No. 1] 27 8. Magnitude-Frequency Relation of Earthquakes and its Bearing on Geotectonics By Setumi MIYAMURA EarthquakeResearch Institute, University of Tokyo (Comm.by C. TsuBOI,M.J.A., Jan. 12, 1962) A formula log N= a+b (8-M) was introduced by B. Gutenberg and C. F. Richter'' for expressing the number N of earthquakes in relation to their magnitudes M. The coefficient a which represents the logarithm of the number of earthquakes having a magnitude 8±dM/2 depends on the extent of area and the length of time taken into account, but the other one b does not and is believed to be a physical constant related to the mechanical behaviour of the portion of the earth in which the earthquakes occur. The values of the coefficients a and b were numerically deter- mined by Gutenberg and Richter for shallow, intermediate and deep earthquakes for both the entire world and various selected regions. Although the value of b determined by Gutenberg and Richter ranges from 0.45 to 1.5 for various regions, they suspected it is more or less constant so that the rate of increase in frequency of earthquakes with decreasing magnitude does not differ much for all regions. They did not fail to point out, however, that in South America and Central Asia, earthquakes having very large magnitudes are dispro- portionately numerous, while in the Atlantic and Indian oceans, they are disproportionately rare. This study of Gutenberg and Richter has been followed by many similar ones, which were made for various other regions. Most of the authors who have made the studies seem to be inclined to support the view that the rate of increase in frequency of earthquakes with decreasing magnitude does not differ much from a region to another. Re-arranging the seismicity materials which were given by C. F. Richter,2' according to seismic belts and magnitudes as shown in Table I, the present author has found that the rate of increase in frequency of earthquakes according to decreasing magnitudes undeniably differs from one region to another and that the difference appears to be systematically related to that in geotectonic charac- teristics of the respective regions. C. Tsuboi3' also determined the b values for each of the three areas A, B and C, into which Japan and her vicinity are devided, to be 1.06, 0.72 and 0.66 respectively. The area A is the Pacific side of NE Japan, B that of SW Japan and C the Japan Sea side of the 28 S. MIYAMURA [Vol. 38, whole Japan. The b value for the whole Japan was found to be 1.01 which is close to that for the area A and this is only natural because a greater portion of seismic activity in and near Japan is concentrated in A where two thirds of epicenters of the whole Japan are located. It is noteworthy that the b value differs significantly among A, B and C. According to a study of three dimensional distribution of earth- quake foci in and near Japan,4' the earthquakes i n A area are mostly sub-crustal, while those in B and C areas are mainly supra- and intra-crustal, using the terminology of L. Glangeaud and J. P. Rothe.5' Table I. Magnitude-frequency relation of large earthquakes for the main seismic belts of the world From the standpoint of tectonic development of the Japanese Islands, the sub-crustal activity in A is related to rather recent Pacific phase movements along the Kurile-Mariana arc accompanied by trenches, volcanoes, gravity anomalies arranged in the well-known parallel pattern. The activities in B and C are likely to be related to the older orogenic sequences of the Honshu geosyncline. It may therefore be safely said that, at least so far as the Japanese area is concerned, the value of b is larger for a young arc structure than for an old block structure. The values given in Table I for the world also point out the same tendency. The relative frequency of earthquakes having larger magnitudes is low for the Atlantic and Indian oceans in contrast with the Kansu and Pamir-Baikal belts where it is high. The Circum-Pacific and Alpide belts lie between those oceanic and continental zones in this respect, indicating transient stages from arc structures to block structures. High b values of 1.8-1.0 are found for the oceanic regions, in- cluding mid-oceanic ridges and island arcs of small islets. Moderate b values of 1.0-0.7 are for the Circum-Pacific and Alpide orogenic zones, including island arcs of big islands and peninsulas, while low b values of 0.7-0.6 are for continental rift zones and platform block zones. Very low b values of 0.6-0.4 are for old shield zones. It may be noted that an experimental study of the magnitude- No. 1] Magnitude-Frequency Relation of Earthquakes 29 Fig. 1. Relation of the coefficients a and b for the various earthquake regions of the world. N.B. 1: East Pacific, 2: South-east Pacific, 3: Arctic Ocean, 4: Atlantic Ocean, 5: Indian Ocean, 6: Indian-Antarctic Swell, 7: Tonga-Kermadec Is., 8: Aleutian Is., 9: Caroline-Mariana Is., 10: Solomon Is., 11: Sunda Is., 12: Mexico-Central America, 13: Southern California, 14: New Zealand, 15: Japan-Kamchatka, 15': NE Japan-Pacific side, 15": SW Japan-Pacific side, 15": Inner Japan-Japan Sea side, 16: Turkey, 17: Caucasus, 17': Djavakhet plateau (Caucasus), 17": Pri-kazbek region (Caucasus), 18: Baikal, 19: Pamir to East Asia, 20: Hungary, 21: Western Rift Valley (East Africa), 22: China (continent), 23: Fennoscandia, 24: South America (north of 37°S), 25: Australia. Data References: 1-16,19, 24... Gutenberg and Richter. 15',15", 15"... Tsuboi. 17,17' 17"... Tskhakaya. 18. .. Soloviev. 20. .. Csomor and Kiss 21... Sutton and Berg. 22. .. Mei Shi-Yun. 23... Bath. 25... Burk-Gaffney. frequency relation of fracture has been made by K. Mogi5' using heterogeneous materials and results were obtained which are very suggestive to explain the difference of b values in various tectonic regions. The coefficient a, which is the logarithm of the number of earthquakes having a magnitude 8±dM/2, depends on the extent of area and the length of time taken into account as well as on the class interval of magnitude dM. In order to make use of the coefficient as a comparative measure of seismic activity, the a values must be reduced to refer to certain standards. Here the area is taken to be 106 km2, the time 1 year and the class interval dM 1.0. Fig. 1 is the result of the plot of the b values against the reduced a values. A notable fact to be seen in Fig. 1 is that the points are distributed in a systematic way and a curve may be drawn through these points as shown in the figure. Starting from high b values which correspond to oceanic regions, the curve slopes down towards the right following the order of arcs of small islets 30 S. MIYAMURA [Vol. 38, and of bigger islands in the Circum-Pacific belt and Cenozoic arcuate mountains of the Alpide belt. Then the curve shows a bent beyond which it slopes down gently to the left. This portion corresponds to continental structures geographically. The sequence which is stated above appears to correspond to that in the development of geotectonic structures, which, starting from an infant stage, pass through young and mature stages to terminate at an old quiet end. References 1) B. Gutenberg and C. F. Richter : Seismicity of the Earth and Associated Phenomena, Princeton University Press (1949). 2) C. F. Richter : Elementary Seismology, Freeman, San-Fransisco (1958). 3) C. Tsuboi: Magnitude-frequency relation for earthquakes in and near Japan, Journ. Phys. Earth, 1, 4?-54 (1952). 4) S. Miyamura: Earthquake province and its bearing on geotectonics, Read at the XII General Assembly of IUGG at Helsinki (1960). 5) L. Glangeaud et J. P. Rothd : Cause tectonophysiques et effets morphologiques des sdismes d'Orldanville et du Chdliff, Comptes Rendus, Paris, 1829-1831 (1945). 6) K. Mogi : Study of elastic shocks caused by the fracture of heterogeneous materials and its relations to earthquake phenomena, Bull. Earthq. Res. Inst., 40 (1962)..