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

This paper presents an efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes. The Eikonal equation, and the broader class of Hamilton-Jacobi equations to which it belongs, have a wide range of applications from geometric optics and seismology to biological modeling and analysis of geometry and images. The ability to solve such equations accurately and ...

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 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...

We present a fast algorithm for solving the eikonal equation in three dimensions, based on the fast marching method. The algorithm is of the order O(N log N), where N is the total number of grid points in the computational domain. The algorithm can be used in any orthogonal coordinate system and globally constructs the solution to the eikonal equation for each point in the coordinate domain. Th...

S U M M A R Y In this paper, several methods for the solution of the eikonal equation are investigated. Using the method of characteristics, traveltimes are computed along rays. Approximate solutions of the eikonal equation can also be obtained. From Fermat’s principle, first-order changes in the traveltime can be found by integrating along initial ray trajectories. Alternatively, linearized ra...

In this paper, an adaptation of the eikonal equation is proposed by considering the latter on weighted graphs of arbitrary structure. This novel approach is based on a family of discrete morphological local and nonlocal gradients expressed by partial difference equations (PdEs). Our formulation of the eikonal equation on weighted graphs generalizes local and nonlocal configurations in the conte...

In the high frequency regime, the geometrical-optics approximation for the Helmholtz equation with a point source results in an eikonal equation for traveltime and a transport equation for amplitude. Because the point-source traveltime field has an upwind singularity at the source point, all formally high-order finite-difference eikonal solvers exhibit first-order convergence and relatively lar...