Lyapunov exponents for 2-D ray tracing without interfaces

Ludek Klimes


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.


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

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