Microwave Imaging of Soil Water Diffusion Using the Linear Sampling Method

This letter deals with the monitoring of the volumetric water content of a soil column in a fully controlled environment by means of a noninvasive microwave imaging system. Indeed, soil moisture is an important piece of information to improve fluid flow modeling or to better understand the water uptake by plant roots. In this letter, we address the problem of recovering the footprint of soil moisture evolution with respect to time using a built-in laboratory microwave setup coupled to a robust qualitative microwave imaging method: the linear sampling method (LSM). The evolution of the water content in the soil is ruled by the Richards equations and stored at different time steps. The associated maps of soil water content are converted into permittivity maps using the Dobson model. Electromagnetic scattered fields are then computed with finite-element software. We have tested the LSM in a situation that can be encountered in agricultural soils where the water content is not homogeneous. We show that the evolution of the soil water content can be qualitatively monitored with the LSM. We also point out that the source is more precisely located by considering the evolution in time of the singular system of the multistatic matrix (multiple signal classification method).

[1]  Marc Saillard,et al.  Decomposition of the Time Reversal Operator for Electromagnetic Scattering , 1999 .

[2]  Fawwaz T. Ulaby,et al.  Dielectric properties of soils in the 0.3-1.3-GHz range , 1995, IEEE Trans. Geosci. Remote. Sens..

[3]  Peter Monk,et al.  A Regularized Sampling Method for Solving Three-Dimensional Inverse Scattering Problems , 1999, SIAM J. Sci. Comput..

[4]  A. Litman,et al.  Imposing Zernike representation for imaging two-dimensional targets , 2009 .

[5]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[6]  Roland Potthast,et al.  A survey on sampling and probe methods for inverse problems , 2006 .

[7]  Evert Slob,et al.  7. Ground-Penetrating Radar , 2010 .

[8]  Marc Saillard,et al.  A Two-Step Procedure for Characterizing Obstacles Under a Rough Surface From Bistatic Measurements , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[9]  A. P. Annan,et al.  Measuring Soil Water Content with Ground Penetrating Radar: A Review , 2003 .

[10]  Johan Alexander Huisman,et al.  Measuring soil water content with ground penetrating radar , 2003 .

[11]  Francois Bastardie,et al.  Assessment of earthworm contribution to soil hydrology: a laboratory method to measure water diffusion through burrow walls , 2005, Biology and Fertility of Soils.

[12]  Lorenzo Crocco,et al.  An Imaging Method for Concealed Targets , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[13]  Ekaterina Iakovleva,et al.  A MUSIC Algorithm for Locating Small Inclusions Buried in a Half-Space from the Scattering Amplitude at a Fixed Frequency , 2005, Multiscale Model. Simul..

[14]  Michele Piana,et al.  Numerical validation of the linear sampling method , 2002 .

[15]  Margaret Cheney,et al.  The Linear Sampling Method and the MUSIC Algorithm , 2001 .

[16]  L. A. Richards Capillary conduction of liquids through porous mediums , 1931 .

[17]  Francesco Soldovieri,et al.  GPR based soil electromagnetic parameters determination for subsurface imaging , 2008 .

[18]  Evert Slob,et al.  Measuring soil surface water content in irrigated areas of southern Tunisia using full-waveform inversion of proximal GPR data , 2008 .

[19]  Francesco Simonetti,et al.  Time-Reversal MUSIC Imaging of Extended Targets , 2007, IEEE Transactions on Image Processing.

[20]  Claude Doussan,et al.  Water Uptake by Plant Roots: I – Formation and Propagation of a Water Extraction Front in Mature Root Systems as Evidenced by 2D Light Transmission Imaging , 2006, Plant and Soil.

[21]  Carretera de Valencia,et al.  The finite element method in electromagnetics , 2000 .

[22]  P. M. van den Berg,et al.  Removal of undesired wavefields related to the casing of a microwave scanner , 2003 .

[23]  Peter Monk,et al.  Recent Developments in Inverse Acoustic Scattering Theory , 2000, SIAM Rev..

[24]  Jean-Michel Geffrin,et al.  Measurement strategies for a confined microwave circular scanner , 2009 .

[25]  D. Daniels Ground Penetrating Radar , 2005 .

[26]  Jean-Michel Geffrin Imagerie microonde : etude d'un scanner a 434 mhz pour applications biomedicales , 1995 .

[27]  A. Kirsch The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media , 2002 .

[28]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

[29]  T. Isernia,et al.  On Simple Methods for Shape Reconstruction of Unknown Scatterers , 2007, IEEE Transactions on Antennas and Propagation.

[30]  Evert Slob,et al.  Ground Penetrating Radar in Hydrogeophysics , 2008 .