Inversion of zoepritz equations and their approximations

In this study, the inversion of precritical P-wave reflection offset-amplitude by the generalized linear inversion (GLI) method is introduced to obtain the elastic parameters, P- and S-wave velocities and density, of the underlying layer of a two layer model. The inversion scheme was applied with the full form of the Zoeppritz equations and their approximate forms to synthetic data to investigate the feasibility of using approximate Zoeppritz equations in this inversion scheme. Because the incident, reflection and refraction angles can be expressed in terms of the source-receiver offset, two-way-travel (twt) time to the reflector, and P- and S-wave velocities of the overlying and underlying layer, the relevant equations are expressed in offset-twt domain to be used with a common mid point (CMP) gather. In the inversion, it is assumed that the two-way-travel time to the reflector, shot receiver offsets and the elastic parameters of the overlying medium are known; the offset-amplitude of the reflected wavelets can be measured by Euclidean norm. The ratios of the second layer parameters to those of first layer are then obtained by using the GLI method. The second layer parameters are solved from these ratios. It is assumed that the data are corrected for geometrical spreading and absorption, and they are noise free.