The eikonal equation is instrumental in many applications in several fields ranging from
computer vision to geoscience. This equation can be efficiently solved using the iterative …

The eikonal equation plays an important role across multidisciplinary branches of science
and engineering. In geophysics, the eikonal equation and its characteristics are used in …

The viscosity solution of static Hamilton-Jacobi equations with a point-source condition has
an upwind singularity at the source, which makes all formally high-order finite-difference …

First-arrival traveltime is commonly used in problems that involve static correction, pre-stack
migration, earthquake location, seismic tomography, etc. The classical eikonal equation …

The solution for the eikonal equation with a point-source condition has an upwind singularity
at the source point as the eikonal solution behaves like a distance function at and near the …

In some applications, it is reasonable to assume that geodesics (rays) have a consistent
orientation so that the Helmholtz equation may be viewed as an evolution equation in one of …

Tong has proposed an adjoint-state traveltime tomography method to determine velocity
heterogeneity and azimuthal anisotropy. This method, however, ignores the Earth's …

Global traveltime modeling is an essential component of modern seismological studies with
a whole gamut of applications ranging from earthquake source localization to seismic …

Topography‐dependent eikonal equation (TDEE) formulated in a curvilinear coordinate
system has been recently established and is effective for calculating first‐arrival travel times …

Accurate numerical computation of wave traveltimes in heterogeneous media is of major
interest for a large range of applications in seismics, such as phase identification, data …