Extension of the kinematic approximations to the multilayered elastic orthorhombic medium

Abstract

Understanding the kinematics of horizontally layered reservoir rocks is important to their proper characterization; to accomplish this, it is necessary to specify the explicit model for these kinematic properties. Accurate approximations for traveltime and relative geometric spreading in an elastic homogeneous orthorhombic (ORT) model have been investigated with different forms: shifted hyperbola form (SHF), Taylor series, and the rational form. We have extended these approximations to the multilayered ORT model by adopting composite coefficients and effective model parameters. The multilayered model is characterized without and with the azimuthal variation among layers. There is an overdetermined problem when the azimuthal variation exists; to address that case, the least-squares method is adopted. To check the feasibility of the expansion, we select the SHF approximation specified in the homogeneous elastic ORT model for the calculation in the numerical example. Four groups of examples are analyzed to investigate the influence on the accuracy of the approximation with the change in rotation angle, degree of anisotropy, and the direction of the orientation. The results indicate that, for the multilayer, the accuracy of the approximation is proportional to the degree of anisotropy and the value of the angle of rotation. The relative errors in traveltime and relative geometric spreading in this multilayered extension are very small and can be implemented in practical applications.