Frechet kernels for finite-frequency traveltimes - I. Theory

We use body wave ray theory in conjunction with the Born approximation toco mpute 3-D Frechet kernels for finite-frequency seismic traveltimes, measure d by cross-correlation of a broad-band waveform with a spherical earth synt hetic seismogram. Destructive interference among adjacent frequencies in th e broad-band pulse renders a cross-correlation traveltime measurement sensi tive only to the wave speed in a hollow banana-shaped region surrounding th e unperturbed geometrical ray. The Frechet kernel expressing this sensitivi ty is expressed as a double sum over all forward-propagating body waves fro m the source and backward-propagating body waves from the receiver to every single scatterer in the vicinity of this central ray. The kernel for a dif ferential traveltime, measured by cross-correlation of two phases at the sa me receiver, is simply the difference of the respective single-phase kernel s. In the paraxial approximation, an absolute or differential traveltime ke rnel can be computed extremely economically by implementing a single kinema tic and dynamic ray trace along each source-to-receiver ray.