## Grid computations of rays and travel times

**Ludek Klimes** ** , **
**Michal Kvasnicka** ** & **
**Vlastislav Cerveny**
### Summary

Grid computations of rays and travel times of seismic body waves play a
very important role in seismological applications, particularly in
seismic exploration. Several methods of
such computations have been proposed. The different methods may yield
different travel times in certain regions of the model. The differences
are caused mainly by different concepts of travel times. Definitions of
four different types of travel times of seismic body waves in
non-dispersive inhomogeneous layered and block structures are
introduced. They are as follows: 1) first arrival travel times, 2)
constrained first arrival travel times, 3) zero-order elementary travel
times, 4) elementary travel times. Appropriate algorithms of computation
of individual travel times are described. There are four basic classes of
such computations: a) "finite-difference" methods, b) network ray
tracing (also called the shortest path ray tracing), c) wavefront tracing,
d) methods based on the numerical ray tracing, supplemented by suitable
interpolation/extrapolation procedures. The advantages and limitations of
these methods are discussed. Particular attention is devoted to the
fourth method, where the interpolation/extrapolation is performed by
weighting paraxial ray approximations. In the method, the standard
initial value ray tracing is performed and supplemented by the dynamic
ray tracing. The computed rays must cover the target zone with a
sufficient density, even though irregularly. At any point of the target zone, the
travel time is then calculated using the weighting paraxial
approximations from the closest ray points. Several alternatives of the
method of weighting paraxial approximations are proposed and numerical
examples are presented. The accuracy of the method is compared with other
approaches. It is shown that the method is computationally very efficient
and yields results of a high accuracy.

### Whole paper

The
image of the paper in GIF 150dpi (9 852 kB!).

In: Seismic Waves in Complex 3-D Structures, Report 1,
pp. 85-114, Dep. Geophys., Charles Univ., Prague, 1994.

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