H41B-01
A new Joint Inversion Approach in Conjunction With Cluster Analysis to Improve the Reliability of Hydrogeophysical Models
Since the inversion of geophysical inversion usually suffers non-uniqueness we try to apply different physical
fields to obtain a more reliable image of the subsurface.
If the underlying parameters are connected by petrophysical laws or empirical relationships we are able construct
a unique inversion scheme that considers all data.
However, in many cases such a relationship does not exist.
Nevertheless we expect structural similaries and want to allow for it without enforcement.
That is basically the idea of our novel joint inversion:
The structure of one parameter, i.e., the gradient of its distribution, is used to weight the other.
For each boundary a weight is defined that determines one row of the derivative matrix.
We use the techniques of robust modelling, the iteratively reweighted least squares method to determine the
individual weights.
The roughness vector of one parameter is the input for the weight of the other.
Thus a large change in one parameter allows for easier change of the other and vice versa at the same position.
Both inversion start and yield the first model iteration independently, then the coupling starts.
By an example involving dc resistivity and refraction data we prove to yield more significant structures with
structural coupling compared to inversion without coupling.
Both images can be combined by means of cluster analysis determining a cluster value for each cell.
By associating the cluster mean to the corresponding cells we obtain a very simple image of the subsurface.
However the clustered model is not able to fit the data appropriately.
Hence, we first try to optimize the values (post-iteration).
As a second step we use a side-result of the fuzzy analysis, the cluster membership function, for model
constraints in the next stage of inversion with the cluster model as reference.
Basically the distance from the cluster center defines how much it may vary.
Finally we end up in a very simple model combining two parameters that is able to explain the data to a high
degree.
The membership function serves as a measure for the reliability and helps to appraise resolution.
http:www.resistivity.net/
H41B-02
Evaluation of Water Flow-Paths and Dispersivities in Three-Dimensional Heterogeneous Porous Media Based on Magnetic Resonance Imaging Experiments
Tracer concentration breakthrough curves (BTCs) depend mainly upon the spatial distribution of hydraulic conductivity (K). Small-scale heterogeneity causes local velocity changes and local concentration gradients which can result in dispersive mixing. To examine the effects of heterogeneity and dispersion coefficients on tracer transport, we used a unique non-intrusive experimental method that measures BTCs from magnetic resonance imaging (MRI) signal intensity profiles at a voxel scale of 0.1875cm x 0.1875cm x 0.225cm in a three-dimensional flowcell (25cm x 8.8cm x 8.5cm) packed with a spatially correlated heterogeneous distributions of K at the 1cm3 scale. Predicted breakthrough profiles obtained with an integrated finite difference code (STOMP) were compared to experimental BTCs averaged over 0.25x0.25 cm2, 1x1 cm2, and the entire heterogeneous flow cell cross sections (8x8 cm2), all in 0.25 cm increments along the main flow direction (x). Different methods of assigning hydraulic conductivity (K) values to these sand fractions based on literature and measured values were tested. At the 0.06525cm2 and 1cm2 scales, the simulated BTCs matched the measured BTCs very well in the highest K sand along the central portion of the flowcell, but matching was poorer in the lower K regions. Root mean squared error (RMSE) values between measured and simulated BTCs were calculated; they were lowest for the flowcell cross-section scale, and increased with decreasing scales (1 cm2 and 0.0625 cm2). The difference is attributed to: (1) a reduction in local effective conductivity caused by the mixing of the coarse and fine sands, and (2) variability between the experimentally packed and the numerical heterogeneous permeability field. The impact of the dispersion coefficients upon the RMSE was also evaluated under the assumption that the ratio of longitudinal to transverse dispersivities equals ten; a minimum RMSE value was obtained when the longitudinal dispersivity was similar to the grain size. The effect of local-scale heterogeneity on differences between measured and predicted BTCs will be further exploited by inverse flow modeling using measured BTCs.
H41B-03
Combined Macroscopic Invasion Percolation and Continuum Modeling of Electrical Resistivity Measurements in Unsaturated Media
When coupled with unsaturated flow models, electrical resistivity techniques (including tomography) offer the promise of non-intrusive characterization of moisture within the unsaturated zone. Most unsaturated flow models (e.g., Richards' equation) are continuum models that are incapable of reproducing the complicated aqueous- phase structure observed in many field and laboratory experiments. This heterogeneous distribution of moisture contributes to highly heterogeneous distributions of electrical conductivity (EC) within unsaturated materials. We explore the influence of this heterogeneity using an experimentally verified modeling study. We simulate the evolution of aqueous phase structures using a macroscopic invasion percolation (MIP) model that accurately reproduces the complicated aqueous phase structures that arise within unsaturated porous media. Unlike traditional invasion percolation (IP) models which specify individual pore throats and necks, MIP models use an up-scaled blocks that are defined by a local threshold spanning (capillary) pressure. Block moisture contents are then mapped to block-specific EC values using the constitutive model of Mualem and Friedman (1991). Resulting heterogeneous EC fields are then used in a finite-difference model to simulate resistivity measurements. This approach is experimentally verified by simulations of laboratory measurements of electrical resistivity in layered samples at various moisture contents. Broader implications are explored through additional simulations.
H41B-04
Determination of Groundwater Velocity and Dispersion Parameters by Borehole Wall Multielectrode Geoelectrics
A single well technique to determine groundwater flow values and transport parameters is presented. Multielectrode arrays are placed at the filtered casing depth by an inflatable packer or are installed on the borehole wall behind the casing.Tracer water with a higher or lower specific electrical conductivity (salinity) which is injected between the electrodes. This tracer plume then moves into the natural groundwater flow field. The observation of this movement by geoelectric logging enables the determination of the groundwater velocity and salinity. The transport parameters "effective porosity" and "dispersion length" can also be derived. The geoelectric logging uses n borehole electrodes and two grounding electrodes. Thus, either n independent two point measurements or n*(n-1)/2 pole-to-pole measurements can be conducted to obtain a full set of geoelectric measurements. This set is used to derive all electrode combinations by applying the law of superposition and reciprocity. The tracer distribution around the borehole during and after injection depends on the hydraulic and transport parameters of the aquifer and the filter sand. The transport parameter "porosity" plus the total injected tracer volume determines the tracer distribution around the borehole. The transport parameter "dispersivity" determines the abruptness of the tracer front. The method was tested by undertaking measurements in a lab aquifer filled with sand. The results are discussed and the limitations of the method are shown. Multielectrode installations behind casing were tested in situ in the two scientific boreholes CAT-LUD-1 and CAT- LUD-1A drilled in the northern part of Germany. A multielectrode packer system was designed, built and tested in these boreholes. The results are compared with colloid observations in the borehole and hydraulic triangulation in surrounded observation wells. Here, the interpretation of these in situ measurements is mainly restricted to two point geoelectric measurements and vertical four point electrode interpretations. The transport equation for NaCl-tracered water is the basic rule to determine the groundwater transport velocity. Numerical calculations to simulate the measurement are carried out with the program FEFLOW. Due to the density contrast, the tracer undergoes vertical movement. Kessels, W., Zoth, G.(1998): Doppelmantel - Packer mit geoelektrischer Meßtechnik zur Bestimmung der Abstandsgeschwindigkeit des Grundwassers, Patent Az:19855048.0, GGA-Institut, Germany, Hannover. KESSELS, W., RIFAI, H., THORENZ, C., ZOTH, G.(2002): Multi Electrode Geoelectric on the Borehole Wall- Determination of groundwater velocity and dispersion parameters, AGU spring meeting, Washington KESSELS, W., ZOTH, G., WONIK, T., FULDA, C. (1999): THE USE OF SALT CARTRIDGES FOR FLUID LOGGING. XXIV GENERAL ASSEMBLY OF E.G.S. THE HAGUE, THE NETHERLANDS PANTELEIT,B., KESSELS, W., BINOT, F (2006): MUD TRACER TEST DURING SOFT ROCK DRILLING; W.R.R., VOL. 42, W11415, DOI:10.1029/2005WR004487
H41B-05
Comparison of Transport Parameters derived from Time-Lapse Electrical Resistivity Tomography, TDR and Effluent Break Through Curves
During the recent years it was shown that time-lapse electrical resistivity tomography (ERT) has potential to image subsurface solute transport processes. In this study we captured the spatio-temporal evolution of an inert salt tracer plume by means of time-lapse ERT in an unsaturated undisturbed soil column (height: 1.4 m, diameter: 1.16 m). The experiment was performed two-fold for 2 different steady state flow conditions, respectively, corresponding to approximately 15 % and 55 % of saturation. The ERT data were inverted with a three dimensional, smoothness-constrained inversion algorithm based on finite-element modelling. Identical error parameters were used for all ERT inversions and experiments. The image time series provides spatially resolved break-through curves (BTCs). Simultaneously, the BTCs in the outflow were measured and local BTCs within the monolith were measured with TDR. Following a stream tube approach, effective transport parameters were obtained by fitting the convective-dispersive equation to all available break-through curves. However, due to the non-uniqueness of the ERT inversion, the parameters derived from time lapse ERT might not be robust. Therefore, we appraised their robustness by comparing them with parameters derived from effluent and TDR measured BTCs. For all break through experiments, the mean ERT derived effective velocities at the TDR positions matched the ones found by TDR with a mean deviation of app. 5 %. The ERT derived dispersivities exceeded the ones found by TDR by a factor of two or more for the upper soil layers. For the deeper soil layers where the electrical contrasts were smoothed by dispersion, ERT and TDR derived effective dispersivities converged. For the four experiments, the effective velocity which was obtained from the effluent BTC matched the mean of the velocities derived from the bottommost ERT voxels with accuracy of 2.5 % to 5.5 %. The dispersivities of the effluent BTCs could be predicted from the variance of the ERT voxel velocities and the mean ERT voxel dispersivities with an accordance of 2.5 % to 23.5 %. The results confirm that smoothness constraint time lapse ERT images can be interpreted quantitatively up to a certain degree. We expect that a greater accuracy could be achieved if time-lapse information was incorporated into the inversion algorithm or a hydro-geophysical joint inversion approach was used.
H41B-06 INVITED
Flow and Transport Monitoring in Soils and Aquifers using Electrical Resistivity Tomography.
Given the importance of soil and aquifer structures on flow and transport processes, tomographic methods enabling a non-invasive monitoring of these processes are of special interest. In this contribution, we demonstrate some applications of electrical resistivity tomography (ERT) for monitoring flow and transport processes. A first application deals with monitoring of salt tracer transport in the soil or groundwater. During groundwater tracer studies the tracer breakthrough was monitored using local groundwater samplers and ERT in two reference planes perpendicular to the mean flow direction. A numerical study illustrated that conditioning the ERT inversion on local salinity measurements may improve the quality of the ERT images considerably. Because of the small spatio-temporal consistency of groundwater sampler measurements, i.e. groundwater concentration measurements varied over small distances and were not consistent in two consecutive tracer experiments, the use of these measurements for conditioning must be questioned. In a second application, salt tracer transport was monitored with ERT in unsaturated soil monoliths. Here, ERT images were validated against TDR measurements and patterns of an infiltrated dye. Since bulk soil electrical conductivity depends on water content, ERT was applied in a third application to monitor soil water content in a forest plot, where we derived correlations between water content and bulk electrical conductivity from TDR measurements. For all our studies, ERT inversions were strongly determined by the noise of the raw resistivity data. A correct estimation of the data noise and its implementation in the inversion algorithm was found to be essential for a quantitative interpretation of the ERT images. Also incorporating process understanding was found to be important for constraining the inversion. An example hereof is monitoring of seawater intrusion in a coastal aquifer. Finally, we give an example where we use resistivity data to parameterise the process model directly. Resistivities monitored during a tension infiltrometer experiment constrained the estimation of hydraulic soil parameters considerably.
H41B-07 INVITED
Aquifer and Vadose Zone Pollution Determined From Geoelectrical Measurements With Multi- Electrode Wells and Surface Multi-Profiling
During the last three years we are developing hydrobiogeological researches to quantitatively describe the underground contamination of a 4.0 km2 area, including two landfill deposits and a tannery industry of Alagoinhas city, Bahia state, Brazil. We used electrical geophysics, geological, geochemical and biological analysis to gain a general understanding of the complex interactions between organic and inorganic pollutants and their environmental impacts. A geological reconnaissance work and a geoelectrical survey using vertical electrical soundings were made around the area to detect and to delineate the extent of the underground contamination plume. The results pointed out the presence of a strong conductive anomaly within the aquifer resulting from invasive fluids both from the landfills and from the surface disposal lagoons from the tannery. Water samples collected at available wells and along the Sauipe river, have shown drastic changes in the total dissolved solids, total chromium, inorganic macro-components, biochemical oxygen demand, chemical oxygen demand, nutrients and bacterial content. As a complimentary work, apparent resistivity and chargeability data were measured as a function of depth along three new multi-electrode wells, and as a function of electrode spacing along five double semi-Schlumberger subsurface profiles. A multi-electrode well is a special monitoring well where we externally install copper electrodes as thin metallic rings spaced by 0.50 m, along its entire filter and casing length. Such electrodes are connected through insulated cables to the ground surface and may be combined into different arrays. Two-side semi-Schlumberger soundings expanded up to 200 m AB/2 spacing and with centers spaced by 50 m along special transverse centered at the plume were inverted using 1D and 2D models. Both techniques were used to detail the groundwater contamination around the Alagoinhas landfills. The electrical measurements performed at the earth surface and within wells, were used both to characterize the plume and to estimate changes in water saturation and water chemistry bellow the water table and throughout the upper vadose section of the Marizal- São Sebastião aquifer system. Well data were acquired during three different campaigns of 2004-2006 years, covering a complete seasonal cycle. The results are quantitativelyinterpreted using the volume conductivity approach described by Lima et al. (2005) extended for condiction of partial water saturation.