Foreshocks, Aftershocks and Earthquake Swarms (I)*

550. 341 Foreshocks, Aftershocks and Earthquake Swarms (I)*

—A Definition of Foreshocks , Aftershocks and Earthquake Swarms and Its Application to Seismicity—

by Norio Yamakawa

Meteorological Research Institute, Tokyo and Meteorological College, Kashiwa, Chiba Pref. (Received February 18, 1967)

Abstract

This is the first part of a study dealing with various seismological, geophysical and geological characteristics such as time and space distributions, energy release and focal mechanisms of foreshocks. aftershocks and earthquake swarms. Seismological data of the Japan Meteorological Agency are chiefly made use of . Before any investigation of foreshock, aftershock and earthquake swarms is undertaken, it is fundamentally important to give a clear definition of these seismic activities which are here tentatively called " abnormal seismic activities " . A definition of abnormal seismic activities based on a statistical method is proposed. This method is applied to distinguish abnormal seismic activities from the normal or background seismic activity in one of the seismically active regions in and near the Japanese islands.

1. Introduction

The Matsushiro earthquake swarm which suddenly occurred in August 1965 in Nagano Prefecture in the central part of Japan is the most marked earthquake swarm ever known in the world. This earthquake swarm itself is one of the most interesting subjects in seismology. Numerous papers on this subject have already been published (See, for instance, vol. 44 of Bulletin of the Earthquake Research Institute, 1966). It can also be regarded as one of the manifestations of the inner geophysical, geo- chemical, and geological state of the crust in the central part of the Japanese islands. In this respect, it is worth notice that the focal mechanism of most of the shocks, especially the larger ones, are closely related to the tectonic system around this region (KASAHARAet al. 1966, PARTY 1966, and ICHIKAWA1967). On the other hand, it was suggested that the study of occurrence of foreshocks and aftershocks might supply important clues to solving the physical mechanism

* Presented at the Eleventh Pacific Science Congress of the Pacific Science Association, held at the University of Tokyo, Japan, August-September 1966, and organized by the Science Council of Japan. 158 Norio Yamakawa Vol. XVII No. 3 of a destructive main shock itself (UTSU 1961, 1962 and 1964, and YAMAKAWA1965). The study of foreshocks is also important from the viewpoint of earthquake prediction. In this study, various characteristics such as, time and space distributions, energy release and focal mechanisms of foreshocks, aftershocks and earthquake swarms are discussed from seismological, geophysical and geological points of view.

But, before any investigation of foreshocks, aftershocks and earthquake swarms is undertaken, a clear definition of these seismic activities must be given. In some cases, however, the definition of foreshocks and aftershocks is not so easy or simple, especially in active seismic regions. As RICHTER (1958) pointed out, it is sometimes doubtful whether a preceding or following event is actually a foreshock or aftershock. In any active region small earthquakes are common, so that the occurrence of small shocks before or after larger one is not necessarily significant. In this paper, a definition of abnormal seismic activities based on a statistical method called THOMPSON'Stest is proposed. This method is applied to distinguish abnormal seismic activities from normal or background seismic activity off Miyazaki Pref., Japan.

2. A definition of foreshocks, aftershocks and earthquake swarms

Numerous papers on aftershocks have been published. But, so far as the present author knows, the definition of aftershocks is somewhat arbitrary in most of the papers. In his former paper (YAMAKAWAet al. 1965), the author pointed out various difficulties concerning the definition of aftershocks, showing several examples. The main features of the difficulties are expressed in the following two questions : (1) How long should an aftershock activity be considered to continue ? and (2) How far should an aftershock area be considered to extend ? Of course, these two questions should not be discussed separately. In other words, time and space distributions of aftershock are closely related to each other. The same kind of difficulties may arise in the definition of foreshocks and earthquake swarms. In the above-mentioned paper, the present author proposed a definition of aftershocks based on THOMPSON'Stest and suggested that this method can also be applied to the definition of foreshocks.

In a sense, foreshocks, aftershocks and earthquake swarms are the same kind of seismic activities (Mom, 1963), and are more or less abnormal seismic activities which should be distinguished from the normal or background seismic activity of the region concerned. So that, if we can determine whether one particular seismic activity is abnormal or not, based on a statistical mothod, it means that we can distinguish foreshocks or aftershocks or earthquake swarms from background seismic activity at a certain level of significance.

There are several tests of rejection of observations which enable us to find whether or not a single datum can be regarded as a sample of size 1 from one particular population. 1966Foreshocks, Aftershocks and Earthquake Swarms (I)159

The test proposed by THOMPSON(1935) is the most suitable in this case. (MURAUCHI 1949, and KUNISAWAand SUZUKI 1961). It makes the following test.

First we calculate the mean and the standard deviation a of a sample of size N already obtained, as follows :

Then, another datum x0, that is, a sample of size 1, can be rejected as a singular sample which does not belong to the same population, if it satisfies one of the following two equations :

where F'N_l(d) is FISHER'S distribution of 1 and N-1 degree of freedom, and a is the level of significance.

This method can be applied to the definition of abnormal seismic activities as follows : First we calculate the mean and standard deviation of earthquake frequencies in a certain region for a certain length of period. The unit time interval here is not necessarily one day, but ten days or one month.

Then, if there is a marked seismic activity in this region, we calculate the earthquake frequency for the above-mentioned unit time interval. This frequency is the x0 of THOMPSON'Smethod. If this frequency can be rejected based on Eq. 4, this means that the activity during this time interval is abnormal.

Usually an abnormally high frequency of shocks is detected with this method. But an abnormally low frequency which means that the region in question is abnormally quiet, can also be detected based on Eq. 3.

3. Seismic activity off Miyazaki Prefecture

The method proposed in the previous section is applied to earthquake sequences off Miyazaki Prefecture. The Miyazaki Local Meteorological Observatory (the former Miyazaki Weather Station) has been recording earthquakes with mechanical and, later, electromagnetic seismographs with almost the same free period (about 5 gec.) and magnification (about 100) for more than 40 years. Fig. 1 shows the locations of epicenters of the major earthquakes off Miyazaki Prefecture, showing also the energies of larger shocks calculated by the formula 160 Norio Yainakawa Vol. XVII No. 3

(5) log E=11. 8+1. 5M.

(GUTENBERGand RICHTER 1956, see also YAMA- KAWA 1965)

As shown by KATSUMATA(1965), almost all the near earthquakes whose S-P time are less than about 15 sec. occur in the region off Miyazaki Prefecture, which is sometimes called the Hyuganada area (See also YAMAKAWAet al. 1965).

Table 1 gives the numbers of earthquakes near Miyazaki during the 40 years from 1926 to 1965. The data were obtained from the Kisho-yoran (Geophysical Review) (1926-1950) and the Seismological Bulletin (1951-1965) of the Japan Meteorological Agency (the former Central Meteorological Observatory) except for 1947, 1948 and 1949, in which detailed seismological data were not published because Fig. 1. Distributions of epicenters of of the confusion after the Second World War. earthquakes off Miyazaki Pref., The data for these three years are obtained showing energies of large shocks. The volumes of spheres whose from the Jishin-chosa-genbo (the Original Data maximum cross sections are shown of Seismological Investigation) kept by the on this map are approximately Seismological Section of the Japan Meteoro- proportional to the energies of logical Agency. The data are often referred to shocks. in case there are some ambiuuities in the Kisho-yoran and the Seismological Bulletin. The following three kinds of shocks were chosen in this table : (1) Shocks whose epicenters were determined to be near Miyazaki, (2) Unfelt shocks solely recorded by the observatory, and (3) Felt shocks reported from the area near Miyazaki.

Fig. 2 shows the general features of seismic activities during these 40 years. The ordinates show numbers of shocks per day. These four figures show the frequencies of earthquakes per one year, three months, one month and ten days respectively. There are several events which point toward marked seismic activities. These events are related to occurrence of the following seven large shocks whose magnitudes are greater than 6. 5 with one exception.

(1) The shock of 22 May 1929. The five parameters are t=01 h 35 in JST, 7°N, 2=132.2°E, h=30 km, M=6. 8. (2) The shock of 2 November 1931. The five parameters are t=19 1103 m JST, co=32. 2°N, 2=132. 1°E, h=20 km., and M=6. 6 (M(=-7. 5). (3) The shock of 6 January 1937. The five parameters are t=06 h 38 m JST, co=31 1/2°N, 2=132 1/2°E, —20 km, and M=6. 5 (MG,----6.3). (4) The shock of 19 November 1941. The five parameters are t=01 h 46 in JST, w=32• 6°N, 2=132. 1°E, h=0-20 km, and M=7. 4 (MG=7. 8). (5) The shock of 22 August 1942. The five parameters are t=18 h 01 m JST, 1966Foreshocks, Aftershocks and Earthquake Swarms (I)161 162 Norio YamakawaVol. XVII No. 3 1966 Foreshocks, Aftershocks and Earthquake Swarms (I) 163

co=32. 2°N, 2.132. 3°E, /7.0 —40 km, and M.6. 2. (6) The shock of 9 May 1948. The five parameters are t=11 h 09 m JST, co.-31. 5°N, A=131. 8°E, h.0 km, and M.6. 7. (7) The shock of 27 February 1961. The five parameters are t=03 h 10 m 48. 1 s +O. 5 s JST, co.31. '361+21, 2.131°51'+2', h.40 km, and M=7.0.

The above-mentioned five parameters are the origin time t, the latitude co, the longi- tude A, the depth of focus h and the magnitude M or MG, where M is TSUBOI'S magnitude determined by the Japan Meteorological Agency and MG is the magnitudes determined by GUTENBERGand RICHTER (1954) and the United States Coast and Geodetic Survey (U. S. C. G. S.). Tsusoi's magnitude is equivalent to the original RICHTER'S magnitude scale (See TSUBOI 1954 and 1957 and RICHTER 1958)

To apply THOMPSON'Stest, it is necessary to calculate the mean and standard deviation of earthquake frequencies in " the normal seismic activity ". So that the data of abnormal seismic activities immediately before and after the above-mentioned large shocks are omitted in the course of calculation of the mean and standard deviation. This procedure may be considered very natural from the physical standpoint, but from the mathematical point of view the data which are omitted in the course of calculation shoud also be selected based on the •statistics. For this purpose, the so- called SMIRNOV-GRUBBS'method which tests outlying observations can be applied to the present problem. (See, SMIRNOV 1941, GRUBBS1950, Research Association of Statistical Sciences 1952, and KUNISAWAand SUZUKI 1961). This problem will be discussed in a later paper of the present study.

The mean of earthquake frequencies of the whole data is 0. 32, and the mean of the data omitting abnormal activities is O. 26. The latter is used in this paper. The standard deviation changes its value according to the unit time interval as naturally expected from Fig. 2. The values from the whole data are 0. 92, and 0. 57 according to the unit time intervals of ten days and one month respectively. The values from the data omitting abnormal activities are O. 31 and O. 20 respectively. The latter values are also used in this paper.

Now if we take O. 05 as the level of significance, the above values and Eq. 4 give the following result. If the average frequency per day during ten days or one month is over O. 88 or O. 66 we can assume that the seismic activity during this time interval is abnormal. So we can distinguish at O. 05 level of significance the abnormal seismic activities such as foreshocks, aftershocks and earthquake swarms.

Making use of this result, we can discuss the abnormal seismic activities before and after the above-mentioned seven large earthquakes. The above-mentioned publica- tions and original data are also made use of in getting the following results.

Fig. 3 shows the seismic activities before and after the earthquake of 22 May 1929. There was no marked foreshock activity which could be detected by THOMPSON'S test. The modified OMORI'S formula proposed by UTSU (1961) *

* The original °MORT'S formula was developed in 1894 . 164Norio YamakawaVol. XVII No. 3

Fig. 4. Earthquake frequencies per day before and after the shock of 2 November 1931. where n is the number of shocks per unit time and t is the time from the main shock occurrence, and n0, c and p are the constants to fit the data, can not express so closely the frequency decrease of aftershock activity for more than ten days, but a month after the main shock an abnormal seismic activity can still be detected by THOMPSON'Stest. The arrow in the figure shows the occurrence of the next main shock.

Fig. 4 shows the seismic activities before and after the earthquake of 2 November 1931. There was a marked foreshock activity in this case. The modified OMORI'S formula can not express the frequency decrease of aftershock activity for more than several days, but more than one hundred days after the main shock an abnormal seismic activity can still be detected.

Fig. 5 shows the seismic activities before and after the earthquake of 6 January 1937. There was a typical foreshock activity in this case. The aftershock activity decreased without fitting the modified OMORI'S formula, and dropped to the normal 1966Foreshocks, Aftershocks and Earthquake Swarms (I)165

Fig. 5. Earthquake frequencies per day before and after the shock of 6 January 1937.

Fig. 6. Earthquake frequencies per day before and after the shocks of 19 November 1941 and 22 August 1942.

level after some dozens of days.

Fig. 6 shows the seismic activities before and after the earthquake of 19 November 1941 and 22 August 1942. The latter shock may be considered, in a sense, the largest aftershock of the former main shock. There was a slight foreshock activity before the former shock. The aftershock activity of this shock decreased roughly in accordance with the modified OMORI'S formula for nearly two hundred days. The seismic activity before the shock of 22 August 1942 was abnormally quiet in the sense mentioned in the previous section. The aftershock activity of the latter shock decreased without fitting the modified OMORI'S formula, and dropped to the normal level about fifteen days after the main shock.

Fig. 7 shows the seismic activities before and after the earthquake of 9 May 1948. There was no marked foreshock activity which could be detected by THOMPSON'S test. The aftershock activity decreased roughly in accordance with the modified OMORI'S formula, and dropped to the normal level about twenty days after the main shock, 166Norio YamakawaVol. XVII No. 3

Fig. 7. Earthquake frequencies per day before and after the shock of 9 May 1948.

Fig. 8. Earthquake frequencies per day before and after the shock of 27 February 1961.

Fig. 8 shows the seismic activities before and after the earthquake of 27 February 1961. (In this figure, the numbers in the ordinate before the main shock should be divided by ten.) There was no foreshock activity. The aftei shock activity decreased roughly agreeing with the modified OMORI'S formula and dropped to the normal level some dozens of days after the main shock.

The general features of the above-mentioned earthquake sequences off Miyazaki Prefecture can be summarized as follows (1) Foreshock activities are not so uncommon. (2) Agreement with the modified °MORI'S formula is not so satisfactory. These results are more or less typical features in earthquake sequences in seismically active regions in Japan. These features will be discussed in detail in later parts of this study.

Of course we must consider several effects of errors of observation. We must 1966Foreshocks, Aftershocks and Earthquake Swarms (I)167

also consider the fact that shocks near Miyazaki do not necessarily occur in the region off Miyazaki which is discussed in this section. But according to the result obtained by KATSUMATA(1965) , the errors due to this fact may be considered under several percents. (See also YAMAKAWAet al. 1965)

4. Discussion

Inthe previous section, a definition of abnormal seismic activities has been applied to the earthquake sequences off Miyazaki Prefecture. But this definition is only a preliminary one to an exact definition of foreshocks, aftershocks and earthquake swarms. There are many difficulties in the exact definition of these abnormal seismic activities as pointed out by the present author (YAMAKAWAet al. 1965). This is only one solution to the first one of the two questions put forward in Section 2.

To get a final solution to these questions, it may be essential to have a detailed knowledge of background seismic activity as well as other geophysical and geological knowledge in the region concerned. This problem will also be discussed in detail in the later parts of this study.

However, there are some exceptions in which abnormal seismic activities are so remarkable that no statistical method such as Thompson's test is needed. The Matsushiro earthquake swarm which was mentioned in the beginning of this paper is just one of these cases. Here we can only point out the importance of a knowledge of background seismicity obtained by the routine observation of the Matsushiro Seismological Observatory of the Japan Meteorological Agency. Because of this knowledge of background seismicity, various characteristics of this swarm can safely be discussed. In this connection, the papers of ASADAet al. (1958) and SUYEHIROet al. (1964) which reported the seismicity near Matsushiro before this swarm should also be mentioned.

Acknowledgment------The present author wishes to express his thanks to Drs. Tokuji UTSU and Kiyoo MOGI and Mr. Mamoru KATSUMATAfor their kind advice. He also wants to express his hearty thanks to Prof. Toshi ASADA and Drs. Takuzo HIRONO,Takashi KIzAwA and Shigeji SUYEHIROand Mmes Kaoru KOIDE and Sachiyo NAKAHIRAand Miss Noriko AKIMOTOfor their kind help.

References

ASADA, T.. S. SUTEITIRO and K. AICAMATU,1958 : Observation of nearby micro-earthquakes occurring in the vicinity of Matsushiro, Japan, Zisin II, 11, 7-19. GRUBBS, F. E., 1950 : Sample criteria for testing outlying observations, A. M. 5., 21, 27-58. GUTENBERG, B., and C. F. RwEITER, 1944 : Frequency of earthquakes in California, Bull. Seism. Soc. Amer., 34, 185-188. ------, 1954 : Seismicity of the earth and associated phenomena, Princeton University Press, Princeton, p. 190. ------, 1956 : Magnitude and evergy of earthquakes, Annali di Geofisica, 9, 1-15. ICHIKAWA, M., 1967 : Mechanism of earthquakes in and near Japan and some related problems, in press. KASAHARA,K., and A. OKADA,1966 : Electro-optical measurement of horizontal strains accumulat- ing in the swarm earthquake area (1), Bull. Earthq. Res. Inst., 44, 335-350. KATSUMATA,M., 1965 : Regional characteristics of magnitude distribution of earthquakes (1), Zisin II, 18, 219-234. KUNISAWA,K. and E. SUZUKI, 1961 : Jitsurei tokeigaku enshu, Seirinshorin, Tokyo, p. 92. Moui, K., 1963 : The fracture of a semi-infinite body caused by an inner stress origin and its relation to the earthquake phenomena (II), Bull. Earthq. Res. Inst., 41, 595-614. MURAUCHI,S., 1948 : A study on the variation in seismic activities before and after great earthquakes (1st report). Zisin, II, 2, 47-51. OMORI,F., 1894 : On the aftershocks of an earthquake, J. Coll. Sci. Imp. Univ. Tokyo, 7, 111- 200. Party for Seismographic Observation of Matsushiro Earthquakes and the Seismometrical Section, 1966 : Matsushiro earthquakes observed with a temporary seismographic netwark, (I), Bull. Earthq. Res. Inst., 44, 309-333. Research Association of Statistical Sciences 1952 : Statistical tables (Revised edition), Kawade & Co., Tokyo, p. 60. RICHTER,C., 1958 : Elementary Seismology, W. H. Freeman and Co. San Francisco, p. 66. SMIRNOV,N. V., 1941 : On the estimation of the maximum term in a series of observations, Doklady Akad., Nauk S. S. S. R. (N. S.), 33, 346. SUYEHIRO,S., T. ASADAand M. OHTAKE, 1964: Foreshocks and aftershocks accompanying a perceptible earthquake in central Japan, Pap. Met. Geophys., 15, 71-87. THOMPSON,W. R., 1935 : On a criterion for the rejection of observations and the distribution of the ratio of the deviation to the sample standard deviation, A. M. S., 6, 214-219. TSUBOI, C., 1954: Determination of Gutenberg-Richter's magnitude of earthquakes occurring in and near Japan, Zisin, II, 7, 185-193.

------, 1957: Energy accounts of earthquakes in and near Japan, J. Phys. Earth., 5, 1-7. UTSU, T., 1961 : A statistical study on the occurrence of aftershocks, Geophysical Mag., 30, 521-605. , ------1962 : The nature of three Alaskan aftershock sequences of 1957 and 1958, Bull. Seism. Soc. Amer., 52, 279-297.

------, 1964: Characteristics of aftershocks in space, time and magnitude. Proc. U.S.-Japan Conference on Res. Earthq. Prediction Problem. 59-60. YAMAKAWA,N., 1965: Some investigations of aftershocks. (Part 1) Local concentration of aftershock energy and crustal deformation accompanying the main shock, Zisin, II, 18, 25-40. YAMAKAWA,N., M. HomAE and E. KOBAYASHI,1965 : Aftershock activity and normal seismic activity, Zisin, II, 18, 68-81. 1966Foreshocks, Aftershocks and Earthquake Swarms (I)169

前震,余震および群発地震(I)

一前震,余震および群発地震の一定義とその地震統計への応用一

山川宜男

前震と余震の研究は,対象それ自身に対する興味だけでなく,本震の発生機構に対する手がかりを与える可能性からも,地震学上重要な研究課題の一つであろう。また前震の調査は地震予防の立場からもかかせない、群発地震もまたいろいろな意味で興味ある対象である。しかしこれらの地震活動ここでは,常時地震活動に対比させて,一まとめに異常地震活動と呼ぶことにするの調査の前に,先ずそれらの定義を明確にする必要があることは論を待たない.この研究は前震,余震および群発地震活動の地震学的あるいは地球物理学的特性を吟味しようとする試みであるが,ここではその手始めにこれら異常地震活動の定義の客観化に対する一つの試みとして,統計学において異常値の検出に用いるトンプソンの検定を利用する方法を提案し,実際に宮崎県沖の地震活動に適用した。その結果0.05の信頼限界をとると,宮崎地方気象台において1日あたり0.7～0.9回程度の近地地震(S-P時間約15秒以内〉が観測されるような期間は,異常地震活動期(たとえば,前震,余震活動期〉であると判定できることがわかった。今後地震学上の知識を加え,スミルノフーグラッブの検定等を採用して改良を加えれば,かなり客観的な前震,余震および群発地震の定義を得ることができるであろう。 170Norio YamakawaVol. XVII No. 3

Table 1-1. Numbers of shocks near Miyazaki during the period from 1926 to 1929. 1966 Foreshocks, Aftershocks and Earthquake Swarms (I) 171 172 Norio Yamakawa Vol. XVII No. 0

Table 1-2. Numbers of shocks near Miyazaki during the period from 1930 to 1933. 1966Foreshocks, Aftershocks and Earthquake Swarms (I)173 174 Norio Yamakawa Vol. XVII No. 2

Table 1-3. Numbers of shocks near Miyazaki during the period from 1934 to 1937. 1966Foreshocks, Aftershocks and Earthquake Swarms (1)175 176 Norio Yamakawa Vol. XVII No. 3

Table 1-4. Numbers of shocks near Miyazaki during the period from 1938 to 1941. 1966Foreshocks, Aftershocks and Earthquaks Swarms (I)177 178 Norio Yamakawa Vol. XVII No. 2

Table 1-5. Numbers of shocks near Miyazaki during the period from 1942 to 1945. 1966Foreshocks, Aftershocks and Earthquaks Swarms (I)179 180 Norio Yamakawa Vol. XVII No.

Table 1-6. Numbers of shocks near Miyazaki during the period from 1946 to 1949. 1966Foreshocks, Aftershocks and Earthquaks Swarms (I)181 182Norio YamakawaVol . XVII No, 3

Table 1-7. Numbers of shocks near Miyazaki during the period from 1950 to 1953. 1966 Foreshocks, Aftershocks and Earthquaks Swarms (I) 184Norio YamakawaVol. XVII No. 3

Table 1-8. Numbers of shocks near Miyazaki during the period from 1954 to 1957. 1.966Foreshocks, Aftershocks and Earthquaks Swarms (I)185 186 Norio Yamakawa, Vol. XVII No. 3

Table 1-9. Numbers of shocks near Miyazaki during the period from 1958 to 1961. 1966 Foreshocks, Aftershocks and Earthquaks Swarms (I) 187 188Norio YamakawaVol. XVII No. 3

Table 1-10. Numbers of shocks near Miyazaki during the period from 1962 to 1965. 1966Foreshocks, Aftershochs and Earthquaks Swarms (I)189