MICROSEISMIC PERIOD SPECTRA AND RELATED 

 PROBLEMS IN THE SCANDINAVIAN AREA 



ByMarkusBath 



Meteorological Institute at Uppsala 



I. Introduction — The problem of microseismic 

 periods is intimately connected with the mi- 

 croseismic problem as a whole. We are here 

 concerned with microseisms in the general pe- 

 riod range of 3-8 sec. Notable theories to ex- 

 plain their origin have been proposed on one 

 hand by British workers on the subject (see 

 Longuet-Higgins, 1950), on the other hand by 

 Press and Ewing (1948). Both theories are 

 capable of explaining the observed microseis- 

 mic periods, but in completely different ways. 

 Therefore the only fact that observed and theo- 

 retical periods coincide cannot be taken as a 

 stronger support of one theory than of the 

 other. Other facts indicate that the observa- 

 tions in Scandinavia are better explained by 

 the former theory than by the latter. A fur- 

 ther discussion of this matter is given by the 

 present author in the paper (1951 b). 



In this paper we will study some charac- 

 teristics of the microseismic periods in the 

 Scandinavian area, leaving aside the question 

 how the periods originate. By periods we usu- 

 ally mean the periods corresponding to the 

 maximum amplitudes. By constructing fre- 

 quency curves of all periods existing at a cer- 

 tain time (period spectra) we will be able to 

 study also the period corresponding to the fre- 

 quency maximum as well as the mean period. 

 It is a well-known fact that the periods increase 

 with distance. But it is still an open question 

 if this is due to a real lengthening of the period 

 of each wave as they propagate or if it is due 

 to a more rapid extinction of the shorter peri- 

 ods, whereas the period of each individual wave 

 is constant. Another fact, which will also be 

 studied, is the tendency of periods to vary in 

 unison with the amplitudes. The fact that the 

 periods of microseisms are functions of several 

 variables (such as distance and intensity of 

 the source) , which usually vary simultaneously, 

 requires great care in period studies in in- 

 dividual cases. 



The periods of microseisms have earlier 

 been studied from various points of view by the 

 present author. See (1949), pp. 8-9 (frequen- 

 cies of periods for different months), pp. 23-24 

 (annual variation of periods), pp. 26-28 (diur- 

 nal variation of periods), pp. 42-44 (beats), pp. 

 60-66 (relation between amplitude and period, 



and mean periods in different situations), p. 

 109 (comparison between periods on N-S and 

 E-W components), pp. 119-142 (period studies 

 in individual cases) ; see also (1951 a), pp. 371- 

 374 (comparison between periods at Bergen 

 and Uppsala). In the latter paper (p. 374) 

 also a hyperbola method for locating the source 

 by means of the periods was indicated. This 

 method will be studied below in the light of the 

 new results. 



II. Materials and Methods Used — Period 

 spectra have been constructed for four differ- 

 ent situations (Oct. 7, 1947, Oct. 28, 1947, Jan. 

 14, 1949, and March 23, 1949, at 07 h M.E.T. in 

 all cases) from the records of the N-S and E-W 

 components of the Wiechert seismographs at 

 Bergen, Copenhagen, and Uppsala, and the 

 Mainka seismograph at Helsinki (all with me- 

 chanical recording). In each case every in- 

 dividual period within ± 15 minutes of 07 h 

 M.E.T. was measured. Due to this concentra- 

 tion of the measurements the period spectra 

 correspond in all cases to well defined weather 

 situations ; the changes of the weather situa- 

 tions taking place during the interval of 30 

 minutes are of no consequence. The number 

 of observations is given in every case in Table 

 2 below. In the mean every frequency curve is 

 based on more than 200 observations. Various 

 sources of error will now be considered. 



1. A certain period spectrum is gener- 

 ated at tbe source. The seismographs do not 

 generally reproduce this spectrum unchanged 

 but act as niters due to their different response 

 to different periods. In comparing the records 

 of different seismographs due account must be 

 taken of this fact. Table 1 gives the seismo- 

 graph constants in our cases, and Figure 1 

 gives a few representative curves of the dy- 

 namic magnification V. As we are not so much 

 concerned with the magnification itself as with 

 its variation with the period T (especially with- 

 in the range of the microseismic periods), the 

 curves in Figure 1 have been displaced so that 

 they all pass through the point V = 200 for 

 T = 5 sec in order to facilitate their compari- 

 son. The circumstance that Copenhagen usu- 

 ally has the shortest free period and Helsinki 

 in all cases has the largest free period necessi- 

 tates some discussion. The free periods are 



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