A novel multi-frequency inversion algorithm for the retrieval of the subsurface properties of layered soil media

The characterization of subsurface structure and dielectric properties of soil media using microwave remote sensing technology has proven very useful in identifying soil stratigraphy, measuring soil moisture content, and assessing soil salinity. Following the formulation of a forward model for scattering from two-interface rough surfaces based on the small perturbation method (SPM), a multi-frequency inversion algorithm is presented in this paper. When backscattering coefficients at an oblique incidence at multiple frequencies are measured, the inversion algorithm is designed to retrieve the dielectric properties and roughness statistics of each distinct soil layer in a layer-stripping fashion. The dielectric constant of the top surface is first determined and then the top surface is mathematically stripped away. Subsequently, the measurements that would have been obtained if the properties of top surface are known are synthesized. The process is repeated and the medium is mathematically stripped away, layer by layer, with the dielectric constants being found in the process. In the development of the proposed inversion algorithm, both HH and VV data are inverted simultaneously for more accurate reconstruction of the dielectric properties of layered media. The premise behind this work lies in the use of virtual time-domain data realized using multi-frequency measurements. The time-domain data consist of a series of time echoes delayed at different times with each time-delayed echoes representing a reflection upon a rough interface. Time-domain data have very attractive features which can facilitate the inversion of material properties and roughness statistics of rough layers. The peak value of a time delay echo is strongly correlated with the dielectric contrast across an interface and the pulse shape of a time delay depends on the rms height and correlation length of a rough interface. The time difference between delay echoes is linearly related to the layer thickne- ss. Numerical simulation results show that the real part of dielectric constants for both top and subsurface layers, the imaginary part of the dielectric constant for the top layer (but not the last layer), the roughness statistics for both rough interfaces, and the layer thickness can be retrieved with great accuracy.