## 3 Materials and Methods
### Simulation Measurements  
For the training and test cases, we used the opensource k-Wave toolbox [30; 31; 32]. The model was based on the k-space pseudospectral time domain (PSTD) method to solve the nonlinear wave equation in a Cartesian coordinate system and simulate linear and nonlinear wave fields in fluid media [31; 32]. This toolbox requires the properties of the computational grid, the medium properties, the source terms, and the reception points used to record the evolution of the wave field over time. For this work, 2D simulations were carried out; therefore, the spatial points were defined along the X and Y axes. The grid size was defined using 600 \(\times\) 600 grid points with \(\Delta\)x = \(\Delta\)y = 1/3 \(\frac{\mathrm{mm}}{\mathrm{point}}\) resolution, resulting in a simulated area of 20 \(\times\) 20 cm\({}^{2}\). The created sample corresponds to a concrete cylinder with a diameter of 10 cm in the center of the simulated area, called the outer cement or P1, which was surrounded by water. Inside of this cylinder, 1 or 2 additional cylinders of another type of cement were added (inner cement or P2). Moreover, the inner cylinders were of random sizes and placed in random positions, but some restrictions were applied: the diameters were uniformly distributed between 2 cm and 6 cm (U(2, 6) cm), there was a minimum distance of 1 cm between the edge of the inner cylinder(s) and the edge of the outer cylinder, and there were two possible cases (case 1 with only 1 inner cylinder and case 2 with 2 non-overlapping inner cylinders). An example of both cases is shown in Figure 10.  
The primary characteristics of the parameters and materials used for simulation are summarized in Table 1. To better approximate the training process to real-world conditions, a uniform distribution of density values was assigned for both cement materials. Figure 11a  
Figure 9: Flow chart of the measuring procedure. illustrates the uniform density distribution with a range of \(\pm 10\%\) relative to the central values: \(\rho_{1}=2.88\) for the outer cement (P1) and \(\rho_{2}=2.19\) for the inner cement (P2). The variations in the remaining parameters were derived from the changes in density and their respective distributions are depicted in Figure 11b-d. This approach is reflected in Table 2, which presents the central values and the corresponding range for each parameter. It is also important to note that the parameters for water were kept constant. As a result, the water column in the table does not present a range; it only includes the fixed value applied across all the simulated cases. Figure 11: Function distribution of the used parameters for simulation: (**a**) density values; (**b**) longitudinal velocity values; (**c**) attenuation values; (**d**) transversal velocity values. Figure 10: Representation of the geometry of simulation cases: (**a**) Single-core sample (**b**) Two-cores sample. For the simulation process, a through-transmission was selected where,  
* The transmitted signal corresponded to a burst signal of 1 MHz and 5 cycles (Figure 12a). The end time was set to 100 us and the sampling frequency was 100 MHz, yielding 10,000 points for each signal. * There were 25 reception transducers, equally distributed from 0 to 180 and placed in front of the transmission transducer. The reception transducers received signals simultaneously; that is, for each signal transmitted, 25 signals were received (Figure 12b). * The transmission transducer was a 2 cm active surface and was placed in water 3 cm from the outer cylinder (Figure 13). * The whole set of transducers was rotated around the cement sample in 2-degree increments from 0 to 358 (Figure 13), resulting  
Therefore, each simulation was composed of 4500 signals: 180 transmission positions multiplied by 25 reception positions for each transmission position. The simulations were carried out using a GPU GEFORCE RTX 2080 super and the simulation time for each case was about 1.58 h. A total of 146 cases were simulated, requiring around 9 days of simulation.