We introduce the cumulative-distribution-based area metric (AM)—also known as stochastic AM—as a scoring metric for earthquake ground-motion models (GMMs). The AM quantitatively informs the user of the degree to which observed or test data fit with a given model, providing a rankable absolute measure of misfit. The AM considers underlying data distributions and model uncertainties without any assumption of form. We apply this metric, along with existing testing methods, to four GMMs in order to test their performance using earthquake ground-motion data from the Preston New Road (United Kingdom) induced seismicity sequences in 2018 and 2019. An advantage of the proposed approach is its applicability to sparse datasets. We, therefore, focus on the ranking of models for discrete ranges of magnitude and distance, some of which have few data points. The variable performance of models in different ranges of the data reveals the importance of considering alternative models. We extend the ranking of GMMs through analysis of intermodel variations of the candidate models over different ranges of magnitude and distance using the AM. We find the intermodel AM can be a useful tool for selection of models for the logic-tree framework in seismic-hazard analysis. Overall, the AM is shown to be efficient and robust in the process of selection and ranking of GMMs for various applications, particularly for sparse and small-sized datasets.
<p>The selection and ranking of&#160; Ground Motion Models (GMMs) for scenario earthquakes is a crucial element in seismic hazard analysis. Typically model testing and ranking do not appropriately account for uncertainties, thus leading to improper ranking. We introduce the stochastic area metric (AM) as a scoring metric for GMMs, which not only informs the analyst of the degree to which observed or test data fit the model but also considers the uncertainties without the assumption of how data are distributed. The AM can be used as a scoring metric or cost function, whose minimum value identifies the model that best fits a given dataset. We apply this metric along with existing testing methods to recent and commonly used European ground motion prediction equations: Bindi et al. (2014, B014), Akkar et al. (2014, A014) and Cauzzi et al. (2015, C015). The GMMs are ranked and their performance analysed against the European Engineering Strong Motion (ESM) dataset. We focus on the ranking of models for ranges of magnitude and distance with sparse data, which pose a specific problem with other statistical testing methods. The performance of models over different ranges of magnitude and distance were analysed using AM, revealing the importance of considering different models for specific applications (e.g., tectonic, induced). We find the A014 model displays good performance with complete dataset while B014 appears to be best for small magnitudes and distances. In addition, we calibrated GMMs derived from a compendium of data and generated a suite of models for the given region through an optimisation technique utilising the concept of AM and ground motion variability. This novel framework for ranking and calibration guides the informed selection of models and helps develop regionally adjusted and application-specific GMMs for better prediction.&#160;</p><p>&#160;</p>
An optimization-based calibration technique, using the area metric, is applied to determine the input parameters of a stochastic earthquake-waveform simulation method. The calibration algorithm updates a model prior, specifically an estimate of a region’s seismological (source, path and site) parameters, typically developed using waveform data, or existing models, from a wide range of sources. In the absence of calibration, this can result in overestimates of a target region’s ground-motion variability, and in some cases, introduce biases. The proposed method simultaneously attains optimum estimates of the median, range and distribution (uncertainty) of these seismological parameters, and resultant ground motions, for a specific target region, through calibration of physically-constrained parametric models to local ground motion data. We apply the method to Italy, a region of moderate seismicity, using response spectra recorded in the European Strong Motion (ESM) dataset. As a prior, we utilise independent seismological models developed using strong-motion data across a wider European context. The calibration obtains values of each seismological parameter considered (such as, but not limited to, quality factor, geometrical spreading and stress drop), to develop suits of optimal parameters for locally adjusted stochastic ground motion simulation. We consider both the epistemic and aleatory variability associated with the calibration process. We were able to reduce the area metric (misfit) value by up to 88% for the simulations using updated parameters, compared to the initial prior. This framework for the calibration and updating of seismological models can help achieve robust and transparent regionally adjusted estimates of ground motion, and to consider epistemic uncertainty through correlated parameters.
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