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Python is at the forefront of scientific computation for seismologists and therefore should be introduced to students interested in becoming seismologists. On its own, Python is open source and well designed with extensive libraries. However, Python code can also be executed, visualized, and communicated to others with "Jupyter Notebooks". Thus, Jupyter Notebooks are ideal for teaching students Python and scientific computation. In this article, we designed an openly available Python library and collection of Jupyter Notebooks based on defined scientific computation learning goals for seismology students. The Notebooks cover topics from an introduction to Python to organizing data, earthquake catalog statistics, linear regression, and making maps. Our Python library and collection of Jupyter Notebooks are meant to be used as course materials for an upper-division data analysis course in an Earth Science Department, and the materials were tested in a Probabilistic Seismic Hazard course. However, seismologists or anyone else who is interested in Python for data analysis and map making can use these materials.
The Seismic Hazard Inferred from Tectonics based on the Global Strain Rate Map (SHIFT_GSRM) earthquake forecast was designed to provide high-resolution estimates of global shallow seismicity to be used in seismic hazard assessment. This model combines geodetic strain rates with global earthquake parameters to characterize long-term rates of seismic moment and earthquake activity. Although SHIFT_GSRM properly computes seismicity rates in seismically active continental regions, it underestimates earthquake rates in subduction zones by an average factor of approximately 3. We present a complementary method to SHIFT_GSRM to more accurately forecast earthquake rates in 37 subduction segments, based on the conservation of moment principle and the use of regional interface seismicity parameters, such as subduction dip angles, corner magnitudes, and coupled seismogenic thicknesses. In seven progressive steps, we find that SHIFT_GSRM earthquake-rate underpredictions are mainly due to the utilization of a global probability function of seismic moment release that poorly captures the great variability among subduction megathrust interfaces. Retrospective test results show that the forecast is consistent with the observations during the 1 January 1977 to 31 December 2014 period. Moreover, successful pseudoprospective evaluations for the 1 January 2015 to 31 December 2018 period demonstrate the power of the regionalized earthquake model to properly estimate subduction-zone seismicity.
Ground-motion prediction equations (GMPE) are essential in probabilistic seismic hazard studies for estimating the ground motions generated by the seismic sources. In low-seismicity regions, only weak motions are available during the lifetime of accelerometric networks, and the equations selected for the probabilistic studies are usually models established from foreign data. Although most GMPEs have been developed for magnitudes 5 and above, the minimum magnitude often used in probabilistic studies in low-seismicity regions is smaller. Disaggregations have shown that, at return periods of engineering interest, magnitudes less than 5 may be contributing to the hazard. This paper presents the testing of several GMPEs selected in current international and national probabilistic projects against weak motions recorded in France (191 recordings with source-site distances up to 300 km, 3:8 <= M-w <= 4:5). The method is based on the log-likelihood value proposed by Scherbaum et al. (2009). The best-fitting models (approximately 2:5 <= LLH <= 3:5) over the whole frequency range are the Cauzzi and Faccioli (2008), Akkar and Bommer (2010), and Abrahamson and Silva (2008) models. No significant regional variation of ground motions is highlighted, and the magnitude scaling could be the predominant factor in the control of ground-motion amplitudes. Furthermore, we take advantage of a rich Japanese dataset to run tests on randomly selected low-magnitude subsets, and confirm that a dataset of similar to 190 observations, the same size as the French dataset, is large enough to obtain stable LLH estimates. Additionally we perform the tests against larger magnitudes (5-7) from the Japanese dataset. The ranking of models is partially modified, indicating a magnitude scaling effect for some of the models, and showing that extrapolating testing results obtained from low-magnitude ranges to higher magnitude ranges is not straightforward.
Ground‐motion prediction equations (GMPEs) are calibrated to predict the intensity of ground shaking at any given location, based on earthquake magnitude, source‐to‐site distance, local soil amplifications, and other parameters. GMPEs are generally assumed to be independent of time; however, evidence is increasing that large earthquakes modify the shallow soil conditions and those of the fault zone for months or years. These changes may affect the intensity of shaking and result in time‐dependent effects that can potentially be resolved by analyzing between‐event residuals (residuals between observed and predicted ground motion for individual earthquakes averaged over all stations). Here, we analyze a data set of about 65,000 recordings for about 1400 earthquakes in the moment magnitude range 2.5–6.5 that occurred in central Italy from 2008 to 2017 to capture the temporal variability of the ground shaking at high frequency. We first compute between‐event residuals for each earthquake in the Fourier domain with respect to a GMPE developed ad hoc for the analyzed data set. The between‐events show large changes after the occurrence of mainshocks such as the 2009 Mw 6.3 L'Aquila, the 2016 Mw 6.2 Amatrice, and Mw 6.5 Norcia earthquakes. Within the time span of a few months after the mainshocks, the between‐event contribution to the ground shaking varies by a factor 7. In particular, we find a large drop in the between‐events in the aftermath of the L'Aquila earthquake, followed by a slow positive trend that leads to a recovery interrupted by a new drop at the beginning of 2014. We also quantify the frequency‐dependent correlation between the Brune stress drop Δσ and the between‐events. We find that the temporal changes of Δσ resemble those of the between‐event residuals; in particular, during the period when the between‐events show the positive trend, the average logarithm of Δσ increases with an annual rate of 0.19 (i.e., the amplification factor for Δσ is 1.56 per year). Breakpoint analysis located a change in the linear trend coefficients of Δσ versus time in February 2014, although no large earthquakes occurred at that time. Finally, the temporal variability of Δσ mirrors the relative seismic‐velocity variations observed in previous studies for the same area and period, suggesting that both crack healing along the main fault system and healing of microcracks distributed at shallow depths throughout the surrounding region might be necessary to explain the wider observations of postearthquake recovery.
We present the results of a consistency check performed over the flatfile extracted from the engineering strong motion (ESM) database. The flatfile includes 23,014 recordings from 2179 earthquakes in the magnitude range from 3.5 to 7.8 that occurred since the 1970s in Europe and Middle East, as presented in the companion article by Lanzano et al. (Bull Earthq Eng, 2018a). The consistency check is developed by analyzing different residual distributions obtained from ad-hoc ground motion prediction equations for the absolute spectral acceleration (SA), displacement and Fourier amplitude spectra (FAS). Only recordings from earthquakes shallower than 40 km are considered in the analysis. The between-event, between-station and event-and-station corrected residuals are computed by applying a mixed-effect regression. We identified those earthquakes, stations, and recordings showing the largest deviations from the GMPE median predictions, and also evaluated the statistical uncertainty on the median model to get insights on the applicable magnitude–distance ranges and the usable period (or frequency) range. We observed that robust median predictions are obtained up to 8 s for SA and up to 20 Hz for FAS, although median predictions for Mw ≥ 7 show significantly larger uncertainties with ‘bumps’ starting above 5 s for SA and below 0.3 Hz for FAS. The between-station variance dominates over the other residual variances, and the dependence of the between-station residuals on logarithm of Vs30 is well-described by a piece-wise linear function with period-dependent slopes and hinge velocity around 580 m/s. Finally, we compared the between-event residuals obtained by considering two different sources of moment magnitude. The results show that, at long periods, the between-event terms from the two regressions have a weak correlation and the overall between-event variability is dissimilar, highlighting the importance of magnitude source in the regression results.
We derive a set of regional ground-motion prediction equations (GMPEs) in the Fourier amplitude spectra (FAS-GMPE) and in the spectral acceleration (SA-GMPE) domains for the purpose of interpreting the between-event residuals in terms of source parameter variability. We analyze a dataset of about 65,000 recordings generated by 1400 earthquakes (moment magnitude 2: 5 <= M-w <= 6: 5, hypocentral distance R-hypo <= 150 km) that occurred in central Italy between January 2008 and October 2017. In a companion article (Bindi, Spallarossa, et al., 2018), the nonparametric acceleration source spectra were interpreted in terms of omega-square models modified to account for deviations from a high-frequency flat plateau through a parameter named k(source). Here, the GMPEs are derived considering the moment (M-w), the local (M-L), and the energy (M-e) magnitude scales, and the between-event residuals are computed as random effects. We show that the between-event residuals for the FAS-GMPE implementing M-w are correlated with stress drop, with correlation coefficients increasing with increasing frequency up to about 10 Hz. Contrariwise, the correlation is weak for the FAS-GMPEs implementing M-L and M-e, in particular between 2 and 5 Hz, where most of the corner frequencies lie. At higher frequencies, all models show a strong correlation with k(source). The correlation with the source parameters reflects in a different behavior of the standard deviation tau of the between-event residuals with frequency. Although tau is smaller for the FAS-GMPE using M-w below 1.5 Hz, at higher frequencies, the model implementing either M-L or M-e shows smaller values, with a reduction of about 30% at 3 Hz (i.e., from 0.3 for M-w to 0.1 for M-L). We conclude that considering magnitude scales informative for the stress-drop variability allows to reduce the between-event variability with a significant impact on the hazard assessment, in particular for studies in which the ergodic assumption on site is removed.
In this study, we analyzed 10 yrs of seismicity in central Italy from 2008 to 2017, a period witnessing more than 1400 earthquakes in the magnitude range 2.5≤Mw≤6.5. The data set includes the main sequences that have occurred in the area, including those associated with the 2009 Mw 6.3 L'Aquila earthquake and the 2016–2017 sequence (Mw 6.2 Amatrice, Mw 6.1 Visso, and Mw 6.5 Norcia earthquakes). We calibrated a local magnitude scale, investigating the impact of changing the reference distance at which the nonparametric attenuation is tied to the zero‐magnitude attenuation function for southern California. We also developed an attenuation model to compute the radiated seismic energy (Es) from the time integral of the squared ground‐motion velocity. Seismic moment (M0) and stress drop (Δσ) were estimated for each earthquake by fitting a ω‐square model to the source spectra obtained by applying a nonparametric spectral inversion. The Δσ‐values vary over three orders of magnitude from about 0.1 to 10 MPa, the larger values associated with the mainshocks. The Δσ‐values describe a lognormal distribution with mean and standard deviation equal to log(Δσ)=(−0.25±0.45) (i.e., the mean Δσ is 0.57 MPa, with a 95% confidence interval from 0.08 to 4.79 MPa). The Δσ variability introduces a spread in the distribution of seismic energy versus moment, with differences in energy up two orders of magnitudes for earthquakes with the same moment. The variability in the high‐frequency spectral levels is captured by the local magnitude (ML), which scales with radiated energy as ML=(−1.59+0.52logEs) for logEs≤10.26 and ML=(−1.38+0.50logEs) otherwise. As the peak ground velocity increases with increasing Δσ, local and energy magnitudes perform better than moment magnitude as predictors for the shaking potential. The availability of different magnitude scales and source parameters for a large earthquake population will help characterize the between‐event ground‐motion variability in central Italy.
Logic trees are widely used in probabilistic seismic hazard analysis as a tool to capture the epistemic uncertainty associated with the seismogenic sources and the ground-motion prediction models used in estimating the hazard. Combining two or more ground-motion relations within a logic tree will generally require several conversions to be made, because there are several definitions available for both the predicted ground-motion parameters and the explanatory parameters within the predictive ground-motion relations. Procedures for making conversions for each of these factors are presented, using a suite of predictive equations in current use for illustration. The sensitivity of the resulting ground-motion models to these conversions is shown to be pronounced for some of the parameters, especially the measure of source-to-site distance, highlighting the need to take into account any incompatibilities among the selected equations. Procedures are also presented for assigning weights to the branches in the ground-motion section of the logic tree in a transparent fashion, considering both intrinsic merits of the individual equations and their degree of applicability to the particular application
Adjustment of median ground motion prediction equations (GMPEs) from one region to another region is one of the major challenges within the current practice of seismic hazard analysis. In our approach of generating response spectra, we derive two separate empirical models for a) Fourier amplitude spectrum (FAS) and b) duration of ground motion. To calculate response spectra, the two models are combined within the random vibration theory (RVT) framework. The models are calibrated on recordings obtained from shallow crustal earthquakes in active tectonic regions. We use a subset of NGA-West2 database with M3.2-7.9 earthquakes at distances 0-300 km. The NGA-West2 database expanded over a wide magnitude and distance range facilitates a better constraint over derived models. A frequency-dependent duration model is derived to obtain adjustable response spectral ordinates. Excellent comparison of our approach with other NGA-West2 models implies that it can also be used as a stand-alone model.
We have analyzed the recently developed pan-European strong motion database, RESORCE-2012: spectral parameters, such as stress drop (stress parameter, Delta sigma), anelastic attenuation (Q), near surface attenuation (kappa(0)) and site amplification have been estimated from observed strong motion recordings. The selected dataset exhibits a bilinear distance-dependent Q model with average kappa(0) value 0.0308 s. Strong regional variations in inelastic attenuation were also observed: frequency-independent Q(0) of 1462 and 601 were estimated for Turkish and Italian data respectively. Due to the strong coupling between Q and kappa(0), the regional variations in Q have strong impact on the estimation of near surface attenuation kappa(0). kappa(0) was estimated as 0.0457 and 0.0261 s for Turkey and Italy respectively. Furthermore, a detailed analysis of the variability in estimated kappa(0) revealed significant within-station variability. The linear site amplification factors were constrained from residual analysis at each station and site-class type. Using the regional Q(0) model and a site-class specific kappa(0), seismic moments (M-0) and source corner frequencies f (c) were estimated from the site corrected empirical Fourier spectra. Delta sigma did not exhibit magnitude dependence. The median Delta sigma value was obtained as 5.75 and 5.65 MPa from inverted and database magnitudes respectively. A comparison of response spectra from the stochastic model (derived herein) with that from (regional) ground motion prediction equations (GMPEs) suggests that the presented seismological parameters can be used to represent the corresponding seismological attributes of the regional GMPEs in a host-to-target adjustment framework. The analysis presented herein can be considered as an update of that undertaken for the previous Euro-Mediterranean strong motion database presented by Edwards and Fah (Geophys J Int 194(2):1190-1202, 2013a).
A transparent and data-driven global tectonic regionalization model for seismic hazard assessment
(2018)
A key concept that is common to many assumptions inherent within seismic hazard assessment is that of tectonic similarity. This recognizes that certain regions of the globe may display similar geophysical characteristics, such as in the attenuation of seismic waves, the magnitude scaling properties of seismogenic sources or the seismic coupling of the lithosphere. Previous attempts at tectonic regionalization, particularly within a seismic hazard assessment context, have often been based on expert judgements; in most of these cases, the process for delineating tectonic regions is neither reproducible nor consistent from location to location. In this work, the regionalization process is implemented in a scheme that is reproducible, comprehensible from a geophysical rationale, and revisable when new relevant data are published. A spatial classification-scheme is developed based on fuzzy logic, enabling the quantification of concepts that are approximate rather than precise. Using the proposed methodology, we obtain a transparent and data-driven global tectonic regionalization model for seismic hazard applications as well as the subjective probabilities (e.g. degree of being active/degree of being cratonic) that indicate the degree to which a site belongs in a tectonic category.
On April 29, 2017 at 0:56 UTC (2:56 local time), an M (W) = 2.8 earthquake struck the metropolitan area between Leipzig and Halle, Germany, near the small town of Markranstadt. The earthquake was felt within 50 km from the epicenter and reached a local intensity of I (0) = IV. Already in 2015 and only 15 km northwest of the epicenter, a M (W) = 3.2 earthquake struck the area with a similar large felt radius and I (0) = IV. More than 1.1 million people live in the region, and the unusual occurrence of the two earthquakes led to public attention, because the tectonic activity is unclear and induced earthquakes have occurred in neighboring regions. Historical earthquakes south of Leipzig had estimated magnitudes up to M (W) ae 5 and coincide with NW-SE striking crustal basement faults. We use different seismological methods to analyze the two recent earthquakes and discuss them in the context of the known tectonic structures and historical seismicity. Novel stochastic full waveform simulation and inversion approaches are adapted for the application to weak, local earthquakes, to analyze mechanisms and ground motions and their relation to observed intensities. We find NW-SE striking normal faulting mechanisms for both earthquakes and centroid depths of 26 and 29 km. The earthquakes are located where faults with large vertical offsets of several hundred meters and Hercynian strike have developed since the Mesozoic. We use a stochastic full waveform simulation to explain the local peak ground velocities and calibrate the method to simulate intensities. Since the area is densely populated and has sensitive infrastructure, we simulate scenarios assuming that a 12-km long fault segment between the two recent earthquakes is ruptured and study the impact of rupture parameters on ground motions and expected damage.
The Seismic Hazard Harmonization in Europe (SHARE) project, which began in June 2009, aims at establishing new standards for probabilistic seismic hazard assessment in the Euro-Mediterranean region. In this context, a logic tree for ground-motion prediction in Europe has been constructed. Ground-motion prediction equations (GMPEs) and weights have been determined so that the logic tree captures epistemic uncertainty in ground-motion prediction for six different tectonic regimes in Europe. Here we present the strategy that we adopted to build such a logic tree. This strategy has the particularity of combining two complementary and independent approaches: expert judgment and data testing. A set of six experts was asked to weight pre-selected GMPEs while the ability of these GMPEs to predict available data was evaluated with the method of Scherbaum et al. (Bull Seismol Soc Am 99:3234-3247, 2009). Results of both approaches were taken into account to commonly select the smallest set of GMPEs to capture the uncertainty in ground-motion prediction in Europe. For stable continental regions, two models, both from eastern North America, have been selected for shields, and three GMPEs from active shallow crustal regions have been added for continental crust. For subduction zones, four models, all non-European, have been chosen. Finally, for active shallow crustal regions, we selected four models, each of them from a different host region but only two of them were kept for long periods. In most cases, a common agreement has been also reached for the weights. In case of divergence, a sensitivity analysis of the weights on the seismic hazard has been conducted, showing that once the GMPEs have been selected, the associated set of weights has a smaller influence on the hazard.
The aim of this paper is to investigate the ability of various site-condition proxies (SCPs) to reduce ground-motion aleatory variability and evaluate how SCPs capture nonlinearity site effects. The SCPs used here are time-averaged shear-wave velocity in the top 30 m (V-S30), the topographical slope (slope), the fundamental resonance frequency (f(0)) and the depth beyond which V-s exceeds 800 m/s (H800). We considered first the performance of each SCP taken alone and then the combined performance of the 6 SCP pairs [V-S30-f(0)], [V-S30-H-800], [f(0)-slope], [H-800-slope], [V-S30-slope] and [f(0)-H-800]. This analysis is performed using a neural network approach including a random effect applied on a KiK-net subset for derivation of ground-motion prediction equations setting the relationship between various ground-motion parameters such as peak ground acceleration, peak ground velocity and pseudo-spectral acceleration PSA (T), and Mw, RJB, focal depth and SCPs. While the choice of SCP is found to have almost no impact on the median groundmotion prediction, it does impact the level of aleatory uncertainty. VS30 is found to perform the best of single proxies at short periods (T < 0.6 s), while f(0) and H-800 perform better at longer periods; considering SCP pairs leads to significant improvements, with particular emphasis on [V-S30-H-800] and [f(0)-slope] pairs. The results also indicate significant nonlinearity on the site terms for soft sites and that the most relevant loading parameter for characterising nonlinear site response is the "stiff" spectral ordinate at the considered period.
We compare the ability of various site-condition proxies (SCPs) to reduce the aleatory variability of ground motion prediction equations (GMPEs). Three SCPs (measured V-S30, inferred V-S30, local topographic slope) and two accelerometric databases (RESORCE and NGA-West2) are considered. An artificial neural network (ANN) approach including a random-effect procedure is used to derive GMPEs setting the relationship between peak ground acceleration (PGA), peak ground velocity (PGV), pseudo-spectral acceleration [PSA(T)], and explanatory variables (M-w, R-JB, and V-S30 or Slope). The analysis is performed using both discrete site classes and continuous proxy values. All "non-measured" SCPs exhibit a rather poor performance in reducing aleatory variability, compared to the better performance of measured V-S30. A new, fully data-driven GMPE based on the NGA-West2 is then derived, with an aleatory variability value depending on the quality of the SCP. It proves very consistent with previous GMPEs built on the same data set. Measuring V-S30 allows for benefit from an aleatory variability reduction up to 15%.
VS30, slope, H800 and f0
(2017)
The aim of this paper is to investigate the ability of various site-condition proxies (SCPs) to reduce ground-motion aleatory variability and evaluate how SCPs capture nonlinearity site effects. The SCPs used here are time-averaged shear-wave velocity in the top 30 m (VS30), the topographical slope (slope), the fundamental resonance frequency (f0) and the depth beyond which Vs exceeds 800 m/s (H800). We considered first the performance of each SCP taken alone and then the combined performance of the 6 SCP pairs [VS30–f0], [VS30–H800], [f0–slope], [H800–slope], [VS30–slope] and [f0–H800]. This analysis is performed using a neural network approach including a random effect applied on a KiK-net subset for derivation of ground-motion prediction equations setting the relationship between various ground-motion parameters such as peak ground acceleration, peak ground velocity and pseudo-spectral acceleration PSA (T), and Mw, RJB, focal depth and SCPs. While the choice of SCP is found to have almost no impact on the median groundmotion prediction, it does impact the level of aleatory uncertainty. VS30 is found to perform the best of single proxies
at short periods (T < 0.6 s), while f0 and H800 perform better at longer periods; considering SCP pairs leads to significant improvements, with particular emphasis on [VS30–H800] and [f0–slope] pairs. The results also indicate significant nonlinearity on the site terms for soft sites and that the most relevant loading parameter for characterising nonlinear site response is the “stiff” spectral ordinate at the considered period.