From the figure 6 (b) it is evident that there is some energy concentration in the S0 mode at a frequency of 410 kHz the group velocity
was cantered at 2.775 m/ms, while the highest energy concentration is in the A0 mode at a frequency of 150 kHz, but the group velocity
was found to be 1.871 m/ms which is far less when compared to 2.775 m/ms, therefore this should be an A0 mode.
Knowing the group velocity
of the modes [A.sub.0] and [S.sub.0]: Vg ([A.sub.0],300kHz)=1268 m/s, Vg ([S.sub.0],300kHz)=5649 m/s, we can calculate the delamination position from the sensor A noted [P.sub.D] by [DELTA][t.sub.1] (Delta 1) and delamination length noted [L.sub.D] by [DELTA][t.sub.2] (Delta 2) as presented in Table 2.
where [L.sub.max] and [L.sub.min] are the maximum and minimum grid size, respectively; [[lambda].sub.min] is the minimum wavelength; [n.sub.min] is the minimum number of elements within one wavelength (usually [n.sub.min] is in the range of 8~10); [c.sub.s] denotes the velocity of shear waves; and [c.sub.min] is the minimum group velocity
of elastic waves.
The results of the joint inversion of the Z and R group velocity
spectra and the RPM frequency curve are presented in Figures 10 and 11.
The group velocity
vg of the wave packet associated with the electron of rest mass [m.sub.0], coincides with its velocity v.
[v.sub.ph] is the phase velocity, and vg is the group velocity
. [r.sub.c] is the optimum radius of the integral surface in the process of U scattering .
In the case of first derivatives we consider the dispersion error, the error in phase velocity, and the error in group velocity
as objective functions.
The cause of this result is that the frequency of DW is determined by the phase-matched condition associated with the nature group velocity
, but SS increases the group velocity
at resonant frequency eventually because it affects the group velocity
in an intensity dependent fashion .
The saddle point method is used to determine the solution with zero group velocity
. In general, there are two distinct spatial branches of solutions of (4) on the complex k* plane.
In this paper, tapered core is used instead of cylindrical core so as to make the light travel with the lesser group velocity
and also to stop the light at the fixed position efficiently.
The Rayleigh-wave group velocity
for the trace of each event registered has been measured by means of the combination of digital filtering techniques: Multiple Filter Technique (Dziewonski et al., 1969) and Time Variable Filtering (Cara, 1973), as shown in the flow chart displayed in Figure 2.
The results focused on waveforms, fast Fourier transforms (FFT), and frequency/time analysis (with superimposed group velocity
curves) of the signals.