EARTH S INTERIOR ADAMS AND WILLIAMSON 



245 



far within the earth. The data obtained from seismograms, more- 

 over, indicate that the material of the earth, except at the surface, 

 may be treated as (megascopically) isotropic. It is fortunate that 

 this is the case, since otherwise the mathematical treatment of seismo- 

 logic data would be extremely difficult. 



Starting from the time-distance curve — that is, the times of arrival 

 of a disturbance at given distances along the surface — by a compara- 

 tively simple process one can calculate the elastic constants of the 

 material of the earth at various depths. The steps in the process are 

 as follows: (a) From the slopes of the time-distance curves the 



'-o 



4 



s 



Fig. 1. 



-The velocities of longitudinal and transverse earthquake waves at various depths 

 below the surface of the earth as calculated from seismologic data 



apparent surface velocities of each of the varieties of through waves 

 is obtained; (&) by graphical integration of a certain function of the 

 surface velocity there is obtained the maximum depth for a wave 

 traveling between two points separated by a specified distance ; (c) 

 from a very simple relation the true velocity at this depth is de- 

 termined; (d) and finally, the bulk modulus K and the rigidity R 

 are calculated from the equations connecting these quantities with 

 the velocities. 9 



With the time-distance curve given by Turner 10 the velocity-depth 

 curve shown in Figure 1 was obtained. In this figure the abscissae 

 represent depth in kilometers and the ordinates the velocity, in 

 km./sec. This curve closely resembles that obtained by Wiechert" 



•Viz: Rlp=v a ', and 25T/p=»t; p «— 4p s j /3 which are obtained directly from the equations in the preceding 

 footnote. 

 10 See Davison, Manual of Seismology, p. 145. 

 « Nachr. Kgl. Ges. Wiss. Gottingen. 1907, pp. 415-549. 



1454—25- 



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