Erwan Gloaguen

Estimation of hydraulic conductivity of an unconfined aquifer using cokriging of GPR and hydrostratigraphic data

Abstract Densely sampled geophysical data can supplement hydrogeological data for estimating the spatial distribution of porosity and hydraulic conductivity over an aquifer. A 3D Ground Penetrating Radar (GPR) survey was performed over a shallow unconfined aquifer consisting of a coarse to medium sand sequence overlying an impermeable clay layer. The site is instrumented with piezometers and water levels are frequently monitored. Vertical determination of moisture and granulometry at a resolution of 10 cm were made at a few locations. The GPR reflection times were correlated with piezometric and stratigraphic information; cokriging of both data yields the spatial distribution of the radar velocities within the layers. Porosity and hydraulic conductivities are estimated using the Complex Refractive Index Method (CRIM) and Kozeny–Carman formulations, respectively. A pumping test and a tracer test, both done using a well in the center of the survey zone, provide a measure of the average hydraulic conductivity and its anisotropy. The results from cokriging in the saturated zone show that the estimated parameters agree very well with the measured hydrogeological data. The geometric mean of the porosity is close to the laboratory measurements. The geometric mean of the GPR-derived hydraulic conductivities fits the values obtained from the pumping and tracer tests. The range of estimated hydraulic conductivities is quite large and indicates that flow could be faster or slower than the one predicted from the pumping test in some places. Radar attenuation is also found to be a good indicator of porosity distribution. From the observed (high) GPR attenuations and electrical conductivities of water sampled in the piezometers, porosity is determined using Archies formula. In the vadose zone, moisture content estimated from the GPR velocities using either CRIM or Topp formulations agree well with the ones from the laboratory measurements. Cokriging of the radar reflection times and of the hydrogeological/stratigraphic data leads to an accurate estimate of the radar velocities with a precision and a spatial resolution much higher than the CDP technique. Within the limits of the interpretative models, porosity, saturation and hydraulic conductivities can accurately be estimated with a high spatial resolution over the survey zone.

bh_tomo-a Matlab borehole georadar 2D tomography package

bh_tomo is an open source borehole georadar data processing and ray-based 2D tomography software package developed at the Ecole Polytechnique of Montreal. bh_tomo runs under Matlab version 7.0 and above, and is therefore portable between computer operating systems supported by Matlab. To perform the tomographic inversions, bh_tomo includes an implementation of the classical LSQR algorithm, as well as an implementation of the recent geostatistical inversion scheme developed at the Ecole Polytechnique of Montreal. One important motivation behind the development of bh_tomo was to ease the data processing sequence necessary to perform tomographic inversion of georadar amplitude data, especially when measured between many adjacent boreholes. The software package relies on a mini database and comprises interactive modules to manage, process and interpret the data.

Heterogeneous aquifer characterization from ground-penetrating radar tomography and borehole hydrogeophysical data using nonlinear Bayesian simulations

It is known that the heterogeneity of hydraulic conductivity drives the groundwater flow and the transport of contaminants. However, in conventional characterization methods, the lack of densely sampled hydrological data does not permit us to describe the aquifer heterogeneity at an appropriate scale. In this study, we integrate ground-penetrating radar (GPR) tomographic data with hydraulic conductivity logs to estimate the hydraulic conductivity of a heterogeneous unconsolidated aquifer at a decimetric scale between two boreholes. The integration of these different data sets is achieved using a nonlinear Bayesian simulation algorithm. The prior hydraulic conductivity distribution is estimated, under Gaussian hypothesis, by simple kriging of the hydraulic well data. The likelihood of hydraulic conductivity given the relative permittivity and the electrical conductivity functions is obtained from a kernel probability density function estimator that describes the in-situ relationship between the electric and the hydraulic properties measured along boreholes. The proposed method is tested on a synthetic heterogeneous model of permeability to validate the methodology. We show that permeability realizations obtained from the proposed algorithm present a higher correlation with the synthetic model than other classical simulation methods. The method is then applied on data acquired over an unconsolidated aquifer located in Saint-Lambert-de-Lauzon, Quebec, Canada. The data set consists of measurements from (i) GPR crosshole acquisition, (ii) cone penetration testing with pressure measurement combined with soil moisture resistivity, and (iii) a borehole electromagnetic flowmeter. By using the presented Bayesian approach, we generated multiple hydraulic conductivity realizations that are in good agreement with the hydrogeological model of the area.

Pseudo-full-waveform inversion of borehole GPR data using stochastic tomography

Electromagnetic full-waveform tomography is computer intensiveandrequiresgoodknowledgeofantennacharacteristics and ground coupling. As a result, ground-penetratingradartomographyusuallyusesonlythefirstwavelet’sarrival timeandamplitudedata.Weproposetoimprovetheclassical approach by inverting multiple slowness and attenuation fields using stochastic tomography. To do so, we model the slowness and attenuation covariance functions to generate geostatistical simulations that are conditional to the arrival times, amplitudes, slowness, and attenuation observed along boreholes. We combine slowness and attenuation fields to compute conductivity and permittivity fields from which we model synthetic radar traces using a finite-difference timedomain full-waveform algorithm. Modeled traces that best match the measured ones correspond to the computed conductivity and permittivity fields that correlate best with the true physical properties of the ground. We apply the method to a synthetic example with known electric properties. We show that a combination of stochastic tomography and fullwaveform modeling allows a better selection of permittivity fields close to the reference field, at a reasonable computing cost.

Permeability Profiles in Granular Aquifers Using Flowmeters in Direct-Push Wells

Numerical hydrogeological models should ideally be based on the spatial distribution of hydraulic conductivity (K), a property rarely defined on the basis of sufficient data due to the lack of efficient characterization methods. Electromagnetic borehole flowmeter measurements during pumping in uncased wells can effectively provide a continuous vertical distribution of K in consolidated rocks. However, relatively few studies have used the flowmeter in screened wells penetrating unconsolidated aquifers, and tests conducted in gravel-packed wells have shown that flowmeter data may yield misleading results. This paper describes the practical application of flowmeter profiles in direct-push wells to measure K and delineate hydrofacies in heterogeneous unconsolidated aquifers having low-to-moderate K (10(-6) to 10(-4) m/s). The effect of direct-push well installation on K measurements in unconsolidated deposits is first assessed based on the previous work indicating that such installations minimize disturbance to the aquifer fabric. The installation and development of long-screen wells are then used in a case study validating K profiles from flowmeter tests at high-resolution intervals (15 cm) with K profiles derived from multilevel slug tests between packers at identical intervals. For 119 intervals tested in five different wells, the difference in log K values obtained from the two methods is consistently below 10%. Finally, a graphical approach to the interpretation of flowmeter profiles is proposed to delineate intervals corresponding to distinct hydrofacies, thus providing a method whereby both the scale and magnitude of K contrasts in heterogeneous unconsolidated aquifers may be represented.

A direct carbon budgeting approach to infer carbon sources and sinks. Design and synthetic application to complement the NACP observation network

In order to exploit the upcoming regular measurements of vertical carbon dioxide (CO2) profiles over North America implemented in the framework of the North American Carbon Program (NACP), we design a direct carbon budgeting approach to infer carbon sources and sinks over the continent using model simulations. Direct budgeting puts a control volume on top of North America, balances air mass in- and outflows into the volume and solves for the surface fluxes. The flows are derived from the observations through a geostatistical interpolation technique called Kriging combined with transport fields from weather analysis. The use of CO2 vertical profiles simulated by the atmospheric transport model MOZART-2 at the planned 19 stations of the NACP network has given an estimation of the error of 0.39 GtC yr-1 within the model world. Reducing this error may be achieved through a better estimation of mass fluxes associated with convective processes affecting North America. Complementary stations in the north-west and the north-east are also needed to resolve the variability of CO2 in these regions. For instance, the addition of a single station near 52◦N; 110◦W is shown to decrease the estimation error to 0.34 GtC yr-1.

Resolution analysis of tomographic slug test head data: Two‐dimensional radial case

Hydraulic tomography inverse problems, which are solved to estimate aquifer hydraulic properties between wells, are known to be ill-conditioned and a priori information is often added to regularize numerical inversion of head data. Because both head data and a priori information have effects on the inversed solution, assessing the meaningful information contained in head data alone is required to ensure comprehensive interpretation of inverse solutions, whether they are regularized or not. This study thus aims to assess the amount of information contained in tomographic slug tests head data to resolve heterogeneity in Kh, Kv/Kh, and Ss. Therefore, a resolution analysis based on truncated singular value decomposition of the sensitivity matrix with a noise level representative of field measurements is applied using synthetic data reflecting a known littoral aquifer. As an approximation of the hydraulic behavior of a real aquifer system, synthetic tomographic experiments and associated sensitivity matrices are generated using a radial flow model accounting for wellbore storage to simulate slug tests in a plane encompassing a stressed well and an observation well. Although fine-scale resolution of heterogeneities is limited by the diffusive nature of the groundwater flow equations, inversion of tomographic slug tests head data holds the potential to uniquely resolve coarse-scale heterogeneity in Kh, Kv/Kh, and Ss, as inscribed in the resolution matrix. This implies that tomographic head data can provide key information on aquifer heterogeneity and anisotropy, but that fine-scale information must be supplied by a priori information to obtain finer details.

Accounting for Aquifer Heterogeneity from Geological Data to Management Tools

A nested workflow of multiple-point geostatistics (MPG) and sequential Gaussian simulation (SGS) was tested on a study area of 6 km(2) located about 20 km northwest of Quebec City, Canada. In order to assess its geological and hydrogeological parameter heterogeneity and to provide tools to evaluate uncertainties in aquifer management, direct and indirect field measurements are used as inputs in the geostatistical simulations to reproduce large and small-scale heterogeneities. To do so, the lithological information is first associated to equivalent hydrogeological facies (hydrofacies) according to hydraulic properties measured at several wells. Then, heterogeneous hydrofacies (HF) realizations are generated using a prior geological model as training image (TI) with the MPG algorithm. The hydraulic conductivity (K) heterogeneity modeling within each HF is finally computed using SGS algorithm. Different K models are integrated in a finite-element hydrogeological model to calculate multiple transport simulations. Different scenarios exhibit variations in mass transport path and dispersion associated with the large- and small-scale heterogeneity respectively. Three-dimensional maps showing the probability of overpassing different thresholds are presented as examples of management tools.

Field characterization and data integration to define the hydraulic heterogeneity of a shallow granular aquifer at a sub-watershed scale

Providing a sound basis for aquifer management or remediation requires that hydrogeological investigations carried out to understand groundwater flow and contaminant transport be based on representative data that capture the heterogeneous spatial distribution of aquifer hydraulic properties. This paper describes a general workflow allowing the characterization of the heterogeneity of the hydraulic properties of granular aquifers at an intermediate scale of a few km2. The workflow involves characterization and data integration steps that were applied on a 12-km2 study area encompassing a decommissioned landfill emitting a leachate plume and its main surface water receptors. The sediments composing the aquifer were deposited in a littoral–sublittoral environment and show evidence of small-scale transitional heterogeneities. Cone penetrometer tests (CPT) combined with soil moisture and electrical resistivity (SMR) measurements were thus used to identify and characterize spatial heterogeneities in hydraulic properties over the study area. Site-specific statistical relationships were needed to infer hydrofacies units and to estimate hydraulic properties from high-resolution CPT/SMR soundings distributed all over the study area. A learning machine approach was used due to the complex statistical relationships between colocated hydraulic and CPT/SMR data covering the full range of aquifer materials. Application of this workflow allowed the identification of hydrofacies units and the estimation of horizontal hydraulic conductivity, vertical hydraulic conductivity and porosity over the study area. The paper describes and discusses data acquisition and integration methodologies that can be adapted to different field situations, while making the aquifer characterization process more time-efficient and less labor-intensive.

Time-domain seismic modeling in viscoelastic media for full waveform inversion on heterogeneous computing platforms with OpenCL

Full Waveform Inversion (FWI) aims at recovering the elastic parameters of the Earth by matching recordings of the ground motion with the direct solution of the wave equation. Modeling the wave propagation for realistic scenarios is computationally intensive, which limits the applicability of FWI. The current hardware evolution brings increasing parallel computing power that can speed up the computations in FWI. However, to take advantage of the diversity of parallel architectures presently available, new programming approaches are required. In this work, we explore the use of OpenCL to develop a portable code that can take advantage of the many parallel processor architectures now available. We present a program called SeisCL for 2D and 3D viscoelastic FWI in the time domain. The code computes the forward and adjoint wavefields using finite-difference and outputs the gradient of the misfit function given by the adjoint state method. To demonstrate the code portability on different architectures, the performance of SeisCL is tested on three different devices: Intel CPUs, NVidia GPUs and Intel Xeon PHI. Results show that the use of GPUs with OpenCL can speed up the computations by nearly two orders of magnitudes over a single threaded application on the CPU. Although OpenCL allows code portability, we show that some device-specific optimization is still required to get the best performance out of a specific architecture. Using OpenCL in conjunction with MPI allows the domain decomposition of large models on several devices located on different nodes of a cluster. For large enough models, the speedup of the domain decomposition varies quasi-linearly with the number of devices. Finally, we investigate two different approaches to compute the gradient by the adjoint state method and show the significant advantages of using OpenCL for FWI. An open source software for viscoelastic full waveform inversion is presented.This software is based on OpenCL and can run on CPUs, GPUs and accelerators.On large clusters, MPI is used and a nearly linear scaling is achieved.Using GPUs, we obtain a speed-up of up to 80x over a single threaded CPU code.