## 1 Introduction
In common azimuth, the seismic data is gathered in a certain straight line (certain azimuth). The seismic data is stacked based on various offsets or angles of incidence, and the famous format is near, mid and far stacked seismic data. Differently, in variable azimuth, seismic data is stacked for a certain angle of incidence in various azimuthal directions and commonly labeled as \(0^{\circ},\ldots,360^{\circ}\). Common azimuth data, well known as partial or pre-stack data, is widely used for reservoir lithological and fluid inversion, while variable azimuth data is used for characterizing the anisotropic behavior of the reservoir. When seismic data is rich in azimuths, it can be used by an anisotropic method to estimate the earth's anisotropy parameters [6]. Anisotropy analysis, such as vertical and horizontal transverse isotropy (VTI/HTI), can be conducted with amplitude versus azimuth (AVAz) reflectivity and azimuthal inversion. Recently, [PERSON] et al. [7] successfully inverted quantitatively the fracture weakness parameter from a vertically fractured reservoir. They predicted the second Fourier coefficient and the azimuth of the symmetry axis of the inverted azimuthal EI datasets and combined them to estimate the fracture weaknesses. They found that the proposed inversion is stable and reliable when the azimuth of the symmetry axis deviates less than \(30^{\circ}\). They explained that the proposed inversion is dependent on the correctness of the constructed anisotropic rock physical model; therefore, the reliability of the inversion remains questioned. Elastic impedance inversion in the common azimuth data domain is also widely used in the industry. While the azimuthal inversion is conducted with AVAz (amplitude versus azimuth) reflectivity, the EI inversion in common azimuth is conducted with AVA (amplitude variation with angle) or AVO (amplitude versus offset) reflectivity. The elastic properties are commonly estimated by solving simultaneously the AVO equation for a given set of angle-stacked data. The main result of the inversion is commonly compressional impedance, shear impedance and density. Compressional velocity, shear velocity and Poisson's ratio are usually inverted as an additional result. Recently, [PERSON] et al. [8] used a simultaneous inversion from commercial software to delineate the hydrocarbon reservoir from a subtle seismic feature that failed to be conducted by traditional seismic inversion. Utilizing four wells and five stacked seismic data, they successfully delineated the reservoir well validated by a blind well test. They show the effectivity of the inversion from the volume of the inverted compressional-impedance, shear-impedance, density, near and far-far lambda-rho, mu-rho and Poisson's-ratio that reveal vertical and lateral continuity of the reservoir. Although the non-zero angle incidence seismic data is believed to bring various elastic properties information, in practice, the AVO equation limits the applicable range of the angle of incidence and when the angle of incidence is very large, it leads the reflectivity value to exceeds one which conflicts with real seismic data. [PERSON] et al. [9] proposed to rotate the AVO equation such that the square sinus of the incidence angle is equal to the tangent of the angle of rotation. The elastic reflectivity is, consequently, not only a function of the incidence angle but also the rotation angle and called extended elastic impedance (EEI) reflectivity. The angle of rotation changes between \(-90^{\circ}\) and \(90^{\circ}\), extending the elastic impedance for any given angle of incidence. The rotation angle that corresponds to the maximum cross correlation between the elastic (or any physical) parameter and EEI and is called the optimum of angle of rotation and can be used to predict the parameter from any given EI at a certain angle of incidence set. [PERSON] et al. [10] conducted a feasibility study to see if EEI spectrum variation exhibits any sensitivity to hydrocarbon reservoir geomechanical parameters.