122 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
RELATION OF THE VELOCITY TO THE DEPTH BELOW THE EARTH’S SURFACE. 
Professor Wiechert’s method enables us to determine the velocities at different depths 
below the surface. For any point on a given path we have 
rsint 7sint 
v v 


where r is the distance from the center of the earth, 7 the angle which the path makes 
with the radius, and v the velocity; the letters in the second member refer to the same 
quantities at the point where the path comes to the surface. 
TaBLE 12.— Surface Velocities and Angles of Emergence. 
First PRELIMINARY TREMORS. SECOND PRELIMINARY TREMORS. 

Surface 
velocity. 
Surface 
velocity. Distance. 
Distance. 


Km. sec. Km. sec. 
2.6 
2.95 
3.75 
5.45 
7.5 







In table 12 we have collected together the values for the surface velocities and for the 
angle of emergence e, for points at several distances from the origin; and from these data 
we can calculate the velocity at the points where the respective waves reach their greatest 
depths. At these points the 
paths are at right angles to 
the radius and sinzvis 1. The 
value of r can be measured in 
fig. 27 and the value of v de- 
termined. This process was 
carried out and the values of v 
given in table 13 were found. 
These values were plotted on 
section paper and a smooth 
curve drawn thru them repre- 
senting the velocity as a func- 
tion of the depth. On ap- 
plying these velocities to the 
various parts of each path 
it was found that the time the wave would take to traverse the path did not correspond 
exactly with the time given by the hodograph. ‘The velocities were slightly altered and, 
by the method of trial and error, new values were found which would make the time 
intervals correspond to those given by the hodographs. The changes in the velocities 
were small. These velocities are shown in table 13 in the column headed wu, and graphi- 
cally in fig. 28. The velocity increases with the depth below the surface, but more and 
more slowly as the depth becomes greater. There is no indication of a sudden change in 
the velocity, such as we should expect if there were any sudden changes in the nature of 
the earth’s interior, but it must be remembered that the greatest depth reached by the 
deepest path we have drawn is only about halfway to the earth’s center, and that our 
values, especially for the deeper paths, leave much to be desired in accuracy ; indeed, the 



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