Translations:The eikonal equation - book/1/en

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If the given wavefront is at time t and the new wavefront is at time , then the traveltime along the ray is dt. If s measures path length along the given ray, then the travel distance in time dt is ds. The increments dt and ds are related by the slowness, that is, dt = nds. Thus, The directional derivative in the direction of the raypath is equal to the slowness, that is, . The directional derivative can be written in terms of its components as