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Physical Ray Tracing Part 1: Understanding the Eikonal …
https://www.youtube.com/watch?v=G1LOsvGGQos
This video describes the Eikonal Equation from the field of Geometric Optics. It can be used to describe rays within mediums where the speed of light (refractive index) changes gradually, instead...
Eikonal Based Ray Tracing Procedure - 6 An Evaluation of Electron ...
https://1library.net/article/eikonal-based-tracing-procedure-evaluation-electron-density-transmitter.zlvwojly
6.2 Eikonal Based Ray Tracing Procedure As already mentioned, oblique ionograms are useful for studying free electron distri- bution along a ray path. To achieve this, an eikonal based ray-tracing was performed (Borovskikh, A. V., 2010), considering the ionosphere as characterized by a slowly varying refractive index that gradually changes only ...
Ray-tracing and eikonal solutions for low-frequency wavefields
https://www.crewes.org/Documents/ResearchReports/2007/2007-45.pdf
The physics of the eikonal equation Physically, the eikonal equation may be thought of as defining an outer envelope which would approximately contain all rays traced from the start timet= 0 to the travel time t. Consider a medium consisting of a homogeneous background velocity of 2000m/s
Eikonal approximation (Chapter 3) - Ray Tracing and …
https://www.cambridge.org/core/books/ray-tracing-and-beyond/eikonal-approximation/B09582EE0BAEA706A59238649960C761
The great advantage of eikonal methods is that they reduce the solution of systems of PDEs, or systems of integrodifferential equations, to the solution of a family of ODEs. This often results in a substantial increase in computational speed in applications. In addition, the ray trajectories themselves often provide useful physical insight.
Ray Tracing and Eikonal Solver
https://mcsc.sc.mahidol.ac.th/courses/pde/slides/08_ray_tracing.pdf
Ray Equation Ray paths are characteristic curves of the Hamiltonian which can be written in various form. In the Hamiltonian formalism of ray tracing, the momentum is corresponding to the slowness vector defined as . The eikonal equation can then be written as with a Hamiltonian 4 Hamiltonian Formalism
Ray-tracing and eikonal solutions for low-frequency …
https://www.academia.edu/16041465/Ray_tracing_and_eikonal_solutions_for_low_frequency_wavefields
This highlights one major difference between eikonal-based modelling and ray-tracing modelling: ray-tracing allows for more natural inclusion of the modelling of multiple reflections, while eikonal solutions are often insen- sitive to multiple reflections∗ . Whether or not either is a benefit or hindrance is dependent on the goals of the modelling.
Eikonal Equation - an overview | ScienceDirect Topics
https://www.sciencedirect.com/topics/earth-and-planetary-sciences/eikonal-equation
The eikonal equation is a nonlinear, partial differential equation of the first order belonging to the Hamilton–Jacobi variety (Kravtsov and Orlov, 1990 ), usually solved in terms of characteristics ( Courant and Hilbert, 1966 ). The characteristics are 3D trajectories x = x (τ) verifying a set of ordinary differential equations (ODEs).
Big ray-tracing and eikonal solver on unstructured
https://pubs.geoscienceworld.org/geophysics/article-abstract/64/1/230/73435/big-ray-tracing-and-eikonal-solver-on-unstructured
Big ray tracing is based on a combination of ray tracing and local solutions of the eikonal equation. Classical ray tracing first discretizes the phase space and defines local zones that possibly overlap where the traveltime field is multivalued. Then an eikonal solver computes traveltimes in these zones called big rays.
Ray tracing in - Stanford University
http://sepwww.stanford.edu/public/docs/sep95/biondo1/paper_html/node2.html
Ray tracing in The solutions to the focusing eikonal can be computed using current methods for solving the standard eikonal, either directly by modern eikonal solvers Fomel (1997); Sethian and Popovici (1997), or by ray tracing. We chose a ray tracing solution, because for reflection tomography is handier to have rays than traveltime maps.
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