Abstract This study presents an innovative probabilistic tsunami inundation assessment for an earthquake scenario to randomly generate tsunami inundation depth distributions by quantitatively evaluating the spatial correlation of tsunami inundation depths using singular value decomposition (SVD) derived from proper orthogonal decomposition and to evaluate the tsunami inundation depths considering the imminent occurrence of an earthquake. We found a good agreement between the evaluation results of the proposed surrogate model and the numerical results of the nonlinear long wave equations for the tsunami inundation depth distribution in Kamakura city, Japan, due to the Sagami Trough megathrust earthquake. Evaluating the spatial correlation using SVD has the advantage that the covariance matrix does not need to be defined in advance but can be defined from the data itself. We also achieved a significant reduction in the number of required tsunami propagation simulations for the probabilistic assessment and attained higher computational efficiency by extracting spatial correlations with SVD. Furthermore, we conducted a probabilistic tsunami inundation assessment focusing on a relatively short period (i.e., 50 years) considering the time‐dependent occurrence probability of the target earthquake. The proposed probabilistic assessment method with mode decomposition is applicable to the general probabilistic tsunami hazard assessment by integrating it with physical stochastic slip models.
Abstract. It is necessary to consider simultaneous damage to multiple buildings when performing probabilistic risk assessment for a portfolio of buildings. In this study, we demonstrate tsunami risk assessment for two buildings using copulas of tsunami hazards that consider the nonlinear spatial correlation of tsunami wave heights. First, we simulated the wave heights considering uncertainty by varying the slip amount and fault depths. The frequency distributions of the wave heights were evaluated via the response surface method. Based on the distributions and numerically simulated wave heights, we estimated the optimal copula via maximum likelihood estimation. Subsequently, we evaluated the simultaneous distributions of the wave heights and the aggregate damage probabilities via the marginal distributions and the estimated copulas. As a result, the aggregate damage probability of the ninety-ninth percentile value was approximately 1.0 % higher and the maximum value was approximately 3.0 % higher while considering the wave height correlation. We clearly showed that the usefulness of copula modeling considering the wave height correlation in evaluating risk of building portfolio. We only demonstrated the evaluation method for two buildings, but the effect of the wave height correlation on the results is expected to increase if more points are targeted.
Abstract. It is necessary to evaluate aggregate damage probability to multiple buildings when performing probabilistic risk assessment for the buildings. The purpose of this study is to demonstrate a method of tsunami hazard and risk assessment for two buildings far away from each other, using copulas of tsunami hazards that consider the nonlinear spatial correlation of tsunami wave heights. First, we simulated the wave heights considering uncertainty by varying the slip amount and fault depths. The frequency distributions of the wave heights were evaluated via the response surface method. Based on the distributions and numerically simulated wave heights, we estimated the optimal copula via maximum likelihood estimation. Subsequently, we evaluated the joint distributions of the wave heights and the aggregate damage probabilities via the marginal distributions and the estimated copulas. As a result, the aggregate damage probability of the 99th percentile value was approximately 1.0 % higher and the maximum value was approximately 3.0 % higher while considering the wave height correlation. We clearly showed the usefulness of copula modeling considering the wave height correlation in evaluating the probabilistic risk of multiple buildings. We only demonstrated the risk evaluation method for two buildings, but the effect of the wave height correlation on the results is expected to increase if more points are targeted.
We created a fault model with a Tohoku-type earthquake fault zone having a random slip distribution and performed stochastic tsunami hazard analysis using a logic tree. When the stochastic tsunami hazard analysis results and the Tohoku earthquake observation results were compared, the observation results of a GPS wave gauge off the southern Iwate coast indicated a return period equivalent to approximately 1,709 years (0.50 fractile), and the observation results of a GPS wave gauge off the shore of Fukushima Prefecture indicated a return period of 600 years (0.50 fractile). Analysis of the influence of the number of slip distribution patterns on the results of the stochastic tsunami hazard analysis showed that the number of slip distribution patterns considered greatly influenced the results of the hazard analysis for a relatively large wave height. When the 90 % confidence interval and coefficient of variation of tsunami wave height were defined as an index for projecting the uncertainty of tsunami wave height, the 90 % confidence interval was typically high in locations where the wave height of each fractile point was high. At a location offshore of the Boso Peninsula of Chiba Prefecture where the coefficient of variation reached the maximum, it was confirmed that variations in maximum wave height due to differences in slip distribution of the fault zone contributed to the coefficient of variation being large.
Abstract Probabilistic tsunami inundation assessment ordinarily requires many inundation simulations that consider various uncertainties; thus, the computational cost is very high. In recent years, active research has been conducted to reduce the computational cost. In this study, we successfully reduced the number of random tsunami sources to 20% of the original numbers by applying proper orthogonal decomposition (POD) to tsunami inundation depth distributions obtained from random tsunami sources. Additionally, we stochastically treated the failure degree of seawalls and incorporated its impact into the evaluation model for tsunami inundation hazard because the failure degree of seawalls has a significant impact on the tsunami inundation depth assessment for land areas. Although the randomness of the slip distribution in tsunami sources has been studied extensively in the past, the idea of simultaneously modelling the failure degree of seawalls is an outstanding feature of this study. Finally, we developed tsunami inundation distribution maps to represent the probability of occurrence of inundation depth for the next 50 years and 10 years by using a number of tsunami inundation distributions that consider the randomness of the tsunami sources and the failure probability of the seawalls.
