Related papers: Solving the Eikonal equation for compressional and…
The eikonal equation is utilized across a wide spectrum of science and engineering disciplines. In seismology, it regulates seismic wave traveltimes needed for applications like source localization, imaging, and inversion. Several numerical…
Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order…
First-arrival traveltime computation is crucial for many applications such as traveltime tomography, Kirchhoff migration, etc. There exist two major issues in conventional eikonal solvers: the source singularity issue and insufficient…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
The concept of physics-informed neural networks has become a useful tool for solving differential equations due to its flexibility. There are a few approaches using this concept to solve the eikonal equation which describes the…
The recent deep learning revolution has created an enormous opportunity for accelerating compute capabilities in the context of physics-based simulations. Here, we propose EikoNet, a deep learning approach to solving the Eikonal equation,…
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 Fast Sweeping (FS) methods and the direct Fast Marching (FM)…
We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the…
We use a Schr\"odinger wave equation formalism to solve the eikonal equation. In our framework, a solution to the eikonal equation is obtained in the limit as Planck's constant $\hbar$ (treated as a free parameter) tends to zero of the…
We present a numerical method for computing the solution of a partial differential equation (PDE) for modeling acoustic pressure, known as an extra-wide angle parabolic equation, that features the square root of a differential operator. The…
Seismic traveltime is critical information conveyed by seismic waves, widely utilized in various geophysical applications. Conventionally, the simulation of seismic traveltime involves solving the eikonal equation. However, the efficiency…
In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…
Since the original algorithm by John Vidale in 1988 to numerically solve the isotropic eikonal equation, there has been tremendous progress on the topic addressing an array of challenges including improvement of the solution accuracy,…
Fast and differentiable solvers for anisotropic and asymmetric distance fields are a key primitive in geometry processing, enabling gradient-based optimization over metrics, drift fields, and downstream objectives that depend on geodesic…
In this paper, we propose a direct probing method for the inverse problem based on the Eikonal equation. For the Eikonal equation with a point source, the viscosity solution represents the least travel time of wave fields from the source to…
Seismic forward and inverse problems are significant research areas in geophysics. However, the time burden of traditional numerical methods hinders their applications in scenarios that require fast predictions. Machine learning-based…
We introduce a fast Eikonal Phase Retrieval (EPR) formulation that accelerates eikonal phase retrieval by more than two orders of magnitude while retaining controlled accuracy. The method is derived from a second-order asymptotic expansion…
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane…
The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing wave spacetimes and then extracts approximate solutions of the physical problem, with…
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady state solutions of hyperbolic partial differential equations (PDEs). As other types of fast sweeping…