基於脆弱性函數之地震經濟損失機率估計：以2024年能登半島地震為例

Abstract

既有關於日本地震損失估計的研究，多以震度等級對應固定損壞率的方式進行推估。這種方法有助於災後快速掌握初步損失規模，但在處理損壞率的不確定性，或將經濟損失表示為機率分布時，仍有其限制。基於此，本論文導入機率式脆弱性函數，嘗試改進災後地震損失估計方法，並以2024年1月能登半島地震作為實證應用案例。 本文以2024年能登半島地震的受災區域為研究對象，分析範圍主要涵蓋石川縣、富山縣與新潟縣。在地震危害方面，本文採用日本氣象廳震度，並使用依地震動加速度換算而得的連續近似震度值，以呈現地震動強度。暴露量部分則以市町村層級的資本存量表示，並將全國及縣層級的資本存量分配至六類資產，包括住宅、非住宅建築、電力、瓦斯與自來水等公用事業、港灣、港灣以外之社會基礎設施，以及其他社會資本。上述資本存量的分配，主要依據戶數、從業人數、基礎設施相關指標與設施位置等行政統計資料進行推估。 在脆弱性函數的建構上，本文分別處理住宅與非住宅資產。住宅資產部分，本文利用觀測到的損壞率資料估計probit迴歸模型，並將地震動強度、1981年建築基準修正前後之木造住宅比例，以及是否位於沿海地區等因素納入分析。非住宅資產部分，則依據震度別損壞率設定，以probit函數近似各資產類別的損壞率曲線。經濟損失估計則是將市町村層級的資本存量暴露量，與各資產類別相對應的損壞率函數結合計算；此外，本文亦透過蒙地卡羅模擬，檢視估計結果所包含的不確定性。 估計結果顯示，研究區域的確定性點估計總損失為2.14兆日圓。蒙地卡羅模擬結果則顯示，總損失分布呈現正偏態，其中位數為2.05兆日圓，95%區間介於1.47兆至3.30兆日圓之間。若從機率分布觀察，總損失低於2兆日圓的機率為44.9%，而超過3兆日圓的機率為5.37%。整體而言，本文估計結果與既有地震損失估計研究大致一致；同時，機率式估計也能呈現單一確定性估計難以處理的不確定性與上尾風險。本文的分析可作為未來以機率式方法檢討地震損失估計的參考，並有助於改進日本災後快速經濟損失評估方法。

Previous seismic loss estimation studies in Japan have often relied on fixed damage-rate assumptions for each seismic intensity class. While this approach is useful for rapid estimation, it has limited ability to evaluate uncertainty in damage rates or express economic loss as a probabilistic distribution. This thesis aims to improve post-earthquake seismic loss estimation by introducing probabilistic vulnerability functions and applying them to the January 2024 Noto Peninsula Earthquake. The study area covers the affected area of the 2024 Noto Peninsula Earthquake, focusing on Ishikawa, Toyama, and Niigata Prefectures. Seismic hazard is represented by Japan Meteorological Agency seismic intensity and its continuous approximation based on ground acceleration. Capital stock is calculated as municipal-level exposure by allocating national and prefectural stock values to six asset categories: housing, nonresidential buildings, electricity/gas/water utilities, ports, social infrastructure excluding ports, and other social capital. The allocation uses administrative statistics such as households, employees, infrastructure indicators, and facility locations. Vulnerability functions are constructed separately for housing and non-housing assets. For housing, a probit regression model is estimated from observed damage-rate data, incorporating ground-motion intensity, wooden housing shares before and after the 1981 building code revision, and coastal location. For non-housing assets, asset-specific damage-rate curves are approximated using probit functions based on seismic-intensity damage-rate settings. Economic loss is estimated by combining municipal capital stock exposure with the corresponding damage-rate functions, and Monte Carlo simulation is conducted to examine uncertainty. The deterministic point estimate for the three-prefecture study area is 2.14 trillion yen. The Monte Carlo simulation showed a positively skewed distribution, with a median total loss of 2.051 trillion yen and a 95% interval ranging from 1.469 to 3.302 trillion yen. The probability that total loss remained below 2 trillion yen was 44.9%, while the probability of exceeding 3 trillion yen was 5.37%. These results are broadly consistent with previous seismic loss estimation studies, while also quantifying uncertainty and upper-tail risk that cannot be obtained from a deterministic estimate alone. These findings suggest that probabilistic vulnerability functions can extend conventional seismic loss estimation by adding information on uncertainty, supporting more informative post-earthquake economic loss assessment in Japan.