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In this section we introduce the key ideas of *nonclassical solution*
and *viscosity solution* of eikonal equations and related problems,
which underlie our treatment of traveltime calculations. Our
approach is based on this conjecture: *The first-arrival
time field is a viscosity solution of the eikonal equation*.
The conjecture is supported by some theoretical results
and by a great deal of numerical ediffvidtimeence. The notion of viscosity
solution was developed first for *hyperbolic conservation
laws*, particular instances of which are satisfied by the gradient
components of the time field. Numerical methods for these conservation laws use
*upwind finite differencing*, and may be adapted
to produce viscosity solutions of the eikonal equation.
Here we introduce these ideas in a non-technical, heuristic way.
Formal mathematical treatment can be found in subsequent sections,
or in the references.

** Next:** Nonclassical and viscosity solutions
** Up:** Van Trier & Symes:
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Stanford Exploration Project

1/13/1998