### 3D finite-difference reflection traveltimes

**J. A. Hole and B. C. Zelt**
A method has been developed to compute seismic reflection travel times in complex 3D
velocity models with complex 3D reflector geometry. An existing finite-difference
algorithm for calculating first-arrival travel times was modified to
properly handle large, sharp velocity contrasts.
The modified algorithm is faster and more accurate than several alternative schemes, and
was incorporated in a
procedure to compute reflection travel times.
Snell's law for reflections is used in the vicinity of the reflecting interface. The reflector
model is allowed to vary smoothly in depth, increasing the accuracy as compared to a
discretized reflector model. Reflection travel times are computed simultaneously for all
receivers, requiring only two applications of the finite-difference algorithm for each shot.
This results in a significant savings in computation time in comparison to other algorithms
which require one pass of the finite-difference algorithm for each shot and each receiver.
The reflection travel-time procedure is well suited for incorporation in inversion schemes
for 3D velocity and reflector structure.

1995. Geophysical Journal International, **121**, 427-434.