Spatial Retrieval of Broadband Dielectric Spectra

Abstract

A broadband soil dielectric spectra retrieval approach (1 MHz–2 GHz) has been implemented for a layered half space. The inversion kernel consists of a two-port transmission line forward model in the frequency domain and a constitutive material equation based on a power law soil mixture rule (Complex Refractive Index Model—CRIM). The spatially-distributed retrieval of broadband dielectric spectra was achieved with a global optimization approach based on a Shuffled Complex Evolution (SCE) algorithm using the full set of the scattering parameters. For each layer, the broadband dielectric spectra were retrieved with the corresponding parameters thickness, porosity, water saturation and electrical conductivity of the aqueous pore solution. For the validation of the approach, a coaxial transmission line cell measured with a network analyzer was used. The possibilities and limitations of the inverse parameter estimation were numerically analyzed in four scenarios. Expected and retrieved layer thicknesses, soil properties and broadband dielectric spectra in each scenario were in reasonable agreement. Hence, the model is suitable for an estimation of in-homogeneous material parameter distributions. Moreover, the proposed frequency domain approach allows an automatic adaptation of layer number and thickness or regular grids in time and/or space.

Physical observations of the transient evolution of the porosity distribution during internal erosion using spatial time domain reflectometry

“…Scheuermann (2012) demonstrated that the TDR trace, especially the section between the first and second main reflection, contains information enabling the determination of the permittivity profile from the measured TDR signal, either in time domain or frequency domain. The classical approach to achieve this is based on the calculation of the wave propagation along the transmission line due to an incident voltage step (Lundstedt and He, 1996;Norgren and He, 1996;Feng et al, 1999;Heimovaara et al, 2004;Greco, 2006;Bumberger et al, 2018). An alternative approach was proposed by Schlaeger (2005) which allows the fast computation of soil moisture profiles along elongated probes from TDR signals, using either one-or two-ended measurements.…”