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LI. The Analysis of Microseismoqrams. 

 By 5. B. Dale, ALA. * 



1. TN his monograph on Modern Seismology, Walker has 

 _I_ called attention to the interesting records traced 

 by seismographs when undisturbed by earthquakes. 



Microseismic motion falls into two classes, of which one is 

 due to the motion of: wind and is wholly irregular, while the 

 other prevails even in calm weather and at all times of the 

 year, although it is more marked in winter than in summer. 

 It is this latter type which is discussed in the present paper. 



The general characteristics of the records of this seismic 

 motion are smooth sinusoidal curves of fairly constant period, 

 but with an amplitude which rises and falls at somewhat 

 irregular intervals whose average length is about 1 minute. 

 The period of the oscillations ranges from 4 to 8 seconds, 

 the longer periods and larger average amplitudes occurring 

 in the winter months. 



Although the main features of the motion are obvious, their 

 exact specification is by no means easy, and analysis discloses 

 the simultaneous existence of oscillations of different periods. 

 There also appear to be discontinuities in phase and period. 



2. The method of analysis employed is that published by 

 the writer a few years ago f, and the following summary 

 will explain the notation. It is assumed that a function 

 y of t can be expressed in the form 



y = c Q + %c n sin (0 n t + u n ) , . . . . (1) 



when c , c n , 9 n , a n are constants to be determined from the 

 observational data. 



It is further assumed that the values of y are known for a 

 sufficient number of . equidistant values of t, the values corre- 

 sponding to £ = 0, 1, 2, ... n being denoted by y G , yi,y 2 , • . • y n - 



As a first step c is eliminated by forming differences 

 which are denoted by a, so thai 



a r =yr+i-y, (2) 



Next an operator E is defined hy the relation 



Ea r =a r+1 +a r _i, (3) 



and in a similar manner E 2 a r , E 3 <x r are derived. 



The number of times the operation E is to be performed 

 is equal to the number of independent periods. In practice 



* Communicated by the Author. 



t " The Resolution of a Compound Periodic Function into Simple 

 Periodic Functions/' Monthly Notices, R. A. S., May 1914. 



