Surface Nuclear Magnetic Resonance Tomography - Semantic Scholar
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Surface Nuclear Magnetic Resonance Tomography Marian Hertrich, Martina Braun, Thomas Günther, Alan G. Green, and Ugur Yaramanci
Abstract—Groundwater is the principal source of freshwater in many regions worldwide. Expensive drilling, borehole logging, and hydrological testing are the standard techniques employed in groundwater exploration and management. It would be logistically beneficial and cost-effective to have surface-based nonintrusive methods to locate and quantify groundwater occurrences and to estimate other key hydrological parameters. Surface nuclear magnetic resonance (SNMR) techniques, which are based on the spin magnetic-moment precession of protons in the hydrogen atoms of water, offer the possibility of achieving these goals. Current SNMR practices are based on 1-D inversion strategies. These simple strategies impede applications of SNMR techniques in hydrologically complex areas. To address this issue, we introduce a very fast 2-D SNMR tomographic-inversion scheme and apply it to four series of measurements simulated for a perched water-lens model. Whereas the new 2-D scheme correctly reconstructs all important characteristics of the original model, 1-D strategies produce highly inaccurate/misleading results. Index Terms—Hydrogeophysics, inversion, surface nuclear magnetic resonance (SNMR), tomography.
I. I NTRODUCTION
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EARLY 97% of the Earth’s liquid freshwater, which, arguably, is our most precious natural resource, is stored underground in aquifers. This groundwater is the principal source of drinking water for at least 30% of the world’s population. As examples, groundwater comprises 50% of the drinking water in North America and up to 80% in some European countries. Many people in other areas of the planet, mostly in developing countries, lack easy access to the freshwater supplies that are essential for their development and survival. Groundwater is ubiquitous; we need more efficient ways to search for it and manage it in a sustainable fashion. Earth scientists and civil engineers have been seeking nonintrusive means to locate and quantify groundwater aquifers for more than a century. With the introduction of shallow highresolution 3-D geophysical methods and innovative approaches for integrating diverse data sets, the new field of hydrogeophysics has evolved over the past decade. Although a broad range of geophysical methods (e.g., electric, electromagnetic, georadar, or seismic methods that operate from the surface, within boreholes, or between boreholes) provide much useful information related to groundwater occurrence and flow, until recently, there has been no reliable technique that will directly map the position and amount of water. A rapidly developing Manuscript received March 9, 2007; revised May 18, 2007. M. Hertrich and A. G. Green are with the Institute of Geophysics, ETH Zurich, 8093 Zurich, Switzerland (e-mail: [email protected]). M. Braun and U. Yaramanci are with the Department of Applied Geophysics, TU-Berlin, 13355 Berlin, Germany. T. Günther is with the Leibniz Institute for Applied Geosciences, Geoelectrics and Borehole Logging Methods, 30631 Hannover, Germany. Digital Object Identifier 10.1109/TGRS.2007.903829
method that has the potential to provide this information (and possibly also flow-related parameters) in a wide variety of environments is the surface nuclear magnetic resonance (SNMR) technique. The principle of NMR has widely been employed in the earth sciences for many decades (e.g., in proton-precession magnetometers for > 50 years and in borehole and core exploration tools for > 40 years), but its application to surfacebased groundwater exploration has been somewhat checkered. Although the idea of SNMR was first proposed in an early 1960s U.S. patent, it was not until the late 1970s that Russian scientists successfully conducted SNMR soundings and in the 1980s that they designed and constructed relatively robust instruments [1]. Most western scientists first became aware of the Russian developments in the early 1990s [2]. Since the introduction of commercially available SNMR equipment in 1996, practically all SNMR publications have been concerned with 1-D models of water content versus depth (i.e., soundings; see reviews in [3] and [4]). Recent theoretical formulations [5], methodological developments, critical assessments, and numerous case studies (see special issues edited in [6] and [7]) have exclusively involved actual or presumed 1-D situations. Conceptually, 1-D strategies are inappropriate in investigating isolated water occurrences (e.g., perched water aquifers) and hydrologically complicated environments (e.g., mountainous terrains, karsts, and fractured hardrock). To broaden significantly the applicability of SNMR techniques, we have developed a very fast 2-D SNMR tomographicinversion scheme. We solve the forward and inverse problems using an irregular mesh and a Gauss–Newton approach, respectively. After presenting the essential components of our new scheme, we demonstrate its ability to reconstruct both the structure and water content of a perched water-lens model based on only four series of simulated measurements. In contrast, 1-D inversions of the same measurements yield highly erroneous information. We demonstrate the influence of background resistivity and random measurement noise in a series of model studies presented in the Appendix. II. F ORWARD M ODELING At the beginning of an SNMR measurement cycle, a relatively large (5–150 m) surface coil transmits a short pulse of electromagnetic energy at the local Larmor angular frequency ωL . During this period, energy is effectively pumped into subsurface water protons, forcing their spin magnetic moments to tilt with respect to the Earth’s “static” magnetic field. A short time after the current is switched off, the same coil is usually used to measure the electromagnetic field generated by
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HERTRICH et al.: SURFACE NUCLEAR MAGNETIC RESONANCE TOMOGRAPHY
the spin magnetic moments as they precess around the ambient magnetic field, releasing their excess energy. Progressively deeper regions of the subsurface are probed by increasing the pulse moment q = I0 τ p
(1)
where I0 is the current through the coil, and τp is the pulse duration. The signal-to-noise ratio is improved by repeating the measurement cycle tens to hundreds of times and by stacking the results. The amplitude of the SNMR signal after extinction of the current is given by [5] V (q) = 2ωL M0 f (r) B− (r) e2iζ(r) sin γq B+ (r) d3 r
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and ∂f (y)/∂y = 0.
(7)
For a model represented by an irregular mesh of N elements and a field survey that comprises p pulse moments at each of M measurement locations, the total number of data points P = M p and the forward problem can be written in matrix notation as f1 K11 · · · K1N V1 V2 K21 · · · K2N f2 . . = (8) .. . .. . . VP KP 1 · · · KP N fN or
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(2) where M0 is the magnetization of hydrogen protons, and the integral represents the superposition of signals generated by the precessing spin magnetic moments. In the integral, the following can be seen: 1) f (r) is the amount of water at location r, which scales the response of each volume element by the number of hydrogen nuclei within it; 2) B− (r) and B+ (r) are the counter-rotating (for the received signal) and corotating (for the transmitted signal) components of elliptically polarized alternating electromagnetic fields normalized for unit currents in the coil; 3) ζ(r) are phase lags associated with the distances between the coil and points r in the subsurface; and 4) sin(γq|B+ (r)|) is a measure of the SNMR signal that is induced at point r, where γ is the gyromagnetic ratio for hydrogen protons. We emphasize that V (q) is complex as a result of the e2iζ(r) term. The imaginary component (i.e., phase) is important at locations where the resistivity is low [8], [9] (see the Appendix). As resistivity decreases, the penetration depth for a given pulse moment decreases, and the imaginary component increases. Equation (2) can be rewritten with the kernel containing the constants and input variables (3) K(q, r) = 2ωL M0 B− (r) e2iζ(r) sin γq B+ (r) and the dependent variable f (r) as V (q) = f (r)K(q, r)d3 r.
(4)
For 2-D conditions in which the system extends to infinity in the ±y-directions, the voltage response is determined by ∞ ∞ f (x, z) · K2D (q; x, z)dxdz
(5)
0 −∞
where ∞ K2D (q; x, z) =
K(q; x, y, z)dy −∞
(9)
From the aforementioned equations, we can see that, for a given suite of coil deployments and pulse moments, the SNMR signal V is linearly related to the water-content distribution f , such that the kernel K is the sensitivity or Jacobian matrix of the inverse problem. III. I NVERSION S CHEME For the inversion component of our SNMR tomographic scheme, we employ the Gauss–Newton algorithm developed for geoelectric methods in [10]. The data functional Φd to be minimized is the l2 -norm of the misfit between the observed and modeled data given by Φd (V) =
P Vi − Kij fj 2 = D(V − Kf )2 2 i
(10)
i=1
where the standard deviations i of measurements Vi result in a weighting matrix D = diag(1/i ) [Einstein’s summation convention is used in (10)]. As for many geophysical problems, this system of equations is underdetermined, such that additional constraints are required. By using a smoothing constraint [11], we define the model functional Φm as Φm (f ) = Cf 22
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V (q) =
V = Kf .
(11)
where C is Menke’s [12] flatness matrix. The functional to be minimized is then Φ = Φd + λΦm → min
(12)
where λ is a weighting factor. We modify the Jacobian matrix (the SNMR kernel K) to allow only plausible water-content values (i.e., 0%–100%). Although the inverse problem that is represented by (8)–(12) is linear, this modification makes the system slightly nonlinear, thus requiring an iterative solution. The model vector at the kth iteration f k is updated as follows:
(6) f k+1 = f k + η k ∆f k
(13)
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where η k is the line search parameter. The model update is determined by solving the following Gauss–Newton system of equations [10] (KT DT DK+λCT C)∆f k= KT DT D(V−Kf k )−λCT Cf k . (14) For the perched water lens and numerous other synthetic examples, the weighting factor λ was determined after extensive testing. It was chosen to avoid unnecessarily complex models that overfitted the data and avoid excessively smooth models that did not explain the data within the simulated measurement accuracies. The line search parameter η was automatically selected to optimize the inversion process, such that large step lengths did not lead to oscillations on either side of the minimum. Only four iterations were required for inversion to satisfactory solutions. The original Jacobian K did not change during the inversion process; it was simply scaled to constrain the range of water-content values. Since the problem was nearly linear, the inversions took only a few minutes on a standard personal computer. IV. T ESTS B ASED ON D ATA S IMULATED FOR A 2-D P ERCHED W ATER -L ENS M ODEL To investigate the influence of heterogeneity on SNMR measurements and to test our new 2-D tomographic-inversion scheme, we simulate readings across the perched water-lens model in Fig. 1(a) and (b). This symmetric lens, which is centered at a depth of 24 m, is 72 m wide and has a maximum thickness of 24 m. The water content within the lens is 25% by volume, whereas that outside is only 5% [Fig. 1(b)]. The resistivity throughout the model shown in Fig. 1 is 100 Ω · m. To demonstrate the effect of varying the background resistivity (1000, 100, and 10 Ω · m) and measurement noise (0 and ±10-nV Gaussian noise), we present the results of a supplementary series of model tests in the Appendix. Data are simulated for four positions of a 48-m-diameter coil with two turns and centers that are separated by 24 m. The four overlapping coil positions cover a total distance of 120 m. A. Synthetic Data Two SNMR measurement series were simulated for the four coil positions: one for laterally homogeneous models with 1-D water distributions equal to those of the water-lens model directly below the coil centers (dashed lines in Fig. 2), and one for the 2-D water-lens model (solid lines in Fig. 2). Vertically beneath P2 and P3, the 25% water content of the lens between 14 and 34 m in depth is overlain and underlain by regions of 5% water content, whereas vertically below P1 and P4, the water content is uniformly 5%. Comparisons of the 1-D and 2-D SNMR simulations in Fig. 2 demonstrate the strong influence of the lateral variations represented by the water-lens model. Since the 1-D curves for P2 and P3 are based on the assumption that the zones of anomalous water content maintain their 20-m thickness to large distances on either side of the coils, their amplitudes are generally much higher than those of the 2-D curves. In contrast, because the
Fig. 1. Two-dimensional model of a perched water lens (blue object) and the locations of four synthetic coincident transmitter/receiver coil SNMR measurements [red loops in (a)] centered along lines P1–P4. Coil center increment is 24 m, and the diameter of the two-turn coil is 48 m (i.e., 50% overlap between coils). Water content in the lens is 25% by volume and that of the surroundings is 5%. Synthetic measurements shown in Fig. 2 are calculated for maximum pulse moments—∼10 As, Earth’s magnetic field—48 000 nT at 60◦ inclination, profile azimuth—45◦ NE, and half-space resistivity—100 Ω · m.
1-D curves for P1 and P4 are computed for models with no anomalous water content, their amplitudes are uniformly much lower than those of the 2-D curves, which are affected by the presence of the water lens. Our 1-D and 2-D inversions are based on the simulated measurements for the water-lens model (i.e., solid curves in Fig. 2). We contaminated the data with 10 nV of Gaussian noise (which corresponds to 3%–10% of the signal), which is comparable to that encountered under favorable field conditions. All inversions were initiated using a homogeneous input model with 10% water content. B. One-Dimensional Inversion Our 1-D inversion algorithm forces the water content to vary smoothly within a stack of uniformly thin layers. The rather different resultant models at equivalent locations on either side of the lens [compare Fig. 3(a) and (d) and Fig. 3(b) and (c)] are a consequence of the different amplitude versus pulse moment curves (Fig. 2) that result from the oblique inclination of the Earth’s magnetic field and the associated asymmetry of the 2-D kernel. For all SNMR measurement series, the 5% water content in the upper 10–18 m of the original 2-D model is correctly predicted by the 1-D inversions, but the deeper water-content estimates are inaccurate. At P1 and P4, the 1-D models include
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Fig. 2. (a)–(d) Synthetic SNMR real amplitudes at positions P1–P4 in Fig. 1 (note that, for this model, the imaginary parts are practically zero; see the Appendix). Dashed lines are the signals for 1-D models with water-content distributions equal to those of the 2-D model vertically below the respective coil centers. Solid lines are the signals for the 2-D water-lens model. Note, that the 2-D synthetic measurements are not symmetric about the center of the lens; the oblique inclination of the Earth’s magnetic field results in an asymmetry of the 2-D kernel.
Fig. 3. Results of 1-D inversions of the four synthetic measurements P1–P4 (solid lines in Fig. 2). Results of 1-D inversions are shown by the blue areas and color bars. Dashed black lines show the true water content directly below the coil centers. There is no anomalous concentration of water directly below the centers of coils P1 and P4 (see Fig. 1); the apices of the lens at these locations are delineated by arrows in (a) and (d). RMS is the percentage root mean-square difference between the simulated and model-predicted data.
10–20-m-thick zones that contain 10%–17% water. Clearly, these models substantially overestimate the thicknesses, depth extents, and average water contents in relatively broad regions on either side of the coil centers (see also Fig. 4). We conclude that the lateral sensitivity or footprint of the individual measurement series exceeds the coil dimension. Although the 1-D models are influenced by the water lens, portions of which underlie the two coil deployments, neither water-bearing zone in the models is centered about the apices of the lens. At P2 and P3, the 1-D models approximately delineate the upper boundary of the water lens, but the depths to its lower boundary, its total water content, and water content below the lens are significantly underestimated. C. Two-Dimensional Inversion A full 2-D tomographic inversion of the four SNMR measurement series reproduces well the boundaries and wa-
Fig. 4. Two-dimensional inversion of the four coincident loop SNMR data sets simulated for the perched water-lens model (see Fig. 1). The black dashed lines delineate the original model in Fig. 1, whereas the four discrete columns are the 1-D inversions. RMS is the percentage root mean-square difference between the simulated and model-predicted data.
ter content of the perched water lens (Fig. 4). It is noteworthy that the boundary surrounding most of the lens is correctly shown to be relatively sharp and that the water
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Fig. 5. Results of the 1-D and 2-D inverting four coincident loop SNMR data sets that are simulated for the perched water-lens model (see Fig. 1) using 1000 Ω · m [diagrams (a)–(d)], 100 Ω · m [diagrams (e)–(h)], and 10 Ω · m [diagrams (i)–(l)] background resistivities. The simulated data are noise-free. (a), (e), and (i) show the simulated real (green dots) and imaginary (red dots) data, and 1-D model-predicted values (green and red lines). (c), (g), and (k) show the same information, but for the 2-D model-predicted values. (b), (f), and (j) show the true water-content-depth profiles beneath the center of each loop (dashed lines) and the 1-D models (blue areas and color bars). (d), (h), and (l) show the 2-D models. The black dashed lines delineate the original model in Fig. 1, whereas the four discrete columns in each diagram are the 1-D inversions. RMS is the percentage root mean-square difference between the simulated and model-predicted data.
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Fig. 6. As for Fig. 5, but for simulated data contaminated by 10-nV Gaussian noise (≈5%), which is comparable to that encountered under favorable field measurement conditions.
contents at locations P1 and P4 are accurately predicted to be very close to the background 5% value. Furthermore, the 2-D model is practically symmetric, verifying that the tomographicinversion scheme has properly accounted for the asymmetry
of the data caused by the inclination of the Earth’s magnetic field. The gradual transitions at the two ends of the reconstructed lens (Fig. 4) are a direct result of the applied smoothing.
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In addition to confirming the advantages of the new 2-D tomographic-inversion scheme, Fig. 4 further highlights the shortcomings of employing 1-D approaches in laterally heterogeneous environments. Combining details provided by the 1-D models would lead to false definitions of the boundaries and erroneously low water-content determinations. V. C ONCLUSION We have described the key elements of the first 2-D SNMR tomographic-inversion scheme. By using simulated data from only four measurement series, the rapid new scheme accurately reconstructed the boundaries and average water content of a perched water lens. In contrast, 1-D inversions of the same data produced highly misleading models, with significant overestimates of water content below the outer coil positions, underestimates below the inner coil positions, and an average water content that was much too low. Holes drilled on the basis of erroneously predicted high water contents (i.e., 10%–17%) beneath the outer positions would practically be dry. Results from the tests shown in the Appendix demonstrate the robustness of the 2-D SNMR inversion scheme for background resistivities that vary from 1000−10 Ω · m. As resistivity significantly decreases to below 100 Ω · m for the 48-m-diameter transmitter–receiver loop, it is necessary to include the effects of the imaginary components of (2)–(9), which our scheme accomplishes by treating the relevant parameters as complex. Two further related advances in SNMR techniques are expected in the near future: 1) application of the 2-D tomographicinversion scheme to multioffset SNMR data and 2) full 3-D strategies. Our analysis has been concerned with simulated coincident transmitted/receiver coil data. The 2-D inversion results demonstrate that these conventional data are adequate for imaging relatively large water-bearing features at depths of the same order as the coil radius. Separated transmitter and receiver coils supply data with markedly improved sensitivity in mapping features situated at shallow depths [13]. As for seismic and geoelectric methods, 2-D tomographic inversions of data acquired using a range of transmitter–receiver offsets have the potential to provide high-resolution images of waterbearing structures throughout the 0–150-m depth range of SNMR techniques. Our investigation required the computation of 3-D electromagnetic fields generated and received by the coil and, then, the reduction of the problem to 2-D for the final forward modeling steps and the inversion process. Accordingly, extension of the tomographic-inversion scheme to 3-D should be relatively straightforward, such that, once fast multicoil SNMR data acquisition systems are available, it should be possible to record, process, and tomographically invert the 3-D SNMR data in the field. A PPENDIX Previous studies based on 1-D inversions of SNMR data have demonstrated the potentially important role that is played by background electrical resistivities in estimating water content [8], [14]. To investigate these effects on 2-D samples, we have
conducted a series of tests using simulated data with background resistivities of 1000, 100, and 10 Ω · m and with and without ±10-nV Gaussian noise (Figs. 5 and 6). At locations where the resistivity is quite low, it is necessary to consider not only the real components of the measured amplitudes but also the imaginary components that contain the phase information. The imaginary components of the data are very small for the two relatively high-resistivity models [Figs. 5(a) and (e) and 6(a) and (e)], but significant for the low-resistivity model [Figs. 5(i) and 6(i)]. Figs. 5(a)–(h) and 6(a)–(h) demonstrate that the results for both the 1-D and 2-D inversions are practically invariant for background resistivities greater than 100 Ω · m. By considering the low values of the imaginary components, these results are not surprising. Addition of noise slightly changes the watercontent estimates, but the 1-D and 2-D models shown in Figs. 5 and 6 reveal the same general patterns. We note that the percentage root mean-square (rms) differences between the simulated and model-predicted data are slightly higher for the data contaminated with noise than for the noise-free data. From Fig. 5(i) and (k) and Fig. 6(i) and (k), it is clear that the imaginary components are important at locations where the background resistivities are significantly below ≈100 Ω · m. Nevertheless, by including the imaginary components in the inversion process, the results are very similar to those derived for the higher resistivity models (Figs. 5 and 6). ACKNOWLEDGMENT The authors would like to thank the journal reviewers for their constructive comments on an earlier version of this paper. R EFERENCES [1] M. Schirov, A. Legchenko, and G. Creer, “A new direct non-invasive groundwater detection technology for Australia,” Explor. Geophys., vol. 22, pp. 333–338, 1991. [2] M. Goldman, B. Rabinovich, M. Rabinovich, D. Gilad, I. Gev, and M. Schirov, “Application of the integrated NMR-TDEM method in groundwater exploration in Israel,” J. Appl. Geophys., vol. 31, no. 1–4, pp. 27–52, 1994. [3] A. Legchenko and P. Valla, “A review of the basic principles for proton magnetic resonance sounding measurements,” J. Appl. Geophys., vol. 50, no. 1/2, pp. 3–19, May 2002. special issue. [4] U. Yaramanci, A. Kemna, and H. Vereecken, “Emerging technologies and approaches in hydrogeophysics,” in Hydrogeophysics, ser. Water Science and Technnology Library, vol. 50, S. Hubbard and R. Yoram, Eds. New York: Springer-Verlag, 2005, pp. 468–487. [5] P. B. Weichman, E. M. Lavely, and M. H. Ritzwoller, “Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems,” in Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 62, 2000, pp. 1290–1312. [6] P. Valla and U. Yaramanci, “Surface nuclear magnetic resonance—What is possible,” J. Appl. Geophys., vol. 50, pp. 1–229, 2002. [7] U. Yaramanci and A. Legchenko, “Magnetic resonance sounding, aquifer detection and characterization,” Near Surf. Geophys., vol. 3, pp. 119–222 and 255–310, 2005. [8] M. Braun, M. Hertrich, and U. Yaramanci, “Complex inversion of MRS data,” Near Surf. Geophys., vol. 3, no. 3, pp. 155–163, 2005. [9] M. Müller, M. Hertrich, and U. Yaramanci, “Analysis of magnetic resonance sounding kernels concerning large scale applications using SVD,” in Proc. SAGEEP, EEGS, 2006. [10] T. Günther, C. Rücker, and K. Spitzer, “Three-dimensional modelling and inversion of dc resistivity data incorporating topography—II. Inversion,” Geophys. J. Int., vol. 166, no. 2, pp. 506–517, Aug. 2006.
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[11] S. C. Constable, R. L. Parker, and C. G. Constable, “Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data,” Geophysics, vol. 52, no. 3, pp. 289–300, Mar. 1987. [12] W. Menke, Geophysical Data Analysis: Discrete Inverse Theory, ser. International Geophysics Series, vol. 45. San Diego, CA: Academic, 1989. revised ed. [13] M. Hertrich, M. Braun, and U. Yaramanci, “Magnetic resonance soundings with separated transmitter and receiver loops,” Near Surf. Geophys., vol. 3, no. 3, pp. 131–144, Aug. 2005. [14] P. B. Weichman, D. R. Lun, M. H. Ritzwoller, and E. M. Lavely, “Study of surface nuclear magnetic resonance inverse problems,” J. Appl. Geophys., vol. 50, no. 1/2, pp. 129–147, 2002.
Thomas Günther received the M.Sc. and doctoral degrees from the University of Mining and Technology Freiberg, Freiberg, Germany, in 2000 and 2004, respectively. He is currently a Researcher with the Leibniz Institute for Applied Geosciences, Hannover, Germany. His research is mainly focused on modeling and inversion methods as applied to near surface geophysics, with particular emphasis on joint inversion methods.
Marian Hertrich received the M.Sc. and doctoral degrees from the Technical University of Berlin, Berlin, Germany, in 2000 and 2005, respectively. He is currently a Research Associate and Lecturer with the Applied and Environmental Geophysics Group, ETH Zurich, Zurich, Switzerland. His research interests include the development and application of surface nuclear magnetic resonance techniques, as well as geoelectric and electromagnetic methods for groundwater investigations.
Martina Braun received the M.Sc. degree from the Technical University of Berlin, Berlin, Germany, in 2002, where she is currently working toward the Ph.D. degree at the Applied Geophysics Group. Her research interests include the development and improvement of modeling and inversion algorithms for surface nuclear magnetic resonance data, with special focus on the influence of electrical resistivity.
Alan G. Green completed his studies at British universities before moving to Canada in 1973. After a one-year Postdoctoral Fellowship at the Earth Physics Branch, Ottawa, ON, Canada, he became an Assistant Professor of geophysics at the University of Manitoba, Winnipeg, MB, Canada. In 1979, he accepted an invitation to become the Head of the Lithospheric Geophysics Section, Geological Survey of Canada, Ottawa. During his 19 years in Canada, he further developed and applied seismic reflection methods in investigations of the continental crust, studies associated with nuclear waste disposal, and mineral exploration in crystalline terranes. Shortly after a one-year sabbatical leave in Switzerland, he accepted an invitation to become a Professor of applied and environmental geophysics at the Institute of Geophysics, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland.
Ugur Yaramanci received a degree from the Technical University of Clausthal, Clausthal, Germany, in 1975 and the doctoral degree from the University of Liverpool, Liverpool, U.K., in 1978. He was a Junior Scientist and eventually became an Associate Professor of applied geophysics with the Technical University of Istanbul, Istanbul, Turkey. Supported by an Alexander von Humbold Scholarship, he conducted research at the University of Kiel, Kiel, Germany, before joining the Research Center of Environment and Health, Braunschweig, Germany, in 1987 to work on geophysical investigations that are associated with the disposal of nuclear waste. In 1993, he was appointed as a Full Professor of petrophysics with the Technical University of Clausthal, and in 1996, he became a Full Professor of applied geophysics with the Technical University of Berlin, Berlin, Germany.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 45, NO. 11, NOVEMBER 2007
Surface Nuclear Magnetic Resonance Tomography Marian Hertrich, Martina Braun, Thomas Günther, Alan G. Green, and Ugur Yaramanci
Abstract—Groundwater is the principal source of freshwater in many regions worldwide. Expensive drilling, borehole logging, and hydrological testing are the standard techniques employed in groundwater exploration and management. It would be logistically beneficial and cost-effective to have surface-based nonintrusive methods to locate and quantify groundwater occurrences and to estimate other key hydrological parameters. Surface nuclear magnetic resonance (SNMR) techniques, which are based on the spin magnetic-moment precession of protons in the hydrogen atoms of water, offer the possibility of achieving these goals. Current SNMR practices are based on 1-D inversion strategies. These simple strategies impede applications of SNMR techniques in hydrologically complex areas. To address this issue, we introduce a very fast 2-D SNMR tomographic-inversion scheme and apply it to four series of measurements simulated for a perched water-lens model. Whereas the new 2-D scheme correctly reconstructs all important characteristics of the original model, 1-D strategies produce highly inaccurate/misleading results. Index Terms—Hydrogeophysics, inversion, surface nuclear magnetic resonance (SNMR), tomography.
I. I NTRODUCTION
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EARLY 97% of the Earth’s liquid freshwater, which, arguably, is our most precious natural resource, is stored underground in aquifers. This groundwater is the principal source of drinking water for at least 30% of the world’s population. As examples, groundwater comprises 50% of the drinking water in North America and up to 80% in some European countries. Many people in other areas of the planet, mostly in developing countries, lack easy access to the freshwater supplies that are essential for their development and survival. Groundwater is ubiquitous; we need more efficient ways to search for it and manage it in a sustainable fashion. Earth scientists and civil engineers have been seeking nonintrusive means to locate and quantify groundwater aquifers for more than a century. With the introduction of shallow highresolution 3-D geophysical methods and innovative approaches for integrating diverse data sets, the new field of hydrogeophysics has evolved over the past decade. Although a broad range of geophysical methods (e.g., electric, electromagnetic, georadar, or seismic methods that operate from the surface, within boreholes, or between boreholes) provide much useful information related to groundwater occurrence and flow, until recently, there has been no reliable technique that will directly map the position and amount of water. A rapidly developing Manuscript received March 9, 2007; revised May 18, 2007. M. Hertrich and A. G. Green are with the Institute of Geophysics, ETH Zurich, 8093 Zurich, Switzerland (e-mail: [email protected]). M. Braun and U. Yaramanci are with the Department of Applied Geophysics, TU-Berlin, 13355 Berlin, Germany. T. Günther is with the Leibniz Institute for Applied Geosciences, Geoelectrics and Borehole Logging Methods, 30631 Hannover, Germany. Digital Object Identifier 10.1109/TGRS.2007.903829
method that has the potential to provide this information (and possibly also flow-related parameters) in a wide variety of environments is the surface nuclear magnetic resonance (SNMR) technique. The principle of NMR has widely been employed in the earth sciences for many decades (e.g., in proton-precession magnetometers for > 50 years and in borehole and core exploration tools for > 40 years), but its application to surfacebased groundwater exploration has been somewhat checkered. Although the idea of SNMR was first proposed in an early 1960s U.S. patent, it was not until the late 1970s that Russian scientists successfully conducted SNMR soundings and in the 1980s that they designed and constructed relatively robust instruments [1]. Most western scientists first became aware of the Russian developments in the early 1990s [2]. Since the introduction of commercially available SNMR equipment in 1996, practically all SNMR publications have been concerned with 1-D models of water content versus depth (i.e., soundings; see reviews in [3] and [4]). Recent theoretical formulations [5], methodological developments, critical assessments, and numerous case studies (see special issues edited in [6] and [7]) have exclusively involved actual or presumed 1-D situations. Conceptually, 1-D strategies are inappropriate in investigating isolated water occurrences (e.g., perched water aquifers) and hydrologically complicated environments (e.g., mountainous terrains, karsts, and fractured hardrock). To broaden significantly the applicability of SNMR techniques, we have developed a very fast 2-D SNMR tomographicinversion scheme. We solve the forward and inverse problems using an irregular mesh and a Gauss–Newton approach, respectively. After presenting the essential components of our new scheme, we demonstrate its ability to reconstruct both the structure and water content of a perched water-lens model based on only four series of simulated measurements. In contrast, 1-D inversions of the same measurements yield highly erroneous information. We demonstrate the influence of background resistivity and random measurement noise in a series of model studies presented in the Appendix. II. F ORWARD M ODELING At the beginning of an SNMR measurement cycle, a relatively large (5–150 m) surface coil transmits a short pulse of electromagnetic energy at the local Larmor angular frequency ωL . During this period, energy is effectively pumped into subsurface water protons, forcing their spin magnetic moments to tilt with respect to the Earth’s “static” magnetic field. A short time after the current is switched off, the same coil is usually used to measure the electromagnetic field generated by
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the spin magnetic moments as they precess around the ambient magnetic field, releasing their excess energy. Progressively deeper regions of the subsurface are probed by increasing the pulse moment q = I0 τ p
(1)
where I0 is the current through the coil, and τp is the pulse duration. The signal-to-noise ratio is improved by repeating the measurement cycle tens to hundreds of times and by stacking the results. The amplitude of the SNMR signal after extinction of the current is given by [5] V (q) = 2ωL M0 f (r) B− (r) e2iζ(r) sin γq B+ (r) d3 r
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and ∂f (y)/∂y = 0.
(7)
For a model represented by an irregular mesh of N elements and a field survey that comprises p pulse moments at each of M measurement locations, the total number of data points P = M p and the forward problem can be written in matrix notation as f1 K11 · · · K1N V1 V2 K21 · · · K2N f2 . . = (8) .. . .. . . VP KP 1 · · · KP N fN or
vol
(2) where M0 is the magnetization of hydrogen protons, and the integral represents the superposition of signals generated by the precessing spin magnetic moments. In the integral, the following can be seen: 1) f (r) is the amount of water at location r, which scales the response of each volume element by the number of hydrogen nuclei within it; 2) B− (r) and B+ (r) are the counter-rotating (for the received signal) and corotating (for the transmitted signal) components of elliptically polarized alternating electromagnetic fields normalized for unit currents in the coil; 3) ζ(r) are phase lags associated with the distances between the coil and points r in the subsurface; and 4) sin(γq|B+ (r)|) is a measure of the SNMR signal that is induced at point r, where γ is the gyromagnetic ratio for hydrogen protons. We emphasize that V (q) is complex as a result of the e2iζ(r) term. The imaginary component (i.e., phase) is important at locations where the resistivity is low [8], [9] (see the Appendix). As resistivity decreases, the penetration depth for a given pulse moment decreases, and the imaginary component increases. Equation (2) can be rewritten with the kernel containing the constants and input variables (3) K(q, r) = 2ωL M0 B− (r) e2iζ(r) sin γq B+ (r) and the dependent variable f (r) as V (q) = f (r)K(q, r)d3 r.
(4)
For 2-D conditions in which the system extends to infinity in the ±y-directions, the voltage response is determined by ∞ ∞ f (x, z) · K2D (q; x, z)dxdz
(5)
0 −∞
where ∞ K2D (q; x, z) =
K(q; x, y, z)dy −∞
(9)
From the aforementioned equations, we can see that, for a given suite of coil deployments and pulse moments, the SNMR signal V is linearly related to the water-content distribution f , such that the kernel K is the sensitivity or Jacobian matrix of the inverse problem. III. I NVERSION S CHEME For the inversion component of our SNMR tomographic scheme, we employ the Gauss–Newton algorithm developed for geoelectric methods in [10]. The data functional Φd to be minimized is the l2 -norm of the misfit between the observed and modeled data given by Φd (V) =
P Vi − Kij fj 2 = D(V − Kf )2 2 i
(10)
i=1
where the standard deviations i of measurements Vi result in a weighting matrix D = diag(1/i ) [Einstein’s summation convention is used in (10)]. As for many geophysical problems, this system of equations is underdetermined, such that additional constraints are required. By using a smoothing constraint [11], we define the model functional Φm as Φm (f ) = Cf 22
vol
V (q) =
V = Kf .
(11)
where C is Menke’s [12] flatness matrix. The functional to be minimized is then Φ = Φd + λΦm → min
(12)
where λ is a weighting factor. We modify the Jacobian matrix (the SNMR kernel K) to allow only plausible water-content values (i.e., 0%–100%). Although the inverse problem that is represented by (8)–(12) is linear, this modification makes the system slightly nonlinear, thus requiring an iterative solution. The model vector at the kth iteration f k is updated as follows:
(6) f k+1 = f k + η k ∆f k
(13)
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where η k is the line search parameter. The model update is determined by solving the following Gauss–Newton system of equations [10] (KT DT DK+λCT C)∆f k= KT DT D(V−Kf k )−λCT Cf k . (14) For the perched water lens and numerous other synthetic examples, the weighting factor λ was determined after extensive testing. It was chosen to avoid unnecessarily complex models that overfitted the data and avoid excessively smooth models that did not explain the data within the simulated measurement accuracies. The line search parameter η was automatically selected to optimize the inversion process, such that large step lengths did not lead to oscillations on either side of the minimum. Only four iterations were required for inversion to satisfactory solutions. The original Jacobian K did not change during the inversion process; it was simply scaled to constrain the range of water-content values. Since the problem was nearly linear, the inversions took only a few minutes on a standard personal computer. IV. T ESTS B ASED ON D ATA S IMULATED FOR A 2-D P ERCHED W ATER -L ENS M ODEL To investigate the influence of heterogeneity on SNMR measurements and to test our new 2-D tomographic-inversion scheme, we simulate readings across the perched water-lens model in Fig. 1(a) and (b). This symmetric lens, which is centered at a depth of 24 m, is 72 m wide and has a maximum thickness of 24 m. The water content within the lens is 25% by volume, whereas that outside is only 5% [Fig. 1(b)]. The resistivity throughout the model shown in Fig. 1 is 100 Ω · m. To demonstrate the effect of varying the background resistivity (1000, 100, and 10 Ω · m) and measurement noise (0 and ±10-nV Gaussian noise), we present the results of a supplementary series of model tests in the Appendix. Data are simulated for four positions of a 48-m-diameter coil with two turns and centers that are separated by 24 m. The four overlapping coil positions cover a total distance of 120 m. A. Synthetic Data Two SNMR measurement series were simulated for the four coil positions: one for laterally homogeneous models with 1-D water distributions equal to those of the water-lens model directly below the coil centers (dashed lines in Fig. 2), and one for the 2-D water-lens model (solid lines in Fig. 2). Vertically beneath P2 and P3, the 25% water content of the lens between 14 and 34 m in depth is overlain and underlain by regions of 5% water content, whereas vertically below P1 and P4, the water content is uniformly 5%. Comparisons of the 1-D and 2-D SNMR simulations in Fig. 2 demonstrate the strong influence of the lateral variations represented by the water-lens model. Since the 1-D curves for P2 and P3 are based on the assumption that the zones of anomalous water content maintain their 20-m thickness to large distances on either side of the coils, their amplitudes are generally much higher than those of the 2-D curves. In contrast, because the
Fig. 1. Two-dimensional model of a perched water lens (blue object) and the locations of four synthetic coincident transmitter/receiver coil SNMR measurements [red loops in (a)] centered along lines P1–P4. Coil center increment is 24 m, and the diameter of the two-turn coil is 48 m (i.e., 50% overlap between coils). Water content in the lens is 25% by volume and that of the surroundings is 5%. Synthetic measurements shown in Fig. 2 are calculated for maximum pulse moments—∼10 As, Earth’s magnetic field—48 000 nT at 60◦ inclination, profile azimuth—45◦ NE, and half-space resistivity—100 Ω · m.
1-D curves for P1 and P4 are computed for models with no anomalous water content, their amplitudes are uniformly much lower than those of the 2-D curves, which are affected by the presence of the water lens. Our 1-D and 2-D inversions are based on the simulated measurements for the water-lens model (i.e., solid curves in Fig. 2). We contaminated the data with 10 nV of Gaussian noise (which corresponds to 3%–10% of the signal), which is comparable to that encountered under favorable field conditions. All inversions were initiated using a homogeneous input model with 10% water content. B. One-Dimensional Inversion Our 1-D inversion algorithm forces the water content to vary smoothly within a stack of uniformly thin layers. The rather different resultant models at equivalent locations on either side of the lens [compare Fig. 3(a) and (d) and Fig. 3(b) and (c)] are a consequence of the different amplitude versus pulse moment curves (Fig. 2) that result from the oblique inclination of the Earth’s magnetic field and the associated asymmetry of the 2-D kernel. For all SNMR measurement series, the 5% water content in the upper 10–18 m of the original 2-D model is correctly predicted by the 1-D inversions, but the deeper water-content estimates are inaccurate. At P1 and P4, the 1-D models include
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Fig. 2. (a)–(d) Synthetic SNMR real amplitudes at positions P1–P4 in Fig. 1 (note that, for this model, the imaginary parts are practically zero; see the Appendix). Dashed lines are the signals for 1-D models with water-content distributions equal to those of the 2-D model vertically below the respective coil centers. Solid lines are the signals for the 2-D water-lens model. Note, that the 2-D synthetic measurements are not symmetric about the center of the lens; the oblique inclination of the Earth’s magnetic field results in an asymmetry of the 2-D kernel.
Fig. 3. Results of 1-D inversions of the four synthetic measurements P1–P4 (solid lines in Fig. 2). Results of 1-D inversions are shown by the blue areas and color bars. Dashed black lines show the true water content directly below the coil centers. There is no anomalous concentration of water directly below the centers of coils P1 and P4 (see Fig. 1); the apices of the lens at these locations are delineated by arrows in (a) and (d). RMS is the percentage root mean-square difference between the simulated and model-predicted data.
10–20-m-thick zones that contain 10%–17% water. Clearly, these models substantially overestimate the thicknesses, depth extents, and average water contents in relatively broad regions on either side of the coil centers (see also Fig. 4). We conclude that the lateral sensitivity or footprint of the individual measurement series exceeds the coil dimension. Although the 1-D models are influenced by the water lens, portions of which underlie the two coil deployments, neither water-bearing zone in the models is centered about the apices of the lens. At P2 and P3, the 1-D models approximately delineate the upper boundary of the water lens, but the depths to its lower boundary, its total water content, and water content below the lens are significantly underestimated. C. Two-Dimensional Inversion A full 2-D tomographic inversion of the four SNMR measurement series reproduces well the boundaries and wa-
Fig. 4. Two-dimensional inversion of the four coincident loop SNMR data sets simulated for the perched water-lens model (see Fig. 1). The black dashed lines delineate the original model in Fig. 1, whereas the four discrete columns are the 1-D inversions. RMS is the percentage root mean-square difference between the simulated and model-predicted data.
ter content of the perched water lens (Fig. 4). It is noteworthy that the boundary surrounding most of the lens is correctly shown to be relatively sharp and that the water
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Fig. 5. Results of the 1-D and 2-D inverting four coincident loop SNMR data sets that are simulated for the perched water-lens model (see Fig. 1) using 1000 Ω · m [diagrams (a)–(d)], 100 Ω · m [diagrams (e)–(h)], and 10 Ω · m [diagrams (i)–(l)] background resistivities. The simulated data are noise-free. (a), (e), and (i) show the simulated real (green dots) and imaginary (red dots) data, and 1-D model-predicted values (green and red lines). (c), (g), and (k) show the same information, but for the 2-D model-predicted values. (b), (f), and (j) show the true water-content-depth profiles beneath the center of each loop (dashed lines) and the 1-D models (blue areas and color bars). (d), (h), and (l) show the 2-D models. The black dashed lines delineate the original model in Fig. 1, whereas the four discrete columns in each diagram are the 1-D inversions. RMS is the percentage root mean-square difference between the simulated and model-predicted data.
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Fig. 6. As for Fig. 5, but for simulated data contaminated by 10-nV Gaussian noise (≈5%), which is comparable to that encountered under favorable field measurement conditions.
contents at locations P1 and P4 are accurately predicted to be very close to the background 5% value. Furthermore, the 2-D model is practically symmetric, verifying that the tomographicinversion scheme has properly accounted for the asymmetry
of the data caused by the inclination of the Earth’s magnetic field. The gradual transitions at the two ends of the reconstructed lens (Fig. 4) are a direct result of the applied smoothing.
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In addition to confirming the advantages of the new 2-D tomographic-inversion scheme, Fig. 4 further highlights the shortcomings of employing 1-D approaches in laterally heterogeneous environments. Combining details provided by the 1-D models would lead to false definitions of the boundaries and erroneously low water-content determinations. V. C ONCLUSION We have described the key elements of the first 2-D SNMR tomographic-inversion scheme. By using simulated data from only four measurement series, the rapid new scheme accurately reconstructed the boundaries and average water content of a perched water lens. In contrast, 1-D inversions of the same data produced highly misleading models, with significant overestimates of water content below the outer coil positions, underestimates below the inner coil positions, and an average water content that was much too low. Holes drilled on the basis of erroneously predicted high water contents (i.e., 10%–17%) beneath the outer positions would practically be dry. Results from the tests shown in the Appendix demonstrate the robustness of the 2-D SNMR inversion scheme for background resistivities that vary from 1000−10 Ω · m. As resistivity significantly decreases to below 100 Ω · m for the 48-m-diameter transmitter–receiver loop, it is necessary to include the effects of the imaginary components of (2)–(9), which our scheme accomplishes by treating the relevant parameters as complex. Two further related advances in SNMR techniques are expected in the near future: 1) application of the 2-D tomographicinversion scheme to multioffset SNMR data and 2) full 3-D strategies. Our analysis has been concerned with simulated coincident transmitted/receiver coil data. The 2-D inversion results demonstrate that these conventional data are adequate for imaging relatively large water-bearing features at depths of the same order as the coil radius. Separated transmitter and receiver coils supply data with markedly improved sensitivity in mapping features situated at shallow depths [13]. As for seismic and geoelectric methods, 2-D tomographic inversions of data acquired using a range of transmitter–receiver offsets have the potential to provide high-resolution images of waterbearing structures throughout the 0–150-m depth range of SNMR techniques. Our investigation required the computation of 3-D electromagnetic fields generated and received by the coil and, then, the reduction of the problem to 2-D for the final forward modeling steps and the inversion process. Accordingly, extension of the tomographic-inversion scheme to 3-D should be relatively straightforward, such that, once fast multicoil SNMR data acquisition systems are available, it should be possible to record, process, and tomographically invert the 3-D SNMR data in the field. A PPENDIX Previous studies based on 1-D inversions of SNMR data have demonstrated the potentially important role that is played by background electrical resistivities in estimating water content [8], [14]. To investigate these effects on 2-D samples, we have
conducted a series of tests using simulated data with background resistivities of 1000, 100, and 10 Ω · m and with and without ±10-nV Gaussian noise (Figs. 5 and 6). At locations where the resistivity is quite low, it is necessary to consider not only the real components of the measured amplitudes but also the imaginary components that contain the phase information. The imaginary components of the data are very small for the two relatively high-resistivity models [Figs. 5(a) and (e) and 6(a) and (e)], but significant for the low-resistivity model [Figs. 5(i) and 6(i)]. Figs. 5(a)–(h) and 6(a)–(h) demonstrate that the results for both the 1-D and 2-D inversions are practically invariant for background resistivities greater than 100 Ω · m. By considering the low values of the imaginary components, these results are not surprising. Addition of noise slightly changes the watercontent estimates, but the 1-D and 2-D models shown in Figs. 5 and 6 reveal the same general patterns. We note that the percentage root mean-square (rms) differences between the simulated and model-predicted data are slightly higher for the data contaminated with noise than for the noise-free data. From Fig. 5(i) and (k) and Fig. 6(i) and (k), it is clear that the imaginary components are important at locations where the background resistivities are significantly below ≈100 Ω · m. Nevertheless, by including the imaginary components in the inversion process, the results are very similar to those derived for the higher resistivity models (Figs. 5 and 6). ACKNOWLEDGMENT The authors would like to thank the journal reviewers for their constructive comments on an earlier version of this paper. R EFERENCES [1] M. Schirov, A. Legchenko, and G. Creer, “A new direct non-invasive groundwater detection technology for Australia,” Explor. Geophys., vol. 22, pp. 333–338, 1991. [2] M. Goldman, B. Rabinovich, M. Rabinovich, D. Gilad, I. Gev, and M. Schirov, “Application of the integrated NMR-TDEM method in groundwater exploration in Israel,” J. Appl. Geophys., vol. 31, no. 1–4, pp. 27–52, 1994. [3] A. Legchenko and P. Valla, “A review of the basic principles for proton magnetic resonance sounding measurements,” J. Appl. Geophys., vol. 50, no. 1/2, pp. 3–19, May 2002. special issue. [4] U. Yaramanci, A. Kemna, and H. Vereecken, “Emerging technologies and approaches in hydrogeophysics,” in Hydrogeophysics, ser. Water Science and Technnology Library, vol. 50, S. Hubbard and R. Yoram, Eds. New York: Springer-Verlag, 2005, pp. 468–487. [5] P. B. Weichman, E. M. Lavely, and M. H. Ritzwoller, “Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems,” in Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 62, 2000, pp. 1290–1312. [6] P. Valla and U. Yaramanci, “Surface nuclear magnetic resonance—What is possible,” J. Appl. Geophys., vol. 50, pp. 1–229, 2002. [7] U. Yaramanci and A. Legchenko, “Magnetic resonance sounding, aquifer detection and characterization,” Near Surf. Geophys., vol. 3, pp. 119–222 and 255–310, 2005. [8] M. Braun, M. Hertrich, and U. Yaramanci, “Complex inversion of MRS data,” Near Surf. Geophys., vol. 3, no. 3, pp. 155–163, 2005. [9] M. Müller, M. Hertrich, and U. Yaramanci, “Analysis of magnetic resonance sounding kernels concerning large scale applications using SVD,” in Proc. SAGEEP, EEGS, 2006. [10] T. Günther, C. Rücker, and K. Spitzer, “Three-dimensional modelling and inversion of dc resistivity data incorporating topography—II. Inversion,” Geophys. J. Int., vol. 166, no. 2, pp. 506–517, Aug. 2006.
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[11] S. C. Constable, R. L. Parker, and C. G. Constable, “Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data,” Geophysics, vol. 52, no. 3, pp. 289–300, Mar. 1987. [12] W. Menke, Geophysical Data Analysis: Discrete Inverse Theory, ser. International Geophysics Series, vol. 45. San Diego, CA: Academic, 1989. revised ed. [13] M. Hertrich, M. Braun, and U. Yaramanci, “Magnetic resonance soundings with separated transmitter and receiver loops,” Near Surf. Geophys., vol. 3, no. 3, pp. 131–144, Aug. 2005. [14] P. B. Weichman, D. R. Lun, M. H. Ritzwoller, and E. M. Lavely, “Study of surface nuclear magnetic resonance inverse problems,” J. Appl. Geophys., vol. 50, no. 1/2, pp. 129–147, 2002.
Thomas Günther received the M.Sc. and doctoral degrees from the University of Mining and Technology Freiberg, Freiberg, Germany, in 2000 and 2004, respectively. He is currently a Researcher with the Leibniz Institute for Applied Geosciences, Hannover, Germany. His research is mainly focused on modeling and inversion methods as applied to near surface geophysics, with particular emphasis on joint inversion methods.
Marian Hertrich received the M.Sc. and doctoral degrees from the Technical University of Berlin, Berlin, Germany, in 2000 and 2005, respectively. He is currently a Research Associate and Lecturer with the Applied and Environmental Geophysics Group, ETH Zurich, Zurich, Switzerland. His research interests include the development and application of surface nuclear magnetic resonance techniques, as well as geoelectric and electromagnetic methods for groundwater investigations.
Martina Braun received the M.Sc. degree from the Technical University of Berlin, Berlin, Germany, in 2002, where she is currently working toward the Ph.D. degree at the Applied Geophysics Group. Her research interests include the development and improvement of modeling and inversion algorithms for surface nuclear magnetic resonance data, with special focus on the influence of electrical resistivity.
Alan G. Green completed his studies at British universities before moving to Canada in 1973. After a one-year Postdoctoral Fellowship at the Earth Physics Branch, Ottawa, ON, Canada, he became an Assistant Professor of geophysics at the University of Manitoba, Winnipeg, MB, Canada. In 1979, he accepted an invitation to become the Head of the Lithospheric Geophysics Section, Geological Survey of Canada, Ottawa. During his 19 years in Canada, he further developed and applied seismic reflection methods in investigations of the continental crust, studies associated with nuclear waste disposal, and mineral exploration in crystalline terranes. Shortly after a one-year sabbatical leave in Switzerland, he accepted an invitation to become a Professor of applied and environmental geophysics at the Institute of Geophysics, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland.
Ugur Yaramanci received a degree from the Technical University of Clausthal, Clausthal, Germany, in 1975 and the doctoral degree from the University of Liverpool, Liverpool, U.K., in 1978. He was a Junior Scientist and eventually became an Associate Professor of applied geophysics with the Technical University of Istanbul, Istanbul, Turkey. Supported by an Alexander von Humbold Scholarship, he conducted research at the University of Kiel, Kiel, Germany, before joining the Research Center of Environment and Health, Braunschweig, Germany, in 1987 to work on geophysical investigations that are associated with the disposal of nuclear waste. In 1993, he was appointed as a Full Professor of petrophysics with the Technical University of Clausthal, and in 1996, he became a Full Professor of applied geophysics with the Technical University of Berlin, Berlin, Germany.
