## 3 Experimental Program
### Methodology
First arrival detection methods can be affected as well by near field effects with low-frequency input waves [51; 53], which result from BEs generating lateral P-waves reflection and refraction from specimen boundaries, and by signal noise at higher frequencies. Several researchers, like [PERSON] and [PERSON] [57] have proposed the frequency domain methods, because they potentially allow automation of signal processing and avoid the difficulties associated with picking the first arrival. On the other hand, these techniques are either unreliable or require considerable user intervention to provide a reasonable result. A unique criterion for the travel time determination is here elusive [48]. Cross-correlation is considered to be one of the time domain methods, although all calculations are performed in the frequency domain. Cross-correlation essentially measures the level of correspondence between the transmitted and received signals: transmitted, \(T(t)\) and received, \(R(t)\), as expressed by the cross-correlation coefficient, CCTR (\(t_{s}\)):  
\[CC_{TR}(t_{S})=\lim_{T_{r}\rightarrow\infty}\frac{1}{T_{r}}\int\limits_{T_{r}}T (t+t_{S})R(t)dt, \tag{3}\]  
where \(T_{r}\) is the time record and \(t_{S}\) is the time shift between the two signals. Using the same signals as for previously mentioned techniques, the cross-correlation function is plotted alongside the transmitted and received signals (see Figure 6). The cross-correlation values are calculated from the source and received element signals at each time stamp of the data. The time at  
Figure 5: Receiver time charts: A) first deflection; B) first bump; C) zero crossing; D) first major peak. An example of test results from pure RCA specimen No. 2, \(T=0.16\) ms, \(p^{\prime}=90\) kPa. which the maximum cross-correlation value occurs is then used to estimate the travel time of shear wave [58]. In order to apply this technique, it is convenient to convert the time domain signals to the frequency domain, whereby decomposition of the signals produces groups of harmonic waves with known amplitude and frequency. A common algorithm used for this purpose is the Fast Fourier Transform (FFT), which transforms the signals to their linear spectrums, giving the magnitude and phase shift of each harmonic component in the signal, respectively. The complex conjugate of the linear spectrum of the transmitted signal is next computed, and the cross-power spectrum of the two signals established [59]. [PERSON] and [PERSON] [56] also first proposed implementation of the cross-spectrum method in analyzing results from the gender element test. It is essentially to have an extension of the procedure used in the cross-correlation method, where the frequency spectra of the signals are further manipulated to obtain the absolute cross-power spectrum. The cross-power spectrums, obtained via FFT, are used to create a phase angle versus frequency plot. The slope of this plot is then used to estimate the shear wave travel time, based on a linear best fit across a defined frequency window [58]. An example of the unwrapped phase is displayed in Figure 7. The frequency domain calculations are related in this paper to the cross-spectrum analysis.