Ray tracing in anisotropic media with a linear gradient
نویسندگان
چکیده
In general, ray paths in anisotropic media can be found by solving the sixth-order kinematic ray equations. In this paper it is shown that in media where the density-normalized elastic parameters depend quadratically on one coordinate, i.e. the velocities vary linearly, the projection of the ray path on to the slowness vector plane, which is fixed, is the same shape as the cross-section of the slowness surface. Thus the ray path can be found by solving a polynomial equation. The deviation of the ray path from the plane and the travel time can be calculated by evaluating a simple integral along the ray.
منابع مشابه
Velocity Modeling in a Vertical Transversely Isotropic Medium Using Zelt Method
In the present paper, the Zelt algorithm has been extended for ray tracing through an anisotropic model. In anisotropic media, the direction of the propagated energy generally differs from that of the plane-wave propagation. This makes velocity values to be varied in different directions. Therefore, velocity modeling in such media is completely different from that in an isotropic media. The vel...
متن کاملRay-Optics Analysis of Inhomogeneous Uniaxially Anisotropic Media
Uniaxial optical anisotropy in the geometrical-optics approach is a classical problem and most of the theory is known for at least fifty years. Although the subject appears frequently in the literature, it is nearly silent about wave propagation through inhomogeneous anisotropic media. At the same time, the rapid advances in liquid-crystal lenses call for a good overview of the theory on wave p...
متن کاملRay-tracing and Interferometry in Schwarzschild Geometry
Here, we investigate the possible optical anisotropy of vacuum due to gravitational field. In doing this, we provide sufficient evidence from direct coordinate integration of the null-geodesic equations obtained from the Lagrangian method, as well as ray-tracing equations obtained from the Plebanski’s equivalent medium theory. All calculations are done for the Schwarzschild geometry, which resu...
متن کاملAttenuation analysis for heterogeneous transversely isotropic media
Attenuation coefficients obtained from seismic data may provide sensitive attributes for reservoir characterization and increase the robustness of AVO (amplitude variation with offset) analysis. Here, we present an algorithm for ray tracing in attenuative anisotropic media based on the methodology of C̆ervený and Ps̆enc̆ik. Both kinematic and dynamic ray tracing are carried out in an elastic refer...
متن کاملInteractive Rendering of Non-Constant, Refractive Media Using the Ray Equations of Gradient-Index Optics
Existing algorithms can efficiently render refractive objects of constant refractive index. For a medium with a continuously varying index of refraction, most algorithms use the ray equation of geometric optics to compute piecewise-linear approximations of the non-linear rays. By assuming a constant refractive index within each tracing step, these methods often need a large number of small step...
متن کامل