The amplitude computation requires an accurate approximation for the traveltime gradient and Laplacian. Since it is hard to compute the traveltimes with a secondor higher-order accuracy in realistic media, the di erence approximations of the traveltime derivatives may not be suitable for accurate amplitudes unless special cares are taken. This article is concerned with a concurrent simulation o...

Traveltime computation is an important part of seismic imaging algorithms. Conventional implementations of Kirchhoff migration require precomputing traveltime tables or include traveltime calculation in the innermost computational loop . The cost of traveltime computations is especially noticeable in the case of 3-D prestack imaging where the input data size increases the level of nesting in co...

Traveltime computation is an important part of seismic imaging algorithms. Conventional implementations of Kirchhoff migration require precomputing traveltime tables or include traveltime calculation in the innermost computational loop . The cost of traveltime computations is especially noticeable in the case of 3-D prestack imaging where the input data size increases the level of nesting in co...

[1] The channel network (S) is a nonconvex set, while its basin [C(S)] is convex. We remove open-end points of the channel connectivity network iteratively to generate a traveltime sequence of networks (Sn). The convex hulls of these traveltime networks provide an interesting topological quantity, which has not been noted thus far. We compute lengths of shrinking traveltime networks L(Sn) and a...

Full waveform inversion (FWI) can generate high-resolution subsurface models, but often suffers from an objective function with local minima caused mainly by an absence of low frequencies in seismograms. These local minima cause cycle skipping when the initial model for FWI is far from the true model. To avoid cycle skipping, traveltime inversion is often used to compute initial models for FWI....

We present a practical regular grid wave traveltime calculation that is based on Huygens wavefront expansion and grid traveltime mapping. Wavefront expansion is carried out by finite difference approximations to the equations that are equivalent to the Eikonal equation with a fixed time interval. Mapping traveltime from wavefront to regular grids is based on a dynamic ray tracing paraxial appro...

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...

S U M M A R Y A new theory for the calculation of later seismic arrivals in heterogeneous media is presented. We introduce the concept of a ‘raylet’, which is a segment of a later arriving ray path between source and receiver defined by joint properties of forward and reciprocal traveltime fields. We show that all rays between a single source and receiver in arbitrary heterogeneous media can be...

Traveltime calculations amount to solving the nonlinear eikonal equation for a given source location. We analyze the relationship between the eikonal solution and its perturbations with respect to the source location and develop a partial differential equation that relates the traveltime field for one source location to that for a nearby source. This linear first-order equation in one form depe...