INPUT PARAMETERS IN CIVA
PROBE ParamEtERs
The diameter of the probe defined in CIVA is the one given by the manufacturer:
 Probe diameter : 6.35mm
The central frequency of the input signal is the nominal frequency given by the manufacturer:
 Central frequency = 2.25 MHz
The two other parameters of the input signal, the bandwidth and phase, are determined by fitting the temporal shapes of the measured and simulated echoes from a reference reflector which CIVA predictions have been validated.
The reference reflector chosen for this probe is a SDH of diameter D = 2mm located at 44mm depth in a steel calibration block. This reference echo has been measured for a water depth of 20mm.
The bandwidth and the phase of the signal are (Figure 14):
 Bandwidth =55%
 Phase = 40°
INCLUSION ParamEtErs
The inclusions diameters defined in CIVA are the ones provided by the manufacturer:
 Inclusion diameter = 1, 2, 4 and 6 mm
Longitudinal and shear waves velocities in the inclusions couldn't be measured precisely. However, they were determined thanks to a small parametric study with CIVA by using the fact:
 that a shear wave variation close to 3000m/s (velocity in steel) has an effect on the position and amplitude of the echoes arriving after the specular echo (Figure 15, top).
 that a L wave velocity variation has little effect on the amplitude of these echoes and not only on their positions (Figure 15, bottom)
 that the specular echo does not depend on the values of these velocities (Figure 15)
Thus, the speed of Twaves in the inclusion is determined by adjusting the temporal positions of the echoes arriving after the first experimental and COMPLETE_SOV simulated specular echo (Figure 16, top).
The value that has been obtained is:
 v_{T}_{steel} = 3300 m/s (Figure 16 bottom).
Note : the SOV and COMPLETE_SOV models simulate the same echoes after adjustment (Figure 17). The determined velocity does not depend on the chosen model for simulation.
Then, the L wave velocity in the inclusion was determined by adjstment of the amplitude of the simulated and experimental amplitude echo following the first specular echo (Figure 18 top).
The value that was obtained is (Figure 18 bottom):
 v_{L}_{steel} = 5850 m/s.
The L and T wave velocities that were determined for the Ø2mm inclusion were used as input data in CIVA for the other inclusion beacuse we suppose that they are identical.
Note: this method for determining the L and T waves velocities in the inclusion is not very accurate and makes the assumption that COMPLETE_SOV model predicts accurately the echoes following the specular one whereas this model is still being validated. Nevertheless we kept this adjustment because it has no consequence for the rest of the study since it concerns the inclusions specular echo which do not depend on the values of these speeds.
WATER ParamEtERs
This velocity was measured sing the successive bounces of a surface echo on an infinite plan.
 vL_{water} = 1483 m/s
The attenuation in the water has been neglected in simulations with a frequency of 2.25MHz, because it is very small. Moreover, we verified by comparing simulations with and without attenuation that it is has no effect on the probe/reflector distances chosen in this study.
 Attenuation in water neglected for the 2.25 MHz probe
REfErence FOR THE AMPLITUDES FOR EXPERIMENTS VS SIMULATED AMPLITUDES
BEAM OF THE 2.25 mhZ PROBE IN WATER
The maximal amplitude emitted by the probe is at 15.5 mm distance form its axis. At this point, the 3dB focal spot width measures 1.9 mm and increases on each size (Figure 20).
The Ø4 and 6 mm inclusions are also much larger than the focal spot, as it can be seen on the Figure 21, where inclusions are represented with the same scale as the one of the field cartography in order to compare their dimensions to the focal spot dimensions.
REsults obtAINED WITH STEEL INCLUSIONS
2.25MHZ 
Inclusion Ø 1mm 
Inclusion Ø 2mm 
Inclusion Ø 4mm 
Inclusion Ø 6mm 
SOV 
yes 
yes 
yes 
no 
COMPLETE_SOV 
yes 
yes 
yes 
no 
SPECULAR 
no 
no 
no 
yes 
EXPERIMENTAL RESULTS
The experimental amplitude/distance echodynamic curves are presented on Figure 22. On the top, the amplitudes are relative to the reference echo amplitudes, on the bottom they are normalized:
 the maximal echo amplitude increases with the inclusion diameter. The amplitude increases by 5 to 6 dB when the inclusion diameter is doubled. It can as well be noted an increase by 3.5 dB between the 4 mm and 6 mm inclusions.
 the « d_{max }» distance at which the echo amplitude is maximal do practically not depend on the inclusion diameter : d_{max } = 14 or 14.5 mm.
 beyond « d_{max }», the decreasing slope do not depend on the inclusion diameter.
The experimental XY curves obtained for the 4 inclusions are presented on Figure 23 (normalized amplitudes). The focal spot width does not depend on the inclusion diameter.
The specular echoes shape of the inclusions located at a focal distance of 14.5 mm or in the probe far field (60mm) do not depend on the inclusion diameter (Figure 24). The echo coming after the first contribution is even more far in time from the first echo than the inclusion diameter is great. The origin of the echoes appearing after the specular contribution is not accurately known, it appears a mix between the creeping waves and the waves penetratingthe inclusion in which they propagate, rebound with eventually modes conversions, interfere ...
EXPERIMENTS/CIVA COMPARISON

Amplitude/distance curves
The comparisons of the measured and with SOV, COMPLETE_SOV and SPECULAR simulated amplitude/distance curves are presented Figure 25 (Ø1 mm and Ø2 mm inclusions) and Figure 26 (Ø4 mm et Ø6 mm inclusions)
The d_{max } distance at which the amplitude/distance curve amplitude is maximal is indicated in the Table 3. The differences between d_{maxEXPERIMENTAL } and d_{maxCIVA} are indicated in the table 4.
Distance “D” of amp max (mm) /+0.5mm 
Simulated beam 
Inclusion Ø1mm 
Inclusion Ø2mm 
Inclusion Ø4mm 
Inclusion Ø6mm 

15.5 




Measure 

14 
14.5 
14 
14 
SOV 

15 
14.5 
13.5 
13 
COMPLETE_SOV_BEAM 

13.5 
14 
13.5 
13.5 
SPECULAR 

14 
14 
13 
14 
ΔD_{sim/exp} of amp max (mm) 
Inclusion Ø1mm 
Inclusion Ø2mm 
Inclusion Ø4mm 
Inclusion Ø6mm 
SOV 
1 
0 
0.5 
1 
COMPLETE_SOV_BEAM 
0.5 
0.5 
0.5 
0.5 
SPECULAR 
0 
0.5 
1 
0 
COMPLETE_SOV and SPECULAR Models : a very good agreement is obtained with the experiment for the 4 inclusions at every distances. The differences do not exceed 2 dB except for small distances. « d_{max} » positions are well predicted for those 4 inclusions.
More in detail:
 In far field, the measures/simulations differences are less than 1 dB for every inclusions except in the case of the Ø6 mm inclusion and of the COMPLETE_SOV model for which the measures/simualtions difference reaches a little bit more than 2 dB while SPECULAR model is closer to the measure. This gap greater than 2 dB can be attributed to a model limitation concerning the diffraction coefficient computation for the great « ka » (see here).
 Around « d_{max }» the amplitude/distance curves predicted by COMPLETE_SOV and SPECULAR models are in good agreement with the measure (differences of less than 2 dB).
 The deviations are more important at the very small distances but do not exceed 4 dB.
 « d_{max }» distance do almost not depend on the inclusion diameter according to COMPLETE_SOV and SPECULAR (Table 3) as experimentally. Both models slightly tend to underestimate « d_{max }» relatively to the measures, but the differences between the measured and simulated values are still less than 1 mm (Table 4).
SOV Model: the agreemnt with the measure is not so good as for the 2 previous models when the inclusions are close to the probe.
More in detail:
 In far field, the measures/simulations differences are less than 1 dB for every inclusions except in the case of the Ø6 mm inclusion for which the measures/simualtions difference reaches a little bit more than 2 dB (as with COMPLETE_SOV this gap can be attributed to a model limitation concerning the diffraction coefficient computation for the great « ka »).
 Around « d_{max }» the amplitude/distance curves shape predicted by SOV are not in good agreement with the measures. The gaps measures/simulations reach more than 8 dB at the distances lower than the focal distance. At the focal distance, the maximal amplitudes predicted by the SOV model are underestimated of about 2 dB for the Ø1 mm inclusion and overestimated of about 3 dB for the Ø6 mm inclusion. For the Ø2 mm and Ø4 mm inclusions, the simulated and experimental maximal amplitudes show a good agreement.
 The « d_{max }» distance at which the echo amplitude is maximal slightly decreases with the inclusion diameter increasing: d_{max} varies from 13 mm to 15 mm (Table 3) what is not in agreement with the measure. But the differences between the measures and SOV simulated values are lower than 1 dB (Table 4).
Those measures/simulations comparisons of the amplitude/distance curves point out:
 the necessity to use COMPLETE_SOV and SPECULAR rather than SOV to simulate the inclusions echoes when theu are not in far field.
 the fact that in the probe far field, the SOV and COMPLETE_SOV models give similar results.
 that the SPECULAR model predictions for the Ø6 mm inclusion in far field are closer th the measure than those obtained with the COMPLETE_SOV model for which the deviations stay low. This last observation validates the restriction that only allows SPECULAR model for the Ø6 mm inclusion in CIVA.
Simulated and experimental Ascans exemples of inclusions echoes with SOVCOMPLET and SPECULAR are rerpesented on the figure here below for both distances « D » between the probe and the inclusion. The specular echo is well predicted by SOVCOMPLET and SPECULAR. The SOVCOMPLET model also predicts quite well the contribution arriving after this echo (except for the Ø1 mm inclusion). The SPECULAR model do not simulate this contribution.
The XY experimental and with SOV, COMPLETE_SOV and SPECULAR simulated echodynamic curves, extrated at the probe/inclusion distance of 14.5 mm (experimental focal distance) as well as the 6 dB focal spot width are close (see figure here below).
Results obtained with the infinite plan
Note: the figure below shows that the consideration of the attenuation in water (0.0087 dB/mm at the frequency of 2 MHz) is negligible for this probe. It is recalled that for the computation of the inclusions echoes it has not been taken into account because the probe/inclusion maximal distance for the inclusions echoes measures is only 74 mm.
The experimental and with SPECULAR models predicted Ascans in the infinite plane are in very good agreement (Figure 30).
ECHOES SPECTRUM OF INCLUSION AND INFINITE PLAN
NB : the bandwidth indicated in MHz in the tables below is the spectrum width at the half of its maximum.
Infinite plane 

Distance probe/plane 
14.5mm 
60mm 


fc (MHz) 
BW (MHz) 
fc (MHz) 
BW (MHz) 
Measure 
2 
1.2 
2.2 
1.25 
SPECULAR 
2 
1.25 
2.15 
1.25 
The same extracted experimental and simulated characteristics of inclusions echoes spectra have been compared with the characterictics from the infinite plane. The Table 6 shows an example of Ø1mm inclusion results.
Inclusion Ø1mm 

Distance probe/inclusion 
14.5mm 
60mm 


fc (MHz 
BW (MHz) 
fc (MHz) 
BW (MHz) 
Measure 
2 
1.2 
2.1 
1.2 
SOV 
2 
1.1 
2.1 
1.1 
SOVCOMPLETEBEAM 
1.9 
1 
2.1 
1.05 
SPECULAR 
1.9 
1.1 
2.1 
1.3 
Those results show that CIVA correctly predicts the central frequencies and bandwidths of the echoes of the infinite planes in both inclusions. The values do almost no depend on the reflector.
EFFECT OF small CHANGEs IN the central frequency
Before studying this effect on the inclusions echoes and infinite plane, the experimental/simulated good agreement for the SDH reference echo for the three evaluated frequencies (2.2 MHz, 2.3 MHz and 2.4 MHz) has been verified because it is essential to allow the measure/simulation comparisons for other reflectors.
The reference echo Ascans (SDH) simulated at the three frequencies are in agreement with the measure (Figure 31).
In the same way, the reference SDH amplitude (at 44 mm depth) varies a little bit with the central frequency: almost 0.5 dB (Figure 32).
The inclusions ampitude/distance curves has been simulated at the 3 central frequencies « fc » with the COMPLETE_SOV models for the Ø1, 2 et 4 mm inclusions (Figure 33) and SPECULAR model for the Ø6 mm inclusion (Figure 34).
Those results show the a probe central frequency variation modifies the maximal amplitude of the amplitude/distance curves by 2 dB to 2.5 dB. However, when the inclusions move away from the probe, the amplitudes of their echoes vary a little with fc.
Also, if the CIVA entry signal central frequency is modified by 0.1 MHz, the maximal amplitudes of the inclusions amplitude/distance curves can vary by almost 2 dB if the reference for the amplitudes is the SDH at 44 mm depth. Moreover, the amplitude/distance curve maximal position varies by 1.5 mm. Those variations can be considered as uncertainties on CIVA simulation results related to the value uncertainty of the entry signal of the central frequency.
Synthesis
 the amplitude/distance curves and the inclusions and the infinite plane,
 the « XY » curves and the inclusions,
 the echoes Ascans and their spectra.
The overestimation of the Ø6 mm inclusions echoes amplitude in far field with SOV and COMPLETE_SOV justify the current restriction in CIVA which only allow echoes computation of this inclusion with SPECULAR model. The COMPLETE_SOV contribution related to SOV has been pointed out for the inclusions echoes when they are close to the probe.
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