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The Leading Edge; October 2009; v. 28; no. 10; p. 1220-1224; DOI: 10.1190/1.3249778
© 2009 Society of Exploration Geophysicists
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SPECIAL SECTION: Hydrogeophysics

Mapping root zones of small plants using surface and borehole resistivity tomography

Torsten Petersen and Said Attia al Hagrey

University of Kiel

Corresponding author: torstenp{at}geophysik.uni-kiel.de

The main function of roots is absorbing water and nutrients (sap) required for the development of plants and trees and anchoring them to the ground. The increasing water shortage in many countries calls for a better understanding of root structure, root volume, water uptake by roots, and water redistribution in the soil-plant zone to serve as the base for a well-directed and sustainable supply of water. Root zones mainly consist of a mixture of root branches and soil material. The root branches within the root envelope are of two kinds: fine, soft roots that absorb the sap from the surrounding soils and thick, wooden roots that transport the sap to the trunk and leaves. The sap is used mainly for transpiration processes and slightly for growth processes (photosynthesis and formation of carbon).

The soft, fine roots are electrically conductive with low resistivities. The thicker, isolated roots are electrically resistive with higher resistivities. Root zones may show either a conductive anomaly (young, fine, soft branches of young plants within a partially saturated resistive soil) or a resistive anomaly (old thick wooden branches of old trees) or possibly both conductive and resistive anomalies together.

Multi-electrode/multichannel measurement systems and adequate 2D and 3D inversion algorithms have been developed and increasingly applied in resistivity surveys over the last two decades. Electrical resistivity tomography (ERT) from the surface and in boreholes (BRT) allows quadrupole measurements using many combinations of current (C) and potential (P) electrode positions (Hagrey, 2008). They are conducted in the tripotential electrode configurations of {alpha} (CPPC) and β (CCPP) and their reciprocals after excluding the erroneous (CPCP) one ({gamma}).

For an N collinear multi-electrode array, a complete data set contains N(N–1)(N–2)(N–3)/8 independent nonreciprocal quadrupole configurations (Noel and Xu, 1991). The comprehensive data set results from excluding the redundant configurations of less stable inversion and very low-voltage measurements from the complete set (Stummer et al., 2004). For instance, a linear array of 32 electrodes yields 107,880 and 68,621 complete and comprehensive data sets, respectively. A pair of 16 vertical borehole electrode arrays produces 122,760 and 80,698 complete and comprehensive data sets, respectively. To map subsurface targets such as a root zone, the huge comprehensive data set results in the highest possible resolution but also in a very long acquisition time (i.e., poor temporal resolution) and high costs. Therefore, we applied a new approach (Loke et al., 2007) to generate optimized data sets of practical, predefined sizes and acceptable spatiotemporal resolution.

We investigated the resolution of these optimized data sets for three different survey designs in experiments conducted at the surface, in boreholes, and using a surface-borehole arrangement. We numerically tested six electrode configurations—five standard and nonstandard {alpha} and β and one optimized—using synthetic data sets generated from forward simulation of two (conductive and resistive) root-zone scenarios. Results of the modeling study were tested on a real young hibiscus.

The aim of these was to investigate the resolution of the different applied configurations in mapping root zones of different scenarios (conductive and resistive) and target scales. The 2D and 3D forward and inverse modeling used the Geotomo software.

Analytic methods and results

We considered three survey designs: (1) from the surface using two crossing profiles, each with 16 electrodes; (2) borehole to borehole with each having an array of eight electrodes; and (3) surface to borehole (Figure 1). The surface-borehole data set includes the sum of the data sets from the surface and borehole-borehole arrays in addition to surface-borehole measurements. The borehole-borehole results include inhole and crosshole data sets. From the general quadrupole electrode configurations, we investigated five standard (and nonstandard) configurations and one optimized configuration. The former were {alpha}vc (vc = vertical circulating), βvc, {alpha}vcs (s = symmetrical around the midpoint), βvcs, and {alpha}βvcs (sum of {alpha}vcs and βvcs). The unconventional {alpha}vc and βvc arrays include all possible electrode combinations within these arrays whereas their corresponding subconfigurations {alpha}vcs and βvcs include only the conventional symmetrical arrangements (Wenner, Schlumberger, and dipole-dipole). The {alpha}βvcs array reflects the advantages of both the {alpha}vcs and βvcs arrays.


Figure 1
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  		Figure 1. Schematic arrangements of tripotential quadrupole electrode configurations {alpha} and β for surface (a), borehole-borehole (b), and surface-borehole (c) survey designs. Borehole-borehole surveys are arranged in {alpha} vertical circulating ({alpha}vc) and β vertical circulating mode (βvc). C = current electrode, P = potential electrode. (After Hagrey, 2008)

 
Optimized data sets of different sizes were generated by the algorithm described by Loke et al. (2007) for surface arrays and Hagrey (2009) for borehole-borehole and surface-borehole surveys. The resolution (R) for these optimized data sets is shown in Figure 2 along with their relative value with regard to that of the respective comprehensive data set for each of the three survey designs. The curves reflect the enhancement of R with increasing data size. The improvement in R (and relative R) of the optimized data sets is steeply linear in the first 7% (relative to that of the comprehensive data sets, i.e., 100–200 data points), then gradual in the range of 7–15% (200–600 data points), and becomes very small above 15%, where all curves approach the horizontal asymptotically for all survey designs. The resolution is best for the surface-borehole surveys, moderate for borehole-borehole data sets, and poor for surface measurements. This reflects the potential of the optimization approach to generate data sets with ≤15% of the comprehensive data set but having almost the same resolution.


Figure 2
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  		Figure 2. Resolution (R) and relative resolution with the comprehensive data set (rel. R) of an optimized electrode configuration data set for survey designs of surface, borehole-borehole, and surface-borehole. Note that the R borehole curve overlaps that of rel. R surface.

 
An adequate subsurface model scenario for the root zone was obtained from the work of Wilderotter (2001) who used numerical simulation of root growth (Figure 3). For calculating the synthetic data sets of apparent resistivity ({rho}a), this model of the root zone was created by forward modeling using finite-element methods with four nodes between electrodes. The electrical resistivity ({rho}) of the starting model was assumed to be 100 {Omega}-m for the partially saturated soil and 20 {Omega}-m and 500 {Omega}-m for the conductive and the resistive roots, respectively.


Figure 3
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  		Figure 3. (a) Model of plant root growth simulated by an adaptive refined grid (after Wilderotter, 2001). (b) Corresponding 2D starting resistivity model with conductive ({rho}root = 20 {Omega}-m)/resistive ({rho}root = 500 {Omega}-m) root zone within the partially saturated soil (100 {Omega}-m). Dots show the positions of 16 surface and 16 borehole electrodes.

 
We generated 72 2D and 3D data sets from the six electrode configurations, three survey designs (surface, borehole-borehole, and surface-borehole), and two root types (conductive and resistive). Each data set has been inverted eight times using different inversion parameters for robust and smoothed normalization. The next section presents examples of the results of 2D modeling.

Analytic results

For each 2D data set, we show the inverted tomograms with the best-fitting results from its eight inversions. Our criteria to identify the best data set for evaluating the reconstructed models of the root zone, included: (1) the shape of anomalies, (2) the amplitude of anomalies, (3) the number of data points, (4) the least root mean square error (rmse), and (5) the number of iterations. Figure 4 shows the reconstructed 2D inversion models for numerical ERT/BRT measurements of the conductive and resistive root zones. The tomograms offer a direct visual comparison and evaluation of the shape and amplitude of the reconstructed root-zone anomalies and the surrounding soils with respect to the starting model. Our forward and inversion modeling for the root zone show the following general results:

  1. Most configurations can generally map the root zone within the partially saturated soil. The amplitudes and shapes are well resolved by the different configurations for both conductive and resistive anomalies. The data size and resulting rmse and number of inversions are nearly similar between the corresponding configurations for both cases.
  2. Resolution of the root zone is best for the surface-borehole surveys. The surface surveys resolve the upper boundary only; the borehole-borehole surveys map the lower boundary. Note that the surface-borehole data set includes the sum of the surface and borehole-borehole data sets and thus accumulates their advantages.
  3. Anomalies are best resolved by the {alpha}vc array followed by the βvc and opt arrays. {alpha}vc and βvc have the lowest rms errors but also the largest number of data points (> 1700 points), which increases measurement time. The optimized array has <15% of the data points of {alpha}vc and βvc but shows almost similar results. It can be conducted in a shorter time and still provide good spatiotemporal resolution. The {alpha}vcs had the worst resolution.
  4. The anomalies for the surface-borehole arrangement are best resolved by the {alpha}vc, βvc, and opt arrays. All six configurations show acceptable resolution.
  5. Although the "small" optimized data sets (nearly 7% of their corresponding comprehensive sets) are nearly half of their corresponding "large" optimized data set, their resulting tomograms show nearly the same resolution. It means that small optimized data sets provide a very good spatial resolution with the shortest possible measurement time and have the lowest survey costs. So it is possible to use optimized data sets with lower array numbers to increase the temporal resolution and better monitoring of soil and root processes.
  6. In general, the larger the data set, the higher the resolution of the anomalies. The surface-borehole arrangement produces the most reliable mapping of the root zone.


Figure 4
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  		Figure 4. Reconstructed 2D inversion models of electrical resistivity for conductive (a) and resistive (b) root zones with number of data points and root mean square errors for six quadrupole electrode configurations (rows) and three survey designs (columns). Dots show positions of surface and borehole electrodes and solid lines outline root zones. All models have error ≤ 0.5%.

 
Lab experiment and first results

As a practical example, we selected a very young (some weeks old) hibiscus (Hibiscus rosa-sinensis) that had a height of 24 cm and with fine white roots (electrically conductive), maximum length = 10 cm for a mapping experiment. The plant was carefully washed and planted in the center of a cylindrical plastic pot (diameter = 60 cm and height = 35 cm). The pot was filled with partially saturated (40%) soil that was 92% fine sand and 8% silt with an effective porosity of 28% (e.g., Hagrey et al., 2003). The controlled experiment was carried out in June at nearly constant temperature, and the soil surface was isolated by plastic foil to minimize evaporation from the pot surface.

Figure 5 shows the geoelectric setup: two surface profiles (each with 16 electrodes) crossing each other at 90o and four vertical borehole profiles (each with 12 electrodes). All electrodes are fine stainless steel (length = 2–3 mm) at 1-cm spacing except for the central surface electrodes (2 cm) directly around the stem. One TDR probe and thermometer were next to the hibiscus during the experiment.


Figure 5
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  		Figure 5. Experiment setup and first resulting model of electrical resistivity tomography measurements on a young hibiscus plant in the laboratory: (a) two surface and four vertical electrode arrays (solid dots) placed symmetrically around the plant; (b) 3D tomograph inverted from crosshole measurements only.

 
Geoelectrical measurements were carried out for two days using the {alpha}vcs, βvcs, and optimized configurations for surface, borehole-borehole, and surface-borehole arrangements. We excluded the comprehensive {alpha}vc and βvc data sets to minimize effects of the temporal change in soil moisture (due to uptake by roots) during acquisition. The geoelectric setup was kept in the central third of the pot to assure infinitesimal boundary conditions.

The first inversions of the 3D data sets from optimized borehole-borehole measurements only (nearly 1000 data points from the different applied configurations) show the capability of the technique to map the young fine roots as a negative anomaly. Figure 5b shows a broad conductive anomaly of oval shape (nearly 10 x 8 x 12 cm3) with two minima (nearly 20 {Omega}-m) exists near the soil surface (probably water-content heterogeneity and electrode effects) and at a depth of 5 cm (corresponding to highest root density). This broad anomaly is surrounded by high resistivity values (with maxima up to 500 {Omega}-m). The broad conductive anomaly is positioned exactly within the zone envelope of the plant. This first result clearly reflects the capability of the technique for mapping such sparse, young roots in humid fine sand (i.e., low electrical contrast).

After finalizing these results and their interpretation, we will apply the optimization approach to improve the spatiotemporal resolution of geoelectrical techniques.

Suggested reading

"2D optimisation of electrode arrays for borehole surveys" by Hagrey (EAGE 2009 Extended Abstracts). "First numerical ERT models for CO2 plumes in saline reservoirs using crosshole configurations" by Hagrey (Expanded Abstracts for First EAGE CO2 Geological Storage Workshop, 2008). "Geophysical imaging of root zone, trunk and moisture heterogeneity" by Hagrey (Journal of Experimental Botany, 2007). "Optimisation of electrode arrays used in 2D resistivity imaging" by Loke et al. (ASEG 2007 Expanded Abstracts). "A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion" by Loke and Dahlin (Journal of Applied Geophysics, 2002). "Archaeological investigation by electrical resistivity tomography: a preliminary study" by Noel and Xu (Geophysical Journal International, 1991). "Experimental design: Electrical resistivity data sets that provide optimum subsurface information" by Stummer et al. (GEOPHYSICS, 2004). "An adaptive numerical method for the Richards equation with root growth" by Wilderotter (Plant and Soil, 2001).

Acknowledgments:

Thanks to Tina Wunderlich for MATLAB programs and Wolfgang Rabbel for supporting this study and to Professor Meissner for critical reading this manuscript. The array optimization program used here has been developed in the framework of German research program GEOTECHNOLOGIEN funded by the Federal German Ministry of Education and Research (BMBF) and a consortium of energy companies (E.ON, EnBW AG, RWE Dea AG, Stadtwerke Kiel AG, Vattenfall Europe Technology Research GmbH and Wintershall Holding AG).





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