12 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
First: a glance at fig. 2, where f represents the focus of the shock, will show very clearly 
that the distance from the focus to the various stations depends upon its depth, and if we 
knew the exact time of the shock, the time of 
the arrival at the stations and the velocity of 
propagation, we could immediately calculate 
the depth of the focus. As a matter of fact 
we do not know the exact time of the shock, 
nor do we know the exact velocity, but by 
observations at a number of stations all these quantities could be determined, provided 
the observations were sufficiently accurate. Here, however, is where the difficulty lies. 
The table on page 119, which gives the time of the arrival of a disturbance according 
to the distance of the station from the epicenter and the depth of the focus, shows 
that this time is very slightly affected by the depth of the focus when the distances are 
as great as three or four times this depth; and therefore to get from time observations 
an even fairly approximate value of the depth we must have a number of stations very 
close to the epicenter, and the observations must be extremely accurate — to within a 
second or so. Neither of these conditions have been satisfactorily fulfilled heretofore, 
and determinations of the depth of the focus based on this method are unreliable. In the 
case of the California earthquake the observations at the four stations considered are 
probably more favorable, both as to the situations of the stations and the accuracy of the 
observations, than has been realized at any former earthquake; but nevertheless it has 
been shown that they are not sufficiently accurate to determine the various unknown 
quantities in the problem, and they merely indicate that the depth at which the violent 
shock originated is probably not more than 40 km. The variation of this method by the 
use of Seebeck’s or Schmidt’s hodographs can not yield more reliable results; and its 
application when the time of arrival, not of the beginning of the shock, but of a strong 
reénforcement of the motion, is used is by no means to be recommended; for in this case 
“we can not say that the special part of the disturbance observed has traveled directly 
thru the body of the earth; and the whole theory of the method depends upon this sup- 
position. In some cases it is quite evident that the time of arrival of the long waves has 
been used, and these waves are supposed to be propagated along the surface.* 
Second: the distance of points from the focus will increase more slowly with their dis- 
tance from the epicenter for deep than for shallow foci, and therefore the intensity of the 
action at the surface will diminish more slowly. Maj. C. E. Dutton has shown that if we 
consider the extent of the origin small and the damage done by the shock at the surface 
proportional to the energy of the motion there, the change in the amount of damage will 
be most rapid at a distance from the epicenter of about 1.7 times the depth of the focus; 
and this distance is independent of the actual intensity of the shock.’ 
If we attempt to apply this method to the California earthquake, we meet with many 
difficulties. The disturbance was by no means confined to a small area, but was spread, 
more or less unevenly, over the whole fault-plane. It probably did not take place simul- 
taneously, but varied in time at different parts of the fault. If it had occurred simultane- 
ously, the method might be applied by adding up the effects due to the different parts of 
the fault, but if the movement occurred even at slightly different times in different parts 
of the fault, their effects at some points would be successive and at some points simultane- 
ous. The general averaging of these results might, however, enable us to form a rough 



1 See for example Faidiga; “Das Erdbeben vom Sinj am 2 Juli, 1898,” Mitt. Erdb.-Com., K. Akad. 
Wiss. Wien, No. xvi, 1903. The time of arrival of the second preliminary tremors would be a better 
time to use than that of the first preliminary tremors; for they travel only about two-thirds as fast, and 
therefore the differences in their times of arrival would be somewhat greater at two stations of slightly 
different distances from the centrum. 
Ppl pases Earthquake of August 31, 1886. 9th Ann. Rep. U. S. Geol. Surv., 1887-1888, 
pp. —-317. 
