Determining elastic constants of an orthorhombic material by physical seismic modeling
Faranak Mahmoudian, Gary F. Margrave, P. F. Daley, Joe Wong, Eric V. Gallant
Vertically fractured media are commonly described by an HTI (horizontal transverse isotropy) model, which is a degenerate case of the more general orthorhombic symmetry. To study the seismic effects of such a medium, a model from phenolic LE material, which exhibits the orthorhombic symmetry, was constructed. To characterize the anisotropy of the phenolic model the set of nine elastic constants is determined. Elastic constants are most often found from measurements of the phase velocity in a variety of directions, but finding this plane-wave velocity is problematic. Instead of the phase velocity, group velocity, which can be measured easily and more reliably, is used. Scaled physical modeling experiments in the laboratory in which ultrasonic elastic waves are propagated through the phenolic model are used to measure the P- and S-wave group velocity in different directions in the principal planes. A linear expression between the P-wave group velocity in an arbitrary direction and elastic constants, has allowed us to estimate all nine elastic constants. Although actually slightly orthorhombic, the phenolic model exhibits approximate HTI symmetry requiring only five elastic constants to characterize the medium.