An approximation is of practical interest whenever an exact approach is not available or is too complicated to be used. Kinematic properties of wave propagation in orthorhombic media are generally more complicated than in transversely isotropic media — an issue that emphasizes the necessity of proper approximate equations that keep a balance between accuracy and simplicity. Exact phase velocity equation in orthorhombic media is algebraically too complicated for some practical purposes, even after acoustic assumption. Although the exact phase velocity equation is readily calculated, there is not an explicit equation for the exact group velocity as a function of group angle nor for the traveltime as a function of offset. Accordingly, we have developed new approximate phase velocity, group velocity, and moveout equations for acoustic orthorhombic media in a simple and uniform functional form. They fit to their corresponding exact kinematic properties, within and outside the orthorhombic symmetry planes. We find a higher accuracy of our approximations compared with other existing approximations in a variety of orthorhombic models. As an example, we convert our phase velocity approximation to a dispersion relation in the frequency domain and use it for wavefield modeling in a heterogeneous orthorhombic model. Our dispersion relation is simpler and more accurate than the original equation being in use in the wave extrapolation modeling by low-rank approximation.
Design and analysis of parts constructed from weft-knitted textile composites need the elastic and fracture behavior of the composite. To avoid time-consuming and expensive experimental procedures, micromechanical models and finite element simulations can be used to estimate stiffness matrix of these composites. In the present study, at first, a 3D model of a plain weft-knitted fabric is presented. Then a micromechanical approach is proposed to derive the mechanical properties of the weft-knitted composite using this geometrical model. A finite element simulation is carried out to extract the elastic properties of the composite as an alternative procedure. Finally, obtained moduli from both methods are validated by comparing them with existing experimental values. Results show a good agreement between the calculated and measured data. It can be concluded that the proposed micromechanical approach can predict weft-knitted composite behavior well without any great effort; however, the finite element analysis gives acceptable results too. The effects of composite variables on the stiffness are investigated and discussed.
Normal moveout (NMO) correction is routinely applied to traces of each common-midpoint (CMP) gather before forming a stack section. Conventional NMO correction has the drawback of producing stretching as a natural result of convergence of the NMO trajectories. Although this problem exists on completely hyperbolic reflections, the reflections will be further deviated from the desirable zero-offset equivalent if they indicate nonhyperbolic behavior. We have addressed this issue and developed a new method of stretch-free NMO correction in two steps: first, a novel way of rectifying NMO correction trajectories in a shifted hyperbolic NMO base, and second, a prioritized successive process of mapping data samples into an NMO-corrected gather. We have determined the advantage of the proposed method over two preceding methods: isomoveout and local stretch zeroing. The effectiveness of the new method in producing a stretch-free NMO gather was tested on synthetic data generated by ray tracing and a real data set of 200 CMP gathers of an Iranian oil field. The proposed method can be used in the presence of hyperbolic and nonhyperbolic events, and it recovers the amplitudes of interfering reflections to extend the usable offsets.
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