K. Helbig; A graphical method for the construction of rays and travel times in spherically layered media: Part I: Isotropic case. Bulletin of the Seismological Society of America ; 55 (3): 641–651. doi:
A method is described which allows the graphical construction of rays and travel times. The velocity versus radius curve is graphically converted into a “normalized slowness graph,” in which all variables describing a ray and its travel time can be represented by geometric quantities. It is found that most of the well-known analytic relations between the properties of the velocity versus radius distribution and the form of rays have their geometric counterparts and that these geometric relations can be derived rather simply.