## 2 Problem Statement  
It was shown that seismic imaging in seismic data with above mentioned properties is technically a challenging task due to several reasons. The first is complexity of the media. These complexities will introduce lateral velocity changes, make reduction in quality of data and reduce SNR of data. These problems prevent application of conventional imaging methods and require advanced methods, such as RTM and FWI, to be modified accordingly. The FWI method estimates subsurface properties affecting the seismic wave-field via minimizing the field data and synthetic seismogram generated from forward modeling. An ultimate FWI method should take attenuation and dispersions into account, which means considering the wave propagation medium as a viscoelastic medium. An appropriate choice of model parameterization is also very important in viscoelastic FWI. Various approaches are presented for FWI in viscous media in the frequency and time domain [21]. Shot parallelization, variable grids in the near future and better free surface implementation are also other compatibilities of an appropriate FWI method. Obviously, to make the inversion process converge to the correct and accurate response, the initial velocity model needs to be close enough to the real field velocity model. The focal issue here is to resolve the problem of imaging on data which contains a high-velocity layer and causes less energy of transmitted wavefield reach to the structures under this layer. Presence of steep dips, low SNR, and energy absorption by thick layers of evaporites--which dramatically reduce the quality of images in deeper parts--are obstacles in obtaining high quality images. Since the data suffer from reduction in quality due also to faults and variations in the thickness of the high-velocity layer, it is required that the FWI method modified accordingly in considering attenuation and wavelet estimations [22]. The lateral velocity changes due to the evaporites will reduce the sensitivity of the FWI method in reconstruction of the velocity models. Therefore, it is important to define appropriate initial velocity models. Furthermore, since the FWI package of the Karlsruhe institute of technology (KIT) could model the viscoelastic properties of the media in wave propagation simulation, it is assumed that the data quality will increase in regions with above mentioned problem [23]. The model parameterization and discretization of the media is also challenging in application of FWI method in such regions. Discretization should be flexible and appropriate for boundaries of abrupt changes in elastic properties of the media, which is the result of complex mud intrusions [24]. This complexity will also introduce problems in model parameterization, which needs to be optimized via parameter analysis. In this study, the performance of the 2D pseudo-viscoelastic FWI proposed by [20] to image a synthetic model with velocity complexity is investigated. A time-domain multi-parameter FWI is applied to reconstruct the P- wave velocity, S- wave velocity, and density models. The forward problem is solved using the finite difference method (FD) and the viscoelastic wave equation is discretized considering the convolutional perfectly matched layers (PMLs) absorbing boundary condition to prevent the edge effects. To solve the inverse problem, the preconditioned conjugate gradient (PCG) is used. The gradients are computed with the adjoint-state method. A simple model generated by the 1D linear gradient is considered as the initial model.