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Mau sam (J979). SO. 2 & 3, :!61-2 i3 550 .34 1.5 :5 19. 24 (5·1I) Estimated earthquake Probabilities in the northeast India and Andaman-Nicobar islands P. SITAPATHI RAO and B. RAMALINGESWARA RAO Department of G,ophysi£s , Andhra University, lVallair ABS",:RACT. G umbel's extreme val ue: theory has been app l.ied to estimate the probability of occurrence and return periods of the largest earthquakes 10 the northeast India and Andaman , icobar Islands. The stati- snca! model of Epstein and Lomnitz (l966) is discussed with reference 10 the G umbel's extreme value theory. The lines of expected extremes based on 46 years data of yearly extreme values of earthquakes in the three re- grons are plotted separa telyand the meanreturn periods of the largest possible earthquakes with their probabilit y of recurrence are es tima ted, The most probable largest earthquakes in the Richter scale that may occur in an year and in an interval of SO years are also estimated and reported. Lomnitz (1966) in America. Dick (1965) used it for the a na lysis or the New Zealand ear thquakes Mil ne and Dev enport (1969) for the ear thq uakes, Karn ik and Hu bern ova ( 1968) and Schenkova and Karnik (1970) for the Euro- pean earthquakes. For the North Circum-Paci_ fie seismic belt, Shakal and Willi s ( 1972) have applied thi.s theory and esti. ,,:, ated the earthquake r eturn periods and pr ob abi lites as envisaged by Gumbel ( 1958) in his model. In general, th e extreme value methods, their limitations and the earthquake risk involved have been b rought forth by Lomnitz (1974) in two articles. O n th e e art hq ua ke d ata of the Indi an sub-coml, nent, hitherto no application of Gumbel's extreme value theory bas been made and Rao an d Rao (1978). has reported elsewhere. the pr eli min ary ana lysis and results on the Indian Ocean seismic belts. An extension of this work to northeast India-Andaman-I -icobar Islands forms the subject matter of this pape r. 2. Tbe 3reueal model r, The theoretical model originally proposed by Gumbel (1941) for the an alysis of flood dat a is based on the random variable function G (x I). II requires n independent observations continuously over an appreciably long time which should be amenable for division into .N·number of independent sets each having an equal time-length T. The }/ sets o btaine d include .N nu m ber of ex treme s as each set contributes invariably an ex treme . T he parent population must follow , as proposed, a known statistical distribution such as the normal, exponential, chi-squa re or gamma In the last one decade, extremal value theory was di strib ution. Thus, the earthquake data may be developed and appl ied by Gayskiy and K at ok modelled int o N-sets and th e largest magnitude ( 1965) in Soviet Un ion a nd by Epstein and earthquakes may be picked up fr om each of the (267) Among the Stochastic models used in the esti- mation of earthquake risk, the extreme value methods, originaIly proposed by Gumbel du ring the 1930's for the flood anal ysis, have been applied in recent years to earthquake data for obtaining re curren ce period and probabilit y of occ urrence of the largest earthquakes. In this, giv en a fun- ction G(x, t) of a random variable x on time scale t and is divisible into equal intervals of time T, each segment contains among a minimum and a maximum in the interval T. Th e maxim um value r = [(X"")] T called here the extreme val ue. is an independent earthquake event with the highest magnitude in the inte rva l T [ee one yea r). In a p opu lation of data collected over an appreciably long period, an extreme is obtain- ed in each of the in terval spiked. Since the true probability of occurrence of these extrem es may be estimated with their return periods, a number of authors have applied the theory of extremes and analysed eart hquake data in diffe rent regi ons of the world. The first attempt was, however, by Nordquist (1945) on the eart hquakes of southern California and also on the largest e arthq uakes of the world. H is observed distrib ut ion of the magnit ude of the largest ea rthqua kes was found to be in good agreement with the ext remal theory, envisaged, O ver the tim es, as the statistical theories and models are in increasing use in all the fields . of geophysics, Arnold Court ( 19 52) has broug ht out a full review of the theory of ex tremes and its impor tance to hel p the civil c lIginecring d l.osigns, However, Gum bel ( 1958) publ ished a complete theory or the extremes and its application.
