Eigendecomposition of TDR waveforms: a novel method to determine water content and pore fluid concentration of sandy soils

Abstract

In this study, an incident pulse signal of several harmonics (i.e., multiples of the fundamental frequency) was used as a source in the time domain reflectometry (TDR) probing technique. Reflected signals were captured by an oscilloscope and their characteristics were determined via eigendecomposition. Autoregressive modeling and singular value decomposition were used to calculate the eigenvalues and the most significant ones were identified based on power spectrum. A multivariate statistical analysis was performed for the two most dominant eigenvalues, which are dependent on water content and salt concentrations, and regression equations were obtained. To determine the water content and salt concentrations in terms of the first and second eigenvalues, a modified Powell hybrid algorithm was used to solve the obtained system of nonlinear equations. Actual and predicted results are in agreement indicating that the developed method is very successful in predicting water content and salt concentrations. Furthermore, on comparing the eigendecomposition method with Fourier spectral analysis, one can observe that the former is superior in predicting water content and salt concentrations.