## Interpolation of travel times and ray amplitudes

**Johana Brokesova**
### Summary

The seismic wavefield, in its high-frequency asymptotic approximation, can be
interpolated from a low- to a high-resolution
spatial grid of receivers and,
possibly, point sources by interpolating the eikonal
(travel time) and the amplitude. These quantities
can be considered as functions of position
only. The travel time and the amplitude are assumed to vary
in space only slowly, otherwise the validity conditions of the theory
behind would be violated. Relatively coarse spatial sampling is then
usually sufficient to obtain their reasonable interpolation. The
interpolation is performed in 2-D models of different complexity.
The interpolation geometry is either 1-D, 2-D, or 3-D according to
the source-receiver distribution.
Several interpolation methods are applied: the Fourier interpolation
based on the sampling theorem, the linear interpolation, and the
interpolation by means of the paraxial approximation. These techniques,
based on completely different concepts, are tested by comparing
their results with a reference ray-theory solution computed for
gathers and grids with fine sampling. The paraxial method
turns out to be the most efficient and accurate in evaluating
travel times from all investigated techniques. However, it is
not suitable for approximation of amplitudes, for which the linear
interpolation has proved to be universal and accurate enough to provide
results acceptable for many seismological applications.

### Revised version

Brokesova, J.:
Construction of ray synthetic seismograms
using interpolation of travel times and ray amplitudes.
PAGEOPH, **148** (1996), 503-538.

In: Seismic Waves in Complex 3-D Structures, Report 4, pp. 151-181,
Dep. Geophys., Charles Univ., Prague 1996.