## 5 Results  
In this study, 314 iteration steps are calculated, and the inversion takes about 10 h when using a system with four cores with 3.1 GHz speed and 16 Gb of ram. The true, initial, and inverted P- wave velocity models are shown in Figure 1. The same order is given, for the S- wave velocity and density models in Figures 2 and 3, respectively. Figure 4 shows the vertical profiles through the P- wave and S- wave velocity and density models that are considered to compare the results with the true model in more detail. Vertical profiles through the models are obtained at \(x=25\) m. The reconstructed models are in good accordance with the true models, especially for the S- wave velocity model. In the inverted S- wave velocity model, the upper edge of the high-velocity layer can be seen more sharply compared to the two other models. The bottom edge of the high-velocity layer is reconstructed in each model but not in the accurate location. Some artifacts are seen in the low-velocity zone of the density and P- wave velocity models. Regarding the low sensitivity of surface waves with respect to the P- wave velocity and density model [41], inaccurate results of inversion for the P- wave velocity and density models can be expected, also because the amplitude of surface waves is much higher than the amplitude of P- waves. The sensitivity of surface waves with respect to the P- waves is low and it leads to an inaccurate P- wave velocity model at each iteration step. Because the density model is in relation to the P- wave velocity model using an empirical relation. Therefore, it affects the density model and the result of these two models is not as accurate as of the inverted S- wave velocity model [42]. To assess the results precisely, the final synthetic shot gathers are compared with the observed data. The vertical velocity seismogram of the shot at \(x=9\) m is obtained and the seismograms for the initial models are calculated for trace 36 of the shot and compared with the seismogram of the observed and inverted model. The comparison of the synthetic and observed seismograms of the shot at \(x=9\) m is shown in Figure 5a and the comparison of the initial, observed, and inverted data for trace 36 at this shot is shown in Figure 5b. Each seismogram is normalized to its maximum amplitude. The comparison of the initial and inverted data indicates the good performance of the inversion method and application of the software IFOS2D (Inversion of Full Observed Seismograms (2D)) in reconstructing model parameters. The calculated data agreeably fit the observed data. Therefore, the inversion result is a model which better explains the observed data. In the following, the true and initial models are built considering the \(\frac{v_{p}}{v_{s}}\) ratio of 2.5 that is more realistic in the case of studying the soft rocks near the surface. In this case, due to the increase in the velocity values, the wavelengths propagated through the medium are increased and the resolution is influenced by the wavelength. The high-velocity layer is not resolved with the P- wave velocity model. Therefore, to reconstruct the model, a broad bandwidth of the source signal is needed. A broad bandwidth signal cannot be generated by a hammer source, thus a vibroseis source can be used to generate a signal which has a higher center frequency and covers a broader frequency range than a cubed sine wavelet [43; 44]. Since a Ricker wavelet is similar to a Klauder wavelet generated by vibroseis source and is used in the synthetic seismic modeling, in the following a Ricker wavelet with a center frequency of 50 Hz is considered as the source signal. Figure 1: Multi-parameter synthetic example when using a low-frequency source signal: (**a**) the true P- wave velocity model for the calculation of the observed data, (**b**) the initial P- wave velocity model, and (**c**) the inverted P- wave velocity model. The CPML frame is marked by a thin black line.