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Eikonal equation - Wikipedia, the free encyclopedia
The eikonal equation (from German Eikonal , which is from Greek εἰκών, image) is a non-linear partial differential equation encountered in problems of wave propagation, when the wave equation is a...
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yields the eikonal equation. ... Note that if identically and on the boundary of a region , then for outside , the solution to the eikonal equation measures the distance from to . At least, I think it should ... It’s called the eikonal equation because eikonal is something like the greek word for image.
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Download this paper (pdf) ... This paper is part of the course: Introduction to Seismology, Spring 2005 - MIT OCW ... 4 - Wave Equation (cont.)
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Consider the problem of finding a unit speed trajectory x(t) that minimizes the integral of a cost function g(x(t)). The numerical solution of this problem involves the solution of the discretization of the eikonal equation, a nonlinear partial differential equation, which is a special case of the Hamilton-Jacobi equation.
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Solutions to the eikonal equation sweep out trajectories in (x,w,φ) space satisfying the following system of ordinary differential equations. ...
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A Maxwellian Derivation of the Eikonal Equation of Ray Optics: ... We may now derive the all important eikonal equation. To that end, we first take a derivative along the ray direction -- viz. ... We may use the eikonal equation to find an equation for the approximate ray trajectory -- i.e. an equation for ray height x as...
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Often the eikonal equation f = a = const. is solved for given boundary data consisting of an interface in the form of a curve c R2 and g = 0 along c. The construction of a solution is equivalent to evaluate the distance function of the curve c, which is in fact a planar problem.
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Enders A. Robinson ... New York, New York, U.S. ... One of the most popular methods uses the eikonal equation, whose derivation goes back to the work of Pythagoras about 2500 years ago.
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As we can express the familiar Eikonal equation for the travel time in high frequency domain, V. Khare proposes from equation (4) the following paraxial approximation of Eikonal equation for time migration: ...
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The eikonal equation, describing the traveltime propagation in an isotropic medium, has the form ... which is the linearized version of the eikonal equation ( 1). The accuracy of the linearization depends on the relative ratio of the slowness perturbation n1 and the true slowness model n. Though it is difficult to give...
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