First-break traveltime tomography is based on the eikonal equation. Because the eikonal equation is solved at fixed-shot positions and only receiver positions can move along the raypath, the adjoint-state tomography relies on inversion to resolve possible contradicting information between independent shots. The double-square-root (DSR) eikonal equation allows not only the receivers but also the...

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...

The eikonal equations in spaces of different dimensions and different types have many applications in the geometric optics, acoustics of inhomogeneous media, theoretical physics, etc. The details on this theme can be found in [1–7] (see also the references therein). Sheng, Guha and Gonzalez (see [8,9] and the references therein) proposed new effective methods for solving many problems of comput...

Abstract. Acoustic waves in porous media are subject to dispersion and strong attenuation. A rigorous asymptotic solution of Biot’s equation involves a complex eikonal function and its numerical implementation requires complex space-time ray tracing. Attenuation is represented by the imaginary part of the eikonal. Non-negativity of timeaveraged dissipation in time-periodic motions implies that ...

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...

This work explores the celebrated AdS/CFT correspondence [1] in the regime of high energy scattering in Anti–de Sitter (AdS) spacetime. In particular, we develop the eikonal approximation to high energy scattering in AdS and explore its consequences for the dual Conformal Field Theory (CFT). Using position space Feynman rules, we rederive the eikonal approximation for high energy scattering in ...

We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an example, we combine the probability generating function technique with an eikonal approximation to evaluate the exponentially large increase in the extinction ...

Traveltime computation is widely used in seismic modeling, imaging and velocity analysis. The two most commonly used methods are ray tracingand numerical solutions to the eikonal equation. Eikonal solvers are fast and robust, but are limited to computing only the first arrival traveltimes. Ray tracing can compute multiple arrivals, but lacks the robustness of eikonal solvers. Here, we propose a...

Using an eikonal analysis, we examine the validity of the factorization theorem for nucleon-nucleon, γp and γγ collisions. As an example, using the additive quark model and meson vector dominance, we directly show that for all energies and values of the eikonal, that the factorization theorem σnn/σγp = σγp/σγγ holds. We can also compute the survival probability of large rapidity gaps in high en...