An Analysis of Time-Domain Dort Method for Ultrawideband Probing of Embedded Objects in Dispersive and Random Media

Time-reversal (TR) techniques were first developed in acoustics1 and they involve the re-transmission of signals acquired by a set of transceivers in a time-reversed fashion. In lossless and stationary media, time-reversed signals yield optimal focusing around the original scatter locations due to the TR invariance of the wave equation. An important application of TR is the selective focusing on desired scatterer(s) in media with multiple scatterers. This involves the eigenvalue decomposition (EVD) of the TR operator (TRO) of a TR antenna array (TRA) and uses these eigenvectors as the TRA excitations. This TR-based technique is known as the DORT method (French acronym for decomposition of the time reversal operator), which was first applied to electromagnetic (EM) waves by using time-harmonic signals and a full aspect sensor configuration4. Then, extensions to limited aspect configuration and ultrawideband (UWB) signals have been considered. Most of the previous works on TR have assumed lossless media. However, when the intervening medium is dispersive and/or lossy, TR invariance is broken and compensation techniques become necessary for satisfactory TR operation. A Short Time Fourier Transform (STFT) based method has recently been introduced to compensate for the cumulative and frequency-dependent attenuation in homogeneous dispersive background media. In this work, this compensation technique is extended for the application of the time-domain (TD)-DORT method in both dispersive and random inhomogeneous media. For this end, the effects of dispersion and conductivity on the eigenvalue and eigenvector structure of the TRO are studied first. Then, time-dependent wideband inverse filters are designed and applied for compensation. Additionally, a numerical compensation method proposed for conductive medium only8 is extended to both dispersive and conductive media. The simulation scenarios considered are based on typical subsurface sensing scenarios, where UWB signals under limited aspect sensor configurations are employed. The random media models are based on inhomogeneous soil models with fluctuating dielectric permittivity having prescribed correlation functions and variances