## Lyapunov exponents for 2-D ray tracing without interfaces

**Ludek Klimes**
### Summary

The Lyapunov exponents quantify the exponential
divergence of rays asymptotically, along infinitely long rays.
The Lyapunov exponent for a finite 2-D ray and
the average Lyapunov exponents
for a set of finite 2-D rays and for a 2-D velocity model
are introduced.
The equations for the estimation of the average Lyapunov exponents
in a given smooth 2-D velocity model
without interfaces are proposed and illustrated by a numerical example.
The equations allow the average exponential divergence of rays
and exponential growth of the number of travel-time branches
in the velocity model to be estimated prior to ray tracing.

### Keywords

Velocity models, travel times, ray tracing, paraxial rays,
deterministic chaos.

### Whole paper

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*Pure and appl. Geophys.*, **159** (2002), 1465-1485.

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