We study the importance of accurately recording
signal amplitudes for the quantitative analysis of GPR data sets.
Specifically, we measure the peak amplitudes of signals emitted by
GPR antennas with different central frequencies and study their
amplitude decay with distance, in order to extrapolate the peak
amplitude of the wavelet initially transmitted by each antenna. The
purpose is to compare the reference and reflected amplitudes in
order to accurately estimate the subsurface EM impedance contrasts.
Moreover, we study how sampling-related amplitude
distortions can affect the quantitative analysis, and subsequently
the resulting subsurface models, even in the absence of aliasing
effects. The well-known Nyquist–Shannon theorem gives practical
lower limits for the sampling rate in order to preserve the spectral
content of a digitized signal; however, we show that it does not
prevent possible amplitude distortions. In particular, we demonstrate
that significant and unrecoverable loss of amplitude
information occurs even at sampling rates well above the Nyquist–
Shannon threshold. Interpolation may theoretically reduce such
amplitude distortions; however, its accuracy would depend on the
implemented algorithm and it is not verifiable in real data sets,
since the actual amplitude information is limited to the sampled
values. Moreover, re-sampling the interpolated signal simply
reintroduces the initial problem, when a new sampling rate is
selected. Our analysis suggests that, in order to limit the maximum
peak amplitude error within 5%, the sampling rate selected during
data acquisition must be at least 12 times the signal central frequency,
which is higher than the commonly adopted standards.
