## 6 Conclusions  
In this study, a 2D multi-parameter pseudo-viscoelastic time domain is applied to a synthetic shallow complex velocity model where a dipping high-velocity layer near the surface with varying thicknesses is used as the case study and both surface and body waves are present. Investigation of these problems requires consideration of various aspects in the presented FWI methods. Some of these aspects that need to be considered in this workflow could be noise contamination, initial velocity model building, elastic and viscoelastic effects, Q factor estimation, and handling long offsets. The other concern about the presented FWI is the convergence speed and computational time of both the forward and inverse steps. Obviously, the size of the velocity model and observed data for near-surface application is not comparable with deep reflection data. The forward modeling step for generating synthetically predicted data from the initial model, back propagation, and computing the gradient, are time consuming steps in the proposed strategy. Thus, to speed up the processing time and increase the converge speed, the nonlinear conjugate gradient method was used. Defining the order of the finite difference operator, discretization, built-in wavelet, Q factor approximation, optimization method, and boundary condition definitions also need to be considered. The first synthetic example shows that when the velocity values in the model are not high, P- wave and S- wave velocity, and density models can be reconstructed well using a low frequency source signal. When the velocity values in the model are higher, the high-velocity layer cannot be resolved with the P- wave velocity model because of the large p-wavelength propagated through the medium. Therefore, the use of a wavelet with a broader bandwidth and higher center frequency can be the solution. In the second experiment, a Ricker wavelet is used to fulfill this issue. Both experiments provide satisfactory and reasonable results as the high-velocity layer near the surface is fairly reconstructed and the structures below this layer are also partially imaged. Reconstruction of the S- wave velocity model is more reliable and accurate compared to p-wave velocity and density models, due to less sensitivity of the surface waves with respect to the P- wave velocity and density parameters. This issue needs to be studied and improved in the future. However, it should be noted that a better image of subsurface structures would be obtained if attenuation of P- and S- waves are inverted simultaneously with the model parameters.  
Figure 10: Fitting of the data in the shot at \(x=9\) m when using a high-frequency source signal. (**a**) Comparison of the vertical velocity observed and inverted seismograms. (**b**) Comparison of the normalized seismograms calculated for the initial, inverted, and observed data for trace 36.  
**Author Contributions:** Conceptualization, N.A., M.S.M. and T.B.; Methodology, T.B.; Software, N.A., M.S.M. and T.B.; Validation, N.A.; Formal analysis, N.A., M.S.M. and T.B.; Data curation, T.B.; Writing--original draft preparation, N.A.; Writing--review and editing, M.S.M.; Supervision, M.S.M., A.R.K. and T.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.