Correlogram Analyses of Seismograms by Means of. By Keiiti AKI Geophysical Institute, Faculty of Science, Tokyo University.

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1 JOURNAL OF PHYSICS OF THE EARTH, VOL. 4, No. 2, Correlogram Analyses of Seismograms by Means of a Simple Automatic Computer. By Keiiti AKI Geophysical Institute, Faculty of Science, Tokyo University. Summary An automatic relay computer for calculating autocorrelation coefficients, based on the simplified method of its computation proposed by Y. TOMODA, has been built for the purpose of analysing seismograms. Seismograms of about one hundred near earthquakes recorded at the Central Meteorological Observatory in Tokyo and at the Mizusawa Latitude Observatory were used for the analyses. Each seismogram was divided into several portions, and within each portion, the dependence of the prodominant period of seismic waves upon the magnitude of the earthquakes and upon the crustal structure of the wave path were studied. What are the main factors that determine the frequency spectrum of seismic waves? This is a very interesting question from the standpoint of pure and applied seismology. The spectrum may depend both on the crustal structure at the origin of the seismic waves and also that along the passage through which the waves are propagated, as well as on the mechanism of wave generation at the origin. Although many studies have been made about the change in wave period with the epicentral distance, the variation in period with the earthquake magnitude, and so on, there still remain many questions to be investigated. In the present paper, the writer has made correlogram analyses of actual seismograms. The correlogram of a time series is the FOURIER transform of the periodogram or the spectrum density of the series, and involves the same amount of information about the series as that of the spectrum density. Moreover, in many cases we can infer the spectrum directly from the correlogram without troublesome FOURIER transformations. To make the computation process simpler, an automatic computer is urgently needed. Our computer is that based on the simplified method of computation of correlation coefficient proposed by Y. TOMODA (1956). The computor is very easy to operate and maintain. The cost of its construction is low and the high speed computation is possible. Let y(t) be a given time series, of which the mean value y(t) is 0 and the variance y2(t) equals to 1, and let the values of y(t) at A computer to calculate the autocorrelation coefficient according to the formula (1) needs the following parts; input devices such as tapes or cards, arithmetic elements to make additions and multiplications, and output devices such as a printing machine or some other indicators. So far as we stick to this regular method of computation, the computing machine will become a large one, which cannot be very inexpensive. If we try to deduce the correlation coefficient using the simplified method proposed by Y. TOMODA, however, the computer will become a very simple one. According to this method, the autocorrelation coefficient of y(t) is given as (1)

2 72 Keiiti AKI Fig. 1. Autocorrelation computer. (2) (3) similar way, the kth relays Ak and Bk are made to be in the same state as that of P, t before the moment. y(t). What we must know about y(t) are only its sign, so that the input and output systems and the arithmetic elements become very simple. In tracing the record to be analysed, the sign of y(t) is read from it at regular time intervals, and when y(t) is positive, a contact key is closed manually, while when y(t) is negative, the key is made open. This contact key is connected to an input relay, designated by P, in the computer. Thus we can send input data into the computer directly from the original record without any input devices such as a tape system. The multiplication in this computer is limited to the following four cases: and we can easily construct a circuit of relays for making this arithmetic. The addition in this case is essentially a counting, and can be performed by means of an electromechanical counter. The results of counting of N+(k)'s are given at the indicator of the counter. To calculate N+(k)'s up to k=10 in one cycle of input data, a delay operation is necessary in our computer. Ten sets of two relays are provided for this purpose. The first two relays A1 and B1 are made to be in the same state at any moment as that of the Now we shall explain the details of our computer. A drum on which a seismogram to be analysed is wound as shown in Fig. 2 is revolved with an appropriate speed. The reading of signs from the record of seismic waves is done through a cross wire, of which the intersection point is adjusted to coincide with the zero line of the recorded curve y(t). kƒ

3 Correlogram Analyses of Seismograms by Means of a Simple Automatic Computer 73 Fig. 2. Computer with appurtenances. With the revolution of the drum, the recorded curve y(t) moves along the time axis, and when y(t) is positive the contact of the key is closed manually. While y(t) is positive, the contact is kept closed, and at the time when the curve passes through the intersection point of cross wire from the positive side of the zero line to the negative, the contact is made to open and kept opened as long as y(t) is negative. The input relay P in the computer is connected to the contact of the key, and works just in the same way as the manually operated key. For the control of the operation of addition, multiplication and delay, there is a control unit composed of four relays. The four relays 1,1,2 and 2 of the unit work according to the time table shown Fig. 3 (left), in which the line represents the duration of closed contact of each relay designated at the top, and the blank represents the duration of open from outside of the computer. We can obtain by combining the above relays a set of contacts of which the time table of operation is as shown in Fig. 3 (right). In this Fig. 3. Time table of operation. Fig. 4. Delay circuit. Fig. 5. Multiplication and addition circuit.

4 74 Keiiti AKI A unit of delay circuit is shown in Fig. 4. When the contact of the input relay P is closed (opened) at the time of closure of This computer was constructed by the Fuji Tsushinki Seizo K. K. (Fuji Communication Apparatus Mfg. Co., Ltd.), and was completed in January, The seismograms used in this study are those recorded at the Central Meteorological Observatory in Tokyo and at the Latitude Observatory at Mizusawa, sixty from the former and fifty from the latter. The epicentres of all these earthquakes and the depths of focus for some of them are determined by the Central Meteorological Observatory. Their magnitudes were independently estimated by C. TSUBOI and H. KAWASUMI (1952). The geographic distribution of the earthquake epicentres recorded at the Central Meteorological Observatory is shown in Fig. 6, and of those recorded at the Latitude Observatory is shown in Fig. 7. As shown in these maps, these earthquakes are grouped according to their epicenters into seven, in order to study the variations of statistical properties of seismograms with respect to epicentral areas from which they come. Fig. 6. Geographic distribution of epicentres of earthquakes recorded at the Central Meteorological Observatory in Tokyo. The Mizusawa Latitude Observatory has a history of fifty years of seimological observations and there are abundant available data. Furthermore, this observatory is located just above the line of the very steep increase of gravity anomaly as revealed by C. TSUBOI

5 Correlogram Analyses of Seismograms by Means of a Simple Automatic Computer 75 and his collaborators (1955). The area to the west of this line (named as the Morioka- Shirakawa line) is characterized by thick Tertiary formations which are developed only poorly in the eastern area. As the statistical properties of seismograms will depend on the crustal structure at the wave origin and also that along the wave path, it is expected that the correlograms of seismograms for the eastern origin earthquakes may differ appreciably from those of the western origin ones. The seismometer at the Central Meteorological Observatory is of the Wichert type with the notable facts revealed by the analyses. 1) The seismograms of earthquakes coming from the same or nearly the same epicentral area and with the similar magnitude have nearly the same correlograms when recorded at a station. Fig. 8. Correlograms of coda waves of earthquakes occurring in the area E. Fig. 7. Geographic distribution of epicentres of earthquakes recorded at the Latitude Observatory at Mizusawa. the static magnification 80 to 100, the free period 3.5 to 5.5 seconds and the damping ratio 2.8 to 5.7. Because of the magnification characteristics of the seismometer and the recording paper speed, the range of reliable Period is estimated to be between sec and sec. The seismometer at the Mizusawa Latitude Observatory is the Omori type with the static magnification 20, the period being sec. with no damper. More than one hundred seismograms are loaned from the above two laboratories and put into the relay computer for correlogram analyses. We shall now enumerate some of Fig. 9. Correlograms of coda waves of earthquakes occurring in the area W. The correlograms of the coda parts of seismograms of earthquakes originated from the area E and W are given in Fig. 8 and 9 respectively. All of these earthquakes have

6 76 Keiiti AKI rather simple form. By averaging the correlograms in each figure, we have a mean correlogram for each epicentral area. Both of the mean correlograms are of very simple types as shown in Fig. 10, so that we may assume the spectrum density of the following types. (5) seismogram does not always take such a simple form as above, but it is necessary for the reduction of data to assume a spectrum with a single predominant period for each part of a seismogram. We shall hereafter study mainly on the predominant period read from the spectrum or directly from the correlogram. 2) How the predominant period changes with time after the beginning of P wave depends almost on the crustal structure at the epicentre and that along the wave path. In the case of a simple crustal structure, the predominant period is very short in the early part of seismograms and later increases to approach gradually to a steady value in the coda part. On the other hand in the case of Fig. 10. Averaged correlograms, the thick line for the area E and the dotted line for the area W. Fig. 12. Change of the mean predominant period with time for earthquakes of the magnitude 6.0. Fig. 11. Spectrum densities corresponding to the averaged correlograms. Fig. 13. Change of the mean predominant period with time for earthquakes of the magnitude 6.5. a complex crustal structure, the predominant period in the early part is nearly the same as that in the latter part. The change of average predominant period with time for the earthquakes of magnitude

7 Correlogram Analyses of Seismograms by Means of a Simple Automatic Computer 77 Fig. 14. Change of the mean predominat period with time for earthquakes occured in the areas E and W. Fig. 15. Correlograms of seismograms arranged in the order of the magnitude. 6.0 and the epicentral areas B1, C and D, is shown in Fig. 12, and that for the earthquakes of magnitude 6.5 and the epicentral areas A, C and D in Fig. 13. The earthquakes occurring in the area C are deep focus ones and the wave passage from there is regarded as of a simple oceanic type, while on the other hand the wave path from the area D is of a complex inland type, and that from the area A and B1 is of an intermediate type. Fig. 14 shows the period change in seismograms recorded at Mizusawa for the earthquakes of magnitude 6.0 occurring in the areas E and W. As refered to before, the crust of the western area W of Mizusawa is more complex than that of the eastern area E. The way of period change in the Figs. 12, 13 and 14 agrees with the above statement. 3) As to earthquakes having the same magnitude, the predominant period in the early part of seismogram shows a conspicuous variation with the place of epicentral area and wave passage, but the variation diminishes or dies out in the coda part as seen from the preceding figures. We may say, therefore, that the period of the coda wave is almost determined by the magnitude of earthquake 4) As to earthquakes coming from the same epicentral area, the predominant period of every part of seismogram increases with the magnitude. But the rate of increase with the magnitude differs among parts of a seismogram, it is rapid in early parts and slow in later parts. The correlograms of the motions for 50 seconds after the beginning of S wave are arranged in the order of magnitude in Fig. 15. The largest magnitude is 6.8 and the smallest (the top one in the figure) is 5.2. All of these earthquakes occured in the area D. It is evident from the figure that the larger the magnitude, the longer becomes the period. To see the way of variation of the predominant period with the magnitude, we plotted in Fig. 16 the period read from the correlograms of waves for 50 seconds after the beginning of S wave against the magnitude. The plotted points are scattered widely, but they may be divided into three groups according to their epicentral areas. The first group of earthquakes is of inland origin such as those from

8 78 Keiiti AKI the area D, and shows the longest period. The second guoup is of the deep focus type with the shortest period. The last has the origin in the area A and B, and its period is intermediate. ours. As stated before, the predominant period of coda waves is mainly determined by the magnitude of earthquake. The periods of coda waves are plotted against the magnitudes of earthquakes in Fig. 17, in which earthquakes of the epicentral area D are omitted. Fig. 16. Variation of predominant period of S wave with the magnitude. Assuming the following formula for each group (6) H. HONDA and H. ITO (1939) found a relation between the period of P waves and the magnitude of earthquake, and K. KANAI, K. OSADA and S. YOSHIZAWA (1953) extended the study. They got T2=A between the period T of P waves and the amplitude A reduced to the place 100km from the origin. The magnitude M can be written as M=log10A+ const., so that we can convert the above rela- After KANAI, the relation between the period of S wave and the reduced amplitude A is the same as that for P wave, but in the case of S wave his diagram seems to as in the case of coda waves, but the value of the constant in the formula is different. According to the study of Hawaiian local earthquakes by A. E. JONES (1938), the upper limits of amplitudes of P and S waves of local shocks are found to vary with the cube The writer is very much obliged to Dr. W. becomes 1/3, and approximately agrees with Fig. 17. Variation of predominant period of coda wave with the magnitude. Fitting the same formula we obtain l og10 T= M as (6) to this case, In Fig. 17, the periods of coda waves of local earthquakes in California are plotted against the magnitudes. These values are given in a paper by P. BYERLY (1947) who analysed numerous seismograms obtained by a seismometer of the Wood-Anderson type. The points are located on an extrapolated part of our formula. B. GUTENBERG and C. F. RICHTER (1942) obtained the relation log10 T= M between the periods T of the wave group of the maximum amplitude and the magnitude Thus the period of the coda wave is 4.8 times of that of the wave group of the maximum amplitude.

9 Correlogram Analyses of Seismograms by Means of a Simple Automatic Computer 79 INOUYE, Mr. Y. IWAI and other officials of the GUTENBERG, B. and RICHTER, C. F.: Seismological Section of the Central Meteorological 1942 Earthquake Magnitude, Intensity, Energy Observatory and to Mr. T. SUGAWA and Acceleration. Bull. Seis. Soc. Amer., and other officials of the Mizusawa Latitude 32, 163. Observatory, who kindly lent him valuable HONDA, H. and ITO, H.: 1939 On the period of the P waves and the seismograms recorded at the observatories or magnitude of the earthquake. Geophys. helped him to copy them. Mag. 13, 155. The writer's thanks are also due to Mr. T. JONES, A. E.: IKEDA and other staff members of the Fuji 1938 Empirical Studies of some of the Seismic Tsushinki Seizo K. K. (Fuji Communication Phenomena of Hawaii. Bull. Seis. Soc. Apparatus Mfg. Co. Ltd.) for their helpful Amer., 28, 313. advises given him about the design of the KANAI, K., OSADA, K, and YOSHIZAWA, S.: computer The Relation between the Amplitude and The writer is greatly indepted to Prof. C. the Period of Earthquake Motion. Bull. TSUBOI for his guidance and encouragement. Earthq. Res. Inst., 31, 44. The Central Meteorological Observatory, Tokyo: This study was made with the help of a 1952 The Seismological Bulletin of C. M. 0., Grant from the Department of Education. Japan for the year 1950, 99. TSUBOI, C., JITSUKAWA, A. and TAZIMA, H.: References 1956 Gravity Survey along the lines of Precise AKAMATU, K.: Levels throughout Japan by means of a 1956 in this issue. WORDEN Gravimeter, Part 7, Tohoku District. BYERLY, P.: Bull. Earthq. Res. Inst., Suppl. Vol The Periods of Local Earthquake Waves 4, in Central California. Bull. Seis. Soc. TOMODA, Y.: Amer., 37, in this issue.