対数正規分布モデルによる地震長期発生確率の計算

• 岡田 正実

  気象庁精密地震観測室

書誌事項

タイトル別名

• Probabilistic Estimation of Large Earthquake Occurrence from Several Earthquakes Using Lognormal Distribution Model
• 対数正規分布モデルによる地震長期発生確率の計算--宮城県沖地震の再検討
• タイスウ セイキ ブンプ モデル ニ ヨル ジシン チョウキ ハッセイ カクリツ ノ ケイサン ミヤギケンオキ ジシン ノ サイケントウ
• 宮城県沖地震の再検討
• Re-evaluation for the Oncoming Earthquake off Miyagi Prefecture, Japan

抄録

I statistically discuss the method for estimating the probability of the next characteristic earthquake in a given time interval from the data on date of earthquakes in the past by using lognormal distribution model, based on the Bayesian approach. We assume that n+1 earthquakes have occurred on a fault or in a source area separated by n time intervals, T_i, of which logarithm, x_i=ln(T_i), are considered to follow a normal distribution, N(μ, σ²). Here, μ and σ² are mean and variance parameters of a normal population distribution, respectively. Then the likelihood accounted for aseismic period since the last event is defined as L(μ, σ²)=(1-F_N(x_p;μ, σ²))Πⁿ_i=1f_N(x_i;μ, σ²), where x_p, F_N and f_N are the logarithm of the time interval of aseismic period, T_p, since the last event, the cumulative distribution function, and the probability density function for N(μ, σ²), respectively. We expect that normalized likelihood represents the density distribution of μ, σ² based on Bayesian rule with a prior distribution of π(μ, σ²)=1. If μ and σ² are known, the probability of the next earthquake occurring in the forthcoming period from T_p through T_p+ΔT is denoted by a conditional probability, P_q=(F_N(x_f;, μ, σ²))/(1-F_N(x_p;μ, σ²)), where x_f=ln(T_p+ΔT). However it is impossible to estimate real values from a small number of data without large error, and we can only know the distribution of parameters to calculate numerically the distribution of P_q as shown in this paper. The distribution of expected time interval, T, from the last event to the next event is computed analytically from a law that √n-3(ln(T)-x)/√(n+1)s² follows t-distribution of n-3 degrees of freedom. Here x and s2 are mean and variance of data, x_i=ln(T_i). And the expected probability of characteristic earthquake occurrence in a time interval ΔT given that no earthquake has occurred in T_p, is the mean of variable P_q or a conditional probability of t-distribution. For the characteristic earthquakes off Miyagi prefecture, Japan, the estimates of probability in the periods of 10, 20 and 30 years after January 2001 are 0.28, 0.62 and 0.80, respectively, using the data set compiled by the Earthquake Research Committee of Japan. These estimates for 20 and 30 years are smaller than those, about 0.8 and larger than 0.9, given by the committee, respectively. Interval estimates of P_q for those periods are 0.15-0.41, 0.42-0.82 and 0.75-1.0.

収録刊行物

• 地震　第２輯

  地震　第２輯 56 (4), 327-336, 2004

  公益社団法人 日本地震学会

キーワード

• probabilistic prediction
• characteristic earthquake
• Miyagi-oki earthquake
• lognormal distribution
• Bayesian approach

詳細情報

• CRID: 1390282679282103936
• NII論文ID: 10012965209
• NII書誌ID: AN00305741
• DOI: 10.4294/zisin1948.56.4_327
• ISSN: 18839029
• ISSN: 2186599X
• ISSN: 00371114
• NDL書誌ID: 7000734
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7000734
• Web Site: https://www.jstage.jst.go.jp/article/zisin1948/56/4/56_4_327/_pdf
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