Time Rate of Energy Release by Earthquakes in and near Japan

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1 JOURNAL OF PHYSICS OF THE EARTH, Vol. 12, No. 2, Time Rate of Energy Release by Earthquakes in and near Japan By Chuji TSUBOI Geophysical Institute, Faculty of Science University of Tokyo Abstract 1231 earthquakes have taken place in and near Japan from 1885 through 1963 which were 6.0 or more in magnitude. The points which are plotted in Fig. 4 according to year represent the cumulative sum of energy which has been released by earthquakes since the beginning of 1885 until the end of the year to which each of the points refers. The points are bounded between two parallel straight lines, of which the upper one is expressed by where t is the number of years counted from The distance between the upper representing the amount of energy which is stored in the crust or the mantle of the earth from which earthquakes originate. In Fig. 5, the amount of energy actually released Large earthquakes are seen to have occurred when the deviation for the previous year had been large. No large earthquakes have occurred when the deviation for the previous year had been small. 1. The object of the present study is to make a synoptic survey regarding the time rate of energy release by earthquakes in and near Japan in a more or less quantitative way, based on the well-known wealth of material useful for the purpose, and to see if there is any peculiarity to be found in the mode of earthquake energy release in this region. The first fundamental thing needed for this study is to prepare a comprehensive list of magnitude of large earthquakes which have taken place in the region of interest. Several sources of material are available for this purpose. H. KAWASUMI elaborately traced back into a mass of Japanese historical documents, in which descriptions of large earthquakes and resulting damage can be found. From these investigations, KAWASUMI succeeded in assigning magnitude to 193 earthquakes which took place before 1900 in this region. A list which was prepared by him is published in "Rikanenpyo" (Science Calendar, Tokyo Astronomical Observatory). The list contains date of occurrence, geographical location of epicentral area, estimated magnitude and other pertinent facts related to these earthquakes. The oldest earthquake which KAWASUMI could assign magnitude to is that of 599 A.D. (M=7.0). With regard to the 193 earthquakes, the magnitude-frequency statistics is as given in Table I. The well-known regular decrease of earthquake number according to magnitude is not seen in Table I. This appears to be due mainly to the fact that existing historical documents were naturally biased in describing those earthquake damage phenomena that were observed in areas highly populated at the time and there must have been many ommissions of earthquakes which, in spite of their large physical magnitude, were left unrecorded because they took place in thinly

2 26 Chuji TSUBOI Table I. Historical Earthquakes in and near Japan according to Magnitude (599 A.D A.D.) (KAWASUMI). which were 8.0 or more in his magnitude: M=8.1: 1611, 1677 M=8.2: 1703 M=8.3: 684, 1096, 1361, 1707, 1843, 18541, 18541, 1891 M=8.6: 869, 887, By means of the GUTENBERG-RICHTER's formula: loge= m. which gives the energy E of an earthquake in terms of its magnitude M, the energy of each of the above 14 earthquakes can be according to time. Although the increase is populated areas or offshore with little associated damage. According to KAWASUMI, release appears to be around several tenths very irregular, the overall rate of energy the following 14 earthquakes took place from in the unit of 1023erg/year. In the above, the very beginning of the written history of earthquakes with magnitude 8.0 or more only Japan down to the end of the 19th century have been considered. Inclusion of earth- Fig. 1. Cumulative Sum of Energy Released by 14 Major Earthquakes according to Time.

3 Time Rate of Energy Release by Earthquakes in and near Japan 27

4 28 Chuji TSUBOI quakes with magnitude 7.9 or less, even if it were possible, will not change the estimated rate drastically. The rate of release after 1650 A.D. appears to be several times as large as the overall value. This discrepancy may again be attributed to the increase of earthquake damage and its descriptions in the relatively recent history. After all, such an incomplete nature of data related to old historical earthquakes will not justify any further quantitative study to be made. 2. More modern data about the seismic activity in and near Japan are provided by B. GUTENBERG and C. RICHTER in their book "Seismicity of the Earth (1954) (Japan to Kamchatka, Region 19)." In this book, the two authors give a list of time of occurrence, geographical co-ordinate of the origin and magnitude of a number of earthquakes which took place in this region from 1904 through Table II is a summary which has been constructed from their list. Only those earthquakes having magnitude of 7.0 or more are energy has been calculated as before, the result being shown in Fig. 2. It is remarkable that the points in Fig. 2 are bounded between two parallel straight lines S and S', both of energy of an earthquake having the magnitude a little over 8.5-the largest conceivable earthquake. The facts which are revealed in Fig. 2 are so interesting in connection with the energy account of earthquakes that the author has been led to go further into the problem on the basis of more exhaustive and up-to-date material available in Japan. 3. The magnitude of recent earthquakes which have taken place in and near Japan since 1885 has been determined by H. KAWASUMI (1952), C. TSUBOI (1952, 1957) and by the Seismological Section of the Japan Meteorological Agency (1956 and additional material for later years) for various periods Fig. 2. Cumulative Sum of Energy Released by 63 Earthquakes in Japan to Kamchatka ( ).

5 Time Rate of Energy Release by Earthquakes in and near Japan 29 of years as follows: KAWASUMI's and J.M.A.'s data is compared in Table III. The straight lines which best express the relation between logn and the magnitude M are as follows: KAWASUMI: logn= (8-m) and Since KAWASUMI's determination of magnitude J.M.A.: logn= (8-m). depends mainly on macroseismic data while If, on the assumption of uniform occurrence that of TSUBOI and of J.M.A. on seismometrical of earthquakes with respect to time, the data, they do not necessarily constitute a above equations are reduced to one year, they uniform material. The numbers in the resolve to be: parentheses following the names of each of KAWASUMI: logn= (8-m) (1) and J.M.A.: logn= (8-m), (2) which are graphically represented in Fig. 3 with the letter K and J. The disagreement of the two straight lines, K and J, is very big. The inclination of the K and J lines in Fig. 3 does not differ much, however. It is therefore suspected that a systematic difference exists between the magnitude as determined by KAWASUMI and by J.M.A. If the K line in Fig. 3 is shifted by 0.4 toward smaller magnitude (or the J line toward larger magnitude by the same amount), the two lines will come much closer. If (M+0.4) is used instead of M in eq. (1), it becomes logn= {8-(m+0.4)} = (8-M) (3) which is fairly close to eq. (2). 18 years from 1926 through 1943 are commonly involved in the statistics both of KAWASUMI and of J.M.A. In this period, there were 42 earthquakes for which M(J) is 6.0 or more and for which M(K) is given. Table IV gives the frequency of occurrence of the difference between M(K) and M(J) which were given to the same earthquakes. Notwithstanding of large scattering of number, there is here also an indication that M(K) is relatively larger than M(J), the average of {M(K)-M(J)} being about 0.3. Both of the above two comparisons indicate that {M(K)-0.4}, instead of M(K) itself, appears to be equivalent to M(J). In the subsequent studies, therefore, {M(K)-0.4} will be used for the earthquakes which took place

6 30 Chuji TSUBOI Fig. 3. Relation between logn and M. Table IV. Number of Earthquakes according to the Difference M(K)-M(J) ( ) from 1885 through 1925* and M(J) as such for those from 1926 through This adjustment has been made for the purpose of unifying the existing material. To do justice to KAWASUMI, the present author does not mean to say that {M(K)-0.4} and M(J) are the better representation of the real M. It is possible that M(K) and {M(J)+0.4} are, however. Owing to this adjustment, the number of earthquakes from 1885 through 1925 which were 6.0 or more in magnitude has been reduced to 798 from 1296 as originally given

7 Time Rate of Energy Release by Earthquakes in and near Japan 31

9 Time Rate of Energy Release by Earthquakes in and near Japan 33

10 3 4 Chuji TSUBOI

Time Rate of Energy Release by Earthquakes in and near Japan 35 5. As was stated before, the cumulative sum of energy released by earthquakes increases linearly with time as a whole.

11 Time Rate of Energy Release by Earthquakes in and near Japan As was stated before, the cumulative sum of energy released by earthquakes increases linearly with time as a whole. To be precise, however, the curve of increase is meandering and occasionally is stepwise. A portion of slow increase is sometimes followed by an abrupt one, which is due to the occurrence of a big earthquake and this makes the upper boundary line S become straight as a whole. The supply of energy from the interior of the earth for the whole Japan may be assumed to be pretty uniform with respect to time. From time to time, a sensible portion of it is stored up in some parts of the crust or the mantle of the earth in some form of potential energy. During this storage stage, no big earthquakes occur and the amount of stored energy increases gradually with time. When the stored energy reaches a certain limit in amount, the crust or the mantle of the earth will not be capable of storing energy any more and it comes into the state of saturation. The distance between the two straight lines, S and S', in Fig. 4, be interpreted as representing this saturation value. By some mechanism which is still unknown, either a portion or nearly the whole of the stored energy is suddenly released in the form of earthquake waves and the amount of energy which remains to be stored is reduced considerably. 6. The year-to-year variation of the devia- energy from the straight line S is given in Table V and is shown in Fig. 5. The deviation is interpreted as representing the amount of energy which is stored in the crust or the mantle of the earth. The deviation varies in the form of a saw with respect to time. A series of horizontal lines drawn in Fig. 5 represent the stored energy in terms of M. The thick vertical lines in Fig. 5 represent the amount of energy actually released in each year. An evident fact to be seen in Fig. 5 is that it is when the stored energy is large that earthquakes with large magnitude occur. If the stored energy at a particular time is less than the energy of an earthquake of magnitude M, it may safely be said that an earthquake of that magnitude or more is very unlikely to occur. This may be said to be a kind of negative prediction. M also represents the upper limit of magnitude of an earthquake which may possibly occur. This latter statement should not be taken, however, as meaning that an earthquake of that magnitude will occur. If the stored energy is E, this does not necessarily mean that this amount of energy will be released by one single earthquake. From the energetic point of view, it does not make any difference if this amount of energy is released by n earthquakes, each with the energy E/n. The facts which have been found in the above therefore cannot be useful for the earthquake prediction in the ositive sense. p 7. Much has been said about the prediction of earthquake occurrence. When the word prediction is used, it appears to mean some statement about what will occur. In contrast to this, the facts which have been found by the present study appear to be useful for making some statement what will not occur. Although the argument presented in this article may appear to involve much of hypothetical nature, it is hardly anything more than a paraphrasing of the important facts that the cumulative energy plots are bounded between two parallel straight lines and that the distance between the two lines approximately corresponds to the energy of the largest conceivable earthquake. If the whole area under consideration is divided into several units and the plot of the cumulative sum of released energy is made for each unit separately, the overall uniformity of the rate of increase does not show up within the period of 79 years of the present statistics. A question which naturally arises in this connection is how large a region needs to be and how long the time of statistics needs to be in order that the energy release rate in it can be regarded to be generally uniform. The region which has been considered in the above is several thousand kilometers in horizontal extent. In order that the rate of energy release in it to be uniform

12 36 Chuji TSUBOI as a whole, its northern end, for example, has to know what is going on in the other end which is at a distance of several thousand kilometers. How can this be possible in spite of the fact that the earthquake province (TSUBOI, 1958) is several hundred kilometers in horizontal extent at most? Although there are several such important problems which are difficult to solve, the conclusions arrived at in this study must be accepted as telling us something which is phenomenologically true. References JAPAN METEOROLOGICAL AGENCY: Catalogue of Major Earthquakes which occurred in and near Japan ( ). H. KAWASUMI: Seismological Bulletin of the Central Meteorological Observatory, Japan, for the Year 1950 (1952). C. TSUBOI: Seismological Bulletin of the Central Meteorological Observatory, Japan, for the Year 1950 (1952). Magnitude-Frequency Relation for Earthquakes in and near Japan, Journ. Phys. Earth, 1 (1952), 47. Energy Accounts of Earthquakes in and near Japan, Journ. Phys. Earth, 5 (1957), 1. Earthquake Province-Domain of Sympathetic Seismic Activities, Journ. Phys. Earth, 6 (1958), 35. A. SUGIMURA et al.: Quantitative Distribution of Late Cenozoic Volcanic Materials in Japan, Bull. Volcanologique, 26 (1963), 125.

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