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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 07h 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 07h 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 the source. The seismographs do not generally reproduce this spectrum unchanged but act as filters 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 56

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MICROSEISMIC PERIOD SPECTRA AND RELATED PROBLEMS SCANDINAVIAN AREA 57 usually all larger than the microseismic peri- ods and there seems to be no influence from the different constants. This is obvious for the following reasons. • a. The periods corresponding to frequency maxima and amplitude maxima are not con- sistently larger at Helsinki, nor are they con- sistently lower at Copenhagen. b. The upper limit of the period spectra is not larger at Helsinki than at the other stations. c. The lower limit of the period spectra in- creases from Bergen to Uppsala in spite of equal free periods; it also increases from Ber- gen to Copenhagen in spite of generally lower free periods at Copenhagen than at Bergen. d. Also the mean periods increase from Bergen to Copenhagen and from Bergen to Uppsala. Therefore the conclusion seems to be justi- fied that the different seismographs have the same response to the microsisms under con- sideration, and the spectra at the different sta- tions are directly comparable. 5 6 7 12345 6 7 IJ 9T se(!0 Figure 1. Dynamic magnification curves. V E Valid for 180 2.4 Bergen N 129 2.7 Bergen E 220 1.4 Bergen K 200 4.3 Copenhagen N.K 140 3.5 Helsinki N.E " 189 3.9 Uppsala N.E All curves have been displaced so as to pass through the point T0 = 5 sec, V r 200. Explanation: Curve Jo • 9.3 b 9.2 e 7.7 d 8.2 • 12 f 9.2 2. The ground (from the source to the station) also acts as a filter. Bergen (gneiss), Uppsala (granite), and Helsinki (gneiss) are all within Fennoscandia, and no general dif- ferences exist. Copenhagen (chalk) is outside Fennoscandia, but owing to the relatively small part of the path, consisting of sediments, as well as owing to the uncertainties of any cor- rection for their influence, the Copenhagen pe- riod spectra have also been used without modi- fication. 3. An essential requirement is that the microseisms at the different stations compared have the same source. This has earlier been shown to be the case for Bergen and Uppsala by the author (1951 a) as well as for Copen- hagen (1952). In the light of our present ex- perience the statement is justified that the microseisms at Helsinki also have the same source as at the other three stations (for fur- ther discussion see below). 4. Only measurable periods have natural- ly been included. The smaller number of ob- servations in a few cases depends on weak mi- croseisms, i.e. fewer measurable periods. This procedure necessarily entails a certain selec- tion, depending on the sensitivity of the seismo- graph. With regard to what has been said in 1. above as well as to the results (Table 2) this circumstance does not seem to be of any impor- tance. 5. The drum speeds are 12mm/min at Copenhagen, 15 mm/min at Bergen and Upp- sala, and 20 mm/min at Helsinki. The meas- urements were made to 0.1 mm and then con- verted into seconds and tenths of seconds. There was a clear tendency in all cases of ob- taining frequency maxima at 1.0, 1.5, 2.0 mm (the measurements were made with a glass scale, divided into half millimeters). As they were certainly not real, smoothing has been made according to the formula 14 (a -j- 2 b + c). The frequency curves thus obtained are certainly nearer to the truth than curves based directly on the original observations. 6. In a procedure like this where succes- sive periods are measured, false periods may arise at points where one wave train gives place to another wave train. A too long false period may arise if a small quiet interval sep- arates the two wave trains. Likewise too short false periods may occur where one wave train is replaced by another wave train without sep- aration. However, this source of error is of no influence if due account is taken of it in the measurements; moreover, the microseisms measured are generally regular and continuous. III. Discussion of the Results—For conveni- ence in writing we introduce the following no- tations :

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58 SYMPOSIUM ON MICROSEISMS T, = period, corresponding to frequency maximum, TB = mean period, T. = period, corresponding to amplitude maximum, n = number of observations, N = N-S component, E = E-W component, B = Bergen, C = Copenhagen, H = Helsinki, U = Uppsala, I = October 7, 1947, at 07h M.E.T., II = October 28, 1947, 07h M.E.T., III = January 14, 1949, 07h M.E.T., IV = March 23, 1949, 07h M.E.T. The period spectra are given in Figs 2-5. Table 2 contains values of Tf, Tm, and T. with standard errors for Tm and Ta and the number of observations in each case. Tf, TB, and Ta have also been indicated in Figs. 2-5 by vertical lines, the shortest for Tf, the next longer for Tm, and the longest for T,. The whole in- vestigation is based upon 7083 individual pe- riod measurements on the records. The weath- er situations at 07h M.E.T. are obvious from Fig. 6, copied from the official Swedish weath- er maps. The agreement with the official Brit- ish weather maps is very good. The aim in the following study has mainly been to establish general rules for the periods. The statistical significance of these rules has been investigated in every case, usually by ap- plication of Bernoulli's theorem. The devia- tions from the general rules which may occur in individual cases, require more detailed studies of the particular cases in order to be explained. 1. The shape of the frequency curves. The frequency curves have in general only one pronounced maximum around which the curves are symmetrical. The microseisms may therefore be characterized as regular. Notable exceptions occur at Bergen, especially for N. This component has usually two maxima at Bergen. As the main source of the micro- seisms in Scandinavia lies along the Norwegian coast, we understand that the shape of a fre- quency curve depends on the position of the station in relation to this coast. If the posi- tion is such that the coast length takes up a large distance interval, from the station, as the case is for Bergen, a wider and less regu- lar spectrum is obtained. In case IV the mi- croseisms are less regular at all stations than in cases I-III. 20 * 15 10 5 ( 25 20 15 10 5 ( 20 15 1C 5 20 «/ /a 24 6 8 sec 0 24 6 8 sec Berqjn N-S Bergen, E-W 25 •A, 20 Copenhagen N-S 8 sec 0 Copenhagen E-W 2 4 6 8 S-*. 0 Helsinki N-S 20 15 10 246 Helsinki E-W sec 2 4 6 8 sec 0 Uptsala -N-S 2 4 6 8 sec Uppsala E - W Figure 2. Period spectra on October 7, 1947, at07h M.E.T. The shortest vertical line indicates Tf, the next longer TB , and the longest T,. 2. Comparison of stations. The mean periods (n = 8; calculated from Table 2) for both components and all situations are as follows: T, sec Tm sec T. Station sec B C H U 4.79 5.05 5.45 5.43 4.71 5.10 5.44 5.35 5.76 5.52 5.85 5.65 For Tf it seems to be an increase from B to H: B < C < U < H. The various differences, B < C, C < U, U < H, B < U, and C < H are, however, not statistically significant. But

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MICROSEISMIC PERIOD SPECTRA AND RELATED PROBLEMS SCANDINAVIAN AREA 59 CO ON •* CO CO ^ • • 1 • CO CO rH • • l • O O rH 00 00 rH »- E E « « 1 • • • 1 • 0 i— 1 O i-H l— ( O i-H O O -H 0 r- co i n o f- ON in O •^ CM in ON ^i C5 in ON u CM Tj- CO •* CM CM CO •* 1— 1 Tf CO CO i•—I ^* CO CO H- o B • 1 •a LU ON O O NO CM O TJ1 CO ON O O VO CM O -^f CO 0 0 O I— CM O •«*• CO CM CM '— 1 rH O O O 1— e o * rH CM i— I i-H CM r-l Tf CO CM CM i— 1 i— 1 0) TJ II -1 0| 0 CM CO CO • • CM • ON CO I-H ON CM ^t CO • • CM • r- \o co t— i-H CO • • CM • h~ 4) ON OO rH ON . . CM • « O* Is™ CO rH ^J^ +J c c CM CM CO CO CM NO CO CO CM CO Tj- CM CO Tf eo 0 . td U1 u Z H- o c en t— O O CM t~- O ^ ON f- O O CM f- ON •*)• O\ CM O O CM CO O ••* ON CM 0 O CM (d e CO I-H Tf ON o •*' 4-> 1- ' in ol « in r- CM in ••* CM 0 CM r-t . . CM • O O •— i • . CM • • • • CM • • • CM « •o o ON t— i-H ON ON CO i-H ON ON CO r~t ON ON CO i— I ON c g C V c o 4) 60 -H 4) 60 -H bo **H B »M • 60 -H (8 _* CO C J= C — i a -* a 4-1 C -C C -H 4) C -H (0 60 4) 01 03 fc, CX -H 0. D o 4) CL OQ 0 = 3 C JC S — i 4) C -H 10 (1C 4) 03 03 k. Q. -H O, 4) a f Q. CQ U E 3 C J3 C — i 1) C -H C8 (1C D W M i) a -H • V* IH a. — c a. 60 4) Bl 03 ti D- — i Q. V C V Q. CQ O X 3 L. 4) C 4J Cu '•*- CO O E 3 O t-l CO CM Tf « ON CO CM e • r- • I— A O ON fci T* 1 e •* O ON O ON O -< CO ON CO Q\ O -1 1-5 rH

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60 SYMPOSIUM ON MICROSEISMS B < H is significant. Therefore we may con- clude that there is no pronounced difference of Tf between the different stations except for a slight indication in the manner already men- tioned. For Tm there is a very clear increase from B to H: B < C < U < H, very well sub- stantiated by the individual cases. Every dif- ference is significant, possibly with the excep- tion for U < H. For Ta there is no very ob- vious difference between the different stations, except that H has generally larger values. The only difference which is no doubt significant is C < H. The relatively large values of T. at B for our situations are remarkable. Earlier re- sults (1951 a, p. 373) have indicated that in general Ta is less at B than at U. By means of the data used in (1951 a, p. 373) this was shown to be significant. By means of the cor- responding data for Copenhagen (1952) it has been shown that for Ta B < C with a high de- gree of significance, whereas for the same data there was no difference of Ta between C and U. The main reason for the sequence B < C < U < H, especially clear for Tm, is the stronger extinction of shorter periods (see below). The fact that C comes between B and U is probably explained by a relatively larger importance at C of the southwestern part of the Norwegian coast, from where the microseisms arrive at C before they arrive at U. At U and H the whole Norwegian coast is of about equal im- portance. 3. Comparison of components. The mean periods (n = 16) for all sta- tions and all situations are as follows: Tf sec Tm sec T. Comp. sec N E 5.35 5.01 5.20 5.10 5.82 5.57 For all three periods E < N. This result may be considered significant only for Ta, but the tendency of E < N exists for all three periods. The result that E < N for Ta confirms my earl- ier results for Bergen and Uppsala (1951 a, pp. 372-373). It has a high degree of significance for Uppsala, but not for Bergen. It has also been proved for Copenhagen with a high de- gree of significance, using the observations cor- responding to those at Bergen and Uppsala in (1951 a, p. 373). This is therefore a charac- teristic feature of Scandinavian microseisms. The most probable reason is a distance effect. The N component is most sensitive to actions at the more remote northern part of the Nor- wegian coast, whereas the E component reacts strongest to actions at the west coast (around B). This has been established beyond doubt from numerous cases at Uppsala. An increase of the period T. with increas- ing distance has been observed in several in- vestigations. But the nature of the phenome- non is not clear: if it is mainly an actual in- crease of period with distance, or if it is only a more rapid extinction of the shorter periods. No decision seems to be possible only from a knowledge of the increase of T. with distance as both effects produce the same result (for further discussion see 6, below). 4. Comparison of the different periods. The mean periods (n = 32) for all sta- tions, both components, and all situations are T, = 5.18 sec, T. = 5.15 sec, T. = 5.69 sec. The result T. < T. is valid in practically every case (exceptions are UIIE and HUE) and has a very high degree of significance. The result Tf < T. is also highly significant, but there are a few more exceptions to this rule than to the rule T. < T.. This result is a reflection of the fact that the amplitudes corresponding to the shorter periods are relatively small. Further- more, 2f ~.T., i.e. no significant difference, cor- responding to the generally symmetrical nature of the frequency curves. sec 24 6 8 sec Uppsala E-W Figure 3. Period spectra on October 28, 1947, at 07h M.E.T.

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MICROSEISMIC PERIOD SPECTRA AND RELATED PROBLEMS SCANDINAVIAN AREA 61 CM •— 1 O CO OO O -^ ON O ^H i-H 0 O i— 1 VO ON O CM O O CO ^ CO CM CM r-H i— 4 1— 1 ,-H i-H i— 1 CM O O O O O 0 0 0 +1 +1 +1 -H O IN CO C— ** ON CO OO o o o o +1 +1 +1 +1 t— o t— t— m co ON t— O O O O + 1 +1 +1 +1 Ull +1 +1 +1 +1 co m o co •-H ON in co CM m o o CO OO VO CO m r* m m in ** ** in in Tf T}I Tt m •*f r!• in m TJ* vn in in cl f- i-l •— 1 CO OO CM VO 00 VO CM O VO in I-H ON vo co ON ON o CM CM —1 CM vo o oo vo in vo o •— i t— Tj* Tf r-H e Z (M CM t-H i— 1 •— 1 CM CM i— 1 CM CM CM Q. oa u s: 3 m u s: 3 CO CJ 3= 3 m u i 3 00 CM Tt co 4 » t— • ^- 1— 1 CM 1 1 • t— *^** • ON I-H C Tf 1— ( O ON I-H _C O ON ^» P •* > CO ON 1— 1 *J Tf x-» u ^I '1— 1 H O Ov H-l o av HH O •— i — ' o •— ' *-- "•5 ^H -~- S -1 ^ •o o CM

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SYMPOSIUM ON MICROSEISMS 2C % 15 10 5 0 2 4 6 8 sec o 2 4 6 6 sec Bergen N-S Bergen E-W 20 15 % 10 5 I 20 % tr to 5 0 2 4 6 6 sec 0 Copennagefl N-S 15 2 4 Copenha 2 4 6 d sic 0 Helsinki N-.S 20 15 10 5 2 4 6 8 sec Helsinki E-W 2 4 6 8 sec 0 Uppsala N-S 2468 Uppsala E-W Figure 4. Period spectra on January 14, 1949, at 07h M.E.T. 5. Comparison of situations. The mean periods (n = 8) for all stations and both components are as follows: Case Tf sec T. sec T. sec I II III IV 4.99 4.58 5.44 5.71 4.91 4.82 5.23 5.64 5.32 5.13 5.73 6.60 These values indicate the sequence II < I < III < IV for all three periods. This sequence is in general well established from the individ- ual cases. All differences II < I, I < III, III < IV are significant for T. (BE is the only partial exception). The differences are also significant for T«, possibly with exception for the difference II < I (exceptions occur for T« for CN and BE). On the other hand, the dif- ferences for Tf are not significant, not even II < IV; nevertheless, the general trend is the same for Tf as for T« and T.. The differences between the different situ- ations can hardly be explained as only distance effects, e.g. in II both active coast and cyclone center are at the greatest distance, neverthe- less the periods are shortest. On the other hand, the different intensities of the storms seem to afford an explanation. This is another in- stance of the parallel behaviour of amplitudes and periods. The maximum ground ampli- tudes, expressed in n, are given in the follow- ing table. B C H U Mean Case N E N E N E N E I 2.2 0.9 (6.2) 1.8 1.9 1.2 2.1 0.6 1.1 1.4 1.4 2.5 2.7 2.3 1.8 2.3 2.2 2.1 1.6 3.0 2.0 1.0 0.7 2.1 2.5 0.8 1.0 2.0 2.0 1.6 1.2 2.1 (2.9) 2.2 II III IV 1.3 2.8 3.8 If the anomalous amplitude BNIII is excluded, we get the amplitude sequence II. < I < III < IV, i.e. the same as for the periods. Plotting the periods against the mean amplitudes we find that I-II-III forms a reasonable sequence, whereas the small amplitude difference between III and IV is not in good accord with the rela- tively large period differences. This could pos- sibly be due to a distance effect, as in IV the more active part of the Norwegian coast is in the northern part. A numerical calculation of the rate of change of T. with distance to cen- ter of the active coast gives approx. 2.10'Jsec/ km, a value which lends further support to this idea (1949). 6. Upper and lower limits of the period spectra. From an inspection of the period spectra (Figures 2-5) it is clear that the upper limit is remarkably constant from station to station in a given situation with no general variation, whereas the lower limit shows a very pro- nounced increase in the direction B-C-U-H. This increase occurs for both components in every case without exception. The increases of the lower limit are in the mean from B to C about 0.25 sec, from C to U about 0.7 sec, from U to H about 0.6 sec. The total increase from B to H is in the mean about 1.5 sec. The results concerning the upper and low- er limits of the period spectra strongly support the conclusion that the change of the spectrum with distance is due to a more rapid extinction of the shorter waves rather than to an actual increase of periods. It would naturally be valuable to extend such investigations to great- er distances, wherever possible, provided the source of the microseisms is the same for the whole area investigated. 7. The hyperbola method. A hyperbola method for locating the source of microseisms from the periods ob- served at a number of stations has been given in my paper (1951 a, p. 374). This method

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MICROSEISMIC PERIOD SPECTRA AND RELATED PROBLEMS SCANDINAVIAN AREA 68 rests on the observation that the observed pe- riod T. apparently increases with distance. The method may briefly be described as follows. For a mean apparent increase of T. with dis- dT tance A from the source f=-rJ da we get the following equations, combining three different stations two and two: T." — T.' = f (A" — A') T.'" — T.' = f (A'" — A' ) T."' — T." = f (A"' — A") f is assumed to be the same in all three equa- tions as a first approximation. This set of equations means that (A" — A') : (A"' — A") : (A"' — A") is given, geometrically denning the source. As f is not exactly known, the source can be located by trial and error, until all three hyperbolas intersect in a point, as- suming a point source. When the source has been located, it is possible to calculate f. The method can only be used with success if the source of the microseisms is exactly the same for all stations for which the periods are used. For a common point source the method may be expected to lead to results. In our case, how- ever, we have a line source, the length of which is comparable with and often larger than the mutual distance between the stations. Differ- ent parts of the Norwegian coast are of differ- ent importance to the different stations as al- ready indicated above, i.e. the source is not exactly the same for all our stations. There- fore the hyperbola method may not be expected to lead to any useful results in these conditions. Among further desirable investigations the following may be mentioned: a. Extension of the investigation of periods by means of period spectra to greater distances. b. Application of the hyperbola method to cases with a point source. c. Correlation of microseismic periods with other phenomena, notably the periods of sea waves and swell. Investigations of the last- mentioned kind have been done by British in- vestigators, but an extension to other localities is desirable. Summary—Microseismic period spectra have been constructed for four different situations (I = Oct. 7, 1947, 11 = Oct. 28, 1947, 111 = Jan. 14, 1949, IV = March 23, 1949) for both components (N, E) at Bergen (B), Copenha- gen (C), Helsinki (H), and Uppsala (U). The microseisms studied are usually regular and continuous in the general period range 3-8 sec. The following results have been obtained for the period Tf, corresponding to frequency maxi- mum, for the mean period T., and for the period T., corresponding- to amplitude maxi- mum. 1. Especially T. increases clearly from B to H:B OCR for page 56
64 SYMPOSIUM ON MICROSEISMS Figure 6. Weather situations at 07 M.E.T. on October 7, 1947, October 28, 1947, January 14, 1949, and March 23, 1949. Acknowledgments—This investigation has been made at the Seismological Laboratory of the Meteorological Institute, Uppsala. The Direct- ors of the Seismological stations at Bergen, Co- penhagen, and Helsinki have lent me their original records and given information on seis- mograph constants, etc. Miss I. L. Andersson, Uppsala, has assisted me in drawing the fig- ures. My best thanks for valuable help are due to all the above-mentioned persons. REFERENCES BATH, M., An investigation of the Uppsala -micro- seisms, Medd. Met Inst. Uppsala, No. 14, p. 168, 1949. 0 BATH, M. The distribution of microseismic energy with special reference to Scandinavia, K. Svenska Vet.-akad., Arkiv for Geofysik, (Medd. Met. Inst. Uppsala no. 22) v. 1, No. 13, pp. 359-393, 1951. BATH, M., Review over investigations of microseisms in Scandinavia, Pontificia Academia Scientiarum, Rome, (not yet printed), 1951b. BATH, M., The problem of microseismic barriers with special reference to Scandinavia (not yet printed), 1952. LONGUET-HIGGINS, M. S., A theory of the origin of tnic- roseisms, Phil. Trans. Roy. Soc. London, Ser. Q, No. 857, v. 243, pp. 1-35, 1950. PRESS, F., and EWING, M., A theory of microseisms with geologic applications, Trans. Am. Geophys. Un., v. 29, No. 2, pp. 163-174, 1948. Discussion J. B. MACELWANE, S.J. St. Louis University o In the brief space of a few pages Doctor Bath has assembled a surprisingly large volume of first hand observational data on the periods of microseisms recorded in the Scandinavian area. Anyone familiar with such measure- ments realizes what an expenditure of time and painstaking labor is involved. Seismolo- gists the world over will be unanimous in their appreciation of the factual material thus made available.

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MICROSEISMIC PERIOD SPECTRA AND RELATED PROBLEMS SCANDINAVIAN AREA 65 A few similar studies have been published in the past for other regions. But one won- ders what is the overall significance of a peri- od spectrum which seems to take no account of superposition of wave trains simultaneously ar- riving from different directions. There would be less likelihood of inhomogeneity if only the periods accompanying the maximum ampli- tudes of well-formed groups are considered; but care is required even in this case to select only groups of regular waves. Neither from one microseismic storm to another nor within a group in the same storm has the writer found the period to increase consistently with ampli- tude. Recently Gotch under the writer's direc- tion made a study of the relation between am- plitude and period in the most regular portions of wave groups in nineteen microseismic storms recorded by Galitzin-Wilip seismographs at Florissant in 1949, 1950 and 1951. The aver- age period of the maxima for all nineteen storms was 6.66 seconds. The shortest period was 5 seconds and the longest was 8.8 seconds. In the four storms in which the average peak period was over eight seconds the amplitudes were only moderate; while in those storms in which the mean peak amplitudes were largest the corresponding periods were less than the overall average. The writer has not succeeded in finding a tenable storm to storm relationship between amplitudes and periods in the mid- continent area of North America. Within a given microseismic storm after it is fully de- veloped the period tends to remain approxi- mately constant. The periods generally recorded at Floris- sant and Saint Louis are sensibly longer than those shown by Donn and by Gilmore in rec- ords of east coast stations. This might be and has been interpreted as a distance effect. How- ever, the Florissant periods are approximately the same as those listed by Thompson for the Palmer Land station in Antarctica and yet the probable source fronts were often very near to that station and sometimes over relatively shallow waters. Many seismologists will fail to see the cogency of the argument for a linear source at a given distance drawn from the variation of the plane of vibration of microseismic waves at single stations. Even the actual instantaneous directions of travel of well-formed groups of waves across a tripartite station vary through many degrees of arc so that an average of many observations is necessary to determine a bear- ing that is representative of the energy flow across the network. How then can it be shown from observations at single stations that the source is linear and not a real? And in view of the inconclusive relationship of period to distance how can the source be considered as certainly lying along a given coast line? Measurements Made by Mr. Gotch on Florissant Seismograms T = period; A = amplitude in mm = microns/ 600 approx. Microseismic Storm T Amax T Amax T Amax T Amax Average T (Seconds) of Maximum Amplitude January 1, 1949 V N-S E-W January 15, 1949 V N-S E-W January 30, 1949 V N-S E-W February 8, 1949 V N-S E-W February 11, 1949 V N-S E-W February 18, 1949 j 5.5 5.5 3.5 3.75 5.75' 5.75 4.0 5.75 3.5 5.75 3.5 3.75 5.5 5.5 2.75 3.5 5.6 6.9 5.4 5.4 6.4 6.1 .... 7.25 7.0 2.75 4.25 7.0 7.25 2.5 6.5 6.5 2.75 3.25 6.75 2.75 3.5 3.25 6.75 5.25 1.25 5.75 5.25 5.25 1.0 1.75 2.5 5.25 5.75 5.5 1.75 2.25 2.25 5.75 2.0 5.0 3.0 5.25 5.25 2.25 2.75 5.25 5.5 2.0 5.25 5.5 2.25 2.75 5.75 3.0 5.75 2.75 5.5 2.0 2.75 6.25 6.75 6.75 3.75 3.0 3.75 6.5 6.0 6.0 3.0 3.5 3.75 6.25 6.5 6.25 3.25 3.5 4.5 N-S E-W 6.25 6.0 2.25 3.5 6.0 6.25 2.75 2.75 6.0 6.0 2.5 2.5

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SYMPOSIUM ON MICROSEISMS I T Amax Average T Microseismic Storm T Amax T Amax T Amax (Seconds) of Maximum March 1, 1949 V N-S E-W March 8, 1949 V N-S E-W March 26, 1949 V N-S E-W March 31, 1949 V N-S E-W November 1, 1949 V N-S E-W November 9, 1949 V N-S E-W December 8, 1949 5.25 2.5 Amplitude 4.75 8.75 2.0 5.25 8.75 2.25 2.5 4.75 8.25 2.25 2.5 6.0 2.75 8.25 7.75 2.6 8.75• 1.75 7.25 2.0 1.75 8.75 2.0 8.6 1A 7.75 2.5 7.75 2.25 7.25 7.5 2.75 2.25 7.75 7.75 7.5 1.75 2.25 3.0 8.5 B.I 8.8 8.4 6.2 6.3 6.2 6.7 6.9 8.75 4.75 4.0 8.0 3.75 5.75 4.0 8.5 4.5 8.75 3.75 3.25 4.75 6.0 3.25 4.75 9.0 3.75 5.75 3.5 9.0 4.0 3.75 4.75 3.75 3.25 8.5 3.5 9.0 8.25 3.0 4.5 8.75 8.75 8.75 4.25 4.25 2.75 v 8.25 7.75 8.75 4.75 4.75 5.5 N-S E-W December 29, 1949 V N-S E-W November 26, 1950 V N-S E-W November 28, 1951 V N-S E-W December 9, 1951 V N-S E-W December 17, 1951 V N-S E-W December 19, 1951 V N-S E-W 8.25 4.75 9.0 3.75 8.5 6.25 4.25 6.75 5.75 5.75 6.5 6.5 6.25 4.75 3.75 3.75 5.75 6.25 4.75 3.75 6.5 4.75 6.25 6.25 3.75 6.75 6.25 3.5 6.5 4.75 6.25 6.25 6.0 5.75 4.25 4.5 6.0 7.5 4.0 5.0 6.5 6.0 6.25 6.5 6.75 5.5 4.0 2.5 6.5 7.0 3.5 3.25 6.5 3.75 6.75 7.0 3.0 2.5 6.75 7.25 7.0 4.75 3.0 3.25 6.75 7.0 6.75 4.5 3.5 2.75 6.75 7.25 7.0 3.5 3.0 2.75 6.25 6.0 6.25 9.75 5.25 6.25 6.5 6.0 10.25 5.5 6.25 6.25 6.75 10.75 4.75 6.5 6.5 11.75 6.0 9.5 7.0 6.5 6.4 T. A. 6.66 Discussion GAEL F. ROMNEY Geotechnical Corporation at Troy Microseismic motions over a wide range of periods have been detected and reported in the literature; however, quantitative informa- tion on the ground amplitudes associated with the various periods is surprisingly difficult to find. Further, measurements describing the spectrum existing at a given locality and time are generally found to include only a narrow band of periods, usually of about one octave band width selected by the filter characteris- tics of conventional observatory seismographs. Most of the known information deals with the same "storm microseisms" discussed by Dr. Bath's paper, which is chiefly concerned with periods in the range 4-8 seconds. The spectra to be presented here cover a much wider band width, extending over nearly four octaves. Such data describe more completely the state of earth activity during a given meteorological situation, and in addition, variations in spectra due to location and time provide some insight into the problem of extinction of short period microseisms, which is studied by Dr. Bath. During August of 1950, identical horizon- tal seismographs were operated at the Harvard College Observatory, Harvard, Massachusetts, and at the Rensselaer Polytechnic Institute's Pinewoods Observatory, near Troy, New York,

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MICROSEISMIC PERIOD SPECTRA AND RELATED PROBLEMS SCANDINAVIAN AREA 67 through the cooperation of Dr. L. Don Leet of Harvard and Dr. Roland F. Beers of R. P. I. Seismometers were of the capacitance-bridge type, and ground motion was recorded on pa- per by means of a Brush Instrument Company penmotor after suitable amplification. Prior to installation, both seismographs were cali- brated by means of a shaking-table at the Pinewoods Observatory, and a field calibra- tion technique was developed to insure that changes in the instrumental constants would be known. The seismometers were operated with a free period of 1.5 seconds and with crit- ical damping. Both stations were in operation during the period from August 20 through August 23, at which time an intense hurricane was moving parallel to the Atlantic coast line between Cape Hatteras and a point south of Greenland. This storm produced a rapid rise in microseismic amplitudes at both stations, reaching a maxi- mum on the early morning of the 21st, and decreasing to essentially the normal level by the 23rd. Measurements were made of the microseisms on August 21, near the time of the storm's least distance of about 200-350 miles from the stations, and again on August 23, when the storm was about 1700 miles, away. The measurement technique consisted of find- ing amplitudes (peak to trough and associated periods for the largest nearly sinusoidal groups appearing on the records; special attention was directed toward finding groups with as widely different periods as possible. Seismogram am- plitudes were reduced through the experiment- ally known steady-state response curves to ground motion in microns, and plotted as a function of period on logarithmic paper. Dis- played in this manner, the points show a rather surprising regularity. Figures 1 and 2, for the "normal" day, when the storm had moved off to a great distance, show the observed spec- tra at Harvard and at Pinewoods. Within the range from 1.4 to 5.0 seconds, the peak micro- seismic ground motions were found to increase very nearly as the cube of.the period. Impor- tant differences were observed, however. Note that while both stations showed ground motion for the long period (5.0 seconds at about 0.7- 1.0 microns, the shorter (1.5 second) periods were noticeably smaller at Pinewoods, approxi- mately 120 miles inland from Harvard. A marked change in the spectrum at each Figure 1. Microseismic Spectrum for Harvard, 23 August 1952. Normal day.

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68 SYMPOSIUM ON MICROSEISMS station was found on August 21, when the hur- ricane was at a minimum distance from the stations. As seen in Figures 3 and 4, not only did the general activity increase, but the shape of the spectra changed so that amplitudes were found to increase nearly as the fourth power of the period. A comparison of all of this data is shown in Figure 5 relative to the Harvard spectrum on 23 August 1950, here used as a standard spectrum. If all amplitudes are re- duced to ratios of those at Harvard on the normal day, the following emerges. First, on a normal day the long period noise, presumed to originate in the Atlantic, is reduced by only a small amount in traveling the distance be- tween Harvard and Pinewoods, while the short period noise (also presumed to originate in the ocean) is reduced by a factor of about 3:1. This is interpreted as being in agreement with Dr. Bath's conclusions, that there is a greater extinction rate for short period waves than for long period waves. Second, on the day of the hurricane's near approach, both stations showed a marked increase in amplitude, with The long period waves increasing in size much more than the shorter periods. It may be ob- served that Pinewoods, at roughly 50% great- er distance from the storm than Harvard, showed an amplitude increase of 500% at 5 seconds, while Harvard showed an increase of 1,000% at 5 seconds; short period amplitudes about doubled at each station. This, incidental- ly, tends to verify the assumption that the short period (1.5 second) microseisms also originate in the ocean, as evidenced by the in- crease in amplitude associated with the hurri- cane. • Further knowledge of the microseismic spectrum in the vicinity of Troy, New York, was obtained on November 12, 1950. On that date, between the hours of 1100 to 1200 E.S.T., means of a vertical shaking table, so that the total response characteristic at any filter set- ting was determinable by simply adding the known filter response to that of the seismome- ter. Results are shown in Figure 6. The first line shows electrical noise in the system, which may be seen to be rather unimportant corn- instrumental data were obtained showing mi- croseismic amplitudes over a considerably wid- er frequency range. The instrumental setup consisted of a conventional vertical component electromagnetic seismometer whose output was amplified, played through a Krohn-Hite Ultra- Low Frequency Band-Pass Filter (model 330- Figure 2- Microseismic Spectrum for Pinewoods, 23 August 1952. Normal day.

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MICROSEISMIC PERIOD SPECTRA AND RELATED PROBLEMS SCANDINAVIAN AREA 69 A), and recorded by means of a Brush recorder. The Krohn-Hite is a selective filter which will pass frequencies of an input signal, with no loss in gain, within any desired band between 2,000 cps and 0.02 cps (or 50 seconds period). High and low cut-off frequencies are independ- ently adjustable. Outside of the pass band, the response falls off at 24 db per octave. Using this detector system, it was possible to examine the microseisms within a one octave region of the spectrum, and to vary the pass band so that it was possible to observe activity in sev- eral regions of the spectrum without interfer- ing "noise" from other frequencies of ground noise. The seismometer was calibrated by pared to the recorded microseisms. Although the total instrumental magnification at suc- cessively larger periods decreases roughly as the cube of the period due to the response of the seismometer (T0 = 1.2 seconds, damping critical) it was found necessary to further re- duce the gain for longer periods; from this we infer that the ground amplitudes increase fast- er than the cube of the period. Calculated true ground amplitudes are shown on Figure 7, which shows an amplitude increase about pro- portional to the fourth power of the period in the range 0.5 <. T <. 5 seconds. Indications are that the ground amplitude was maximum at 5.0 seconds, decreasing slowly for longer periods. Measurements on wave periods be- yond 5 seconds are not shown, since there were evidences of instrumental instability at ex- tremely long periods. It was estimated, how- ever, that the waves with periods exceeding ten seconds had about 20% of the amplitude of the five second microseisms. Synoptic me- teorological conditions on this date have not been studied. No evidence for the existence of discrete microseismic "bands" at Harvard or Pinewoods was found during the investigation described here. In all cases, the sprectrum appeared to be continuous, or nearly so, with no wave peri- od exhibiting amplitudes departing to any marked extent from the very regular rate of increase of amplitude with period. On the other hand, Macelwane and his colleaques have published examples showing narrow and sharp- ly defined short period microseismic bands. It is tentatively suggested that the difference in these findings is attributable to regional geolog- ical differences; both Harvard and Pinewoods are situated on relatively homogeneous meta- morphics, in contrast to the horizontal sedi- Figure 3. Microseisraic Spectrum for Harvard, 21 August 1952. Hurricane at nearest approach to station.

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70 SYMPOSIUM ON MICROSEISMS mentary strata prevailing throughout the central United States. Considering the great amplitude differ- ences found for the different frequencies of motion, it is apparent that a "flat" seismograph response curve is useless for studying the mi- croseismic spectrum over a wide frequency range. In such a case, the limiting factor is the dynamic range of the recorder, which will seldom exceed 40 db (100:1), whereas the phe- nomenon to be observed has an amplitude range of at least 60 db (1000:1). Under these con- ditions, analysis of the seismogram by any method will not reveal useful information on the short period components — such informa- tion being irretrievably lost in recording. Two approaches are possible in obtaining broad band microseismic coverage. One is a method used here, employing the selectivity character- istics of low frequency filters; or equivalently, using tuned detectors. The second approach is to use a seismograph response characteristic that is nearly the inverse of the microseismic spectrum. In this case, the product of ground motion and seismograph magnification will be nearly constant, and all ground frequency com- ponents will be registered equally well on the recorder. Fourier analysis or autocorrelation methods may then be used to obtain true ground amplitudes over a wide frequency range. It may be observed that the short peri- od Benioff seismograph when critically damped, has nearly the correct characteristics for the spectra discussed here, since the Benioff re- sponse decreases nearly as the cube of the period for periods longer than one half second. Mechanical seismographs, or seismographs with capacitance — bridge transducers will not have as great a microseismic band coverage, be- cause their response decreases as only the square of the period on the long period side of the peak magnification. Conclusions from the foregoing are that the microseismic spectrum at Pinewoods is es- sentially continuous in the range from */2 to 5 seconds, increasing at a rate about proportional to the third or fourth power of the period, de- pending to some extent on meteorological con- ditions over the adjacent regions on the North Atlantic Ocean; that the ocean is the source of at least part of the short period microseismic activity; and that the shorter period micro- seisms suffer a more rapid attenuation due to dist'ance traveled than the longer periods. It Figure 4. Microseismic Spectra for Pinewoods, 21 August 1952. Hurricane at nearest approach to station.

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MICROSEISMIC PERIOD SPECTRA AND RELATED PROBLEMS SCANDINAVIAN AREA 71 is also shown that broad band microseismic recording may be obtained on one seismograph, if the instrument and instrumental parameters are correctly selected. Discussion from the Floor (Caldwell asked how the periods for the period-amplitude graphs were selected. Rom- ney replied, by looking for each period on the record and then measuring its amplitude. Bonn inquired from B&th whether or not his fixed maxima of eight seconds and variable minumum corresponded with water depth. Bath replied that there was no connection ap- parent.) (After Father Macelwane's paper, Deacon said that the lack of any relationship between microseism periods and amplitudes at Florris- sant was not surprising if it was assumed that the microseisms were made by sea waves of twice their period. Father Macelwane had not examined short microseisms partly because they did not reach Florissant and partly be- cause he had examined the most prominent groups. He was dealing with microseisms in the period range of GVfc to 814 seconds. There is no relationship between the amplitude of waves of 13 to 17 seconds periods. Thirteen seconds would be the dominant wave period produced by a surface wind of 35 knots blowing for a long time, and there would be 17 seconds waves present in the complex wave-pattern produced by such a wind, but they would be much smaller than the 13 second waves. It is also possible that the 8V£ second microseisms were made by 17 second swell which had a small amplitude because it had travelled a long dis- tance over the ocean.) 10.0 1.0 9 I 7891 Figure 5. Ratios of Microseismic Spectra to Spectrum at Harvard on 23 August 1952.

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72 SYMPOSIUM ON MICROSEISMS INPUT SHORTED .67 - .33 1.00 - .90 j||^J^/WV~M^v^^ U3' '^|\,VA^^^ ».« t.OO - 2.00 6.33 - 2.67 10.00 - 5.00 Figure 6. Microseismic Spectral Analysis by Krohn-Hite Filter. Figures to the right of each line give pass band of filter, but not of combined seismometer-filter system. Large disturb- ance on third line due to near approach at automobile. System gain reduced for longer periods.

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MICROSEISMIC PERIOD SPECTRA AND RELATED PROBLEMS SCANDINAVIAN AREA 73 Figure 7. Microseismic Spectrum at Pinewoods from data of Figure 6. Only relative ground motion is shown.