Estimation of quality factors by energy ratio method

Elastic waves in particulate glass-rubber mixtures

“…Several methods have been developed to compute experimentally the quality factor Q [30,50,51]. Here, we apply the spectral ratio method based on the assumption that the ratio of the amplitude at two discrete times, t 1 and t 2 (with the travel distance H 1 and H 2 , respectively), varies as a function of frequency during the propagation of the acoustic wave [52][53][54]. Computation of the spectra of the wavelet and evaluation of the logarithmic ratios for two receivers at depth H 1 and H 2 yields to:…”

“…Several methods have been developed to compute experimentally the quality factor Q [30,50,51]. Here, we apply the spectral ratio method based on the assumption that the ratio of the amplitude at two discrete times, t 1 and t 2 (with the travel distance H 1 and H 2 , respectively), varies as a function of frequency during the propagation of the acoustic wave [52–54]. Computation of the spectra of the wavelet and evaluation of the logarithmic ratios for two receivers at depth H 1 and H 2 yields to: ln|A1false(ffalse)A2false(ffalse)|=−πfalse(t2−t1false)Qf+c, where A 1 ( f ) and A 2 ( f ) are the amplitude spectra at different lengths, f is the frequency, t 1 and t 2 are the travel times from the source to the receiver at distance H 1 and H 2 , and c is a constant which contains all frequency-independent terms like transmissivity, geometrical spreading, source and receiver response, etc.…”

Elasticity and Wave Propagation in Granular Materials

“…4.5, and ∆|A( f )| 2 is the change in energy between two points in the sample. Several methods have been developed to compute experimentally the quality factor Q [31,100,101,107,241,244,256]. Here we use the Spectral Ratio method based on the assumption that the ratio of the amplitude at two discrete times during the propagation of the wave, varies as a function of frequency [213].…”