Lyapunov Exponents for 2-D Ray Tracing Without Interfaces

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.