The ability to calculate traveltimes and amplitutdes of seismic waves is useful for many reflection seismology applications such as migration and tomography. Traditionally, ray tracing (cerveny et al., 1977; Julian, 1977), paraxial methods (Claerbout, 1971), or full-wave methods (Alterman and Karal, 1968) are used for such calculations. These methods have in common considerable computational ex...

The Stolt migration extension to a varying velocity case (Stolt stretch) implies describing a vertical heterogeneity by a constant parameter (W ). This paper exploits the connection between modified dispersion relations and traveltime approximations to derive an explicit expression for W . The expression provides theoretically the highest possible accuracy within the Stolt stretch framework. Ap...

Based on minimizing a piecewise differentiable lp function subject to a single inequality constraint, this paper discusses algorithms for a discretized regularization problem for ill-posed inverse problems. We examine computational challenges of solving this regularization problem. Possible minimization algorithms such as the steepest descent method, iteratively weighted least squares (IRLS) me...

The traveltimes of underside shear wave reflections (i.e. SS precursors) are widely used data for mapping the topography of mantle discontinuities in the upper mantle. Here, we examine the accuracy of ray theory in estimating the contribution of shear velocity heterogeneity in the mantle to SS–S400S, SS–S670S and S400S–S670S traveltimes. We analyse stacks of spectral-element method waveforms co...

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...

■ Abstract This paper reviews recent research focused on the Earth’s inner core. Large inner-core traveltime anomalies and the anomalous splitting of core-sensitive free oscillations strongly suggest that the inner core is anisotropic. Initial models involved a simple, constant or depth-dependent cylindrical anisotropy at a level less than a few percent. Recent observations suggest that its eas...

S U M M A R Y Wave-equation traveltime tomography tries to obtain a subsurface velocity model from seismic data, either passive or active, that explains their traveltimes. A key step is the extraction of traveltime differences, or relative phase shifts, between observed and modelled finite-frequency waveforms. A standard approach involves a correlation of the observed and measured waveforms. Wh...

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...

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...

Azimuthal anisotropy or lateral velocity variations cause azimuthal variations in moveout velocity which can lead to seismic image degradation if not properly handled. In cases where apparent azimuthally anisotropic moveout is present, a single picked velocity is inadequate to flatten an event on a 3D CMP gather. Conventional velocity analysis techniques require a significant amount of time and...