Gpr Signal Analysis: Instantaneous Parameter Estimation Using the Wavelet Transform

The classic approach for estimating instantaneous parameters relies on using the Hilbert Transform (HT). The HT method extracts the instantaneous parameters by comparing the imaginary part with the real part of an analytical signal. The instantaneous parameters obtained this way are frequently contaminated by noises. Using the wavelet transform (WT), one can extract the instantaneous parameters even in different scales. Parameters got by WT are able to characterize signals in different resolutions. The time-frequency analysis using WT is particularly useful when the signal is noisy and non-stationary. As a case study, we have used the WT approach to estimate instantaneous amplitudes and instantaneous frequencies associated with subsurface attenuation caused by gasoline contamination from a GPR profile acquired in the former Wurtsmith Air Force Base in Michigan. Variations of these instantaneous parameters in time-frequency-location domains are in good agreement with attenuation features found from other signal processing approaches. Estimation of instantaneous parameters could be used to serve as one supplementary approach to conventional GPR signal processing routines for extracting more information from a GPR dataset.