Fractional derivative-based approximation of acoustic waveform dispersion measured in bubbly water beyond resonance frequency
Résumé
Acoustic pulses transmitted across air bubbles in water are usually analyzed in terms of attenuation coefficient and phase velocity in the frequency domain. The present work expresses an analytical approximation of the acoustic waveform in the time domain. It is introduced by experiments performed with a Gaussian derivative source wavelet, S0(t)0(), with a derivative order, beta(0) = 4, and a peak frequency, nu p00, much larger than the bubble resonance frequency. The measurements highlight a significant shape variability of the waveform Bx(t)(), measured at x <=<= 0.74 m and characterized by a peak frequency nu px similar or equal to nu p0 similar or equal to 0. The results are in good agreement with the approximation Bx(t)proportional to(d gamma x/dt gamma x)S0(delta xt - T)()proportional to(/)0( - ), where gamma(x) is an additional fractional-derivative order determined by an optimization procedure and T is related to the travel time. The time-scale parameter, delta x=beta 0/(beta 0+gamma x)----------root=0/(0+), becomes a free parameter for more general source signals. The correlation coefficient between Bx(t)() and the approximated waveform is used to identify the applicability of the method for a wide range of bubbly waters. The results may be of potential interest in characterizing gas bubbles in the ocean water column and, more generally, in modeling wave propagation in dispersive media with fractional-derivative orders in the time domain. (C) 2023 Acoustical Society of America.
Domaines
Planète et Univers [physics]
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