強烈的地震經常給人類帶來重大的損失與災難，而在之後出現的大餘震可能進一步弱化已經受損的建築結構。為降低主震後的救災風險，即時評估餘震，特別是最大餘震的風險是一項至關重要的研究。本文的資料來源為臺灣中央氣象署的地震與地球物理資料管理系統之完整地震目錄(https://gdms.cwa.gov.tw/catalogDownload.php)。研究中的地震為發生在臺灣地區(東經118°至126°，北緯20°至26°)於1994年至2023年間，規模在3.0以上、震源深度在70公里以內的所有淺層地震。首先利用經驗公式進行分簇研究，選出規模超過5.0的主震，然後找出對應的最大規模餘震。本文探索主震規模的分配，以及主震間隔時間的分配。此外根據關聯結構建立最大餘震與其主震的規模差距、時間差距和距離差距的聯合分布。最後建立未來主震可能的規模及時間，以及當主震發生後，對應最大規模餘震的可能規模、時間及震央之預測方法，並且加以統計評估之。

Strong earthquakes usually bring up significant losses and disasters to humanbeing, and large aftershocks occurred shortly after the major earthquake may further weaken the damaged structures. To carry out a rescue safely, it is crucial to assess the real-time risk of large aftershocks. In this study, we obtain the earthquake catalog from the Taiwan Seismological and Geophysical Data Management System (GDMS，https://gdms.cwa.gov.tw/
\noindent
catalogDownload.php). Of particular interest are earthquakes with magnitude of 3.0 or higher and hypocentral depth within 70 kilometers that occurred between 1994 and 2023 in the Taiwan region (from 118°E to 126°E, 20°N to 26°N). An empiried rule-based declustering method is applied to find main shocks with magnitude 5.0 or greater, and hence the associated largest aftershocks. The distribution of the magnitude of mainshocks, and that of the inter-occurrence time between successive main shocks are investigated. Moreover, the copula-based joint distribution of the differences in magnitude, time, and distance between the mainshock and the associated largest aftershock is studied. Finally, we conducted and evaluated different methods for forecasting the possible magnitude and time of the next mainshock, as well as after the current main shock, the possible magnitude, time, and epicenter of the largest aftershock.

Aki K. (1965), Maximum likelihood estimate of b in the formula log10N=a-bM and its confidence limits., Bulletin of Earthquake Research, 43, 237-239.
Alvarez-G ́omez J.A.（2019）, FMC—Earthquake focal mechanisms data management, cluster and classification., Software X, 9, 299-307.
Cramr, H.(1928), On the composition of elementary errors, Scandinavian Actuarial Journal, 1,13-74.
Chen, K.C., and J.H. Wang (2012), Correlations between the mainshock and the largest aftershock for Taiwan earthquakes, Pure and Applied Geophysics, 169, 1217-1229.
Chen, C.H., J.P. Wang, Y.M. Wu, and C.H Chan (2012), A study of earthquake inter-occorrence times distribution models in Taiwan, Natural Hazards, 69, 1335-1350.
C.H Chan, and Y.M. Wu (2013), Maximum magnitudes in aftershock sequences in Taiwan, Journal of Asian Earth Sciences, 73, 409-418.
Dickey, D.A., and W.A. Fuller (1979), Distribution of the estimators for autoregresive time series with a unit root, Journal of the American Statistical Association,
74,427-431.
Elst, N.J., and B.E. Shaw (2015), Largest aftershock happen farther away: Nonseparability of magnitude and spatial distributions of aftershocks, Geophysical Research
Letters, 42, 5771-5778.
Gutenberg, R., and C.F. Richter (1944), Frequency of earthquakes in California.Bulletin of the Seismological Society of America, 34, 185-188.
Gardner, J., and L. Knopoff (1974), Is the sequence of earthquakes in Southern California, with aftershock removed, poissonian? Bulletin of the Seismological Society of America, 64, 1363-1367.
Hogg, R.V., J.W. McKean and A.T. Craig (2021), Introduction to Mathematical Statistics, Pearson FT Press.
Huang, S., Q. Li, Z. Shu, and P.W. Chen (2023), Copula-based joint distribution analysis of wind speed and wind direction: Wind energy development for Hong Kong, Wind Energy, 26, 900-922.
Kolmogorov, A. (1933), Sulla determinazione empirica di una legge di distribuzione, Giornale dell’Istituto Italiano degli Attuari, 4, 83-91.
Kendall, M. G. (1938), A new measure of rank correlation, Biometrika, 30, 81-93.
Kruskal, W., and W.A. Wallis (1952), Use of ranks in one-criterion variance analysis, Journal of the American Statistical Association, 47, 583-621.
Mann, H.B., and D.R. Whitney (1947), On a test of whether one of two random variables is stochastically larger than the other, The Annals of Mathematical Statistics, 18, 50-60.
Molchan, G.M. and O.E. Dmitrieva (1992), Aftershock identification: methods and new approaches, Geophysical Journal International, 109, 501-516.
Ogata, Y. (1988), Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes, Journal of the American Statistical Association, 83, 9-27.
Ogata, Y. (1998), Space-time point-process models for earthquake occurrences, Annals of the Institute of Statistical Mathematics, 50, 379-402.
Panamtash, H., Q. Zhou, Z. Qu, and K.O. Davis (2021), A copula-based Bayesian method for probabilistic solar power forecasting, Solar Energy, 196, 336-345.
Smirnov, N. (1948), Table for estimating the goodness of fit of empirical distributions,The Annals of Mathematical Statistics, 19, 279-281.
Simard, C., and B. Rmillard (2015), Forecasting time series with multivariate copulas,Dependence Modeling, 3, 59-82.
Tukey, J.H. (1977), Exploratory Data Analysis, Addison-Wesley. Tsapanos, T.M., G.F. Karakaisis, P.M. Hatzidimitriou, and E.M. Scordilis (1988), On the probability of the time of occurrence of the largest aftershock and of the largest foreshock in a seismic sequence, Tectonophysics, 149, 177-180.
Tahir, M., J.R. Grasso., and D. Amorse (2012), The largest aftershock: How strong, how far away, how delayed?, Geophysical Research Letters, 39, L04301.
Utsu, T. (1969), Aftershock and earthquake statistic (I): some parameters which characterize an aftershock sequence and their interrelations, Journal of the Faculty of Science, VII, 129-195.
Van der Elst, N.J., and B.E. Shaw (2015), Larger aftershocks happen farther away: Nonseparabilityof magnitude and spatial distributionsof aftershocks, Geophysical Research LettersVolume , 42, 5679-6127.
Wiemer, S., and M. Wyss (2000), Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western US and Japan, Bulletin of the Seismological Society of America, 90, 859-869.
Wu, Y.M., and C.C. Chen (2006), Seismic reversal pattern for the 1999 Chi-Chi, Taiwan, MW 7.6 earthquake, Tectonophysics, 429, 125-132.
Zhuang, J., Y. Ogata, and D. Vere-Jones (2002), Stochastic declustering of space-time earthquake occurrences, Journal of the American Statistical Association, 97, 369-380.
Zhuang, J., C.P Chang, Y. Ogata, and Y.I. Chen (2005), A study on the background and clustering seismicity in the Taiwan region by using point process models, Journal of Geophysical Research, 110, B05S18.
中央氣象署：地震測報中心30周年專刊(2019), 第四章：結語, https://scweb.cwa.gov.tw/zh-tw/page/intro/83.
謝侑霖 (2020). 2019年美國加州規模7.1理奇克萊斯特地震之餘震風險統計，國立中央大學碩士論文。
李天旭 (2023). 台灣地區主震及其最大規模餘震之研究，國立中央大學碩士論文。