spread become significant only after a large travel distance, but that its contribution to lateral spread occurs at a relatively early travel time.

HYDRO_GEN: A spatially distributed random field generator for correlated properties

This paper describes a new method for generating spatially-correlated random fields. Such fields are often encountered in hydrology and hydrogeology and in the earth sciences. The method is based on two observations: (i) spatially distributed attributes usually display a stationary correlation structure, and (ii) the screening effect of measurements leads to the sufficiency of a small search neighborhood when it comes to projecting measurements and data in space. The algorithm which was developed based on these principles is called HYDRO_GEN, and its features and properties are discussed in depth. HYDRO_GEN is found to be accurate and extremely fast. It is also versatile: it can simulate fields of different nature, starting from weakly stationary fields with a prescribed covariance and ending with fractal fields. The simulated fields can display statistical isotropy or anisotropy.

Hydrogeological parameter estimation using geophysical data: a review of selected techniques

Subsurface environmental, engineering, and agricultural investigations often require characteri- zation of hydraulic parameters. For example, groundwater flow modeling is often performed through an aquifer whose hydrological properties have been created using stochastic simulation techniques; these techniques use as input both hydraulic parameter point values and spatial correlation structure information. Conventional sampling or borehole techniques for measuring these parameters are costly, time-consuming, and invasive. Geophysical data can compliment direct characterization data by providing multi-dimensional and high resolution subsurface mea- surements in a minimally invasive manner. Several techniques have been developed in the preceding decade for using joint geophysical-hydrological data to characterize the subsurface; the purpose of this study is to review three methodologies that we have recently developed for use with geophysical-hydrological data to estimate hydrological parameters and their spatial correla- tion structures. The first two methodologies presented focus on producing high-resolution esti- mates of hydrological properties using densely sampled geophysical data and limited borehole data. Although we find that high-resolution geophysical data are useful for obtaining these estimates, in practice, geophysical profiles often sample only a small portion of the aquifer under investigation, and thus, the estimates obtained from geophysical data may not be sufficient to completely describe the hydraulic properties of the aquifer volume. The third and last section focuses on using high-resolution tomographic data together with limited borehole data to infer the spatial correlation structure of log-permeability, which can be used within stochastic simulation techniques to generate parameter estimates at unsampled locations. Our synthetic case studies suggest that collection of a few tomographic profiles and interpretation of these profiles together with limited wellbore data can yield hydrological point values and spatial correlation structure

Direct reservoir parameter estimation using joint inversion of marine seismic AVA and CSEM data

A new joint inversion algorithm to directly estimate reservoir parameters is described. This algorithm combines seismic amplitude versus angle (AVA) and marine controlled source electromagnetic (CSEM) data. The rock-properties model needed to link the geophysical parameters to the reservoir parameters is described. Errors in the rock-properties model parameters, measured in percent, introduce errors of comparable size in the joint inversion reservoir parameter estimates. Tests of the concept on synthetic one-dimensional models demonstrate improved fluid saturation and porosity estimates for joint AVA-CSEM data inversion (compared to AVA or CSEM inversion alone). Comparing inversions of AVA, CSEM, and joint AVA-CSEM data over the North Sea Troll field, at a location with well control, shows that the joint inversion produces estimated gas saturation, oil saturation and porosity that is closest (as measured by the RMS difference, L1 norm of the difference, and net over the interval) to the logged values whereas CSEM inversion provides the closest estimates of water saturation.

Mapping permeability in heterogeneous aquifers using hydrologic and seismic data

A new method is presented for identification of the permeability distribution in near-surface aquifers. In addition to using the usual sparsely sampled pressure and permeability data, the method incorporates densely sampled seismic data, as obtained from a reflection or tomography survey, along with empirical relationships between seismic and hydraulic properties. The procedure is to first estimate by hydrologic inversion a pressure field. Then the velocity-permeability-pressure relationship is used to map the inverted pressure and measured seismic data to multivalued estimates of the permeability. Of those, the most probable value, based on the hydrologic inversion, is selected. In synthetic case studies the tremendous increase in coverage offered by the seismic data leads to dramatically better results in terms of both accuracy and resolution. An appealing feature is the use of relatively easy to acquire pressure data; a second is the incorporation of geophysical data which can sample an entire aquifer remotely without the need for an expensive and invasive drilling program.

Ground‐penetrating‐radar‐assisted saturation and permeability estimation in bimodal systems

Near-surface investigations often require characterization of vadose zone hydraulic parameters. Conventional sampling or borehole techniques for estimating these parameters are costly, time consuming, and invasive, all of which limit collection of hydrogeological data at a spacing needed for detailed site characterization. Incorporation of two- or three-dimensional densely sampled geophysical data with conventional hydrological data increases the amount of data available for the characterization and thus has the potential to significantly improve the hydraulic parameter estimates over those obtained from borehole data alone. The hydraulic estimation procedure can be greatly improved by incorporating dielectric information potentially available from ground penetrating radar (GPR), a noninvasive, high-resolution geophysical method. The procedures for collecting and processing GPR data in the format needed for the proposed estimation technique are relatively new and still a topic of research; our method requires as a starting point the ability to estimate dielectric constants from GPR data. Numerical experiments were performed to investigate the general utility of the GPR-assisted estimation technique under a range of conditions. Three bimodal systems were investigated, each system being composed of a sand facies together with another facies with a larger clay volume fraction; each facies was defined using characteristic values of clay content, porosity, and permeability. Using dielectric information and petrophysical relations, degree of saturation and intrinsic permeability values at each location within the three systems were identified. For bimodal systems, a dielectric constant measurement corresponds to two possible values of saturation and intrinsic permeability at each location; single values of saturation and intrinsic permeability were estimated from these values using the principle of maximum likelihood. Results from case studies demonstrate that a combination of GPR data with conventional borehole data significantly improves the estimates of saturation and has the potential to improve the estimates of permeability over those obtained from well bore data alone. The proposed method should be especially advantageous for vadose zone characterization in areas favorable for GPR data acquisition, where detailed hydraulic parameter information is required but the drilling of numerous boreholes is prohibited.