Resolving the spatial distribution of the true electrical conductivity with depth using EM38 and EM31 signal data and a laterally constrained inversion model.
|Abstract:||The ability to map the spatial distribution of average soil property values using geophysical methods at the field and district level has been well described. This includes the use of electromagnetic (EM) instruments which measure bulk soil electrical conductivity ([[sigma].sub.a]). However, soil is a 3-dimensional medium. In order to better represent the spatial distribution of soil properties with depth, various methods of inverting EM instrument data have been attempted and include Tikhonov regularisation and layered earth models. In this paper we employ a I-D inversion algorithm with 2-D smoothness constraints to predict the true electrical conductivity (([sigma]) using [[sigma].sub.a] data collected along a transect in an irrigated cotton field in the lower Namoi valley. The primary [[sigma].sub.a] data include the root-zone measuring EM38 and the vadose-zone sensing EM31, in the vertical (v) and horizontal (h) dipole modes and at heights of 0.2 and 1.0 m, respectively. In addition, we collected [[sigma].sub.a] with the EM38 at heights of 0.4 and 0.6 m. In order to compare and contrast the value of the various [[sigma].sub.a] data we carry out individual inversions of EM38v and EM38h collected at heights of 0.2, 0.4, and 0.6 m, and EM31v and EM3 lh at 1.0 m. In addition, we conduct joint inversions of various combinations of EM38 [[sigma].sub.a] data available at various heights (e.g. 0.2 and 0.4 m). Last we conduct joint inversions of the EM38v and EM38h [[sigma].sub.a] data at 0.2, 0.4, and 0.6 m with the EM31 v and EM3 lh at 1.0 m. We find that the values of [sigma] achieved along the transect studied represent the duplex nature of the soil. In general, the EM38v and EM38h collected at a height of 0.2, 0.4, and 0.6 m assist in resolving solum and rootzone variability of the cation exchange capacity (cmol(+)/kg of soil solids) and the electrical conductivity of a saturated soil paste extract ([EC.sub.e], dS/m), while the use of the EM31 v and EM31 h at 1.0 m assists in characterising the vadose zone and the likely location of a shallow perched-water table. In terms of identifying an optimal set of EM [[sigma].sub.a] data for inversion we found that a joint inversion of the EM38 at a height of 0.6 m and EM31 signal data provided the best correlation with electrical conductivity of a saturated soil paste ([EC.sub.p], dS/m) and [EC.sub.e] (respectively, 0.81 and 0.77) closely followed by a joint inversion of all the EM38 and EM31 [[sigma].sub.a] data available (0.77 and 0.56).|
Soils (Environmental aspects)
Electrical conductivity (Research)
Santos, F.A. Monteiro
|Publication:||Name: Australian Journal of Soil Research Publisher: CSIRO Publishing Audience: Academic Format: Magazine/Journal Subject: Agricultural industry; Earth sciences Copyright: COPYRIGHT 2010 CSIRO Publishing ISSN: 0004-9573|
|Issue:||Date: August, 2010 Source Volume: 48 Source Issue: 5|
|Topic:||Event Code: 310 Science & research|
|Product:||Product Code: 8523400 Geophysics NAICS Code: 54171 Research and Development in the Physical, Engineering, and Life Sciences|
|Geographic:||Geographic Scope: Australia; Portugal Geographic Code: 8AUST Australia; 4EUPR Portugal|
Over the last 30 years the application of electromagnetic (EM) induction instruments for natural resource management has increased. For example, the root-zone sensing EM38 has been used to map soil management zones (Triantafilis et al. 2009a) and discern the spatial distribution of average soil moisture (Huth and Poulton 2007; Tromp-van Meerveld and McDonnell 2009), soil salinity (Amezketa and De Lersundi 2008; Wu et al. 2009), clay content (Triantafilis et al. 2001; Doolittle et al. 2002), and cation exchange capacity (Triantafilis et al. 2009b). This is because the EM38 measures the apparent soil electrical conductivity ([[sigma].sub.a]), which is a function of these soil properties. As a consequence, related soil management issues such deep drainage risk (Triantafilis et al. 2003, 2004) and depth to a water table (Buchanan and Triantafilis 2009) have also been mapped using digital soil mapping methods.
However, management of soil also requires information about the vertical distribution of its properties. In order to determine this, various approaches have been proposed. The best examples appear in relation to describing soil salinity and include the development of techniques to calibrate the EM38 using multiple regression (Rhoades and Corwin 1981), simple depth weighted (Cameron et al. 1981 ; Wollenhaupt et al. 1986), empirical (Corwin and Rhoades 1982, 1984), modelledcoefficients (Slavich 1990), and logistic profile modelling (Triantafilis et al. 2000).
A less site-specific approach involves the reconstruction of the true electrical conductivity ([sigma]) profile itself. Cook and Walker (1992) developed a method using linear combinations of [[sigma].sub.a] measurements to estimate o at a depth interval of interest. Borchers et al. (1997) used Tikhonov regularisation for estimating [sigma] within a soil profile. This was similarly the approach of McBratney et al. (2000) and Hendrickx et al. (2002), who compared various methods of inversion. In all cases this was done for single profiles. More recently, Vervoort and Annen (2006) compared various methods of inversion to model the stratigraphy across a prior stream channel at the field level, while Triantafilis and Monteiro Santos (2009) similarly described how EM38 and EM34 [[sigma].sub.a] measurements can be used to reconstruct o using a I-D inversion algorithm with 2-D smoothness constraints to identify pedoderms, and physiographic and stratigraphic units across a district.
In this paper we explore the use of [[sigma].sub.a] measurements made in the vertical and horizontal modes using an EM38 at several heights (0.2, 0.4, and 0.6 m) and an EM31 at a single height (1.0 m) to reconstruct o along a transect in an irrigated field in the lower Namoi valley. We do this because there is little published research in the soil science literature that addresses the issue of reconstructing o, which depends on the (i) frequency of the energising field, (ii) electrical structure of the earth, (iii) coil spacing, and (iv) configuration of the coils. To reconstruct o, we employ a modified I-D inversion algorithm with 2-D smoothness constraints (Monteiro Santos 2004) using various combinations of EM38 and EM31 [[sigma].sub.a] data. We compare these models qualitatively and quantitatively with estimated and measured soil laboratory data including: volumetric moisture content ([theta]), electrical conductivity of a saturated soil paste ([EC.sub.p]) and extract ([EC.sub.e]) (dS/m), clay content (%), and cation exchange capacity (CEC, mmol(+)/kg soil solids).
Materials and methods
The study field is 3km south-east of Wee Waa (Fig. 1) in the lower Namoi Valley of northern New South Wales (30.24[degrees]S, 149.48[degrees]E). The field is 26 ha and is used mostly for irrigated cotton production. A water storage is next to the south-west comer. The field is at the northern edge of the Pilliga Scrub. Stannard and Kelly (1977) described the upper sediments as being coarse to intermediate in texture with ephemeral creeks draining the northern part into the Namoi River. The soil varies considerably and includes: (a) contorted gilgai of fine texture (Dermosol); (b) Red-Brown and transitional Red-Brown earths (Kurosols) with sandy surface layers underlain by heavy clays; (c) Solodized Solonetz (Sodosols) with coarse-textured surface horizons, differentiated from the subsoil either by a well-developed and columnar structure; and (d) Deep Sands (Rudosol) that consist of undifferentiated reddish sandy loams.
Data generation and laboratory analysis
EM data collection involved acquisition along a single transect (i.e. Transect 3) using an EM38 and EM31 in various modes of operation and heights. This was achieved by carrying out several passes using a mobile electromagnetic sensing system (MESS; Triantafilis et al. 2002). Here, EM38 measurements are made in the vertical (EM38v) and horizontal (EM38h) modes of operation. Given the operating frequency of the EM38 (i.e. 14.5 kHz) and coil spacing (1.0 m), the theoretical depth of exploration is, respectively, 1.5 and 0.75 m (McNeill 1990) when the instrument is placed on the ground. In this study we measure EM38v and EM38h [[sigma].sub.a] at heights of 0.2, 0.4, and 0.6 m. In comparison, the larger coil spacing (3.7m) and smaller operating frequency (9.8 kHz) of the EM31 enable theoretical depths of exploration of 6 and 3 m, when measured in the vertical (EM31v) and horizontal (EM31h) mode and a height of 1.0 m (McNeill 1980).
To compliment the [[sigma].sub.a] data and subsequently validate the EM inversions, 9 sampling sites are available along the transect from site 22 in the south to site 14 in the north. These were chosen to account for the range of EM [[sigma].sub.a] data values (Triantafilis et al. 2009b). At each site, soil was sampled at 0.30-m depth increments to 2.1 m. The samples were analysed for gravimetric soil moisture content (w, %), [EC.sub.p] and [EC.sub.c] (dS/m), and the saturation percentage (SP). To convert w into volumetric moisture content ([theta]), we first estimate bulk density ([rho], g/[cm.sup.3]) using [rho] = 1.73-0.0067 x SP, which Rhoades et al. (1989) suggest can be used under most soil conditions. We calculate [theta] ([cm.sup.3]/[cm.sup.3]) from w x [rho]. Particle size fraction is determined using the hydrometer method. From the clay, silt, and sand content, the soil texture class and group are estimated. The Tucker (1974) method is used to estimate CEC (mmol(+)/kg) using a mechanical leaching device (Holmgren et al. 1977), given the method is preferred for alkaline soil containing solid phase carbonates (Loveday et al. 1972).
[FIGURE 1 OMITTED]
Profile reconstruction using a 1-D laterally constrained method
The 1-D laterally constrained method (i.e. EM34-2D) developed by Monteiro Santos (2004) was modified and used to jointly invert the EM38 and EM31 [[sigma].sub.a] data. It is selected, in opposition to the use of a collection of different 1-D inversions, because Monteiro Santos (2004) showed that the performance of EM34-2D is optimal, particularly in environments showing variations in lateral conductivity. The method of inversion is based on the non-linear smoothness-constrained inversion algorithm proposed by Sasaki (1989). Forward and derivatives calculations are based on the cumulative functions (McNeill 1980). The earth model used in the inversion consists of several blocks whose distribution and size depend on the site location and number of inter coil spacings used. The minimisation of an appropriate objective function allows the estimation of the corrections to the model parameters in each iteration. The objective function (Q) to be minimised is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [W.sub.d] is a diagonal matrix, consisting of the reciprocal of data standard deviations; C is the roughness operator as defined by Sasaki (1989); [DELTA][??]p is the vector containing corrections applicable to the parameters (logarithm of block conductivity [p.sub.i]-ln [[sigma].sub.i]) of an initial model (e.g. a uniform medium with [sigma] set equal to the average [sigma] along a profile); and [DELTA][??]d is the vector of differences between the logarithm of calculated and observed [[sigma].sub.a]. Minimisation yields the normal equations (Sasaki 1989):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [bar.J] is the Jacobian matrix whose elements are given by [[bar.J].sub.ij] = [partial derivative][d.sub.i]/[partial derivative][p.sub.j]. The parameter [lambda] is a Lagrange multiplier and is used to control the balance between data fit and smoothness of the initial model, whereby the larger the value of [lambda] the smoother the model. We use a [lambda] of 0.6 with inversions modelled onto a 2-m mesh spacing along the transect at depths of: 0.075, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.95, 1.05, 1.17, 1.28, 1.40, 1.53, 1.67, 1.80, 1.95, and 2.1 m. For each inversion our initial 1-D model consists of 11 layers with values of [sigma] ascribed as follows: 0.3, 0.6, and 0.9m (60mS/m); 1.2, 1.6, 2.0, and 2.5m (90 mS/m); 3.0, 4.0, and 6.0m (120 mS/m); and a bottom layer (120 mS/m).
In order to compare the results achieved using various EM instruments and modes of operation, different inversions are performed. To characterise the root-zone, the EM38 [[sigma].sub.a] available at 0.20 m are inverted. To see if we can improve our ability to resolve differences in topsoil [sigma], and in particular the generally duplex nature of the solum, we invert the EM38 [[sigma].sub.a] data available at heights of 0.40 and 0.6m. Joint inversions of the various heights are then compared and contrasted qualitatively with the inversions of EM38 data achieved at a single height. Using the misfit--i.e.:
= 100x [square root of ([N.summation over (i) [[([sigma].sub.ai] - [[sigma].sup.cal.sub.ai]).sup.2]]/N]
where [[sigma].sub.a] is the measured o[[sigma].sup.cal.sub.a] the model predicted apparent conductivity and N is the number of data being inverted--between data and model response as a quantitative measure of performance, we compare the results of these inversions of [[sigma].sub.a] in terms of which produces the smallest misfit. Similar comparisons are made in this way with regard to joint-inversions conducted using the various EM38 [[sigma].sub.a] data along with the EM31. To understand the distribution of [sigma] in the subsoil the EM31 [[sigma].sub.a] available at 1.0m is also inverted.
Results and discussion
Measured soil [[sigma].sub.a]
Figure 2b shows the spatial distribution of EM38v [[sigma].sub.a] collected across the field. The southern end is characterised by larger [[sigma].sub.a] (i.e. >50 mS/m) than the northern end (i.e. <50 mS/m). Figure 3 shows the spatial distribution of EM38 and EM31 [[sigma].sub.a] measured in various modes of operation and at several heights along transect 3. The following points summarise the [[sigma].sub.a] data: (i) [[sigma].sub.a] patterns are similar; (ii) ca is larger in the vertical than the horizontal mode for both instruments; (iii) EM31 [[sigma].sub.a] is larger than equivalent EM38 [[sigma].sub.a]; (iv) EM38 data decrease with increasing height: (v) [[sigma].sub.a] generally decreases from south to north (i.e. tail ditch); (vi) difference in [[sigma].sub.a] in vertical and horizontal mode is larger in the south.
[FIGURE 2 OMITTED]
With regard to the second summary point, we would expect the o profile to be normal. That is, o of the topsoil (0-0.3 m) and subsurface (0.3-0.6m) would be less than the subsoil [sigma] (>0.6 m). It is noted that at the southern end of the field, a local minimum in [[sigma].sub.a] exists at a Northing of 6651750 (i.e. at site 19), which is equivalent to the values of [[sigma].sub.a] (e.g. EM38v [[sigma].sub.a] ~50 mS/m) that characterise the northern end of the field.
[FIGURE 3 OMITTED]
Spatial distribution: laboratory-measured soil properties
To interpret our profile reconstruction of [sigma], we briefly describe the laboratory-measured soil properties collected from the 9 cores and generated using the Graph-Contour Plot command in JMP (SAS 2002). Figure 4a shows the plot of estimated volumetric soil water content ([theta]) with depth. At the southern end, [theta] is generally larger. This is particularly the case in the deeper subsoil layers of profiles 17, 18, and 19 (i.e. >1.5m). While the values indicated would not be considered saturated, the soil here is commonly waterlogged, as evidenced by mottled soil colours noted during the sampling program (Triantafilis et al. 2002).
[FIGURE 4 OMITTED]
Figure 4b shows the spatial distribution of clay content (%). Topsoil and subsurface clay percentage is small ([less than or equal to] 20%) and equates to a loam to silty loam texture class (Texture Group 3) when considering the other particle size fractions. At the southern end, subsoil clay content (i.e. 22, 21, 20, and 19) is intermediate (i.e. 25-40%), varying from a clay loam (Texture Group 4) to light clay (Texture Group 5). In the centre and northern part of the field (i.e. 18, 17, 16, 15, and 14), subsoil clay content (>40%) falls within the light-medium to heavy clay classes (Texture Group 6).
Since the change in Texture Group is >1.5 (i.e. loamy topsoil to light to medium-heavy clay subsoil), the differences noted in 0 are attributable to the predominantly duplex nature of the soil. Given the duplex nature of the soil and the smaller ca values that characterise the profiles at the northern end (Fig. 4c), we conclude these profiles are equivalent to the Red-brown earths (i.e. Kurosol) which characterise the ephemeral creeks draining the northern part of the Pilliga Scub (Stannard and Kelly 1977). It should be noted that cores 19 and 20 have uniform and gradational Principle Profile Forms, respectively, and that the general increase in clay content from south to north does not match the [[sigma].sub.a] response, which generally decreases in this direction.
As shown in Fig. 4d, the topsoil is characterised by uniformly low CEC (i.e. [less than or equal to]9 cmol(+)/kg soil), with CEC intermediate to high in the subsoil. At the southern end, subsoil CEC is highest (i.e. >18 cmol(+)/kg soil), while in the north, CEC ranges from low (9 cmol(+)/kg soil) to intermediate (12-15 cmol(+)/kg soil). With regard to [EC.sub.e], Fig. 4e shows that a small amount of salt has accumulated in 2 of the cores at the southern end (i.e. 18 and 20). Here, [EC.sub.e] is large (i.e. >4.5dS/m). Interestingly, site 19 coincides with where [EC.sub.e] is small (i.e. <1.5 dS/m), exhibiting salinity levels equivalent to the profiles at the northern end (i.e. [less than or equal to] 1.5 dS/m). This is also the case with sites 22 and 21, where [EC.sub.e] was >1.5 dS/m in the subsoil.
Figure 3e shows the spatial distribution of the measured [EC.sub.p]. It represents the overall [sigma] of the samples collected and is therefore a measure of the various soil properties known to influence [[sigma].sub.a]. As such, the [EC.sub.p] data give us a means to validate our various estimates of [sigma] achieved from the inversion of [EC.sub.a] data from the EM38 and EM31 as well as joint inversions. Note that the change in soil type along the transect can be inferred from the [EC.sub.p], CEC, and [EC.sub.e] data, as well as the [[sigma].sub.a] shown in Fig. 3, given these soil properties change at a Northing of 6 651 950 or at site 17.
Profile reconstruction using multiple EM measurements
We qualitatively describe the results of our profile reconstruction of [sigma] compared with our measured laboratory data. We also quantitatively compare our inversions in terms of total misfit (see Table 1). Figures 5 and 6 show the result of the reconstruction of [sigma] using our 1-D inversion algorithm with 2-D smoothness constraints using the various combinations of EM38 and EM31 [[sigma].sub.a] measurements. Given the short scale variation evident in the [[sigma].sub.a] data (Fig. 3) and our knowledge of the lateral variation in soil properties (Fig. 4), and hence conductivity (as shown by [EC.sub.p] in Fig. 3e), we chose a [lambda] value of 0.6.
Root-zone modelling: using individual EM38 [[sigma].sub.a] heights
Figure 5a shows the spatial distribution of [sigma] to a depth of 2.1 m and considering the inversion of the root-zone measuring EM38v and EM38h [[sigma].sub.a] data collected at a height of 0.20m. The global misfit is 2.86%. The 2-D distribution of [sigma] generally reflects the spatial distribution of 0 (Fig. 4a) and the duplex nature of the soil (Fig. 4b). However, the pattern of c corresponds better with the spatial distribution of CEC (Fig. 4d), [EC.sub.e] (Fig. 4e), and [EC.sub.p] (Fig. 3e).
With reference to soil texture, the sandy to loamy sand topsoil (0-0.3m) and subsurface (0.3-0.6m) horizons are characterised by smaller [sigma] ([less than or equal to]30 mS/m). At the northern end, intermediate--large [sigma] values (60-120mS/m) characterise the medium clay textured subsoil horizon. Interestingly, the largest [sigma] values (>120 mS/m) characterise equivalent medium clay and clay loam textured subsoil horizons in the centre and southern end, respectively. This is because the subsoil at the southern end is more reactive, as evidenced by the higher CEC (see Fig. 4d). This was confirmed by Triantafilis et al. (2002), who reported that while the soil mineralogy within the field is predominantly characterised by kaolinite and illite, the slightly higher CEC and clay ratio at the southern end suggests that smectite is present and is most likely in the form of an interstratified clay mineral (with either kaolinite or illite). This is the likely reason for the placement of the water reservoir at this end of the field (see Fig. 2b).
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
It is also worth mentioning that since the soil profiles along most of the transect are duplex in nature, we might have expected to resolve a sharp change in o at a depth of around 0.30 m. The change in o is gradual, however, with topsoil and subsurface o (30 mS/m) changing to larger values in the subsoil (>120mS/m) over a depth range of 0.6m. Nevertheless, the inversion of the EM38 [[sigma].sub.a] data at a height of 0.2 m has been able to detect the extent era known minor drainage channel evident at a Northing of 6 651 750 and represented by the slot of small to intermediate values of profile o (90-120 mS/m). This location is aligned with soil sampling site 19. In addition, a second minor drainage channel may also have been identified at 6651650. In both cases, o is equivalent to the northern end of the field, which is where a major drainage channel is located.
Figure 5b and c shows the spatial distribution of o considering the inversion of EM38v and EM38h [[sigma]sub.a] data collected at a height of 0.40 and 0.60m, respectively. The global misfit for the former is almost twice as large (4.26), compared with the inversion of the EM38 0.20 m [[sigma]sub.a] data, with the latter producing a misfit 4 times larger (12.01). A possible cause for the larger misfit may be attributable to the short-scale variation of the EM38 [[sigma].sub.a] at these heights. This can be explained by considering how the EM38 was mounted and where it was located on the MESS; the EM38 was mounted within, and at the end of, a 2.5-m-long vinyl-ester tube, and at the rear of the tractor. As a consequence of the weight of the EM38, its location at the end of the vinyl-ester tube, lack of suspension on the articulated tractor, speed of travel (-1 m/s), and fairly rough terrain (i.e. soil clods) along the furrow, a vertical flex (~0.1 m) of the vinyl-ester tube above and below the height at which the instrument was set (i.e. 0.2, 0.4, and 0.6 m) was noticeable.
Owing to the oscillation, the measurement error is likely to be greater because [[sigma].sub.a] is generally smaller. As a result, and as Palacky and Stephens (1990) point out, when the [[sigma].sub.a] is small the relative effect of measurement error increases and leads to less reliable interpretation. Nevertheless, the 2-D distribution of [sigma] for these inversions indicates equivalent topsoil, subsurface, and subsoil patterns, with the main difference being the generally smaller estimates in subsurface and subsoil o of the root-zone.
Solum modelling: using multiple EM38 [[sigma].sub.a] heights
In an attempt to better represent the spatial distribution of o within the solum, we conducted various joint inversions of the EM38 [[sigma].sub.a] data. Figure 5d shows the reconstructed o profile achieved using the EM38 [[sigma].sub.a] collected in the vertical and horizontal mode and at heights of 0.4 and 0.6 m. The global misfit for this model (i.e. 10.48%) is almost 3 times larger than for 0.20 m, and is equivalent to the misfit achieved by jointly inverting the EM38 data available at 0.2 and 0.6m (11.79). As shown in Table l, the smallest misfit is achieved when the 0.2 and 0.4 m [[sigma].sub.a] data are jointly inverted (7.00). There is no improvement in misfit when all 3 EM38 [[sigma].sub.a] datasets are included in a joint inversion (10.57).
Nevertheless, and as with the use of only one EM38 height, these models overall represent the sandy to loamy sand topsoil and subsurface horizons with small values of o ([less than or equal to] 30mS/m) and the subsoil medium clays are characterised by large o (>120mS/m). It is also evident that the change in o occurs over a smaller depth (i.e. <0.30 m). A possible explanation to account for the improvement in our ability to resolve the duplex nature of the near-surface is that as the EM38 is raised (to heights of 0.40 and 0.60m), a larger proportion of the measurement will be contributed by the less reactive topsoil and subsurface loam to silty loam textured soil. This is significant when considering [[sigma].sub.a] obtained in the horizontal mode, because the theoretical depth of exploration of the EM38 at these heights will be ~0.35 and 0.15 m, respectively. As shown in Fig. 4c and d the topsoil and subsurface properties of texture group and CEC are fairly uniform, and as such there is little difference in the [[sigma].sub.a] response. As a consequence, the inclusion of the 0.4 and 0.6 m EM38 [[sigma].sub.a] enhances the near-surface representation of soil properties when coupled with the deeper sensing 0.20 m [[sigma].sub.a] data.
Conversely, the retention of the 0.20 m [[sigma].sub.a] data allows for the delineation of the minor drainage channels, evident at the southern end of the field and at Northings of 66571 500 and 6651650. However, and as indicated by the small to intermediate o (30-90 mS/m) shown between 1.5 and 2.1 m, inclusion of 0.4 and 0.6 m EM38 [[sigma].sub.a] diminishes our ability to correctly represent the larger o of the deep subsoil. This is also the case with respect to differentiating the subsoil clay mineralogy of the southern and northern ends of the field. In this model, the large subsoil o evident at the northern end is not consistent with the lower values of CEC (Fig. 4d) and [EC.sub.p] (Fig. 3e).
Vadose-zone modelling: using only EM31 [[sigma].sub.a]
To better understand the spatial distribution of o within the deeper subsoil and in order to determine whether a shallow perched water table (which is often present at the southern end of the field during an irrigation season) can be inferred, the EM31 v and EM31h [[sigma].sub.a] available at a height of 1.0m is run through the inversion model. The global misfit is very small (0.54). We attribute this to the fact that the EM31 measurements of [[sigma].sub.a] are obtained from a larger volume of soil, which produces more stable [[sigma].sub.a] data.
The reconstructed o plot is shown in Fig. 5e. The results are consistent with the fact that the theoretical depth of measurement of the EM31 instruments is 6 and 3 m, when the instrument is held at a height of 1.0 m, and in the vertical and horizontal modes, respectively. These depths of exploration are a function of the instruments operating frequency (9.8kHz) and coil spacing (3.7 m). As such, it is not surprising that our profile reconstruction model is poor in terms of resolving the subtle change in topsoil and subsoil o (i.e. the generally duplex nature of soil profiles along our study transect). This is similarly the case with regard to identifying the lateral extent of the 2 minor drainage channels at the southern end of the field as well as the equivalence of the topsoil texture group along the transect.
The inversion of the EM31 o~ does, however, indicate that the large values of o that characterise the deeper subsoil at the southern end of the field may be attributable to the presence era shallow perched water table (which sits above the underlying Pilliga Sandstone) and is consistent with the strongly mottled nature of the subsoil, noted by Triantafilis et al. (2002) at the time of soil sampling. The inclusion of the EM31 [[sigma].sub.a] data potentially provides information that will assist the inversion modelling of the root-and vadose-zone interface.
Solum, root, and vadose zone modelling: using EM31 and EM38 [[sigma].sub.a]
The spatial distribution of [sigma] developed from joint inversions between the EM31 and EM38 at individual heights of 0.2, 0.4, and 0.6 m are shown in Fig. 6a-c, respectively. The global misfit increases with increasing height (respectively, 4.44, 6.04, and 11.65) with the misfits generally equivalent to those calculated using only the EM38 [[sigma].sub.a] data. The patterns of reconstructed [sigma] are also generally equivalent to the features described for Fig. 5a-c. Visually, the major difference between the inversions of the individual EM38 [[sigma].sub.a] data and the joint inversions with the EM31 is that the reconstructed o of the latter are smoother. In addition, the joint inversions lead to an improved delineation of (i) the 2 minor drainage channels at the southern end of the field and (ii) the difference in soil mineralogy in the subsoil horizons at the northern and southern end of the field.
With respect to the delineation of the 2 minor drainage channels, this can be discerned in Fig. 6a, whereby the areas associated with sites 21 and 19 are represented as slots of intermediate (60-90 mS/m)to intermediate-small c (30-60 mS/m) between depths of 0.9 and 2.1 m. In terms of soil chemical properties, Fig. 6b shows how the intermediate-large values of [sigma] (90-120mS/m) generally reflect the more reactive clay subsoil horizons at the southern end of the field compared with the clayier, but less reactive, subsoil layers to the north and associated with the major drainage channel (<30 mS/m).
[FIGURE 7 OMITTED]
This is similarly the case with regard to measured soil [EC.sub.e] (Fig. 4e), whereby smaller [sigma] reflects areas of the field where recharge and/or deep drainage is likely to be occurring. At the southern end (associated with core 19), the lower clay content, higher CEC, and intermediate-low [EC.sub.e] (0.5-1.5 dS/m) suggests that the smaller [sigma] modelled represents the minor drainage channel, which acts as a conduit for water to be lost from the adjacent reservoir (see Fig. 2a). This helps explain the mottled nature of the soil and the wetter subsoil conditions experienced at the time of sampling. The smaller G values, modelled throughout the entire profile in the north, suggest that deep drainage is leaching salts (as evidenced by small values of [EC.sub.e] associated with cores 16, 15, and 14), with the water lost perhaps recharging groundwater resources associated with the nearby Namoi River.
Figure 6d shows the EM31 and EM38 [[sigma].sub.a] joint inversion, with the latter at heights of 0.4 and 0.6 m; Fig. 6e shows our final inversion, whereby we use the EM31 and all EM38 [[sigma].sub.a] data available. The misfits of the joint inversion of the EM31 and (i) EM38 using the 0.4 and 0.6m [[sigma].sub.a] data (10.77%), and (ii) EM38 using the 0.4 and 0.6 m [[sigma].sub.a] data (13.72%), are equivalent to those achieved using only the EM38 at the same heights. In terms of a visual comparison, these 2 inversions are equivalent to that achieved by the joint inversion of the EM31 and EM38 at a height of 0.4 m.
True electrical conductivity (or) v. soil properties
To quantitatively compare the inversions, we regress modelled [sigma] against the 4 main soil properties known to most strongly influence [[sigma].sub.a]. As an example, Fig. 7 shows the plot of [sigma] achieved by a joint inversion of the EM31 and EM38 [[sigma].sub.a] at heights of 0.2, 0.4, and 0.6 m, v. estimated volumetric moisture content ([theta], [cm.sup.3]/[cm.sup.3]), clay content (%), CEC, and [EC.sub.e]. In general, the best correlations with o are achieved with CEC (0.53) and [EC.sub.e] (0.56). Table 1 shows the correlations between inversions of modelled o and CEC and [EC.sub.e]. The joint inversions of the EM38 [[sigma].sub.a] produce the smallest correlations (e.g. EM38vh 0.4 and 0.6 m, 0.07 and 0.09). Given the theoretical depth of exploration, it is not surprising that the EM31 [[sigma].sub.a] data, when used in isolation, also performs poorly (i.e. EM31vh, 0.27 and 0.37). A modest improvement is evident when the EM38 [[sigma].sub.a] data at various heights are used independently (e.g. EM38vh 0.6 m; 0.40 and 0.52).
[FIGURE 8 OMITTED]
Larger or equivalent correlations are achieved when we jointly invert one height of EM38 [[sigma].sub.a] with the EM31. This is the case between [EC.sub.e] and estimated o derived from the joint inversions of EM31 and EM38 [[sigma].sub.a] at 0.4 (0.63) and 0.6 m (0.77). In terms of [EC.sub.e] the latter joint inversion achieved the largest correlation between o and any of the 4 soil variables. The next best correlation is achieved when the EM31 [[sigma].sub.a] data are jointly inverted with EM38 at heights of 0.4 and 0.6 m (0.68). Jointly inverting 2 heights of EM38 [[sigma].sub.a] with EM31 also leads to slight improvements in the correlation with CEC. This is the case from the joint inversions of EM31 and EM38 [[sigma].sub.a] at heights of 0.2 and 0.4 m (0.49). In terms of CEC, the highest correlation is achieved when all EM31 and EM38 [[sigma].sub.a] data are jointly inverted to estimate [sigma] (0.53).
In general, the correlations between [EC.sub.p] and [sigma] improve in the same order as described for the CEC and [EC.sub.e]; that is, the smallest correlations are achieved when 2 or 3 heights of EM38 [[sigma].sub.a] are jointly inverted. Progressive improvements are achieved when the EM31 and the individual EM38 [[sigma].sub.a] data are considered. Conversely, and of greater interest, the highest correlations are achieved by jointly inverting the EM31 and EM38 [[sigma].sub.a] data at height of 0.6m (0.81), followed closely by EM31 and all of the EM38 [[sigma].sub.a] data (0.77) and EM31 when jointly inverted with either of the EM38 [[sigma].sub.a] data at heights of 0.2 and 0.6 m (0.75) and 0.4 and 0.6 m (0.75). Figure 8 shows the plots of estimated [sigma] for various inversions v. [EC.sub.p].
Table 1 also shows that with increasing complexity in our inversion modelling, particularly when we conduct joint inversions both with EM31 and EM38 [[sigma].sub.a] data, there is a steady increase in the global misfit. At the same time, we achieve greater correlations with various soil properties. This is particularly the case with [EC.sub.p], which in effect is a cumulative measure of the 4 soil properties known to influence soil [[sigma].sub.a]. When we regress global misfit and [EC.sub.p], the correlation coefficient--when we exclude the 4 correlation coefficients achieved with the joint inversions of either 2 or 3 measurements of the EM38 [[sigma].sub.a] data--is strong (0.69). This relationship is consistent with the conclusions of Palacky (1991), who suggested that while the misfit is useful in assessing the quality of the inversion modelling, a small value does not necessarily mean that the model is satisfactory. He further suggests that a better guide to the usefulness of a given inversion is obtained in association with significant interpretation in the form of drill holes and geological knowledge or ground-truthing. Given the validation results achieved from our soil sampling and laboratory measured soil properties, we agree.
The spatial distribution of topsoil, subsurface, and subsoil properties are discernible by the inversion of EM31 and EM38 [[sigma].sub.a] data collected along an intensively surveyed transect within an irrigated cotton-growing field south-east of Wee Waa. We conclude that the frequency of the energising field and the coil spacing of the EM38 provide [[sigma].sub.a] data that allow us to resolve the electrical structure of the texture contrast or duplex soil profiles at the northern end from uniform to gradational textured profiles with higher subsoil reactivity in the south. With respect to the various root-zone o models, where individual EM38 [[sigma].sub.a] data (EM38v and EM38h) available at heights of 0.2, 0.4, and 0.6 m are considered, we are able to discern the major soil types and physiographic features across the field. Despite this and in terms of calibration, the values of o did not, for the most part, correlate strongly with measured soil laboratory properties such as [EC.sub.e], CEC, and [EC.sub.p]. This is similarly the case when we jointly invert EM38 [[sigma].sub.a] data at various heights.
The use of the EM31 [[sigma].sub.a] data in reconstructing [sigma] in the rootzone is also limited owing to the wider coil spacing and smaller frequency of operation. Its greatest contribution is providing information that assists in modelling the lower boundary of a root zone model. This conclusion is borne out when we develop various joint EM31 inversion models with various EM38 [[sigma].sub.a] data collected at different heights. In terms of identifying an optimal set of EM [[sigma].sub.a] data, we find that a joint inversion of the EM31 and EM38 [[sigma].sub.a] data collected at a height of 0.6m provides the best correlation with regard to [EC.sub.p] and [EC.sub.e] (respectively, 0.81 and 0.77), closely followed by a joint inversion of the EM31 and all 3 available EM38 [[sigma].sub.a] data (respectively, 0.77 and 0.56).
Despite the large and ever growing number of soil scientific publications on the collection and use of EM38 and EM31 for applications in digital soil mapping, and apart from those we mentioned in the Introduction, there are very few which have attempted to demonstrate the applicability of the data to resolve the electrical properties of the soil with depth. One of the reasons is the lack of easy-to-use software. We envisage that the inversion model developed and described herein and the demonstrated case study we have reported will see the proliferation and advancement of mapping soil properties in 2 dimensions and potentially 3 dimensions.
One of the disadvantages of the approach we have described is that multiple passes need to be undertaken in order to collect the EM31 and EM38 [[sigma].sub.a] data at various heights. Alternatively, and as we did here, the EM31 and EM38 instruments can be offset with post-processing conducted to georectify the [[sigma].sub.a] data. However, technological advances in EM instrument design is revolutionising the way [[sigma].sub.a] data can be collected. This is particularly the case with regard to the DUALEM421 because it operates at a single frequency (9 kHz) and collects [[sigma].sub.a] data in 2 orientations and at 3 coil spacing (i.e. 4, 2, and 1 m). This would similarly appear to be the case with respect to the Profiler EMP-400, which is configured to simultaneously measure up to 3 user-defined frequencies (i.e. 1-16kHz) with a fixed coil separation (i.e. 1.21 m). In the former case, the use of the DUALEM421 is akin to collecting [[sigma].sub.a] data with an EM38, EM31, and a hybrid of these instruments. Such instruments will increase efficiencies in [[sigma].sub.a] data acquisition since the information is collected in a single pass (Monteiro Santos et al. 2010a, 2010b).
The Australian Federal Governments Australian Cotton Research and Development Corporation and Australian Cotton Cooperative Research Centre (CRC-11C) provided the funding for this research. The MESS survey, soil coring, and laboratory analysis were funded from the Australian Federal Government Natural Heritage Trust (NHT) program (Project NW0688.99). We acknowledge the landowner who allowed access to his farm. The authors acknowledge Mr Andrew Huckel, who carried out the MESS survey and coring, and Drs Ranjith Subasinghe, Raj Singh Malik, and Mohammad Faruque Ahmed for their laboratory determination of clay content, [EC.sub.e], and exchangeable cations of all soil core samples, respectively. F. A. Monteiro Santos acknowledges the financial support of Fundacao para a Ciencia e Tecnologia (Grant: SFRH/BSAB/902/ 2009).
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Manuscript received 18 August 2009, accepted 9 March 2010
J. Triantafilis (A,C) and F. A. Monteiro Santos (B)
(A) School of Biological, Earth and Sciences, The University of New South Wales, NSW 2006, Australia.
(B) lnstituto Don Luis Laboratorio Associado, Universidade de Lisboa, C8, 1749-016 Lisboa, Portugal.
(C) Corresponding author. Email: firstname.lastname@example.org
Table 1. Global and total misfit of individual and joint inversions of EM31 and EM38 apparent electrical conductivity ([[sigma].sub.a]) data, and correlation coefficients between true electrical conductivity (a, MS/m) and measured and estimated soil properties: cation exchange capacity (cmol(+)/kg), electrical conductivity of a saturated soil paste extract (dS/m), and soil paste (dS/m) Note: EM31 held at 1.0 m Correlation coefficients EM inversion Misfit Source of EM signal data Global CEC [EC.sub.e] EM38vh 0.2m 2.86 0.41 0.37 EM38vh 0.4m 4.26 0.40 0.41 EM38vh 0.6m 12.01 0.40 0.52 EM38vh 0.2, 0.4 m 7.00 0.09 0.01 EM38vh 0.2, 0.6 m 11.79 0.05 0.01 EM38vh 0.4, 0,6 m 10.48 0.07 0.09 EM38vh 0.2, 0.4, 0.6 m 10.57 0.06 0.01 EM31vh 0.54 0.27 0.37 EM31vh and EM38vh 0.2 m 4.44 0.40 0.35 EM31vh and EM38vh 0.4 m 6.04 0.39 0.63 EM31vh and EM38vh 0.6 m 11.65 0.30 0.77 EM31vh and EM38vh 0.2, 0.4 m 9.04 0.49 0.50 EM31vh and EM38vh 0.2, 0.6 m 15.86 0.49 0.54 EM31vh and EM38vh 0.4, 0.6 m 10.77 0.41 0.08 EM31vh and EM38vh 0.2, 0.4 m, 13.72 0.53 0.56 0.6 m Correlation coefficients EM inversion Source of EM signal data [EC.sub.p] EM38vh 0.2m 0.55 EM38vh 0.4m 0.51 EM38vh 0.6m 0.62 EM38vh 0.2, 0.4 m 0.10 EM38vh 0.2, 0.6 m 0.07 EM38vh 0.4, 0,6 m 0.17 EM38vh 0.2, 0.4, 0.6 m 0.09 EM31vh 0.41 EM31vh and EM38vh 0.2 m 0.59 EM31vh and EM38vh 0.4 m 0.72 EM31vh and EM38vh 0.6 m 0.51 EM31vh and EM38vh 0.2, 0.4 m 0.72 EM31vh and EM38vh 0.2, 0.6 m 0.75 EM31vh and EM38vh 0.4, 0.6 m 0.75 EM31vh and EM38vh 0.2, 0.4 m, 0.77 0.6 m
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