Traveltime tomography in anisotropic media-I. Theory

Upwind Nite Diierence Traveltime for Anisotropic Media

The rst arrival quasi-P wave traveltime eld in an anisotropic elastic solid solves a rst order nonlinear partial diierential equation, the qP eikonal equation. Since the qP slowness surface is convex, the rst arrival traveltime along downward propagating rays solves the paraxial qP eikonal equation, an evolution equation in depth. A second order upwind nite diierence scheme solves this paraxial...

Conditioning bounds for traveltime tomography in layered media

This paper revisits the problem of recovering a smooth, isotropic, layered wave speed profile from surface traveltime information. While it is classic knowledge that the diving (refracted) rays classically determine the wave speed in a weakly well-posed fashion via the Abel transform, we show in this paper that traveltimes of reflected rays do not contain enough information to recover the mediu...

Global Extrema in Traveltime Tomography

Multiscale traveltime tomography

Nonuniqueness in traveltime tomographic velocity analysis is largely the result of insufficiency in model parameterization. Traditional tomography parameterizes the model with nonoverlapping cells. Such single-scale tomography (SST) from inverting traveltimes only may produce underdeterminacy at places of insufficient ray coverage. To cope with the poor and uneven ray coverage, a multiscale tom...

On Crosswell Traveltime Tomography

In this paper, we give a theoretical analysis of the crosswell traveltime tomography. In the single arrival case, we prove that the objective function is smooth, and every critical point is a kinematically correct velocity model. A numerical example is presented to demonstrate the properties we prove and the diierence between traveltime tomography and waveform inversion via the output least squ...