The Lyapunov exponents asymptotically quantify the exponential divergence of rays. The "Lyapunov exponent" for a finite 2-D ray and the average "Lyapunov exponents" for a set of finite 2-D rays or lines 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.
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Klimes, L.: Lyapunov exponents for 2-D ray tracing without interfaces. In: Seismic Waves in Complex 3-D Structures, Report 8, pp. 83-96, Dep. Geophys., Charles Univ., Prague, 1999.
Klimes, L.: Lyapunov exponents for 2-D ray tracing without interfaces. Pure and appl. Geophys., 159 (2002), 1465-1485.