# Estimation of Litho-Fluid Facies Distribution from Zero-Offset Acoustic and Shear Impedances
## 3 The Effect of Seismic Anisotropy on Seismic Data
The idea of this method is to model synthetics by using a PP and PS survey such that layer boundaries and material properties are predefined, and then the survey is simulated by the ray tracing method to generate a synthetic model from which the anisotropy parameters are forecasted. The best parameter estimates are selected according to the comparison between the synthetic model and the real seismic data. This method gives reliable results but only at well locations. Another method was set by [PERSON] and [PERSON] [79], who estimated [PERSON]'s parameters from routine well logging data, following a theoretical framework which uses sonic logs to provide a fine-layered isotropic elastic model that can be used to calculate anisotropy parameters as functions of depth and seismic wavelength [80]. [PERSON]'s parameters  
Figure 1: A plot of the reflection coefficient on the Y-axis versus the angle of incidence on the X-axis. The blue and green lines represent the reflectivities obtained based on the isotropic and anisotropic assumptions, respectively. can be also estimated from the average velocity, obtained from sonic data, and the mean inclination angles of deviated wells [81]. However, the results of that study were inaccurate because most of the wells' inclination angles were below \(5^{\circ}\), showing no anisotropy effect on seismic data. The residual moveout analysis of diving waves has been used to estimate anisotropy parameters by applying different parametrization scenarios [82]. This method is reasonably accurate even for large values of velocity gradients, but it assumes that the velocity increases linearly with depth, while the anisotropy parameters do not. However, this assumption can only apply to homogeneous media. The previous methods can be used to obtain the anisotropy parameters and then process seismic data to obtain zero-offset images, which can be inverted into accurate rock properties. However, a different approach is to transform the layer properties, obtained from isotropic inversion, into zero-offset parameters based on Ruger's reflectivity function in horizontal transverse isotropy (HTI) media [83]. Another anisotropic prestack seismic inversion [84] is based on the Markov random field (MRF), which can establish dependencies between the spacial wave propagation field's nodes based on prior constraints [85]. The weights of those constraints have been optimized by the anisotropic diffusion method to remove the anisotropy effect in three different models: the symmetrical, vertical asymmetrical, and asymmetrical models. This method has produced encouraging results for Vp, Vs, and density. Based on the elastic wave equation, the anisotropic elastic waveform inversion was applied to invert for the P- and S-wave velocities, density, and Thomsen's parameters [86]. The method is based on the idea of eliminating the error between the synthetic and field seismic waveform data according to a misfit function [87]. The anisotropic inversion outputs were successfully used to reduce the ground-roll noise in 2D seismic data. Another methodology depends on multiscale phase inversion, assuming an anisotropic medium [88]. The advantage of this method is that it avoids the nonlinearity of the misfit functions [89] by adding wave-number details to the velocity model by a skeletonized inversion. This method assumes a VTI medium with Delta equal to zero, while the zero-offset P-wave velocity and Epsilon are inverted, resulting in more accurate results compared to full-wave inversion. It can be concluded that most of the previous methods have quantified seismic anisotropy only at well locations. The interpolation of the anisotropy parameters between wells is challenging and should be further linked to the effect of the facies distribution. Therefore, the current study has improved a previous anisotropic inversion approach [90] which solves for the zero-offset impedances and anisotropy parameters, Epsilon and Delta, based on partial-stack inversion and [PERSON]'s anisotropy equations [91].