## 5 Discussion
### Comparison of the Measured and Simulated Results  
The aim of acoustical simulations is to obtain predictions that would closely match measured data. A well-calibrated model should minimise the perceivable differences between simulation and measurements for any considered acoustic parameter. The subsequent considerations were also based on the \(\alpha_{\mathrm{w}}\) and s values of the cavea surface and its variations. The differences between the measured and simulated results are shown in Figure 4, which reports the acoustical behaviour during the calibration of both kinds of software, considering the variations due to the 20 alternative combinations (5 scattering coefficients \(\times\) 4 absorption coefficients), for all the receivers, and the average between the 500 Hz and 1 kHz octave-bands. The isolevel curves shown in Figure 4 have been obtained by a two-dimensional data interpolation using the MATLAB function \"interp2\" with the \"spline\" method active. This method was chosen in order to have smooth first and second derivatives throughout the curves. Figure 4a,b, which pertain to O and C, respectively, refer to parameter T\({}_{20}\), while Figure 4c,d refer to C\({}_{80}\) and Figure 4e,f to G. The light yellow colour in the graphs shows the \(\alpha_{\mathrm{w}}\) and s combinations for which the simulated values were closest to the measured ones. These isolevel curves were based on SAD, i.e., the Sum of the Absolute Differences between the simulated values, s\({}_{\mathrm{n}}\), and the measured ones, m\({}_{\mathrm{n}}\), for each receiver position, expressed as follows by Equation (7) [52]:  
\[\mathrm{SAD}=\ \sum_{1}^{\mathrm{n}}\lvert\mathrm{s}_{\mathrm{n}}-\mathrm{m}_{ \mathrm{n}}\rvert \tag{7}\]  
The results show that, depending on which parameter is considered, the best agreement between the simulated and measured values could not be obtained for the same combination of \(\alpha_{\mathrm{w}}\) and s. From the isolevel curves layout it is observable that, apart from T\({}_{20}\), Odeon software is more sensitive to variations of \(\alpha_{\mathrm{w}}\) than of s, while the opposite occurs for CATT-Acoustic. For T\({}_{20}\), lower differences between the simulated and measured values are detectable for both high and low absorption and scattering values in the case of Odeon software, while mainly for high scattering values over the whole range of absorption values in the case of CATT-Acoustic. For C\({}_{80}\), a good matching between measured and simulated values occurs with high absorption values over the whole range of scattering coefficients in the case of Odeon software, while it occurs with low scattering coefficients over the whole range of absorption coefficients in the case of CATT-Acoustic. For G, the best matching between measured and simulated values occurs with low absorption values over the whole range of scattering coefficients in the case of Odeon software, while it occurs with a medium scattering coefficient over the whole range of absorption coefficients in the case of CATT-Acoustic. Only in the case of G do both kinds of software show an agreement that is obtained in a range around the values of \(\alpha_{\mathrm{w}}\) = 0.10 and s = 0.55. Thus, this combination was considered for the calibration of the model. Table 4 shows all the simulation results of the calibrated model of SR, expressed as T\({}_{20}\), C\({}_{80}\), and the G acoustical parameters, considering both O and C. All the values are averaged over the central 500 Hz and 1 kHz octave-band frequencies and spatial values have been added for each row. In this  
way, the results can be compared directly with those of the corresponding measurements. A good agreement has been shown between the results obtained with the two different types of software, as can be also seen from the graph in Figure 5, where the average G for each row is represented along the average distance from the source, in the cases of measurements and simulations with Odeon and CATT-Acoustic.