## 2 3D SIBIE Procedure
### Computing Procedure for 3D SIBIE  
The following steps show one-side access measurement and the computation procedure, developed in this study for the 3D SIBIE procedure. Figure 5 displays the targeted volume of interest and cross sections employed for the computation.  
1. Place the sensor array on one surface of targeted concrete and hammer with steel sphere ball of 10 mm diameter near each sensor (n = 4) for 10 times respectively.
2. Divide 300 (x-direction) \(\times\) 300 mm (z-direction) in depth (y-direction) for volume of interest into 10 mm meshes.
3. Employ the nodal points on the cross sections of x = 0, x = 300, z = 0, z = 300, x = z, x + z = 300 to mitigate computational load.
4. Calculate \(R\) (travel length of elastic wave) from each nodal point to input and output points (R is the shortest linear path as explained).
5. Search for \(f_{R}\) frequencies due to reflection of propagating P-wave with velocity of \(C_{p}\).
6. Normalize the amplitude from 0 to 1 based on the highest peak value in the frequency spectrum to cancel the variability of each manual hammering impact.
7. Stack amplitudes according to \(f_{R}\) and quantify reflection intensity values at each nodal point.
8. Visualize 3D geometry with the stacking data based on local polynomial regression method.  
Figure 6 shows the example of frequency spectrum successfully obtained from the received signal followed by FFT analysis. Sampling rate is set at 100 kHz in the following measurement. Those sampling rates are appropriately determined to discuss the FFT (Fast Fourier Transform) results in this study since the waveform is sampled at 10000 points for FFT to achieve the sufficient resolution less than 50 Hz.  
Meanwhile, some recorded waveform due to an impact of low energy may cause the low S/N (signal-to-noise ratio) signal and FFT indeterminate peaks. The procedure of FFT signal data stacking with/without including low S/N waveforms are shown in Figure 7. Tapping 10 times according to the above-mentioned steps for 3D SIBIE method, FFT peak stacking results in giving an incorrect  
Figure 4: (**a**) Laser doppler vibrometer; (**b**) Detected waveform with application of laser doppler vibrometer for laboratory test.  
Figure 3: (**a**) Accelerometer array unit; (**b**) Overview of on-site implementation.  
data with unclear frequency spectrum when some signals into a sensor are not entirely high S/N, wherein n = 3, 6, 8, 9 for the example. As a consequence, between the process of 5 and 6 for the development of the 3D SIBIE procedure, low S/N signals are removed from the computation to guarantee data quality. The FFT signal data stacking result without signal normalization procedure is indicated numerically as in Figure 8, where the process of 6 is excluded. It is obvious that the spectrum of n:3 is different from others in 5 kHz implying that this is attributed to some noises. As shown in Figure 8a, the stacked amplitude of 10 raw data without the signal normalization is influenced by the noise signal of n:10 but now found in Figure 8b. The normalization for each frequency spectrum before stacking is thus very effective on the data acquisition process of the 3D SIBIE procedure.  
Figure 5: Volume of interest and cross section for 3D SIBIE procedure.  
Figure 6: An example of FFT (Fast Fourier Transform) result of low S/N signal.  
Figure 7: FFT signal data stacking procedure.