Research on the principle and methodology of seismic zonation

Based on the cognizance of the temporal-spatial inhomogeneity of seismicity in North China, adopting the results of earthquake prediction in the past two decades and the currently used methods of seismic hazard analysis, and after some zonation trials in North China, some improvements on the zonation principle and methodology were made:

1. Seismic zones were taken as statistic units where seismicity parameters were obtained. Tendency analysis was introduced. Earthquake annual average occurrence rates were estimated corresponding to the seismicity level in the future period;
2. Average annual earthquake occurrence rates for a given magnitude interval of a specific seismic zone were assigned to potential sources considering the relative risk level among these sources. Thus, the risk of great earthquakes can be estimated.
3. The probabilistic spatial distribution function under the condition of magnitude interval was suggested to reflect the temporal and spatial inhomogeneity of seismicity.
4. An orientation function in the seismic hazard analysis model was adopted, which reflects the real condition of earthquake foci in China.

     

Ground-motion prediction equations for interface earthquakes of M7 to M9 based on empirical data from Japan

Ground motion prediction equations (GMPEs) have a major impact on seismic hazard estimates, because they control the predicted amplitudes of ground shaking. The prediction of ground-motion amplitudes due to mega-thrust earthquakes in subduction zones has been hampered by a paucity of empirical ground-motion data for the very large magnitudes (moment magnitude (M) $>$ 7) of most interest to hazard analysis. Recent data from Tohoku M9.0 2011 earthquake are important in this regard, as this is the largest well-recorded subduction event, and the only such event with sufficient data to enable a clear separation of the overall source, path and site effects. In this study, we use strong-ground-motion records from the M9 Tohoku event to derive an event-specific GMPE. We then extend this M9 GMPE to represent the shaking from other M $>$ 7 interface events in Japan by adjusting the source term. We focus on events in Japan to reduce ambiguity that results when combining data in different regions having different source, path and site effect attributes. Source levels (adjustment factors) for other Japanese events are determined as the average residuals of ground-motions with respect to the Tohoku GMPE, keeping all other coefficients fixed. The mean residuals (source terms) scale most steeply with magnitude at the lower frequencies; this is in accord with expectations based on overall source-scaling concepts. Interpolating source terms over the magnitude range of 7.0–9.0, we produce a GMPE for large interface events of M7–M9, for NEHRP B/C boundary site conditions (time-averaged shear-wave velocity of 760 m/s over the top 30 m) in both fore-arc and back-arc regions of Japan. We show how these equations may be adjusted to account for the deeper soil profiles (for the same value of $\hbox {V}_\mathrm{S30})$ in western North America. The proposed GMPE predicts lower motions at very long periods, higher motions at short periods, and similar motions at intermediate periods, relative to the simulation-based GMPE model of Atkinson and Macias (2009) for the Cascadia subduction zone.     

The Seismotectonics of the Po Plain (Northern Italy): Tectonic Diversity in a Blind Faulting Domain

We present a systematic and updated overview of a seismotectonic model for the Po Plain (northern Italy). This flat and apparently quiet tectonic domain is, in fact, rather active as it comprises the shortened foreland and foredeep of both the Southern Alps and the Northern Apennines. Assessing its seismic hazard is crucial due to the concentration of population, industrial activities, and critical infrastructures, but it is also complicated because (a) the region is geologically very diverse, and (b) nearly all potential seismogenic faults are buried beneath a thick blanket of Pliocene–Pleistocene sediments, and thus can be investigated only indirectly. Identifying and parameterizing the potential seismogenic faults of the Po Plain requires proper consideration of their depth, geometry, kinematics, earthquake potential and location with respect to the two confronting orogens. To this end, we subdivided them into four main, homogeneous groups. Over the past 15 years we developed new strategies for coping with this diversity, resorting to different data and modeling approaches as required by each individual fault group. The most significant faults occur beneath the thrust fronts of the Ferrara-Romagna and Emilia arcs, which correspond to the most advanced and buried portions of the Northern Apennines and were the locus of the destructive May 2012 earthquake sequence. The largest known Po Plain earthquake, however, occurred on an elusive reactivated fault cutting the Alpine foreland south of Verona. Significant earthquakes are expected to be generated also by a set of transverse structures segmenting the thrust system, and by the deeper ramps of the Apennines thrusts. The new dataset is intended to be included in the next version of the Database of Individual Seismogenic Sources (DISS; http://diss.rm.ingv.it/diss/, version 3.2.0, developed and maintained by INGV) to improve completeness of potential sources for seismic hazard assessment.     

Implications of the 2011 M9.0 Tohoku Japan earthquake for the treatment of site effects in large earthquakes

Site response in Japan is characterized using thousands of surface and borehole recordings from events of moment magnitude $(\mathbf{M}) > 5.5$ collected by the KiK-net network, including the 2011 M9.0 Tohoku earthquake. Site amplification is defined by the ratio of motions at the surface to those at depth (within the borehole), corrected for the depth effect due to destructive interference using a technique based on cross-spectral ratios between surface and down-hole motions. Site effects were particularly strong at high frequencies, despite the expectation that high-frequency response may be damped by nonlinear effects. In part, the large amplitudes at high frequencies are due to the prevalence of shallow soil conditions in Japan. We searched for typical symptoms for soil nonlinearity, such as a decrease in the predominant frequency and/or amplification, using spectral ratios of weak to strong ground motions. Localized nonlinearity occurred at some recording sites, but was not pervasive. We developed a general empirical model to express site amplification for the KiK-net sites as a function of common site variables, such as the average shear-wave velocity in the uppermost 30 m ( $\text{ V}_\mathrm{S30})$ and the horizontal-to-vertical (H/V) spectral ratio. We use the model to estimate site-corrected ground-motions for the Tohoku mainshock for a reference site condition; these motions are in reasonable agreement with the predictions of some of the published ground motion prediction equations for subduction zones.     

Tsunami Early Warning Within Five Minutes

Tsunamis are most destructive at near to regional distances, arriving within 20–30 min after a causative earthquake; effective early warning at these distances requires notification within 15 min or less. The size and impact of a tsunami also depend on sea floor displacement, which is related to the length, L, width, W, mean slip, D, and depth, z, of the earthquake rupture. Currently, the primary seismic discriminant for tsunami potential is the centroid-moment tensor magnitude, M _w ^CMT , representing the product LWD and estimated via an indirect inversion procedure. However, the obtained M _w ^CMT and the implied LWD value vary with rupture depth, earth model, and other factors, and are only available 20–30 min or more after an earthquake. The use of more direct discriminants for tsunami potential could avoid these problems and aid in effective early warning, especially for near to regional distances. Previously, we presented a direct procedure for rapid assessment of earthquake tsunami potential using two, simple measurements on P-wave seismograms—the predominant period on velocity records, T _d , and the likelihood, T ₅₀ ^Ex , that the high-frequency, apparent rupture-duration, T ₀, exceeds 50–55 s. We have shown that T _d and T ₀ are related to the critical rupture parameters L, W, D, and z, and that either of the period–duration products T _d T ₀ or T _d T ₅₀ ^Ex gives more information on tsunami impact and size than M _w ^CMT , M _wp, and other currently used discriminants. These results imply that tsunami potential is not directly related to the product LWD from the “seismic” faulting model, as is assumed with the use of the M _w ^CMT discriminant. Instead, information on rupture length, L, and depth, z, as provided by T _d T ₀ or T _d T ₅₀ ^Ex , can constrain well the tsunami potential of an earthquake. We introduce here special treatment of the signal around the S arrival at close stations, a modified, real-time, M _wpd(RT) magnitude, and other procedures to enable early estimation of event parameters and tsunami discriminants. We show that with real-time data currently available in most regions of tsunami hazard, event locations, m _b and M _wp magnitudes, and the direct, period–duration discriminant, T _d T ₅₀ ^Ex can be determined within 5 min after an earthquake occurs, and T ₀, T _d T ₀, and M _wpd(RT) within approximately 10 min. This processing is implemented and running continuously in real-time within the Early-est earthquake monitor at INGV-Rome (http://early-est.rm.ingv.it). We also show that the difference m _b  ? log₁₀(T _d T ₀) forms a rapid discriminant for slow, tsunami earthquakes. The rapid availability of these measurements can aid in faster and more reliable tsunami early warning for near to regional distances.     

Slope instabilities triggered by the 11th May 2011 Lorca earthquake (Murcia,Spain): comparison to previous hazard assessments and proposition of a new hazard map and probability of failure equation

The Lorca Basin has been the object of recent research aimed at studying the phenomena of earthquake-induced landslides and its assessment in the frame of different seismic scenarios. However, it has not been until the 11th May 2011 Lorca earthquakes when it has been possible to conduct a systematic approach to the problem. In this paper we present an inventory of slope instabilities triggered by the Lorca earthquakes which comprises more than 100 cases, mainly rock and soil falls of small size (1–100  \(\hbox {m}^{3}\) ). The distribution of these instabilities is here compared to two different earthquake-triggered landslide hazard maps: one considering the occurrence of the most probable earthquake for a 475-years return period in the Lorca Basin \((\hbox {M}_{\mathrm{w}}=5.0)\) based on both low- and high-resolution digital elevation model (DEM); and a second one matching the occurrence of the \(\hbox {M}_{\mathrm{w}}=5.2\) 2011 Lorca earthquake, which was performed using the higher resolution DEM. The most frequent Newmark displacements related to the slope failures triggered by the 2011 Lorca earthquakes are lower than 2 cm in both the hazard scenarios considered. Additionally, the predicted Newmark displacements were correlated to the inventory of slope instabilities to develop a probability of failure equation. The fit seems to be very good since most of the mapped slope failures are located on the higher probability areas. The probability of slope failure in the Lorca Basin for a seismic event similar to the \(\hbox {M}_{\mathrm{w}}\) 5.2 2011 Lorca earthquake can be considered as very low (0–4 %).     

Aftershock Statistics of the 1999 Chi–Chi, Taiwan Earthquake and the Concept of Omori Times

In this paper we consider the statistics of the aftershock sequence of the m = 7.65 20 September 1999 Chi–Chi, Taiwan earthquake. We first consider the frequency-magnitude statistics. We find good agreement with Gutenberg–Richter scaling but find that the aftershock level is anomalously high. This level is quantified using the difference in magnitude between the main shock and the largest inferred aftershock $ {{\Updelta}}m^{ *}. $ Typically, $ {{\Updelta}}m^{ *} $ is in the range 0.8–1.5, but for the Chi–Chi earthquake the value is $ {{\Updelta}}m^{ *} $  = 0.03. We suggest that this may be due to an aseismic slow-earthquake component of rupture. We next consider the decay rate of aftershock activity following the earthquake. The rates are well approximated by the modified Omori’s law. We show that the distribution of interoccurrence times between aftershocks follow a nonhomogeneous Poisson process. We introduce the concept of Omori times to study the merging of the aftershock activity with the background seismicity. The Omori time is defined to be the mean interoccurrence time over a fixed number of aftershocks.     

\tau_p^{{\rm max}} magnitude estimation, the case of the April 6, 2009 L’Aquila earthquake

Rapid magnitude estimate procedures represent a crucial part of proposed earthquake early warning systems. Most of these estimates are focused on the first part of the P-wave train, the earlier and less destructive part of the ground motion that follows an earthquake. Allen and Kanamori (Science 300:786–789, 2003) proposed to use the predominant period of the P-wave to determine the magnitude of a large earthquake at local distance and Olivieri et al. (Bull Seismol Soc Am 185:74–81, 2008) calibrated a specific relation for the Italian region. The Mw 6.3 earthquake hit Central Italy on April 6, 2009 and the largest aftershocks provide a useful dataset to validate the proposed relation and discuss the risks connected to the extrapolation of magnitude relations with a poor dataset of large earthquake waveforms. A large discrepancy between local magnitude (ML) estimated by means of $\tau_p^{{\rm max}}$ evaluation and standard ML (6.8 ± 1.5 vs. 5.9 ± 0.4) suggests using caution when ML vs. $\tau_p^{{\rm max}}$ calibrations do not include a relevant dataset of large earthquakes. Effects from large residuals could be mitigated or removed introducing selection rules on τ _p function, by regionalizing the ML vs. $\tau_p^{{\rm max}}$ function in the presence of significant tectonic or geological heterogeneity, and using probabilistic and evolutionary methods.     

On the selection of GMPEs for Vrancea subcrustal seismic source

The Vrancea subcrustal seismic source is characterized by large magnitude ( $M_{W} \ge 7$ ) intermediate-depth earthquakes that occur two or three times during a century on average. In this study several procedures are used to grade four candidate ground motion prediction equations proposed for Vrancea source in the SHARE project. In the work of Delavaud et al. (J Seismol 16(3):451–473, 2012) four ground motion prediction models developed for subduction zones (Zhao et al. in Bull Seism Soc Am 96(3):898–913, 2006; Atkinson and Boore in Bull Seism Soc Am 93(4):1703–1729, 2003; Youngs et al. in Seism Res Lett 68(1):58–73, 1997; Lin and Lee in Bull Seism Soc Am 98(1):220–240, 2008) are suggested as suitable for Vrancea subcrustal seismic source. The paper presents the appropriateness analysis of the four suggested ground motion prediction equations done using a dataset of 109 triaxial accelerograms recorded during seven Vrancea seismic events with moment magnitude $M_{W}$ between 5.4 and 7.4, occurred in the past 35 years. The strong ground motions were recorded in Romania, as well as in Bulgaria, Republic of Moldova and Serbia. Based on the ground motion dataset several goodness-of-fit measures are used in order to quantify how well the selected models match with the recorded data. The compatibility of the four ground motion prediction models with respect to magnitude scaling and distance scaling implied by strong ground motion dataset is investigated as well. The analyses show that the Youngs et al. (Seism Res Lett 68(1):58–73, 1997) and Zhao et al. (Bull Seism Soc Am 96(3):898–913, 2006) ground motion prediction models have a better fit with the data and can be candidate models for Probabilistic Seismic Hazard Assessment.     

Scaling Transition in Earthquake Sources: A Possible Link Between Seismic and Laboratory Measurements

We estimate the corner frequencies of 20 crustal seismic events from mainshock–aftershock sequences in different tectonic environments (mainshocks 5.7 < M _W < 7.6) using the well-established seismic coda ratio technique (Mayeda et al. in Geophys Res Lett 34:L11303, 2007; Mayeda and Malagnini in Geophys Res Lett, 2010), which provides optimal stability and does not require path or site corrections. For each sequence, we assumed the Brune source model and estimated all the events’ corner frequencies and associated apparent stresses following the MDAC spectral formulation of Walter and Taylor (A revised magnitude and distance amplitude correction (MDAC2) procedure for regional seismic discriminants, 2001), which allows for the possibility of non-self-similar source scaling. Within each sequence, we observe a systematic deviation from the self-similar \( M_{0} \propto \mathop f\nolimits_{\text{c}}^{ - 3} \) line, all data being rather compatible with \( M_{0} \propto \mathop f\nolimits_{\text{c}}^{ - (3 + \varepsilon )} \) , where ε > 0 (Kanamori and Rivera in Bull Seismol Soc Am 94:314–319, 2004). The deviation from a strict self-similar behavior within each earthquake sequence of our collection is indicated by a systematic increase in the estimated average static stress drop and apparent stress with increasing seismic moment (moment magnitude). Our favored physical interpretation for the increased apparent stress with earthquake size is a progressive frictional weakening for increasing seismic slip, in agreement with recent results obtained in laboratory experiments performed on state-of-the-art apparatuses at slip rates of the order of 1 m/s or larger. At smaller magnitudes (M _W < 5.5), the overall data set is characterized by a variability in apparent stress of almost three orders of magnitude, mostly from the scatter observed in strike-slip sequences. Larger events (M _W > 5.5) show much less variability: about one order of magnitude. It appears that the apparent stress (and static stress drop) does not grow indefinitely at larger magnitudes: for example, in the case of the Chi–Chi sequence (the best sampled sequence between M _W 5 and 6.5), some roughly constant stress parameters characterize earthquakes larger than M _W ~ 5.5. A representative fault slip for M _W 5.5 is a few tens of centimeters (e.g., Ide and Takeo in J Geophys Res 102:27379–27391, 1997), which corresponds to the slip amount at which effective lubrication is observed, according to recent laboratory friction experiments performed at seismic slip velocities (V ~ 1 m/s) and normal stresses representative of crustal depths (Di Toro et al. in Nature in press, 2011, and references therein). If the observed deviation from self-similar scaling is explained in terms of an asymptotic increase in apparent stress (Malagnini et al. in Pure Appl Geophys, 2014, this volume), which is directly related to dynamic stress drop on the fault, one interpretation is that for a seismic slip of a few tens of centimeters (M _W ~ 5.5) or larger, a fully lubricated frictional state may be asymptotically approached.     

The maximum expected earthquake magnitudes in different future time intervals of six seismotectonic zones of Iran and its surroundings

One of the crucial components in seismic hazard analysis is the estimation of the maximum earthquake magnitude and associated uncertainty. In the present study, the uncertainty related to the maximum expected magnitude μ is determined in terms of confidence intervals for an imposed level of confidence. Previous work by Salamat et al. (Pure Appl Geophys 174:763-777, 2017) shows the divergence of the confidence interval of the maximum possible magnitude m_max for high levels of confidence in six seismotectonic zones of Iran. In this work, the maximum expected earthquake magnitude μ is calculated in a predefined finite time interval and imposed level of confidence. For this, we use a conceptual model based on a doubly truncated Gutenberg-Richter law for magnitudes with constant b-value and calculate the posterior distribution of μ for the time interval T_f in future. We assume a stationary Poisson process in time and a Gutenberg-Richter relation for magnitudes. The upper bound of the magnitude confidence interval is calculated for different time intervals of 30, 50, and 100 years and imposed levels of confidence α?=?0.5, 0.1, 0.05, and 0.01. The posterior distribution of waiting times T_f to the next earthquake with a given magnitude equal to 6.5, 7.0, and 7.5 are calculated in each zone. In order to find the influence of declustering, we use the original and declustered version of the catalog. The earthquake catalog of the territory of Iran and surroundings are subdivided into six seismotectonic zones Alborz, Azerbaijan, Central Iran, Zagros, Kopet Dagh, and Makran. We assume the maximum possible magnitude m_max?=?8.5 and calculate the upper bound of the confidence interval of μ in each zone. The results indicate that for short time intervals equal to 30 and 50 years and imposed levels of confidence 1???α?=?0.95 and 0.90, the probability distribution of μ is around μ?=?7.16???8.23 in all seismic zones.     

Compatible ground-motion prediction equations for damping scaling factors and vertical-to-horizontal spectral amplitude ratios for the broader Europe region

In a companion article Akkar et al. (Bull Earthq Eng, doi:10.1007/s10518-013-9461-4, 2013a; Bull Earthq Eng, doi:10.1007/s10518-013-9508-6, 2013b) present a new ground-motion prediction equation (GMPE) for estimating 5 %-damped horizontal pseudo-acceleration spectral (PSA) ordinates for shallow active crustal regions in Europe and the Middle East. This study provides a supplementary viscous damping model to modify 5 %-damped horizontal spectral ordinates of Akkar et al. (Bull Earthq Eng, doi:10.1007/s10518-013-9461-4 2013a; Bull Earthq Eng, doi:10.1007/s10518-013-9508-6, 2013b) for damping ratios ranging from 1 to 50 %. The paper also presents another damping model for scaling 5 %-damped vertical spectral ordinates that can be estimated from the vertical-to-horizontal (V/H) spectral ratio GMPE that is also developed within the context of this study. For consistency in engineering applications, the horizontal and vertical damping models cover the same damping ratios as noted above. The article concludes by introducing period-dependent correlation coefficients to compute horizontal and vertical conditional mean spectra (Baker in J Struct Eng 137:322–331, 2011). The applicability range of the presented models is the same as of the horizontal GMPE proposed by Akkar et al. (Bull Earthq Eng, doi:10.1007/s10518-013-9461-4 2013a; Bull Earthq Eng, doi:10.1007/s10518-013-9508-6, 2013b): as for spectral periods $0.01 \hbox { s}\le \,\hbox {T}\le \,4\hbox { s}$ as well as PGA and PGV for V/H model; and in terms of seismological estimator parameters $4\le \hbox {M}_\mathrm{w} \le 8, \hbox { R} \le 200 \hbox { km}, 150\hbox { m/s}\le \hbox { V}_\mathrm{S30}\le $ 1,200 m/s, for reverse, normal and strike-slip faults. The source-to-site distance measures that can be used in the computations are epicentral $(\hbox {R}_\mathrm{epi})$ , hypocentral $(\hbox {R}_\mathrm{hyp})$ and Joyner–Boore $(\hbox {R}_\mathrm{JB})$ distances. The implementation of the proposed GMPEs will facilitate site-specific adjustments of the spectral amplitudes predicted from probabilistic seismic hazard assessment in Europe and the Middle East region. They can also help expressing the site-specific design ground motion in several formats. The consistency of the proposed models together with the Akkar et al. (Bull Earthq Eng, doi:10.1007/s10518-013-9461-4 2013a; Bull Earthq Eng, doi:10.1007/s10518-013-9508-6, 2013b) GMPE may be advantageous for future modifications in the ground-motion definition in Eurocode 8 (CEN in Eurocode 8, Design of structures for earthquake resistance—part 1: general rules, seismic actions and rules for buildings. European Standard NF EN 1998-1, Brussels, 2004).     

Effects of Location Errors in Pattern Informatics

The effect of location errors in the performance of seismicity-based forecasting methods was studied here using one particular binary forecast technique, the Pattern Informatics (PI) technique (Rundle et al., Proc Nat Acad Sci USA 99, 2514–2521, 2002; Tiampo et al., Pure Appl Geophys 159, 2429–2467, 2002). The Southern Californian dataset was used to generate a series of perturbed catalogs by adding different levels of noise to epicenter locations. The PI technique was applied to these perturbed datasets to perform retrospective forecasts that were evaluated by means of skill scores, commonly used in atmospheric sciences. These results were then compared to the effectiveness obtained from the original dataset. Isolated instances of decline of the PI performance were observed due to the nature of the skill scores themselves, but no clear trend of degradation was identified. Dependence on the total number of events in a catalog also was studied, with no systematic degradation in the performance of the PI for catalogs with events in the cases studied. These results suggest that the stability of the PI method is due to the invariance of the clustering patterns identified by the TM metric (Thirumalai and Mountain, Phys Rev A 39, 3563–3573, 1989) when applied to seismicity.     

Precursory seismic quiescence: Past,present, and future

Precursory seismic quiescence has played a major role in most of the succesful earthquake predictions made to date. In addition to these successes, the number of detailed post-mainshock documentations of precursory quiescence is steadily growing. These facts suggest that precursory quiescence will play an important role in earthquake prediction programs of the future. For this reason it is important to critically evaluate the present state of knowledge concerning this phenomenon. The history of observations of precursory seismic quiescence includes work on seismic gaps and seismic preconditions as well as actual studies of temporal quiescence. These papers demonstrated the importance of quantitative evaluation of seismicity rates and the benefits of systematic analysis. During the early 1980's the impact of man-made effects on seismicity rates was demonstrated for the first time. Despite progress in catalog understanding, the identification and correction of man-made seismicity changes remains as the major barrier to earthquake prediction using these data. Effects of man-made changes are apparent in many past studies of seismicity patterns, making the results difficult to evaluate. Recent experience with real-time anomalies has demonstrated the necessity of determining the false alarm rates associated with quiescence precursors. Determination of false alarm rates depends on quantitative definitions of anomalies and statistical evaluations of their significance. A number of successful predictions, which have been made on the basis of seismic quiescence, provide important lessons for present and future work. There are many presently unanswered questions regarding seismic quiescence which must be answered before we can determine the reliability of this phenomena as a precursor.     

On the ability of Moho reflections to affect the ground motion in northeastern Italy: a case study of the 2012 Emilia seismic sequence

It has been observed that post-critically reflected S-waves and multiples from the Moho discontinuity could play a relevant role on the ground motion due to medium to strong size earthquakes away from the source. Although some studies investigated the correlation between the Moho reflections amplitudes and the damage in the far field, little attention was given to the frequency content of these specific phases and their scaling with magnitude. The 2012 Emilia seismic sequence in northern Italy, recorded by velocimetric and accelerometric networks, is here exploited to investigate Moho reflections and multiples (SmSM). A single station method for group velocity-period estimation, based on the multiple filter technique, is applied to strong motion data to detect SmSM. Amplitude and frequency scaling with magnitude is defined for earthquakes from \(\hbox {Mw}=3.9\) to \(\hbox {Mw}=5.9\) . Finally, the ability of SmSM to affect the ground motion for a maximum credible earthquake within the Po plain is investigated by extrapolating observed engineering parameters. Data analysis shows that high amplitude SmSM can be recognized within the Po plain, and at the boundaries between the Po plain and the Alpine chain, at epicentral distances larger than 80 km, in the period range from 0.25 to 3 s and in the group velocity window from about 2.6 to 3.2 km/s. 5 % damped pseudo-spectral accelerations at different periods (0.3, 1.0 and 2.0 s), and Housner intensities, are obtained from data characterized by large amplitude SmSM. A scaling relationship for both pseudo-spectral accelerations and Housner intensities is found for the earthquakes of the 2012 Emilia seismic sequence. \(\hbox {I}_{\mathrm{MCS}}\) from VII to VIII is estimated, as a result of SmSM amplitude enhancement, at about 100 km for a maximum credible earthquake ( \(\hbox {Mw}=6.7\) ) in the Po plain, showing that moderate to high damage cloud be caused by these specific phases.     

Comparison of ground motions from the 2010 Mw 7.2 El Mayor–Cucapah earthquake with the next generation attenuation ground motion prediction equations

A total of 144 free-field ground motions with closest site-to-rupture distances (R_rup) less than 200 km recorded during the 2010 M_w 7.2 El Mayor–Cucapah earthquake are used to investigate predictive capabilities of the next generation attenuation (NGA) ground-motion prediction equations (GMPE). The NGA GMPEs underpredict observed spectral accelerations at sites with shear wave velocity in the upper 30 m of the site (V_s30) between 180 and 366 m/s with R_rup from about 10 to 50 km and overpredict at sites with R_rup from about 50 to 200 km. Intra-event residuals of the NGA GMPEs exhibit a noticeable negative trend for peak ground acceleration and 0.3, 1.0, and 2.0 s periods. Comparison of the inter-event residual between the 2010 M_w 7.2 El Mayor–Cucapah earthquake and the NGA dataset reveals that short-period inter-event residuals from the 2010 M_w 7.2 El Mayor–Cucapah earthquake is within the scatter of inter-event residuals from the NGA dataset but long-period inter-event residuals do not appear within of the scatter of inter-event residuals from the NGA dataset. Spectral accelerations predicted by the NGA GMPEs are generally unbiased against V_s30 and periods of less than 4.0 s. Observed spectral accelerations show a stronger V_s30 dependence for both short and long periods compared with the NGA GMPEs. The Boore and Atkinson (Earthq Spectra 24(1):99–138, 2008) and Chiou and Youngs (Earthq Spectra 24(1):173–215, 2008) GMPEs perform better in predicting observed short-period spectral accelerations at the sites with V_s30 between 180 and 250 m/s than the Abrahamson and Silva (Earthq Spectra 24(1):67–97, 2008) and Campbell and Bozorgnia (Earthq Spectra 24(1):139–171, 2008) GMPEs.     

Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory

The present work is a continuation and improvement of the method suggested in Pisarenko et al. (Pure Appl Geophys 165:1–42, 2008) for the statistical estimation of the tail of the distribution of earthquake sizes. The chief innovation is to combine the two main limit theorems of Extreme Value Theory (EVT) that allow us to derive the distribution of T-maxima (maximum magnitude occurring in sequential time intervals of duration T) for arbitrary T. This distribution enables one to derive any desired statistical characteristic of the future T-maximum. We propose a method for the estimation of the unknown parameters involved in the two limit theorems corresponding to the Generalized Extreme Value distribution (GEV) and to the Generalized Pareto Distribution (GPD). We establish the direct relations between the parameters of these distributions, which permit to evaluate the distribution of the T-maxima for arbitrary T. The duality between the GEV and GPD provides a new way to check the consistency of the estimation of the tail characteristics of the distribution of earthquake magnitudes for earthquake occurring over an arbitrary time interval. We develop several procedures and check points to decrease the scatter of the estimates and to verify their consistency. We test our full procedure on the global Harvard catalog (1977–2006) and on the Fennoscandia catalog (1900–2005). For the global catalog, we obtain the following estimates: \( \hat{M}_{{\rm max} } \)  = 9.53 ± 0.52 and \( \hat{Q}_{10} (0.97) \)  = 9.21 ± 0.20. For Fennoscandia, we obtain \( \hat{M}_{{\rm max} } \)  = 5.76 ± 0.165 and \( \hat{Q}_{10} (0.97) \)  = 5.44 ± 0.073. The estimates of all related parameters for the GEV and GPD, including the most important form parameter, are also provided. We demonstrate again the absence of robustness of the generally accepted parameter characterizing the tail of the magnitude-frequency law, the maximum possible magnitude M _max, and study the more stable parameter Q _T (q), defined as the q-quantile of the distribution of T-maxima on a future interval of duration T.     

The Area Skill Score Statistic for Evaluating Earthquake Predictability Experiments

Rigorous predictability experimentation requires a statistical characterization of the performance metric used to evaluate the participating models. We explore the properties of the area skill score measure and consider issues related to experimental discretization. For the case of continuous alarm functions and continuous observations, we present exact analytical solutions that describe the distribution of the area skill score for unskilled predictors, and we also describe how a Gaussian distribution with known mean and variance can be used to approximate the area skill score distribution. We quantify the deviation of the exact distribution from the Gaussian approximation by specifying the kurtosis excess as a function of the number of observed target earthquakes. For numerical earthquake predictability experiments that involve discretization of the study region and observations, we explore simulation procedures for estimating the area skill score distribution, and we present efficient algorithms for various experimental scenarios. When more than one target earthquake occurs within a given space/time/magnitude bin, the probabilities of predicting individual events are not independent, and this requires special consideration. Having presented the statistical properties of the area skill score, we describe and illustrate a preliminary procedure for comparing earthquake prediction strategies based on alarm functions.     

An Independent Assessment of the Load/Unload Response Ratio (LURR) Proposed Method of Earthquake Prediction

The Load/Unload Response Ratio (LURR) method is a proposed technique to predict earthquakes that was first put forward by Yin (1987). LURR is based on the idea that when an area enters the damage regime, the rate of seismic activity during loading of the tidal cycle increases relative to the rate of seismic activity during unloading in the months to one year preceding a large earthquake. Since earth tides generally contribute the largest temporal variations in crustal stress, it seems plausible that earth tides would trigger earthquakes in areas that are close to failure (e.g., Vidale et al., 1998). However, the vast majority of studies have shown that earth tides do not trigger earthquakes (e.g., Vidale et al., 1998; Heaton, 1982; Rydelek et al., 1992). In this study, we conduct an independent test of the LURR method, since there would be important scientific and social implications if it were proven to be a robust method of earthquake prediction. Smith and Sammis (2004) undertook a similar study and found no evidence that there was predictive significance to the LURR method. We have repeated calculations of LURR for the Northridge earthquake in California, following both the parameters of X.C. Yin (personal communication) and the somewhat different ones of Smith and Sammis (2004). Though we have followed both sets of parameters closely, we have been unable to reproduce either set of results. Our examinations have shown that the LURR method is very sensitive to certain parameters. Thus it seems likely that the discrepancies between our results and those of previous studies are due to unaccounted for differences in the calculation parameters. A general agreement was made at the 2004 ACES Workshop in China between research groups studying LURR to work cooperatively to resolve the differences in methods and results, and thus permit more definitive conclusions on the potential usefulness of the LURR method in earthquake prediction.     

Numerical Study of Tsunami Generated by Multiple Submarine Slope Failures in Resurrection Bay, Alaska, during the M W 9.2 1964 Earthquake

We use a viscous slide model of Jiang and LeBlond (1994) coupled with nonlinear shallow water equations to study tsunami waves in Resurrection Bay, in south-central Alaska. The town of Seward, located at the head of Resurrection Bay, was hit hard by both tectonic and local landslide-generated tsunami waves during the M _W 9.2 1964 earthquake with an epicenter located about 150 km northeast of Seward. Recent studies have estimated the total volume of underwater slide material that moved in Resurrection Bay during the earthquake to be about 211 million m³. Resurrection Bay is a glacial fjord with large tidal ranges and sediments accumulating on steep underwater slopes at a high rate. Also, it is located in a seismically active region above the Aleutian megathrust. All these factors make the town vulnerable to locally generated waves produced by underwater slope failures. Therefore it is crucial to assess the tsunami hazard related to local landslide-generated tsunamis in Resurrection Bay in order to conduct comprehensive tsunami inundation mapping at Seward. We use numerical modeling to recreate the landslides and tsunami waves of the 1964 earthquake to test the hypothesis that the local tsunami in Resurrection Bay has been produced by a number of different slope failures. We find that numerical results are in good agreement with the observational data, and the model could be employed to evaluate landslide tsunami hazard in Alaska fjords for the purposes of tsunami hazard mitigation.