## 1 Introduction
### SIBIE Procedure  
In order to visualize such defect as crack and void in concrete, SIBIE (stack imaging of spectrum amplitudes based on impact-echo) procedure has been developed [11; 12]. In the procedure, a targeted cross-section is modeled and divided into square elements as shown in Figure 2. Then, resonant frequencies obtained from FFT analysis due to elastic wave reflections at each element are computed. The travel distance from the input, which is excited by hammering (tapping) concrete surface with steel sphere ball of 10 mm diameter, to the output through the elements is calculated by Equation (3).  
\[R=r_{1}+r_{2} \tag{3}\]  
where \(r_{1}\) is the distance from the input (impact) point to the nodal point of an element and \(r_{2}\) is the distance from the nodal point of an element to the output (signal detection) point. The resonant frequencies due to reflections at each element \(f_{R}\) are calculated by Equation (4).  
\[f_{R}=\frac{C_{p}}{R} \tag{4}\]  
In the frequency spectrum, amplitudes corresponding to these resonances are summed up at each nodal point. Thus, the reflection intensity as the data stacking result at all the analytical elements is prepared for the visualized contour image. After the SIBIE analysis, a 2D view of the contour image is displayed, and the high reflected zone is visually identified as the estimated location of anomaly namely damage.  
Figure 1: Schematic of impact-echo method applied to the testing interior concrete.  
Figure 2: Mesh division and results of SIBIE (Stack Imaging of spectral amplitudes Based on Impact-Echo) procedure [3].  
The SIBIE procedure has been applied for the case studies in the author's previous research. The results for detecting grouted and un-grouted PC (pre-stressed concrete) sheaths is illustrated as in Figure 2[11]. The size of each mesh is of dimensions \(10\times 10\) mm. In the figures, it can be observed that both grouted and un-grouted sheaths were clearly identified with the values of reflection intensities. The contour values are given as the relative amplitude, which is obtained by normalizing data with a maximum amplitude provided from the FFT result, of the P-wave intensity computed from frequency spectrum of received signal.  
In the above-mentioned results, after the SIBIE procedure, it is possible to identify the grouting condition only when the sheath location is preliminarily known. When the sum of distance \(R\) in Equation (3) from input point to a nodal point and the nodal point to output point is the same (Figure 2), it is understandable that the same reflection intensities are given. As the location is based on Equation (3), there are many candidates of nodes with the same travel distance, and therefore the conventional the SIBIE procedure with only one receiver cannot occasionally provide correct geometrical information for asymmetrically distributed damage to the vertical axis e.g., in Figure 2. To upgrade the procedure from 2D to 3D with multiple receivers, in this study, an array with multiple sensors over a targeted area is employed. Specifically, four accelerometers and laser doppler vibrometer system, which is innovatively introduced for remote sensing technique, are used to improve the identification of damage in concrete. A concrete slab of existing structures and an experimentally casted slabs embedded by artificial damage with styrofoam are subjected to the expanded SIBIE procedure.