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Home , 1896 Sanriku earthquake, Seismic intensity scales

The late Prof. Tokuji Utsu: His career with Geophysics and

R. S. Matsu’ura1

1Association for the Development of Prediction, 1-5-18, Sarugaku-cho, Chiyoda-ku, Tokyo 101-0064,

Corresponding Author: R. S. Matsu’ura, [email protected]

Abstract: Dr. Tokuji Utsu, Professor Emeritus of the University of Tokyo passed away on August 17, 2004. Among his various works on seismology and geophysics, the thorough research on and the structure model under island arcs (Utsu model) are the most notable. He devoted more than a half century to the study of seismology and geophysics until he fell down to disease at the age of 76. He left us the enormous information on seismicity by the end of the 20th century in his best book “Seismicity Studies: A Comprehensive Review.” Although he was usually a so silent person, who seldom did conversation with anybody, his book tells us a lot about what we found about seismicity so far and what we should attack from now on.

1. Introduction Prof. Utsu was born in a downtown area of Tokyo on April 13, 1928. After he graduated from Geophysical Institute, the University of Tokyo, he was employed by the Central Meteorological Observatory (which became Japan Meteorological Agency in 1956) in 1951. Although his supervisor was Prof. Takeshi Nagata, and his first paper was on the electromagnetic phenomena, he happened to be posted to the seismological section in the observatory. This was the beginning of his career as a seismologist. If he were posted to the meteorological section or the geomagnetic section at that time, we would not have had Omori-Utsu formula as the decay law of aftershocks, nor the thorough catalog of the world destructive . Furthermore, he was lucky enough to have Dr. Win Inouye as his superior at the section. Here I review Tokuji’s various achievements in seismology and geophysics to praise his half-century works until our sorrowful loss of him on August 17, 2004.

2. His major works During his thirteen years at the Central Meteorological Observatory, he derived Utsu-Seki formula (Utsu and Seki, 1955) of the relation between a shallow earthquake magnitude M and its area S,

MS −= 01.402.1log , (1) and the modified Omori formula (Utsu, 1961) as the decay law of aftershocks,

+= ctKtn )/()( p , (2) where n(t) is the rate of aftershock occurrence after time t from a main shock. K shows the level of the activity, p shows the degree of decaying, and c determines the initial rate of aftershocks right after a main shock. Hereafter, we would like to call this formula as Omori-Utsu formula, since the addition of the parameter p to the original Omori formula is

not just the modification as Utsu(1961) modestly named, but the substantial derivation of the formula which enabled us to represent the clustering, which is the fundamental temporal feature of earthquakes, quantitatively only in a few parameters. He took his Ph. D degree from the University of Tokyo in 1962 on the research of aftershocks. He also spent one year from February of 1961 at the United States Coast and Geodetic Survey in Washington D.C. as a visiting scholar sponsored by the National Science Academy of the United States. Furthermore, he introduced telemeter recording of seismograms in JMA. He also found the Japan Sea is the ocean from the observation of Lg wave through its floor. He was promoted to the associate professor of University in 1964. There he experienced the Tokachi-oki earthquake of M7.9 in 1968. It was him who noticed the existence of a seismic gap off the Nemuro Peninsula in the southern part of seismic zone along the Kurile trench in 1972 (Utsu, 1972). In 1973, an M7.4 earthquake occurred off Nemuro Peninsula as expected. He also proposed the method to obtain b value of G-R relation (Utsu, 1965), which was proved as the maximum likelihood estimation by Aki(1965).

Figure 1 Above shows iso-depth contours of deep earthquakes along the Wadati zone in and around Japan. Below shows the Utsu model. Vertical section of the north-east Japan island arc showing anomalous structure [made after Utsu (1987). Utsu and Okada(1968) and Utsu(1971) were modified with contemporary plates and their names].

In Hokkaido, he also found the anomalous structure under the island arc (Fig. 1) and presented the Utsu model (Utsu, 1966, 1967, 1971, Utsu and Okada, 1968) in the dawn of the . The Utsu model shows the high Q - high V subducting slub from a trench under an island arc. The Utsu model and the finding of a seismic gap off Nemuro were achieved by the induction from a lot of data. He was so superior to notice the substantial common feature among data that look scattered at a glance. He became Professor of Nagoya University in 1972. In 1978, he escaped from increasing administrative jobs there to the Earthquake Research Institute, University of Tokyo, where he again was forced to spare a lot of time for administration. I cannot forget his happy face on the last day of his term as the director general of ERI. Even during these days, he wrote a textbook on seismology for undergraduate students (Utsu, 1977, 1984, 2001), which is still the standard textbook of seismology. He also was a good educator. He was fluent when a student asked a serious question. He was a good volunteer for the IASPEI, too. He made several kinds of software that works on cheap personal computers for developing countries. He also wrote three chapters in the handbook published to celebrate IASPEI’s centennial (Utsu, 2002a, 2002b, 200c). He also compiled the catalog of earthquakes in and around Japan from 1885 to 1925 (Utsu, 1979), and the destructive earthquakes in the world (Utsu, 1990). His character to pursue perfection in research fully exhibited in compilation of data. His catalogs have been utilized widely. He also served as the head in revising “Japanese Scientific Terms of Seismology” (Ministry of Edu. and JSS, 2000) . After he retired from ERI in 1989, he spent the happiest days as a seismologist at the Institute of Statistical Mathematics with the courtesy of Prof. Ogata. He reviewed the seismicity research thoroughly (Utsu, 1999), revised his former books, and did research, what he always wanted to do most. He spent the happiest retirement days. He continued doing research until the cancer was found in his stomach in late summer of 2002. After the operation, he spent most of the time listening to various music, what he loved next to seismology. However, he looked tired of life without enough vitality for doing research. He passed away on August 17, 2004. According to his will, a small funeral was held by the close relatives, and he is now sleeping in the temple near Shinjuku in an eternal peace.

Figure 2 Prof. Utsu’s photo taken on the day of retirement from ERI. He looked so happy.

3. Conclusion Prof. Utsu did several substantial findings on seismology and geophysics. He left us various compiled data and a comprehensive review of the study on seismicity. What we should do is to find some rules among them in order to forecast the seismicity process.

4. Acknowledgement We are grateful to all participated to the fourth International Workshop of Statistical Seismology in the memory of Tokuji Utsu. I believe that nothing but the progress in this field will most please his soul, although he had no interest in the world after death.

5. References Aki, K. (1965), Maximum Likelihood Estimate of b in the Formula log-N＝a－bM and its Confidence Limits, Bull. Earthq. Res. Inst., 43, 237-239. Ministry of Education and Japan Seismological Society (2000), Japanese Scientific Terms, Seismology, Revised and Enlarged Ed., (Japan Soc. Prom. Science, Tokyo), pp.310. Utsu, T. and Seki, A. (1955), A Relation between the Area of After-shock Region and the Energy of Main-shock, Zisin (2), 7, 233-240 (in Japanese). Utsu, T. (1961), A statistical study on the occurrence of aftershocks, Geophys. Mag., 30, 521-605. Utsu, T. (1965), A method for determining the value of b in a formula log n = a – bM showing the magnitude-frequency relation for earthquakes, Geophys. Bull. Hokkaido Univ., 13, 99-103 (in Japanese). Utsu, T. (1966), Regional differences in absorption of seismic waves in the upper mantle as inferred from abnormal distributions of seismic intensities, J. Fac. Sci. Hokkaido Univ., Ser. VII, 2, 359-374. Utsu, T. (1967), Anomalies in velocity and attenuation associated with a deep earthquake zone (I), J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 1-25. Utsu, T. (1972), Large earthquakes near Hokkaido and the expectancy of the occurrence of a large earthquake off Nemuro, Rep. Coord. Comm.Earthq. Pred., 7, 7-13 (in Japanese). Utsu, T. (1977), Seismology, (Kyoritsu Shuppan, Tokyo), pp. 286 (in Japanese). Utsu, T. (1979), Seismicity of Japan from 1885 through 1925 – a new catalog of earthquakes of M>=6 felt in Japan and smaller earthquakes which caused damage in Japan, Bull. Earthq. Res. Inst., 54, 253-308 (in Japanese). Utsu, T. (1984), Seismology 2nd Ed., (Kyoritsu Shuppan, Tokyo), pp. 310 (in Japanese). Utsu, T. (1987), Encyclopedia of Earthquakes, (Asakura Shoten, Tokyo, pp.568), 147. Utsu, T. (1990), Destructive earthquakes in the world - from ancient times to 1989), (Utsu Press, Tokyo), pp.243 (in Japanese). Utsu, T. (1999), Seismicity Studies: A Comprehensive Review, (Univ. Tokyo Press, Tokyo), pp. 876 (in Japanese). Utsu, T. (2001), Seismology 3rd Ed., (Kyoritsu Shuppan, Tokyo), pp. 376 (in Japanese). Utsu, T, (2002a), A list of deadly earthquakes in the world: 1500-2000, in International Handbook of Earthquake & Engineering Seismology Part A, Eds. W. H. K. Lee, H. Kanamori, P.C.Jennings, and C. Kisslinger (Academic Press, San Diego), 691-717. Utsu, T, (2002b), Statistical features of seismicity, in International Handbook of Earthquake & Engineering Seismology Part A, Eds. W. H. K. Lee, H. Kanamori, P.C.Jennings, and C. Kisslinger (Academic Press, San Diego), 719-732. Utsu, T, (2002c), Relationship between magnitude scales, in International Handbook of Earthquake & Engineering Seismology Part A, Eds. W. H. K. Lee, H. Kanamori,

P.C.Jennings, and C. Kisslinger (Academic Press, San Diego), 733-746. Utsu, T. and Okada, H. (1968), Anomalies in seismic wave velocity and attenuation associated with a deep earthquake zone (II), J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 65-84.

7. Appendix. Selected publications of Professor Tokuji Utsu Utsu, T. (1953), On energy and frequency of aftershocks, Quart. J. Seism., 18, 66-84 (in Japanese). Utsu, T. (1953), On energy and frequency of aftershocks (continued), Quart. J. Seism., 18, 165-175 (in Japanese). Utsu, T. and Seki, A. (1955), A Relation between the Area of After-shock Region and the Energy of Main-shock, Zisin (2), 7, 233-240 (in Japanese). Utsu, T. (1956), Some remarkable phases on seismograms of near earthquakes (part 1), Quart. J. Seism., 20, 141-144 (in Japanese). Utsu, T. (1956), On deflection of the direction of initial motion of , Quart. J. Seism., 21, 13-20 (in Japanese). Utsu, T. (1956), On some remarkable phases on seismograms of near earthquakes (part 2), Quart. J. Seism., 21, 107-111 (in Japanese). Utsu, T. (1957), Response curves of electromagnetic seismograph (1), Quart. J. Seism., 22, 5-18 (in Japanese). Utsu, T. (1957), Response curves of electromagnetic seismograph (2), Quart. J. Seism., 22, 133-139 (in Japanese). Utsu, T. (1957), Magnitude of earthquakes and occurrence of their aftershocks, Zisin(2), 10, 35-45 (in Japanese). Utsu, T. (1958), On the Lg phase of seismic wave observed in Japan (1), Quart. J. Seism., 23, 61-76 (in Japanese). Utsu, T. (1960), Observations of the Lg waves and crustal structure in the vicinity of Japan, Geophys. Mag., 29, 499-508. Utsu, T. (1961), A statistical study on the occurrence of aftershocks, Geophys. Mag., 30, 521-605. Utsu, T. (1962), On the nature of three Alaskan aftershock sequences of 1957 and 1958, Bull. Seism. Soc. Amer., 52, 279-297. Utsu, T. (1962), On the time interval between two consecutive earthquakes, US Coast & Geodetic Survey Technical Bull., 17, 1-5. Utsu, T. (1964), On the relation betweenαandγin a formula M=log A+α･logΔ+γ for calculating earthquake magnitude, Zisin (2), 17, 236-238 (in Japanese). Utsu, T. (1964), On the statistical formula showing the magnitude-frequency relation of earthquakes (a preliminary report), Quart. J. Seism., 28, 79-88 (in Japanese). Utsu, T. (1964), Magnitude distribution of earthquakes with special consideration for aftershock activities, Quart. J. Seism., 28, 129-136 (in Japanese). Utsu, T. (1964), Characteristics of aftershocks in space, time, and magnitude, Proc. US- Japan Conf. Earthq. Prediction, 59-60. Utsu, T. (1965), A method for determining the value of b in a formula log n = a – bM showing the magnitude-frequency relation for earthquakes, Geophys. Bull. Hokkaido Univ., 13, 99-103 (in Japanese). Utsu, T. (1966), Variations in spectra of P waves recorded at Canadian Arctic seismograph stations, Can. J. Earth Sci., 3, 597-621. Utsu, T. (1966), Regional differences in absorption of seismic waves in the upper mantle as

inferred from abnormal distributions of seismic intensities, J. Fac. Sci. Hokkaido Univ., Ser. VII, 2, 359-374. Utsu, T. (1966), A statistical significance test for the difference in b-value between two earthquake groups, J. Phys. Earth, 14, 37-40. Utsu, T. (1966), Abnormal distributions of seismic intensities and regional differences in absorption of seismic waves, Zisin (2), 19, 226-227 (in Japanese). Utsu, T. (1967), Anomalies in seismic wave velocity and attenuation associated with a deep earthquake zone (I), J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 1-25. Utsu, T. (1967), Some problems of the frequency distribution of earthquakes in respect to magnitude (I), Geophys. Bull. Hokkaido Univ., 17, 85-112 (in Japanese). Utsu, T. (1967), Some problems of the frequency distribution of earthquakes in respect to magnitude (II), Geophys. Bull. Hokkaido Univ., 18, 53-69 (in Japanese). Utsu, T. and Okada, H. (1968), Anomalies in seismic wave velocity and attenuation associated with a deep earthquake zone (II), J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 65-84. Utsu, T. and Hirota, T. (1968), A note on the statistical nature of energy and strain release in earthquake sequences, J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 49-64. Utsu, T. (1968), Seismic activity in Hokkaido and its vicinity, Geophys. Bull. Hokkaido Univ., 20, 51-75 (in Japanese). Utsu, T. (1969), Abnormal distributions of seismic intensities in western Japan, Geophys. Bull. Hokkaido Univ., 21, 45-52 (in Japanese). Utsu, T. (1969), Note on seismic intensity scales, Geophys. Bull. Hokkaido Univ., 21, 53-62 (in Japanese). Utsu, T. (1969), Seismic investigation of rockbursts in Bibai Coal Mine, Hokkaido, Zisin (2), 22, 76-79 (in Japanese). Utsu, T. (1969), Ratio of Vp/Vs in the upper mantle beneath the island arcs of Japan, Zisin (2), 22, 41-53 (in Japanese). Utsu, T. (1969), Time and space distribution of deep earthquakes in Japan, J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 117-128. Utsu, T. (1969), Some problems of the distribution of earthquakes in time (Part 1) – distributions of frequency and time interval of earthquakes, Geophys. Bull. Hokkaido Univ., 22, 73-93 (in Japanese). Utsu, T. (1969), Some problems of the distribution of earthquakes in time (Part 2) – stationarity and randomness of earthquake occurrence, Geophys. Bull. Hokkaido Univ., 22, 95-108 (in Japanese). Utsu, T. (1969), Aftershocks and earthquake statistics (I) - some parameters which characterize an aftershock sequence and their interrelations, J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 129-195. Utsu, T. (1970), Aftershocks and earthquake statistics (II) – further investigation of aftershocks and other earthquake sequences based on a new classification of earthquake sequences, J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 197-266. Utsu, T. (1970), Aftershocks and earthquake statistics (III) – analyses of the distribution of earthquakes in magnitude, time, and space with special consideration to clustering characteristics of earthquake occurrence (1), J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 379-441. Utsu, T. (1970), Aftershocks and earthquake statistics (IV) - analyses of the distribution of earthquakes in magnitude, time, and space with special consideration to clustering characteristics of earthquake occurrence (2), J. Fac. Sci. Hokkaido Univ., Ser. VII, 4,

1-42. Utsu, T. (1970), Some problems of the distribution of earthquakes in time (Part 3) – characteristics of aftershocks, , and earthquake swarms in time, Geophys. Bull. Hokkaido Univ., 23, 49-71 (in Japanese). Utsu, T. (1970), Some problems of the distribution of earthquakes in time (Part 4) – a stochastic model for earthquake occurrence with consideration to clustering of earthquakes, Geophys. Bull. Hokkaido Univ., 24, 107-123 (in Japanese). Utsu, T. (1970), Seismic activity and seismic observation in Hokkaido in recent years, Rep. Coord. Comm. Earthq. Pred., 2, 1-2 (in Japanese). Utsu, T. (1971), Anomalous structure of the upper mantle beneath the Japanese islands, Geophys. Bull. Hokkaido Univ., 25, 99-127 (in Japanese). Utsu, T. (1971), Seismological evidence for anomalous structure of island arcs with special reference to the Japanese region, Rev. Geophys. Space Phys., 9, 839-890. Utsu, T. (1971), Comments on the synodic monthly distribution of destructive earthquakes in Japan, Zisin (2), 24, 369-371 (in Japanese). Utsu, T. (1972), Large earthquakes near Hokkaido and the expectancy of the occurrence of a large earthquake off Nemuro, Rep. Coord. Comm.Earthq. Pred., 7, 7-13 (in Japanese). Utsu, T. (1973), Temporal variations in travel time residuals of P waves from Nevada sources, J. Phys. Earth, 21, 475-480. Utsu, T. (1974), A three-parameter formula for magnitude-distribution of earthquakes, J. Phys. Earth, 22, 71-85. Utsu, T. (1974), Correlation between great earthquakes along the Nankai trough and destructive earthquakes in western Japan, Rep. Coord. Comm.Earthq. Pred., 12, 120-122 (in Japanese). Utsu, T. (1974), Space-time pattern of large earthquakes occurring off the Pacific coast of the Japanese Islands, J. Phys. Earth, 22, 325-342. Utsu, T. (1975), Correlation between shallow earthquakes in Kwanto region and intermediate earthquakes in Hida region, central Japan, Zisin (2), 28, 303-311 (in Japanese). Utsu, T. (1975), Detection of a domain of decreased P-velocity prior to an earthquake, Zisin (2), 28, 435-448 (in Japanese). Utsu, T. (1975), Regional variation of travel-time residuals of P waves from nearby deep earthquakes in Japan and vicinity, J. Phys. Earth, 23, 367-380. Utsu, T. (1977), Probabilities in , Zisin (2), 30, 179-185 (in Japanese). Utsu, T. (1977), Possibility of a great earthquake in the Tokai district, central Japan, J. Phys. Earth, 25, Suppl., s219-s230. Utsu, T. (1978), An investigation into the discrimination of foreshocks sequences from earthquake swarms, Zisin (2), 31, 129-135 (in Japanese). Utsu, T. (1978), Estimation of parameters in formulas for frequency-magnitude relation of earthquake occurrence - in cases involving a parameter c for the maximum magnitude, Zisin (2), 31, 367-382 (in Japanese). Utsu, T. (1979), Calculation of the probability of success of an earthquake prediction (in the case of Izu-Oshima-Kinkai earthquake of 1978), Rep. Coord. Comm. Earthq. Pred., 21, 65-166 (in Japanese). Utsu, T. (1979), The Nemuro-hanto-oki earthquake, Ten years of the Coodinating Committee for Earthquake Prediction, edited by Coord. Comm. Earthq. Prediction, 79-87 (in Japanese). Utsu, T. (1979), Seismicity of Japan from 1885 through 1925 – a new catalog of earthquakes

of M>=6 felt in Japan and smaller earthquakes which caused damage in Japan, Bull. Earthq. Res. Inst., 54, 253-308 (in Japanese). Utsu, T. (1979), Do large earthquakes in Japan correlate with the age of the moon?, Zisin (2), 32, 495-497 (in Japanese). Utsu, T. (1979), Some remarks on a seismic gap off , Rep. Coord. Comm. Earthq. Pred., 21, 44-46 (in Japanese). Utsu, T. (1980), Spatial and temporal distribution of low-frequency earthquakes in Japan, J. Phys. Earth, 28, 361-384. Utsu, T. (1980), Low-Frequency Earthquake Prediction, Rep. Coord. Comm. Earthq. Pred., 24, 274-278 (in Japanese). Utsu, T. (1981), Seismicity of the Izu Peninsula and its vicinity from 1901 through 1980 with some remarks on the characteristics of activities, Bull. Earthq. Res. Inst., 56, 25-41. Utsu, T. (1981), Seismicity of central Japan from 1904 through 1925, Bull. Earthq. Res. Inst., 56, 111-137 (in Japanese). Utsu, T. (1982), Probabilities Related to Earthquake Prediction, Rep. Coord. Comm. Earthq. Pred., 28, 341-343 (in Japanese). Utsu, T. (1982), Seismicity of Japan from 1885 through 1925 (Correction and supplement), Bull. Earthq. Res. Inst., 57, 111-117 (in Japanese). Utsu, T. (1982), Catalog of large earthquakes in the region of Japan from 1885 through 1980, Bull. Earthq. Res. Inst., 57, 401-463 (in Japanese). Utsu, T. (1982), Relation between earthquake magnitude scales, Bull. Earthq. Res. Inst., 57, 465-497 (in Japanese). Utsu, T. (1982), Probabilities of earthquake prediction (the second paper), Bull. Earthq. Res. Inst., 57, 499-524 (in Japanese). Utsu, T. (1983), Probabilities associated with earthquake prediction and their relationships, Earthq. Predict. Res., 2, 105-114. Utsu, T. (1984), Estimation of parameters for recurrence models of earthquakes, Bull. Earthq. Res. Inst., 59, 53-66, 1984. Utsu, T. (1984), Long- and short-term seismic risk estimation from seismicity and precursors, Proc. Int. Conf. Continental Seismicity Earthq. Predic., 818-827. Utsu, T. (1984), Relation between seismic intensity, epicentral distance and magnitude, Part 1, empirical formula for shallow earthquakes in Japan excluding those occurring off the Pacific coast of eastern Japan, Bull. Earthq. Res. Inst., 59, 219-233 (in Japanese). Utsu, T. (1985), Catalog of large earthquakes in the region of Japan from 1885 through 1980 (Correction and supplement), Bull. Earthq. Res. Inst., 60, 639-642 (in Japanese). Utsu, T. (1986), Relation between seismic intensity, epicentral distance and magnitude, Part 2, empirical formula for uppermost mantle earthquakes in Japan excluding those occurring off the Pacific coast of eastern Japan, Bull. Earthq. Res. Inst., 61, 551-561 (in Japanese). Utsu, T. (1987), Relation between seismic intensity, epicentral distance and magnitude, Part 3, empirical formula for earthquakes occurring off the Pacific coast of eastern Japan, Bull. Earthq. Res. Inst., 62, 289-296 (in Japanese). Utsu, T. (1988), Relation between seismic intensity near the, , focal depth and magnitude, Bull. Earthq. Res. Inst., 63, 23-31 (in Japanese). Utsu, T. (1988), A catalog of large earthquakes (M>=6) and damaging earthquakes in Japan for the years 1885-1925 in Historical Seismograms and Earthquakes of the World, Eds. W. H. K. Lee, H. Meysrs and K. Shimazaki, (Academic Press, San Diego), 150-161.

Utsu, T. (1988),η-value for magnitude distribution and earthquake prediction, Rep. Coord. Comm. Earthq. Pred., 39,380-386 (in Japanese). Utsu, T. (1990), Destructive earthquakes in the world - from ancient times to 1989), (Utsu Press, Tokyo), pp.243 (in Japanese). Utsu, T. (1994), Aftershock activity of the 1896 Earthquake, Zisin (2), 47, 89-92 (in Japanese). Utsu, T. (1994), Recurrence of several earthquakes at almost equal time intervals, Zisin (2), 47, 93-95 (in Japanese). Utsu, T. (1994), An earthquake that has been considered to be a foreshock of the , Zisin (2), 47, 183 (in Japanese). Utsu, T., Ogata, Y., and Matsu'ura, R.S. (1995), The centenary of the Omori formula for a decay law of aftershock activity, J. Phys. Earth, 43, 1-33. Ogata, Y., Utsu, T., and Katsura, K. (1995), Statistical features of foreshocks in comparison with other earthquake clusters, Gephys. J. Int., 121, 233-254. Utsu, T. (1999), Representation and analysis of the earthquake size distribution: a historical review and some new approaches, Pure Appl. Geophys., 155, 509-535. Utsu, T, (2002), A list of deadly earthquakes in the world: 1500-2000, in International Handbook of Earthquake & Engineering Seismology Part A, Eds. W. H. K. Lee, H. Kanamori, P.C.Jennings, and C. Kisslinger (Academic Press, San Diego), 691-717. Utsu, T, (2002), Statistical features of seismicity, in International Handbook of Earthquake & Engineering Seismology Part A, Eds. W. H. K. Lee, H. Kanamori, P.C.Jennings, and C. Kisslinger (Academic Press, San Diego), 719-732. Utsu, T, (2002), Relationship between magnitude scales, in International Handbook of Earthquake & Engineering Seismology Part A, Eds. W. H. K. Lee, H. Kanamori, P.C.Jennings, and C. Kisslinger (Academic Press, San Diego), 733-746.