Bayesian analysis on earthquake magnitude related to an active fault in Taiwan

https://doi.org/10.1016/j.soildyn.2015.03.025Get rights and content

Highlights

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    Bayesian analysis on earthquake magnitude related to a high-risk active fault in Taiwan.

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    Using prior data to compensate limited observation.

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    New Bayesian algorithms are given in detail.

Abstract

It is understood that sample size could be an issue in earthquake statistical studies, causing the best estimate being too deterministic or less representative derived from limited statistics from observation. Like many Bayesian analyses and estimates, this study shows another novel application of the Bayesian approach to earthquake engineering, using prior data to help compensate the limited observation for the target problem to estimate the magnitude of the recurring Meishan earthquake in central Taiwan. With the Bayesian algorithms developed, the Bayesian analysis suggests that the next major event induced by the Meishan fault in central Taiwan should be in Mw 6.44±0.33, based on one magnitude observation of Mw 6.4 from the last event, along with the prior data including fault length of 14 km, rupture width of 15 km, rupture area of 216 km2, average displacement of 0.7 m, slip rate of 6 mm/yr, and five earthquake empirical models.

Introduction

The region around Taiwan is known for high seismicity, not to mention a catastrophic event like the Mw 7.6 Chi–Chi earthquake could recur in decades [1]. Recently, there are studies suggesting that the return period of a major earthquake induced by the Meishan fault in central Taiwan might be as short as 160 years, not to mention the very last Meishan earthquake in 1906 was occurring more than one hundred years ago. Under the circumstances, the risk of the active fault inducing a major earthquake in near future is considered relatively high, and the subject has been discussed in several recent studies [2], [3]. Therefore, from a different perspective with new methodology, the target problem of this study is to evaluate the magnitude of the next Meishan earthquake in central Taiwan that could occur in near future given its short return period. More introductions to the background of the Meishan fault in central Taiwan are given in one of the following sections.

One possibility to evaluate such a problem is via statistical study. But on the other hand, it is understood that sample size is important to statistical assessments and inferences. For example, given an active fault is known for inducing a major earthquake in Mw 6.5 (moment magnitude), a best estimate on the magnitude of the next recurrence will be exactly the same size as the observation, although it is less representative based on one magnitude observation only. Unfortunately, this is the same situation for the target problem of the study, aiming to evaluate the magnitude of the next Meishan earthquake but with only one magnitude observation available for the analysis.

In contrast to statistics-based methods, the Bayesian inference is a relatively new approach that is more useful for evaluating a problem with very limited observations. Basically, the Bayesian approach is to use other sources of data to compensate limited statistics, helping develop a new Bayesian estimate by integrating multiple sources/types of data, usually referred to as prior and observation.

The Bayesian approach has been increasingly applied to many different studies to develop a new estimate from multiple sources of data e.g., [4], [5], [6]. In earthquake engineering and engineering seismology, an early study can be dated back to the 1960s [7], introducing the framework of the Bayesian calculation for seismology research. More recently, several other Bayesian methods for earthquake studies were reported, such as the application to earthquake early warning [8], [9], tectonic stress evaluation [10], and earthquake catalog characterizations [11], among others [12], [14].

Although many different applications were reported, the underlying motivation of the Bayesian studies is the same: Integrating multiple sources/types of data to evaluate or re-evaluate a problem, rather than only relying on (limited) statistics from observation. Take those studies above for example, the framework of Bayesian earthquake early warning is to utilize some empirical models to compensate the limited data at the initial stage of earthquake, for estimating its magnitude and location more reliably on a real-time basis [8], [9]. On the other hand, a Bayesian algorithm [11] to evaluate the completeness magnitude (Mc) of an earthquake catalog is facilitated with the prior data in proximity regions, then integrated with the locally observed seismicity. Note that such a Bayesian calculation is similar to a later application to estimate earthquake rates (or frequencies) around a study area, also using the data from proximity areas as priors [14]. Other recent Bayesian applications to earthquake studies include the probability assessment on earthquake-induced landslides [31], evaluation of the source parameters of a major earthquake [32], and structure safety analysis under earthquake condition [33]. Similarly, new Bayesian methods are increasingly developed for other problems [34], [35], [36].

As a result, given the short return period reported, the key scope of the study is to evaluate the magnitude of the next major earthquake induced by the Meishan fault in central Taiwan, on the basis of a novel Bayesian calculation integrating multiple sources/types of data to compensate the lack of adequate statistics from observation. In this study, we first derived a new Bayesian algorithm for evaluating earthquake magnitude distributions related to an active fault, based on both observational and prior data. Next, we applied the methodology to the target problem, showing there should be a 10% probability for the next Meishan earthquake in central Taiwan to exceed Mw 6.9, considering one magnitude observation of Mw 6.4 from the last Meishan earthquake, and the prior data including fault length of 14 km, rupture width of 15 km, rupture area of 216 km2, average displacement of 0.7 m, slip rate of 6 mm/yr, and five earthquake empirical models.

The paper is organized with an overview of the Bayesian approach, followed by the introductions to the Meishan fault in central Taiwan. Next, the observation and prior data for this Bayesian study were introduced and summarized, followed by the developments of the new Bayesian algorithm, and the Bayesian inference to the magnitude of the next Meishan earthquake from the multiple sources/types of data.

Section snippets

The algorithm

As mentioned previously, the Bayesian approach is to integrate prior information with (limited) observation to develop a new estimate, which is different from the one relying on samples or statistics only. To further illustrate the method, we summarized an example from the literature as follows [15]: Fig. 1a shows the prior information or the so-called prior probability mass function about the accident at a given cross road, suggesting the mean rate equal to two accidents per year. It is worth

Overview of the Meishan fault

The region around Taiwan located in the boundary of three tectonic plates is known for high seismicity. Especially after the infamous Mw 7.6 Chi–Chi earthquake in 1999, the Central Geological Survey Taiwan launched a comprehensive investigation on active faults in Taiwan [16], [17], and periodically updated the findings from the research. For example, the Central Geological Survey Taiwan reported their best-estimate return period as 160 years for a major earthquake (like the Meishan earthquake

Estimating earthquake magnitude with the empirical models

Before introducing the new Bayesian analysis, two conventional estimates based on the fault data and empirical relationships are given in the following: (1) the deterministic approach neglecting model error, and (2) the probabilistic approach considering model error. Understandably, the two estimates are irrelevant to the statistics from observation.

The algorithms

In contrast to the two estimates above, this section would like to show how to apply the Bayesian approach to merge the limited observation with the prior data in this study, developing a new estimate for the target problem given limited statistics from observation are only available.

As many Bayesian studies e.g., [4], [6], [14], we also assigned a “diffuse” prior to each of the five scenarios; that is, without further support, we considered each scenario has an equal probability, leading to a

Robustness of the methodology

Understandably, the Bayesian algorithm of this study from the well-established Bayesian approach is by all means transparent and robust, like those Bayesian studies summarized in the paper. For example, the Bayesian calculations for earthquake catalog characterizations are applicable to any databases, although the method was only applied to the seismicity around Taiwan as a demonstration in that paper [11]. Similarly, another Bayesian application to the calculations of “b-value” (i.e., a

Summary and conclusion

Taiwan is known for high seismicity; in particular, the Meishan fault in central Taiwan with a relative short earthquake return period should be “dangerous” to the surrounding areas. As a result, this study is aimed at estimating the magnitude of the Meishan earthquake that could recur in near future, given a best-estimate return period of the event as short as 160 years.

However, with only one magnitude observation from the last Meishan earthquake in 1906, the estimate is not representative

Acknowledgements

We appreciate the comments and suggestions from Editor and reviewers making this submission much improved in so many aspects. The author would also like to thank the Hong Kong University of Science and Technology for the financial support on the study (Grant FSGRF12EG49).

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