A proposed probabilistic seismic tsunami hazard analysis methodology

Since the mid-1980s, there has been accumulating geologic evidence of large local tsunamis generated by earthquakes along the Cascadia subduction zone off the Pacific Northwest. Information from recent geophysical and geological investigations constrains the potential rupture-zone geometry and average repeat time of interplate thrust earthquakes. Based on this information, tsunami hazard maps have been prepared for coastal communities in the Pacific Northwest using sophisticated numerical models to simulate tsunami propagation and inundation. In this study, sources of uncertainty in tsunami hazard calculations are described and a probabilistic hazard analysis for tsunamis, similar to probabilistic seismic hazard analysis (PSHA), is outlined. Though probabilistic tsunami hazard analysis (PTHA) shares many similarities with PSHA, there are specific issues unique to tsunami hazards that need to be accounted for in the probability calculations. For example, the possibility of rupture along splay faults from the Cascadia interplate thrust have a large effect on tsunami generation, but a relatively small impact on peak ground accelerations onshore. The largest sources of uncertainty include the average slip and downdip extent of rupture. Also, it is demonstrated that significant variations in nearshore tsunami amplitude are caused by uncertainty in slip distribution patterns. Correct identification of uncertainties related to tsunami generation and propagation is critical in performing the probability calculations. PTHA has the potential to provide an improved technique for evaluating local tsunami hazards in the Pacific Northwest and elsewhere.

This study applies the unit tsunami method and probabilistic tsunami hazard analysis to investigate the tsunami hazard for the southern region of Pingtung County in southern Taiwan. The FUNWAVE-TVD model is used to calculate the aleatory and epistemic uncertainties. The aleatory uncertainty is analyzed using a comparison of simulated and observed maximum tsunami wave heights and the epistemic uncertainty is evaluated using a scenario caused by earthquakes in the Manila and Ryukyu subduction zones according to probabilistic seismic hazard analysis in Taiwan using Senior Seismic Hazard Analysis Committee Level 3 methodology. A unit tsunami method database is established for the Manila and Ryukyu subduction zones and used to carry out a probability-based offshore tsunami wave height simulation for the southern region of Pingtung County. A hazard map for tsunamis caused by earthquakes in the Manila and Ryukyu subduction zones is also derived.

One of the major challenges in probabilistic seismic hazard analysis (PSHA) studies, particularly for risk-based decision-making, is to constrain epistemic uncertainties. Epistemic uncertainty associated with ground-motion characterization (GMC) models exerts a strong influence on the hazard estimate for a given target level of ground shaking. In the Indian context (mainly along the Himalayan arc), constraining epistemic uncertainty is a significant challenge owing to the lack of recorded data. This study investigates the epistemic uncertainty associated with ground-motion models (GMMs) considered appropriate for the Himalayan region. First, a review of GMMs considered applicable to the Himalayan region is provided. Subsequently, a graphical comparison of median models is performed, followed by residual and statistical analysis. The evaluation utilizes observations from a recently compiled strong-motion dataset across the Himalayas and Indo-Gangetic plains of northern India. The dataset comprises 519 acceleration traces from 150 events in the moment magnitude (Mw) range Mw 3–7.4, recorded at epicentral distances in the range REpi<300 km. The analysis demonstrates significant between-model variability, particularly with regard to median magnitude and distance scaling. The residual analysis also indicates a large bias and aleatory uncertainty. Moreover, some of the GMMs exhibit trends with distance and magnitude. Overall, our evaluation analysis shows that there is clearly significant aleatory and epistemic uncertainty associated with the GMC modeling owing to the paucity of recorded data. The range of epistemic uncertainty represented by the GMMs (available in the literature) is much larger than that typically captured by the (multiple) global models often used in PSHA studies across India.

Evaluation of tsunami disaster risk for a coastal region requires reliable estimation of tsunami hazard, for example, wave amplitude close to the shore. Observed tsunami data are scarce and have poor spatial coverage, and for this reason probabilistic tsunami hazard analysis (PTHA) traditionally relies on numerical simulation of “synthetic” tsunami generation and propagation toward the coast. Such an approach has been extensively studied in the past and it is widely recognized as an important disaster‐risk mitigation tool. PTHA can not only provide less uncertain and spatially coherent hazard estimates in comparison with classical empirical data analysis which is restricted at the tide gauge stations, but also local inundation information. In this paper, we explore a purely statistical alternative to traditional PTHA for evaluation of tsunami amplitude hazard. Here, we use tide gauge measurements of tsunami amplitude along the western United States, specifically California and Oregon, and develop a spatial Bayesian hierarchical model (BHM) to assess tsunami hazard from far‐field earthquake sources at various recurrence intervals. The configuration of our model incorporates latent Gaussian fields that utilize information on the distance between tide gauges as well as on the continental shelf width, that is, a covariate linked to potential dissipative effects on wave energy as the tsunami travels over shallow water. Through our BHM, we produce spatially continuous probabilistic maps of far‐field tsunami hazard which can aid comprehensive tsunami disaster risk reduction and management.

The study on epistemic uncertainty due to the lack of knowledge has received increasing attention in risk assessment, reliability analysis, decision making, and design optimization. Different theories have been applied to model and quantify epistemic uncertainty. Research on sensitivity analysis for epistemic uncertainty has also been initialized. Sensitivity analysis can identify the contributions of individual input variables with epistemic uncertainty to the model output. It then helps guide the collection of more information to reduce the effect of epistemic uncertainty. In this paper, an effective sensitivity analysis method for epistemic uncertainty is proposed when both epistemic and aleatory uncertainties exist in model inputs. This method employs the unified uncertainty analysis framework to calculate the plausibility and belief measures. The gap between belief and plausibility measures is used as an indicator of the effect of epistemic uncertainty on the model output. The Kolmogorov-Smirnov distance between the two measures is used to quantify the main effect and the total effect of each independent variable with epistemic uncertainty. By the Kolmogorov-Smirnov distance, the importance of each variable is ranked. The feasibility and effectiveness of the proposed method is demonstrated with two engineering examples.

The design of engineering systems is often based on analysis models with substantial errors in predicting failures, that is epistemic uncertainty. The epistemic uncertainty is reduced by post design tests, and the safety of unsafe designs restored by redesign. When this process of design, test and redesign is to be based on probabilistic analysis, there is some controversy on whether uncertainty associated with variability (aleatory uncertainty) should be treated differently than the epistemic uncertainty. In this paper we compare several approaches to design and redesign and treatments of the epistemic uncertainties. These include safety factors, probabilistic approach disregarding redesign and regarding redesign, treating epistemic uncertainty and aleatory uncertainty the same, and more conservative treatment of the epistemic uncertainty. We demonstrate that the proposed approach can allow tradeoff of system performance against development cost (probability of redesign), while a standard reliability based design optimization, which does not take into account future redesign, provides only a single point on the tradeoff curve. We also show that the tradeoff can be achieved even with the traditional safety factor approach, without any probabilistic optimization. Furthermore, we investigate different treatments of epistemic error for probability of failure calculation. We find that it is possible to design to the 95th percentile of the probability of failure with modest mass penalty compared to treating epistemic and aleatory uncertainty alike.

In practical engineering design, most data sets for system uncertainties are insufficiently sampled from un- known statistical distributions, known as epistemic uncer- tainty. Existing methods in uncertainty-based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, reliability-based design optimization (RBDO) is integrated with Bayes theorem. It is referred to as Bayesian RBDO. However, Bayesian RBDO becomes extremely expensive when employing the first- or second-order reliability method (FORM/SORM) for reliability predictions. Thus, this paper proposes development of Bayesian RBDO methodology and its integration to a numerical solver, the eigenvector dimension reduction (EDR) method, for Bayesian reliabil- ity analysis. The EDR method takes a sensitivity-free approach for reliability analysis so that it is very efficient and accurate compared with other reliability methods such as FORM/SORM. Efficiency and accuracy of the Bayesian RBDO process are substantially improved after this integration.

Makran subduction zone, along the southern coasts of Iran and Pakistan, has a wide potential seismogenic zone and may be capable of generating large magnitude (M ~ 9) tsunamigenic earthquakes. Considering ambiguities exist in tsunamigenic source characterization for subduction megathrusts like Makran, where detailed geologic, seismic, and geodetic data are insufficient, the probabilistic tsunami hazard analysis (PTHA) is the most prevalent approach to handle uncertainties and estimate more reliable tsunami hazard. Here, PTHA is performed for the coastal region of the western Makran, south-eastern Iran. Using the logic tree approach, we have considered the uncertainty of maximum seismic magnitude, earthquake occurrence model, continuity of seismic zone, seismic coupling coefficient, rupture depth, presence or absence of splay faults, fault locations, and fault slip distribution in PTHA calculation for the western Makran region. We have derived uniform tsunami hazard maps for two return periods of 475 and 2475 years for two confidence levels, the mean and the 84th percentile. Ground subsidence effects are also evaluated in a probabilistic manner. According to the PTHA results, Chabahar and Sirik towns are at the highest and lowest tsunami risk, respectively.

An honest communication of uncertainty about quantities of interest enhances transparency in scientific assessments. To support this communication, risk assessors should choose appropriate ways to evaluate and characterize epistemic uncertainty. A full treatment of uncertainty requires methods that distinguish aleatory from epistemic uncertainty. Quantitative expressions for epistemic uncertainty are advantageous in scientific assessments because they are nonambiguous and enable individual uncertainties to be characterized and combined in a systematic way. Since 2019, the European Food Safety Authority (EFSA) recommends assessors to express epistemic uncertainty in conclusions of scientific assessments quantitatively by subjective probability. A subjective probability can be used to represent an expert judgment, which may or may not be updated using Bayes's rule to integrate evidence available for the assessment and could be either precise or approximate. Approximate (or bounded) probabilities may be enough for decision making and allow experts to reach agreement on certainty when they struggle to specify precise subjective probabilities. The difference between the lower and upper bound on a subjective probability can also be used to reflect someone's strength of knowledge. In this article, we demonstrate how to quantify uncertainty by bounded probability, and explicitly distinguish between epistemic and aleatory uncertainty, by means of robust Bayesian analysis, including standard Bayesian analysis through precise probability as a special case. For illustration, the two analyses are applied to an intake assessment.

Aiming at providing more accurate information for the first restoration, overhaul and maintenance of airborne products, this paper gives a calendar life assessment method for airborne products considering epistemic and aleatory uncertainty on the basis of investigation and analysis for the factors which affect the uncertainty of calendar life assessment. The uncertainty of calendar life is modeled as two types: epistemic uncertainty and aleatory uncertainty. a aleatory uncertainty model of calendar life based on interval analysis and blind number theory is given with parameter sensitivity analysis. Considering the designer's problem of incomplete cognition of failure mechanism, a measurement method of epistemic uncertainty is given based on the concept of confidence reliability.

A novel method for importance measure analysis in the presence of epistemic and aleatory uncertainties

We develop a novel framework of time-dependent probabilistic tsunami hazard analysis (PTHA) and apply it to Western Sumatra, Indonesia, where future tsunamigenic events are anticipated in the Mentawai region of the Sunda subduction zone. An earthquake rupture model taking into account the spatiotemporal interaction of major megathrust segments is used to simulate future tsunamigenic earthquakes. The earthquake rupture process of the segments is characterized by a multivariate Bernoulli model with interarrival times following a Brownian passage‐time distribution and the dependency between segments specified by a spatial correlation function. We calibrate this model with historical ruptures of the Mentawai thrust in the last 450 years. A total of ≥ 100,000 time-dependent earthquake rupture cases are then coupled with a stochastic tsunami simulation method to evaluate tsunami hazards. We generate a total of 6,300 stochastic tsunami source models from six magnitude scenarios between M 7.75 and M 9.0 and obtain time-dependent PTHA results for seven different periods (1, 5, 10, 20, 30, 50 and 450 years). We further compare the time-dependent PTHA results with a time-independent PTHA approach to investigate the influence of the spatiotemporal earthquake rupture model. The space-time interaction model successfully generates annual seismic moment rates consistent with the observations. Moreover, the model can capture the uncertainty of future time-dependent tsunami hazards. On the other hand, the time-independent approach produces slightly higher hazard estimates than the time-dependent model for long-term hazard assessments (> 450 years).

Tsunamis are multiscale phenomena resulting from a water column displacement that may be induced by multiple sources, and range from local scale inundation processes to ocean-wide scale wave propagation. Different strategies may be required to model tsunami evolution at different scales and to characterize various intensity measures. Research in tsunami hazard and risk has focused mostly on the tsunami effects such as the wave heights or flow depths. This chapter reviews the evolution of tsunami hazard and risk assessment methodologies, with particular emphasis on the development of probabilistic approaches. Building on advances in numerical modeling and uncertainty analysis, two main frameworks for Probabilistic Tsunami Hazard and Risk Analysis (PTHA/PTRA) are described. Framework 1 (FW1) focuses on quantitative methods, including fully simulation-based assessments (FW1A), integration of hazard with vulnerability and loss models (FW1B), consideration of dynamic processes such as tidal and sea-level variations (FW1C), and approaches using limited scenario sets (FW1D). Framework 2 (FW2) complements this by incorporating indicator-based vulnerability assessments, both physical (FW2A) and social, multi-dimensional (FW2B).

Key Points Methods are provided to quantify information and uncertainty in data Best achievable model performance for a given data set is estimated Model adequacy is characterized in terms of Aleatory and Epistemic Uncertainties

An approach to combining unreliable pieces of evidence and their propagation in a system response analysis