Excessive Memory Usage of the ELLPACK Sparse Matrix Storage Scheme throughout the Finite Element Computations

Sparse matrices are occasionally encountered during solution of various problems by means of numerical methods, particularly the finite element method. ELLPACK sparse matrix storage scheme, one of the most widely used methods due to its implementation ease, is investigated in this study. The scheme uses excessive memory due to its definition. For the conventional finite element method, where the node elements are used, the excessive memory caused by redundant entries in the ELLPACK sparse matrix storage scheme becomes negligible for large scale problems. On the other hand, our analyses show that the redundancy is still considerable for the occasions where facet or edge elements have to be used

HAZGRIDX: earthquake forecasting model for ML ≥ 5.0 earthquakes in Italy based on spatially smoothed seismicity

We present a five-year, time-independent, earthquake-forecast model for earthquake magnitudes of 5.0 and greater in Italy using spatially smoothed seismicity data. The model is called HAZGRIDX, and it was developed based on the assumption that future earthquakes will occur near locations of historical earthquakes; it does not take into account any information from tectonic, geological, or geodetic data. Thus HAZGRIDX is based on observed earthquake occurrence from seismicity data, without considering any physical model. In the present study, we calculate earthquake rates on a spatial grid platform using two declustered catalogs: 1) the Parametric catalog of Italian earthquakes (Catalogo Parametrico dei Terremoti Italiani, CPTI04) that contains the larger earthquakes from MW 7.0 since 1100; and 2) the Italian seismicity catalogue (Catalogo della Sismicità Italiana, CSI 1.1) that contains the small earthquakes down to ML 1.0, with a maximum of ML 5.9, over the past 22 years (1981-2003). The model assumes that earthquake magnitudes follow the Gutenberg-Richter law, with a uniform b-value. The forecast rates are presented in terms of the expected numbers of ML>5.0 events per year for each grid cell of about 10 km × 10 km. The final map is derived by averaging the earthquake potentials that come from these two different catalogs: CPTI04 and CSI 1.1. We also describe the earthquake occurrences in terms of probabilities of occurrence of one event within a specified magnitude bin, DM0.1, in a five year time period. HAZGRIDX is one of several forecasting models, scaled to five and ten years, that have been submitted to the Collaboratory for the Study of Earthquake Probability (CSEP) forecasting center in ETH, Zurich, to be tested for Italy

Deliverable # D3.01.4 Probability of occurrence for earthquakes generated by individual faults and the associated uncertainties

Probabilities and uncertainties were calculated based on the approach developed by Akinci et al. (2008). The method was applied to the whole Italian territory using a dataset that integrates individual seismogenic sources derived from both geological/geophysical data and macroseismic data (see Basili et al., 2008, for definitions). We designed two model approaches: one that uses geological slip rates; another that uses slip rates derived from the finite element model developed by Barba et al, 2007. As for recurrence we adopted the Poisson and the Renewal BPT models with aperiodicity a equal to 0.3, 0.5 and 0.7, all for a prediction in the next 30 years. Complete results of these procedures are given in tabular form at the end of this document

Charged Droplets in Cryogenic \u3csup\u3e4\u3c/sup\u3eHe Vapor

We have measured the mobility of positive ions in 4He vapor for temperatures between 1.3 and 2.0 K and for saturation ratios between 0.1 and 1.0. We present a model which relates the size of a charged droplet to its mobility and find good quantitative agreement with our data when we calculate the size of the droplet which forms about the ion with classical macroscopic thermodynamic arguments. The radius thus obtained ranges from 7 to 9 Å

High-Frequency Attenuation in the Lake Van Region, Eastern Turkey

We provide a complete description of the characteristics of excitation and attenuation of the ground motion in the Lake Van region (eastern Turkey) using a data set that includes three-component seismograms from the 23 October 2011 Mw 7.1 Van earthquake, as well as its aftershocks. Regional attenuation and source scaling are parameterized to describe the observed ground motions as a function of distance, frequency, and magnitude. Peak ground velocities are measured in selected narrow frequency bands from 0.25 to 12.5 Hz; observed peaks are regressed to define a piecewise linear regional attenu- ation function, a set of excitation terms, and a set of site response terms. Results are modeled through random vibration theory (see Cartwright and Longuet-Higgins, 1956). In the log–log space, the regional crustal attenuation is modeled with a bilinear geo- metrical spreading g r characterized by a crossover distance at 40 km: g r ∝ r^−1 fits our results at short distances (r < 40 km), whereas g r ∝ r^−0.3 is better at larger distances (40 < r < 200 km). A frequency-dependent quality factor, Q f =100( f/fref)^ 0:43 (in which fref 1.0 Hz), is coupled to the geometrical spreading. Because of the inherent trade-off of the excitation/attenuation parameters (Δσ and κ), their specific values strongly depend on the choice made for the stress drop of the smaller earthquakes. After choosing a Brune stress drop ΔσBrune 4 MPa at Mw 3:5, we were able to define (1) an effective high frequency, distance- and mag- nitude-independent roll-off spectral parameter, κeff = 0:03 s and (2) a size-dependent stress-drop parameter, which increases with moment magnitude, from ΔσBrune 4 MPa at Mw 3.5 to ΔσBrune 20 MPa at Mw 7.1. The set of parameters mentioned here may be used in order to predict the earthquake-induced ground motions expected from future earthquakes in the region surrounding Lake Van

Uncertainty analysis for seismic hazard in Northern and Central Italy

In this study we examine uncertainty and parametric sensitivity of Peak Ground Acceleration (PGA) and 1-Hz Spectral Acceleration (1-Hz SA) in probabilistic seismic hazard maps (10% probability of exceedance in 50 years) of Northern and Central Italy. The uncertainty in hazard is estimated using a Monte Carlo approach to randomly sample a logic tree that has three input-variables branch points representing alternative values for bvalue, maximum magnitude (Mmax) and attenuation relationships. Uncertainty is expressed in terms of 95% confidence band and Coefficient Of Variation (COV). The overall variability of ground motions and their sensitivity to each parameter of the logic tree are investigated. The largest values of the overall 95% confidence band are around 0.15 g for PGA in the Friuli and Northern Apennines regions and around 0.35 g for 1-Hz SA in the Central Apennines. The sensitivity analysis shows that the largest contributor to seismic hazard variability is uncertainty in the choice of ground-motion attenuation relationships, especially in the Friuli Region (∼0.10 g) for PGA and in the Friuli and Central Apennines regions (∼0.15 g) for 1-Hz SA. This is followed by the variability of the b-value: its main contribution is evident in the Friuli and Central Apennines regions for both 1-Hz SA (∼0.15 g) and PGA (∼0.10 g). We observe that the contribution of Mmax to seismic hazard variability is negligible, at least for 10% exceedance in 50-years hazard. The overall COV map for PGA shows that the uncertainty in the hazard is larger in the Friuli and Northern Apennine regions, around 20-30%, than the Central Apennines and Northwestern Italy, around 10-20%. The overall uncertainty is larger for the 1-Hz SA map and reaches 50- 60% in the Central Apennines and Western Alps

A regional ground motion excitation/attenuation model for the San Francisco region

By using small-to-moderate-sized earthquakes located within ~200 km of San Francisco, we characterize the scaling of the ground motions for frequencies ranging between 0.25 and 20 Hz, obtaining results for geometric spreading, Q(f), and site parameters using the methods of Mayeda et al. (2005) and Malagnini et al. (2004). The results of the analysis show that, throughout the Bay Area, the average regional attenuation of the ground motion can be modeled with a bilinear geometric spreading function with a 30 km crossover distance, coupled to an anelastic function exp(-pi*f*r/V*Q(f)) , where: Q(f)=180f^0.42. A body-wave geometric spreading, g(r)= r^-1.0, is used at short hypocentral distances (r < 30 km), whereas g(r)= r^-0.6 fits the attenuation of the spectral amplitudes at hypocentral distances beyond the crossover. The frequency-dependent site effects at 12 of the Berkeley Digital Seismic Network (BDSN) stations were evaluated in an absolute sense using coda-derived source spectra. Our results show: i) the absolute site response for frequencies ranging between 0.3 Hz and 2.0 Hz correlate with independent estimates of the local magnitude residuals (dML) for each of the stations; ii) moment-magnitudes (MW) derived from our path and site-corrected spectra are in excellent agreement with those independently derived using full-waveform modeling as well as coda-derived source spectra; iii) we use our weak-motion-based relationships to predict motions region wide for the Loma Prieta earthquake, well above the maximum magnitude spanned by our data set, on a completely different set of stations. Results compare well with measurements taken at specific NEHRP site classes; iv) an empirical, magnitude-dependent scaling was necessary for the Brune stress parameter in order to match the large magnitude spectral accelerations and peak ground velocities with our weak-motion-based model

A Regional Ground Motion Excitation attenuation Model for the San Francisco Region

By using small-to-moderate-sized earthquakes located within ~200 km of San Francisco, we characterize the scaling of the ground motions for frequencies ranging between 0.25 and 20 Hz, obtaining results for geometric spreading, Q(f), and site parameters using the methods of Mayeda et al. (2005) and Malagnini et al. (2004). The results of the analysis show that, throughout the Bay Area, the average regional attenuation of the ground motion can be modeled with a bilinear geometric spreading function with a 30 km crossover distance, coupled to an anelastic function ! exp " #fr $Q( f ) % & ' ( ) * , where: Q(f)=180 f 0.42. A body-wave geometric spreading, g(r)= r -1.0, is used at short hypocentral distances (r < 30 km), whereas g(r)= r -0.6 fits the attenuation of the spectral amplitudes at hypocentral distances beyond the crossover. The frequency-dependent site effects at 12 of the Berkeley Digital Seismic Network (BDSN) stations were evaluated in an absolute sense using coda-derived source spectra. Our results show: i) the absolute site response for frequencies ranging between 0.3 Hz and 2.0 Hz correlate with independent estimates of the local magnitude residuals (dML) for each of the stations; ii) moment-magnitudes (MW) derived from our path and sitecorrected spectra are in excellent agreement with those independently derived using fullwaveform modeling as well as coda-derived source spectra; iii) we use our weak-motionbased relationships to predict motions region wide for the Loma Prieta earthquake, well above the maximum magnitude spanned by our data set, on a completely different set of stations. Results compare well with measurements taken at specific NEHRP site classes; iv) an empirical, magnitude-dependent scaling was necessary for the Brune stress parameter in order to match the large magnitude spectral accelerations and peak ground velocities with our weak-motion-based model

Effect of time-dependence on probabilistic seismic hazard maps and deaggregation for the central apennines, Italy

We produce probabilistic seismic hazard assessments for the Central Apennines, Italy, using time-dependent models that are characterized using a Brownian Passage Time (BPT) recurrence model. Using aperiodicity parameters,  of 0.3, 0.5, and 0.7, we examine the sensitivity of the probabilistic ground motion and its deaggregation to these parameters. For the seismic source model we incorporate both smoothed historical seismicity over the area and geological information on faults. We use the maximum magnitude model for the fault sources together with a uniform probability of rupture along the fault (floating fault model) to model fictitious faults to account for earthquakes that cannot be correlated with known geologic structural segmentation. We show maps for peak ground acceleration (PGA) and 1.0-Hz spectral acceleration (SA1) on rock having 10% probability of exceedence (PE) in 50 years. We produce maps to compare the separate contributions of smoothed seismicity and fault components. In addition we construct maps that show sensitivity of the hazard for different  parameters and the Poisson model. For the Poisson model, the addition of fault sources to the smoothed seismicity raises the hazard by 50 % at locations where the smoothed seismicity contributes the highest hazard, and up to 100 % at locations where the hazard from smoothed seismicity is low. For the strongest aperiodicity parameter (smallest ), the hazard may further increase 60-80 % or more or may decrease by as much as 20 %, depending on the recency of the last event on the fault that dominates the hazard at a given site. In order to present the most likely earthquake magnitude and/or the most likely source-site distance for scenario studies, we deaggregate the seismic hazard for SA1 and PGA for two important cities (Roma and l’Aquila) . For PGA, both locations show the predominance of local sources, having magnitudes of about 5.3 and 6.5 respectively. For SA1 at a site in Rome, there is significant contribution from local smoothed seismicity, and an additional contribution from the more distant Apennine faults having magnitude around 6.8. For l’Aquila, the predominant sources remain local. In order to show the variety of impact of different  values we also obtained deaggregations for another three sites. In general, as  decreases (periodicity increases), the deaggregation indicates that the hazard is highest near faults with the highest earthquakes rates. This effect is strongest for the long-period (1 s) ground motions