Gaussian beams are a well-known high-frequency wavefield approximation. A more accurate representation can be obtained by the complex eikonal equation. We propose a constructive algorithm for solving the complex eikonal equation. By re-writing the complex traveltime as background real and imaginary parts and their respective perturbations, we arrive at an update scheme that aims at solving the ...

We prove that any 2-dimensional solution ψ ∈ W 1+ 1 3,3 loc of the eikonal equation has locally Lipschitz gradient ∇ψ except at a locally finite number of vortex-points. A related regularizing effect is also obtained for general solutions of the Burgers’ equation. DOI: https://doi.org/10.1080/03605302.2014.999939 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: h...

The first-arrival quasi-P wave travel-time field in an anisotropic elastic solid solves a first-order nonlinear partial differential equation, the qP eikonal equation, which is a stationary Hamilton–Jacobi equation. The solution of the paraxial quasi-P eikonal equation, an evolution Hamilton–Jacobi equation in depth, gives the first-arrival travel time along downward propagating rays. We devise...

The quasi-P wave in anisotropic solids is of practical importance in obtaining maximal imaging resolution in seismic exploration. The geometrical optics term in the asymptotic expansion for the wave characterizes the high frequency part of the quasi-P wave by using two functions: a phase (traveltime) function satisfying an eikonal equation and an amplitude function satisfying a transport equati...

A uniformly second order method with a local solver based on the piecewise linear discontinuous Galerkin formulation is introduced to solve the eikonal equation with Dirichlet boundary conditions. The method utilizes an interesting phenomenon, referred as the superconvergence phenomenon, that the numerical solution of monotone upwind schemes for the eikonal equation is first order accurate on b...

Solving the Eikonal equation on a surface allows establishment of a curvilinear coordinate system which facilitates many types of physics-based simulations and measurements. Existing methods that solve the Eikonal equation on surface triangulations suffer from significant limitations prohibiting their use in many applications. First, the surface may not have any holes. Second, every obtuse tria...

We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit (t, x) → (t/ε, x/ε). We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the classical eikonal equation derived from the heat equation with small diffusivity. We prove well-posedness of the phase problem and convergence towards the viscosity sol...

Traveltime, or geodesic distance, is locally the solution of the eikonal equation of geometric optics. However traveltime between sufficiently distant points is generically multivalued. Finite difference eikonal solvers approximate only the viscosity solution, which is the smallest value of the (multivalued) traveltime (‘‘first arrival time’’). The slowness matching method stitches together loc...

The first-arrival quasi-P wave traveltime field in an anisotropic elastic solid solves a first-order nonlinear partial differential equation, the q P eikonal equation. The difficulty in solving this eikonal equation by a finitedifference method is that for anisotropic media the ray (group) velocity direction is not the same as the direction of the traveltime gradient, so that the traveltime gra...