Stray Field Nuclear Magnetic Resonance of Soil Water ...

Stray Field Nuclear Magnetic Resonance of Soil Water: Development of a New,Large Probe and Preliminary ResultsP. Kinchesh, A. A. Samoilenko, A. R. Preston,* and E. W. RandallABSTRACTtial information is encoded in the output signal in conventionaltechniques by using coils that can produce aDevelopment, characterization, and preliminary results of a recenttechnique capable of local measurements of pore-size distribution by field gradient in any direction. Variation of the size anda spatially resolved low resolution nuclear magnetic resonance (NMR) direction of the gradient allows the production of a spatechniqueare described. Potential environmental uses include study- tial image in one, two, or three dimensions. The maxiingthe change in pore-size distribution caused by surface compaction, mum gradient that can be produced by such coils iswhich influences surface runoff, and obtaining information on the limited; moreover, the switching of the gradients takesphysical state of non-aqueous compounds in porous materials, whichtime. The stray field (STRAFI) technique of Samoileshouldaid the selection of appropriate soil remediation methods.nko et al. (1988) uses a static gradient, which is aboutStray field (STRAFI) imaging is an NMR technique that allows distortwoor three orders of magnitude greater: 10 to 100 T/m.tion-free imaging of materials with short NMR relaxation times. Thesample is placed in the strong axial fringe field gradient of a superconorfringe field. The place along the bore where theThis occurs away from the magnet center in the strayducting NMR magnet. We report on a new, unique, large 5-cm-diameon-axisfield is decaying rapidly with distance, z, thatter STRAFI probe, and its use for three preliminary test cases: waterin ceramics of known pore size, paraffin wax and oil in sandstone rock, is, where B z /z is large, occurs near the edge of theand water in soil at different matric potentials. The imaging is confined superconducting solenoid. The short radio frequencyto one dimension with a spatial resolution of the order of 100 m for (RF) pulses that are used to excite the NMR signal areprotons. The optimum position for imaging occurs at 2.62 T and a of finite bandwidth; this means that in general it is notgradient of 12.1 T/m. Water relaxation decay curves can be measured possible to excite the entire sample simultaneously, inatany position in the 8-cm-long sample. These curves are decomposedstead information comes from a narrow “sensitive slice,”into a series of terms each corresponding to a different pore size.Preliminary results show continuum fits to decay curves for a soil which has a width on the order of 100 m for protons.drained to three different matric potentials. Such information will The STRAFI image in one dimension normally is pro-be useful for interpreting water retention curves and will lead to duced by moving the sample through the sensitive planeunderstanding of the behavior of fluids in the vadose zone.between each pulse train. Higher dimensions can bereached by rotations of the sample. Many of the rapidlygrowing number of uses of the STRAFI technique forGaseous, liquid, and solid phases are present simul- the study of problems in materials science are describedtaneously in the vadose zone of a soil. The location in a recent review by McDonald and Newling (1998),of the fluid phases in the porous structure formed by which also treats the basic theory.the soil particles is very important both in soil physics Typically, a STRAFI image is acquired from a sampleand agriculture. In contaminated soil, non-aqueous liqlargersample is desirable. One of the constraints is theless than 1 cm in diameter, but for soils (and rocks) auids may also be present, and knowledge of their locasizeof the internal bore of the magnet, which is normallytion, whether tightly bound to clay platelets or lying indroplets in interaggregate pores, would aid selection of 89 mm. For this work we have used the 330-mm boreappropriate remediation strategies. The study of such a of a horizontal magnet (200/300 Mk II, Oxford Instru-multiphase system is a challenging problem. This paper ments, Oxford, UK) and a Unity Inova 200 consoledescribes the development of an NMR technique to (Varian Associates, Palo Alto, CA).measure both water content and the size distribution of Stray field imaging is advantageous for soil imagingoccupied pores as a one-dimensional function of posigreatlyreduces problems due to magnetic susceptibilitybecause the strong gradient, B z /z, typically 10 to 50 T/m,tion in an undisturbed soil sample. Such depth-depenvariationsarising from ferromagnetic particles in thedent behavior occurs, for example, in soils whose surfacelayers have been compacted by rain impact or the wheels soil and air in partially filled voids (Kinchesh et al.,of agricultural machinery. This compaction decreases 1994). These susceptibility variations produce strong lo-the near-surface porosity and thus increases runoff. cal internal gradients that are negligible in STRAFIMagnetic resonance imaging (MRI) is a well-estabentsused in conventional MRI and thus can lead toimaging but are not negligible compared with the gradilishedtechnique in which a sample is placed in the censevereimage distortions of conventional images.tral region of a strong magnet where the magnetic fluxdensity or field (B) is uniform and homogeneous. Spathanbulk water. The value for any one pore dependsThe water in soil has much shorter relaxation timesP. Kinchesh, A.R. Preston, and E.W. Randall, University of London, on the size of the pore and whether the water is “solid-Queen Mary and Westfield College, Chemistry Dep., London E1 4NS, like,” being bound to the pore surface. The T 2 relaxationUK. A.A. Samoilenko, Russian Academy of Science, Institute of time of water is on the order of 1 s, but the value for iceChemical Physics, Moscow, 117977, Russia.Received 2 June 2000.*Correspondingauthor (a.r.preston@qmul.ac.uk).Abbreviations: MRI, magnetic resonance imaging; NMR, nuclearPublished in J. Environ. Qual. 31:494–499 (2002).magnetic resonance; RF, radio frequency; STRAFI, stray field.494

KINCHESH ET AL.: A NEW STRAY FIELD NMR PROBE 495is only about 5 s (Nunes et al., 2000). Bound water such narrow then the relaxation rate of each pore will beas water of crystallization also has very short relaxation independent of that of its neighbors so that the overalltimes, on the order of microseconds (Randall et al., decay contains contributions from each individual pore.1995). This is normally too short for conventional imaging,The T 1 or T 2 decay curves for the whole sample arewhich can detect only down to milliseconds, so obtained, and are then fitted as the sum of a series ofthat an appreciable fraction of the water present, the discrete exponentials, or to a model distribution as in thebound water and the water in small pores, remains unde- stretched exponential approach (Kenyon et al., 1986), ortected (Hall et al., 1997). Stray field imaging, by contrast to a continuous distribution of decay times, the coeffi-can detect virtually all the water present.cients of which are taken as a measure of the pore-sizedistribution. The relaxation method, in contrast to thewater retention technique, is sensitive to the pore di-PORE-SIZE DETERMINATIONmensions rather than those of the throats. Thus, in par-One of the most important areas of soil physics con- tially drained materials we expect to see a componentcerns the behavior of water within a soil (e.g., Childs, with a long relaxation time corresponding to those large-1969). The water is present in pores of very different sizes diameter pores, which have been unable to drain beconnectedby necks or throats that are also of variable cause they are linked only to the rest of the materialdiameter. One of the common methods used to deter- by narrow necks.mine the pore-size distribution in a soil uses the water We can extend this method to provide spatially reretentioncurve. The water content of a series of samples solved information using the STRAFI technique.of soil is determined gravimetrically after each has been This paper has two parts. In the first half the designequilibrated at a different matric potential. Differentiat- and characterization of the new STRAFI probe are deingthis curve yields the amount of water lost during a scribed, and in the second part, application of the probegiven pressure increment. The soil is modeled as a bun- to three systems is reported. These case studies include:dle of capillary tubes, the pressure at which each drainsdepending on its diameter, and so the water retention(i) A comparison of images from blocks of sand-curve can be converted into a pore-size distribution.stone into which oil and wax have infiltrated.This model is, however, oversimplified, since it ignores(ii) Spatially resolved measurements of the T 1 relaxthenarrow throats. The throat diameter rather than thatation time in a series of water-saturated ceramics,of the pore will control the matric potential at which iteach with a different narrow pore-size distribu-drains. Large pores with particularly narrow throats willtion. Secondly, the spatial dependence of echodrain at the same potential as smaller ones with proporsizesis examined, to test the STRAFI methodtrains from a phantom having two known poretionately larger throats.of measuring the relative numbers of the poreRELAXATION TIMESsizes as a function of position.(iii) A sample of a natural loamy-sand soil is studiedNuclear magnetic resonance spectroscopy is routinelyas a function of matric potential using a speciallyused to measure pore-size distributions in porous materials.made holder that fits inside the STRAFI probe.Spectroscopy, unlike conventional NMR imaging,can reach the very small relaxation times and hence DESIGN AND CHARACTERIZATIONdetect water in small pores. However, there is no spatialOF THE STRAY FIELD PROBEinformation: the whole sample is used. In a porous medium,water molecules in a thin layer adjacent to the Most existing STRAFI probes (see, for example, Mcporesurface are able to relax much more rapidly than Donald and Newling, 1998) take samples with a maxi-those in the bulk. In the fast diffusion limit the time mum diameter of only about 10 mm. For soils, however,taken for a molecule to cross a pore and enter the larger samples are preferred. Soils can be very heterogesurfacelayer is much less than that needed to relax at neous and friable. We wish ultimately to study the porethesurface, thus all molecules in a given pore relax at size distribution of undisturbed material, so it is impor-a fixed rate given by a weighted average of the bulk tant to minimize edge effects caused by compactionand surface decay rates. Thus, the relaxation time for when a sample is extracted from the ground. We have,a given pore is the harmonic mean of the bulk and therefore, constructed a STRAFI probe that can takesurface decay times. So, for a given pore shape the pore samples up to 50 mm in diameter and up to 80 mmsize d is related to the measured relaxation time T i (i long, which can be rapidly installed inside our 330-mm1 or 2 depending on experiment) by: horizontal-bore imaging spectrometer.1/T i 1/T ib i /d [1]The STRAFI probe consists of a silica tube on whichthe double turn RF saddle coil is wound, and into whichwhere T ib is the relaxation time for the bulk liquid and the sample is placed. During preliminary testing of the i is the relaxivity factor, which includes the thickness coil, the field uniformity inside the coil had been empiriofthe surface layer, the efficiency of surface relaxation, cally optimized by placing shaped copper shims adjacentand geometrical factors. The measured relaxation curve to the longitudinal conducting strips.for a porous material will not in general be a simple The probe is contained in an RF shielding box throughexponential decay, and if the throats linking pores are the walls of which the connections are made. This whole

496 J. ENVIRON. QUAL., VOL. 31, MARCH–APRIL 2002ment of the phantom relative to the magnet axis (asdescribed already), and if multiple scans are added toimprove signal to noise, there should be no drift in originof the translational scan.During acquisition of a profile, the sample and thecoil move along the axis of the magnet. At each slicethe signal is generated from a different position in thecoil, thus it is necessary to find the region of the coilover which the signal is uniform. A phantom was assembledfrom Perspex discs separated by successively thin-ner glass spacers, each of 5 cm diameter. The STRAFIprobe was mounted on the translation mechanism andthe latter bolted onto the front face of the magnet. Theexperiment was carried out to determine the resolutionthat would routinely be attainable relying simply on theprecision of the machining.The 1 H profile (Fig. 1) is the result of overnight averaging:2143 complete scans were acquired. Figure 1shows that with a 90-m step size, the slice flatness andprobe alignment are sufficiently good for a 40-m-thickspacer to be detected. It also demonstrates that thePerspex signal is essentially uniform over the length ofthe phantom. The slight variation in the Perspex signalalong the profile shows that the RF production of thecoil is not entirely uniform. The large step size limitsthe spatial resolution, but this could be improved byusing smaller steps. On other occasions with fewer averages,the 40-m spacer was also readily detectable, dem-onstrating the reproducibility of the probe alignment.Overnight scanning is a test of the reliability of thestepper motor and position encoder.The resolution could be improved also by increasingthe pulse duration. This would require a longer echotime and so would only be practical if the phantom wereconstructed from a material with a longer T 2 relaxationtime than 36 3 s (Kinchesh, unpublished data, 2000),which was found by STRAFI for Perspex.probe–assembly is mounted on a platform that can bemoved in and out of the magnet on horizontal rails bya screw thread driven by a stepper motor. The controllerfor the stepper motor (PM341, Mclennan Servo SuppliesLtd., Camberley, UK) includes a position encoder toensure repeatability of the slice locations during multiplerepeat scans. Sample movement, RF pulsing, andimage acquisition are all controlled from the spectrometerconsole. Profiles are obtained by a simple “step andpulse” method, rather than by continuous movement“on the fly.” Currently adjacent slices are acquired consecutivelyrather than in an interleaved fashion.The Selected SliceIn STRAFI imaging, when the RF pulse is appliedthe signal is produced only from a thin slice of the sample,Samoilenko’s so-called “sensitive slice.” At the positionin the field at which B z /z is a maximum the slicewill be at its narrowest, but it will be nonplanar, thusalthough the volume of material contributing to thesignal will be a minimum, the curvature of the slice willdegrade the resolution in a projected one-dimensionalprofile. It is more important that the projected widthof the slice, rather than its local thickness at the slicecenter, be a minimum. This occurs at a slightly different(optimum) position where the curvature 2 B z /r 2 0(cylindrical polar coordinates). This position was locatedfrom an examination of the manufacturer’s fieldplots. The frequency, OPT , at this position, was thenfound to be 111.5 MHz. The gradient, G B z /z, atthis position was measured to be 12.091 0.016 (2)T/m. This measurement was achieved by “field profil-ing”: imaging a phantom consisting of a series of well-defined interfaces between silicone rubber and glassdiscs, and observing the displacement of these featuresat a set of frequencies over a frequency range of 11MHz (Preston et al., 2000).Resolution and Uniformity TestFig. 1. One-dimensional 1 H stray field (STRAFI) image of the resolu-tion test phantom, made from alternating Perspex and glass discseach of 50 mm diameter. Thickness of each glass spacer is givenabove the appropriate minimum in the profile. The slice separation(step size) is 90 m. The intensity profile is the sum of the firstfive echoes of the STRAFI echo train, with one point per echo.It is important that the probe can be easily removedfrom the magnet and replaced without needing carefuladjustment of the orientation of the translation mechanismrelative to the magnet axis. The sensitive slice isat right angles to the magnet axis, z, and ideally thesample should move precisely along z, and should bemounted in the correct orientation in order to realizethe best resolution in the one-dimensional projection.The resolution seen in an image from a phantomconsisting of a series of parallel-sided discs dependsupon both specimen-dependent and instrumental factors.The former include the width of the excited sliceand the intrinsic line width: small for 1 H larger for othernuclei with I 1/2 but significant for those with I 1/2, that is, quadrupolar nuclei (Bodart et al., 1997).The instrumental factors are the gradient and the lengthof the RF pulse: large gradients and long pulses givenarrow slices. The length of the pulse must, however, beshort enough to allow detection of the small relaxationcomponents. The instrumental considerations also includethe curvature of the sensitive slice and the align-

KINCHESH ET AL.: A NEW STRAY FIELD NMR PROBE 497APPLICATIONStimes. The diffusion effect is enhanced by the large sizeSandstoneof the gradient in STRAFI experiments.Two sandstone samples were prepared, each 15 mmthick by 30 mm square. They were placed with one faceCeramicsjust immersed in mineral oil for one sample and in An aim of the work is to use STRAFI to investigatemolten paraffin wax for the other. Capillary absorption pore-size distributions in soils. An initial feasibility testof the liquids was followed visually by observing the was to apply the technique to a series of highly porousside faces of the blocks. The latter were removed from ceramics, each with a narrow pore-size distribution.contact with the liquids when the wetting front was Discs of Coralith (Fairey Industrial Ceramics, Staffs,about halfway up the faces. The paraffin was allowed UK), made of alumina particles bonded by glass withto solidify.mean pore sizes of 300, 30, 20, 3, and 1 m, were used.One-dimensional STRAFI profiles were then acquired(Further details on these materials together with waterof each block using quadrature echo trains, x retention curves are given in Whalley et al., 2001.) Each( y echo) ne , where x and y are square RF disc was 8 mm thick and 31 mm in diameter. They werepulses of duration 20 s, and x and y denote the relative saturated with distilled water by placing them in a waterphases,which differ by 90 degrees. One complex point filled desiccator connected to a vacuum line for twoper echo was recorded for each of ne 32 echoes. The hours. The saturated discs were separated from eachtime, , between the first two pulse centers was 35 s, other by acetate sheets, and stacked into a cylindricalgiving a time between successive echoes, t e ,of70s. phantom that was then wrapped in Parafilm sealingFor the image (Fig. 2a), 140 slices were acquired. In tissue (Gallenkamp, Loughborough, UK) to preventFig. 2b, markedly different behavior for the two samples evaporation during measurement. The STRAFI systemis seen by comparing signal versus echo number. The was then used to address each disc in turn, and T 1 valuessignal for the solid paraffin steadily increases initially were determined for each disc using the progressivewith echo number indicating that a tip angle consider- saturation method with 40 different recovery timesably less than 90 degrees was used. The level after a spaced logarithmically.few echoes shows very little decay, however, unlike the A single exponential was fitted to the relaxation curveoil signal that decays rapidly. This rapid decay is caused of each disc using the Varian VNMR software. Figure 3by the much faster diffusion in the liquid as opposed to shows the linear relationship obtained by plotting thein the solid as well as by differences in the relaxation reciprocal of T 1 against that of pore diameter. This isas expected but the quality of the fit is a good illustrationof the power of NMR to determine pore size. With theSTRAFI method the spatial variation may be studied.The relaxation of water in a pore is an average valuebecause of the fast exchange of hydrogen between sites.The average is a weighted one; so that as the proportionof free to bound water varies, the average relaxationtime will vary. Hence follows the relation between relaxationtime and pore size. It is expected that in Fig. 3,the intercept should equal the relaxation rate of bulkwater, and the slope should be the relaxivity. The valuesFig. 3. Dependence of the longitudinal relaxation time, T 1 , as deter-mined by stray field (STRAFI) nuclear magnetic resonance (NMR)on the nominal pore diameter for a series of water-saturated ceramicdiscs in a single phantom, each with a narrow pore-sizedistribution and high porosity (ca. 35%). The T 1 recovery curvewas fitted with a single exponential. The line is a weighted leastsquares fit to the data.Fig. 2. Stray field (STRAFI) profiles of two sandstone blocks intowhich molten paraffin wax and mineral oil have diffused from theirright faces. Markers were placed in contact with the left faces. (a)Intensity distributions recorded from points at the peak of the first,second, and third echoes of the echo train. (b) Amplitude of theechoes along the echo train for paraffin and mineral oil. Pointsplotted are the averages over six adjacent slices at positions indicatedin the profile by short bars.

498 J. ENVIRON. QUAL., VOL. 31, MARCH–APRIL 2002obtained are T 1b 1.027 0.3s(2) and relaxivity 1 1.96 0.10 m/s (2).The following experiment was performed to checkthe feasibility of using STRAFI data for a phantomcontaining more than one pore size at any one position.A phantom was designed that contained only two poresizes, the proportion of which varied in a controlled waywith position. A composite ceramic cylinder, 31 mm indiameter and 24 mm long, was produced by cuttingtwo Coralith cylinders of mean pore size 1 and 20 mrespectively at an angle of 45 degrees, and combiningone piece from each. The two pieces were separated byan acetate sheet. After the composite bi-wedge cylinderwas saturated with water as described above, it was Fig. 5. Diagram of the apparatus developed to permit variation ofwrapped in Parafilm, and two end pieces of matching the matric potential of a soil sample within the stray field (STRAFI)pore size were added at the appropriate ends. The T coil. The potential can be altered by raising or lowering the reser-2voir. It is important that the sintered plate is saturated with water.values were then measured at eight positions along thephantom with a Carr–Purcell–Meiboom–Gill experimenthaving 912 repeats and 128 echoes.SoilThe T 2 data from the bi-wedge were analyzed by A loamy sand (Kingsmead, 80% sand, 11% silt, 9%SPLMOD, a program by Provencher and Vogel (1983), clay) was selected because its water content could bein which a number of discrete exponentials are fitted varied significantly over the range of matric potentialsto a decay curve. It was decided to find a single pair of obtainable with a vacuum pump. Air-dry soil, which hadexponentials to fit all eight positions across the compos- been passed through a 5-mm sieve, was packed into aite cylinder while letting the program select the propor- glass cylinder in contact with a reservoir of distilledtion of each needed for each slice. These proportions water via a saturated microporous glass sinter (Fig. 5).and their errors are plotted in Fig. 4. The fit to the After the soil had been saturated, the assembly wasexpected form arising from the known geometry is very placed inside the STRAFI probe so that all three regionsgood as indicated in the inset. The phantom is cylindriofthe coil.(soil, sinter, and water) lay within the uniform regioncal, with the bisecting plane cutting the circular endfaces so we do not expect the contribution of the minor As a preliminary test, the matric potential was variedcomponent to vanish at the end slices, nor should the simply by lowering the water level in the reservoir rela-contribution of a given pore size vary strictly linearly tive to the midline of the probe by 20, 40, and 60 cm.with position, as would be expected if a cuboidal phansusposition clearly revealed inhomogeneities in soilTwo-dimensional displays of echo-train amplitude ver-tom had been used. Without the constraint that all sliceshad the same pair of exponentials, the fit was not as packing. A slice with strong intensity was selected andgood. Part of the problem is the noise that occurs in a decay curve obtained for each matric potential. Thethe experimental results.pulse sequence used was [ x ( y echo) ne D] nr with a (pulse center separation) of 55 s, pulselengths of 35 s, a D of 1 s, ne 768, and nr 14000.The amplitude of the echo peaks, omitting the first fourechoes, were fitted to continuous distribution of decayrates using the program CONTIN (Provencher, 1982).Fig. 4. Spatial dependence of the amplitudes of two exponential decayterms needed to fit peak amplitudes in echo trains from a seriesof positions along a cylinder made up from two half cylinders inthe form of a bi-wedge. The mean pore sizes are 1 and 20 m andare shown above the graph.DISCUSSIONThese initial results are encouraging. As the matricpotential is increased, the distribution peak moves tohigher rates (see Fig. 6) and becomes less skewed tothe low rate (i.e., large pore end), and the overall areaof the distribution curve decreases. The reduction inarea occurs due to the reduction in total water contentof the sample, while the preferential loss of low rateterms is evidence for the expected draining of largepores before smaller ones. However, there is not anabrupt cutoff at the large pore end, whose positionmoves steadily to higher rates on draining; instead, thedistributions all start at the same minimum rate. Thisis consistent with the hypotheses that the sample doesnot behave as a bundle of capillary tubes, each drainingat a fixed matric potential, but instead as interlinked

KINCHESH ET AL.: A NEW STRAY FIELD NMR PROBE 499ACKNOWLEDGMENTSThanks to Dr. Richard Whalley and Dr. Nigel Bird at theSoil Science Group of the Silsoe Research Institute for muchuseful advice and the supply of the ceramic and soil samples.Thanks also to John Cowley for construction of the holderfor use in the experiments using variable matric potential. Thiswork was supported by BBSRC Grants 68/E08576 and 68/E09853. The NMR instrumentation was provided by the Universityof London Intercollegiate Research Services schemeand is located at Queen Mary and Westfield College.REFERENCESBain, A.D., and E.W. Randall. 1996. Hahn spin echoes in large staticgradients following a series of 90 degree pulses. J. Magn. Reson.Fig. 6. Distributions of exponential decay terms produced by CON- A123:49–55.TIN analysis of the peak amplitude of successive echoes from a Bodart, P., T. Nunes, and E.W. Randall. 1997. STRAFI imaging oflong train of pulses applied to a loamy sand in the variable matric solids: The spatial resolution for quadrupolar nuclei with I 3/2.potential holder. Three distributions produced by successively Appl. Magn. Reson. 12:269–273.draining the soil to 20 hPa (20 cm), 40, and 60 hPa are shown. Childs, E.C. 1969. An introduction to the physical basis of soil waterFits were made to 54 logarithmically spaced decay terms.phenomena. Wiley-Interscience, London.Hall, L.D., M.H.G. Amin, E. Dougherty, M. Sanda, J. Votrubova,K.S. Richards, R.J. Chorley, and M. Cislerova. 1997. MR propertiespores and throats, and that not all pores of a given of water in saturated soils and resulting loss of MRI signal in waterdiameter are as easy to drain.content detection at 2 Tesla. Geoderma 80:431–448.This preliminary work needs to be expanded. In parandconsistent representation of rock NMR data for permeabilityKenyon, W.E., P.I. Day, C. Straley, and J.F. Willemsen. 1986. Compactticular, the signal from the soil at each potential mustestimation. SPE Paper 15643. Soc. Petrol. Eng., Richardson, TX.be normalized relative to that of the bulk water and Kinchesh, P., E.W. Randall, and K. Zick. 1994. Magnetic-susceptibilitythat in the sinter (which will stay fully saturated at the effects in imaging—Distortion-free images of plant-tissue in soil.matric potentials under investigation) because the RF Magn. Reson. Imaging 12:305–307.properties of the coil vary significantly as the sample McDonald, P.J., and B. Newling. 1998. Stray field magnetic resonanceimaging. Rep. Prog. Phys. 61:1441–1493.drains. The ideal pulse sequence is still being sought; a Nunes, T.G., E.W. Randall, and G. Guillot. 2000. Relaxation studiesbalance is needed between acquisition time, echo time, of ice in a 7 T superconducting magnet: Zero and STRAFI-gradientand the number of points in the decay curve. Additional observations. In Abstr., 41st Exp. NMR Conf., Asilomar, CA. ENC,work is needed on the theory of the form of the echo Santa Fe, NM.trains following the work of Bain and Randall (1996), Preston, A.R., P. Kinchesh, and E.W. Randall. 2000. Calibration ofthe stray field gradient by a new heteronuclear method and bywhich showed that there are contributions from both field profiling. J. Magn. Reson. 146:359–362.T 1 and T 2 to the relaxation characteristics of each of the Preston, A.R., P. Kinchesh, E.W. Randall, N.R.A. Bird, and W.R.echoes in the relaxation curves fitted to produce Fig. 6. Whalley. 2001. STRAFI-NMR studies of water transport in soil.Magn. Reson. Imaging 19:561–563.Provencher, S.W. 1982. CONTIN—A general-purpose constrainedCONCLUSIONSregularization program for inverting noisy linear algebraic andintegral equations. Comput. Phys. Commun. 27:229–242.The advantages of the use of STRAFI-NMR tech- Provencher, S.W., and R.H. Vogel. 1983. Regularization techniquesniques for the study of water in soils have been success- for inverse problems in molecular biology. Progr. Sci. Comput. 2:fully demonstrated on a suitably large probe. Experi- 304–319.Randall, E.W., A.A. Samoilenko, T. Nunes. 1995. NMR imaging ofments have included the production of one-dimensionalparamagnetic solids in the high-field-gradient approximation withprofiles free of distortions produced by magnetic suscep- the STRAFI method. J. Magn. Reson. A116:122–124.tibility artifacts, and the measurement of the spatial Samoilenko, A.A., D.Y. Artemov, and L.A. Sibeldina. 1988. Formationof sensitive layer in experiments on NMR subsurface imagingvariation of relaxation times, yielding information on thespatial variation of pore sizes. Other applications are easy of solids. JETP Lett. 47:417–419.Whalley, W.R., C.W. Watts, M.A. Hilhorst, N.R.A. Bird, J. Ballentovisualize: any liquid in any solid. Work on some of dock, and D.J. Longstaff. 2001. The design of porous materialthe potential applications mentioned in the introductory sensors to measure the matric potential of water in soil. Eur. J.paragraph is in progress (Preston et al. [2001]).Soil Sci. 52:511–519.