Bayesian hierarchical model for variations in earthquake peak ground acceleration within small-aperture arrays

2018 ◽  
Vol 29 (3) ◽  
pp. e2497 ◽  
Author(s):  
Sahar Rahpeyma ◽  
Benedikt Halldorsson ◽  
Birgir Hrafnkelsson ◽  
Sigurjón Jónsson
Keyword(s):  
Hierarchical Model ◽  
Peak Ground Acceleration ◽  
Bayesian Hierarchical Model ◽  
Ground Acceleration ◽  
Small Aperture ◽  
Bayesian Hierarchical ◽  
Aperture Arrays

scholarly journals Frequency-dependent site factors for the Icelandic strong-motion array from a Bayesian hierarchical model of the spatial distribution of spectral accelerations

2021 ◽  
pp. 875529302110369
Author(s):  
Sahar Rahpeyma ◽  
Benedikt Halldorsson ◽  
Birgir Hrafnkelsson ◽  
Sigurjón Jónsson
Keyword(s):  
Ground Motion ◽  
Hierarchical Model ◽  
Response Spectrum ◽  
Ground Motions ◽  
Strong Motion ◽  
Bayesian Hierarchical Model ◽  
Site Factors ◽  
Ground Acceleration ◽  
Small Aperture ◽  
Bayesian Hierarchical

The earthquake ground motions of over 1700 earthquakes recorded on a small-aperture strong-motion array in south Iceland (ICEARRAY I) that is situated on a relatively uniform site condition characterized as rock, exhibit a statistically significant spatial variation of ground-motion amplitudes across the array. Both earthquake and microseismic horizontal-to-vertical spectral ratios (HVSR) have been shown to exhibit distinct and in some cases, bimodal peaks in amplification, indicating site resonance at periods of 0.1–0.3 s, a phenomenon that has been attributed to a surface layer of lava rock lying above a sedimentary layer, a structure that is then repeated with depth under the array. In this study, we implement a Bayesian hierarchical model (BHM) of the seismic ground motions that partitions the model residuals into earthquake event term, station term, and event–station term. We analyzed and compared peak ground acceleration (PGA) with the 5% damped pseudo-acceleration response spectrum (PSA) at oscillator periods of T = 0.05–1.0 s. The results show that the event terms, dominate the total variability of the ground-motion amplitudes over the array. However, the station terms are shown to increase in the period range of 0.1–0.3 s on most stations and to different extents, leading to an increase in the overall variability of ground motions at those periods, captured by a larger inter-station standard deviation. As the station terms are a measure of how much the ground motions at those stations deviate from the array average, they act as proxies for localized site effects and amplification factors. These results, improve our understanding of the key factors that affect the variation of seismic ground motions across the relatively small area of ICEARRAY I. This approach can help to improve the accuracy of earthquake hazard assessments on local scales, which in turn could contribute to more refined seismic risk assessments and engineering decision-making.

scholarly journals Measuring spatial allocative efficiency in basketball

2020 ◽  
Vol 16 (4) ◽  
pp. 271-289
Author(s):  
Nathan Sandholtz ◽  
Jacob Mortensen ◽  
Luke Bornn
Keyword(s):  
Spatial Distribution ◽  
Hierarchical Model ◽  
Opportunity Cost ◽  
Allocative Efficiency ◽  
Bayesian Hierarchical Model ◽  
National Basketball Association ◽  
Spatial Context ◽  
Bayesian Hierarchical ◽  
The Impact

AbstractEvery shot in basketball has an opportunity cost; one player’s shot eliminates all potential opportunities from their teammates for that play. For this reason, player-shot efficiency should ultimately be considered relative to the lineup. This aspect of efficiency—the optimal way to allocate shots within a lineup—is the focus of our paper. Allocative efficiency should be considered in a spatial context since the distribution of shot attempts within a lineup is highly dependent on court location. We propose a new metric for spatial allocative efficiency by comparing a player’s field goal percentage (FG%) to their field goal attempt (FGA) rate in context of both their four teammates on the court and the spatial distribution of their shots. Leveraging publicly available data provided by the National Basketball Association (NBA), we estimate player FG% at every location in the offensive half court using a Bayesian hierarchical model. Then, by ordering a lineup’s estimated FG%s and pairing these rankings with the lineup’s empirical FGA rate rankings, we detect areas where the lineup exhibits inefficient shot allocation. Lastly, we analyze the impact that sub-optimal shot allocation has on a team’s overall offensive potential, demonstrating that inefficient shot allocation correlates with reduced scoring.

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