An overview of joint inversion in earthquake source imaging

We reviewed joint inversion studies of the rupture processes of significant earthquakes, using the definition of a joint inversion in earthquake source imaging as a source inversion of multiple kinds of datasets (waveform, geodetic, or tsunami). Yoshida and Koketsu (Geophys J Int 103:355–362, 1990), and Wald and Heaton (Bull Seismol Soc Am 84:668–691, 1994) independently initiated joint inversion methods, finding that joint inversion provides more reliable rupture process models than single-dataset inversion, leading to an increase of joint inversion studies. A list of these studies was made using the finite-source rupture model database (Mai and Thingbaijam in Seismol Res Lett 85:1348–1357, 2014). Outstanding issues regarding joint inversion were also discussed.     

Intensity predictive attenuation models calibrated in Mw for metropolitan France

In the framework of the SIGMA project, a study was launched to develop a parametric earthquake catalog for the historical period, covering the metropolitan territory and calibrated in Mw. A set of candidate calibration events was selected corresponding to earthquakes felt over a part of the French metropolitan territory, which are fairly well documented both in terms of macroseismic intensity distributions (SisFrance BRGM-EDF-IRSN) and magnitude estimates. The detailed analysis of the macroseismic data led us to retain only 30 events out of 65 with Mw ranging from 3.6 to 5.8. In order to supplement the dataset with data from larger magnitude events, Italian earthquakes were also considered (11 events posterior to 1900 with Mw?≥?6.0 out of 15 in total), using both the DBMI11 macroseismic database (Locati et al. in Seismol Resour Lett 85(3):727–734, 2014) and the parametric information from the CPTI11 (Rovida et al. in CPTI11, la versione 2011 del Catalogo Parametrico dei Terremoti Italiani Istituto Nazionale di Geofisica et Vulcanologia, Milano, Bologna, 2011.  https://doi.org/10.6092/ingv.it-cpti11). To avoid introducing bias related to the differences in terms of intensity scales (MSK vs. MCS), only intensities smaller than or equal to VII were considered (Traversa et al. in On the use of cross-border macroseismic data to improve the estimation of past earthquakes seismological parameters, 2014). Mw and depth metadata were defined according to the Si-Hex catalogue (Cara et al. in Bull Soc Géol Fr 186:3–19, 2015.  https://doi.org/10.2113/qssqfbull.186.1.3), published information, and to the specific worked conducted within SIGMA related to early instrumental recordings (Benjumea et al. in Study of instrumented earthquakes that occurred during the first part of the 20th century (1905–1962), 2015). For the depth estimates, we also performed a macroseismic analysis to evaluate the range of plausible estimates and check the consistency of the solutions. Uncertainties on the metadata related to the calibration earthquakes were evaluated using the range of available alternative estimates. The intensity attenuation models were developed using a one-step maximum likelihood scheme. Several mathematical formulations and sub-datasets were considered to evaluate the robustness of the results (similarly to Baumont and Scotti in Accounting for data and modeling uncertainties in empirical macroseismic predictive equations (EMPEs). Towards “European” EMPEs based on SISFRANCE, DBMI, ECOS macroseismic database, 2008). In particular, as the region of interest may be characterized by significant laterally varying attenuation properties (Bakun and Scotti in Geophys J Int 164:596–610, 2006; Gasperini in Bull Seismol Soc Am 91:826–841, 2001), we introduced regional attenuation terms to account for this variability. Two zonation schemes were tested, one at the national scale (France/Italy), another at the regional scale based on the studies of Mayor et al. (Bull Earthq Eng, 2017.  https://doi.org/10.1007/s10518-017-0124-8) for France and Gasperini (2001) for Italy. Between and within event residuals were analyzed in detail to identify the best models, that is, the ones associated with the best misfit and most limited residual trends with intensity and distance. This analysis led us to select four sets of models for which no significant trend in the between- and within-event residuals is detected. These models are considered to be valid over a wide range of Mw covering?~?3.5–7.0.     

Comment on Pisarenko et al., “Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory”

In this short note, I comment on the research of Pisarenko et al. (Pure Appl. Geophys 171:1599–1624, 2014) regarding the extreme value theory and statistics in the case of earthquake magnitudes. The link between the generalized extreme value distribution (GEVD) as an asymptotic model for the block maxima of a random variable and the generalized Pareto distribution (GPD) as a model for the peaks over threshold (POT) of the same random variable is presented more clearly. Inappropriately, Pisarenkoet al. (Pure Appl. Geophys 171:1599–1624, 2014) have neglected to note that the approximations by GEVD and GPD work only asymptotically in most cases. This is particularly the case with truncated exponential distribution (TED), a popular distribution model for earthquake magnitudes. I explain why the classical models and methods of the extreme value theory and statistics do not work well for truncated exponential distributions. Consequently, these classical methods should be used for the estimation of the upper bound magnitude and corresponding parameters. Furthermore, I comment on various issues of statistical inference in Pisarenkoet al. and propose alternatives. I argue why GPD and GEVD would work for various types of stochastic earthquake processes in time, and not only for the homogeneous (stationary) Poisson process as assumed by Pisarenko et al. (Pure Appl. Geophys 171:1599–1624, 2014). The crucial point of earthquake magnitudes is the poor convergence of their tail distribution to the GPD, and not the earthquake process over time.     

Declustering of Iran earthquake catalog (1983–2017) using the epidemic-type aftershock sequence (ETAS) model

The main goal of this article is to decluster Iranian plateau seismic catalog by the epidemic-type aftershock sequence (ETAS) model and compare the results with some older methods. For this purpose, Iranian plateau bounded in 24°–42°N and 43°–66°E is subdivided into three major tectonic zones: (1) North of Iran (2) Zagros (3) East of Iran. The extracted earthquake catalog had a total of 6034 earthquakes (Mw?>?4) in the time span 1983–2017. The ETAS model is an accepted stochastic approach for seismic evaluation and declustering earthquake catalogs. However, this model has not yet been used to decluster the seismic catalog of Iran. Until now, traditional methods like the Gardner and Knopoff space–time window method and the Reasenberg link-based method have been used in most studies for declustering Iran earthquake catalog. Finally, the results of declustering by the ETAS model are compared with result of Gardner and Knopoff (Bull Seismol Soc Am 64(5):1363–1367, 1974), Uhrhammer (Earthq Notes 57(1):21, 1986), Gruenthal (pers. comm.) and Reasenberg (Geophys Res 90:5479–5495, 1985) declustering methods. The overall conclusion is difficult, but the results confirm the high ability of the ETAS model for declustering Iranian earthquake catalog. Use of the ETAS model is still in its early steps in Iranian seismological researches, and more parametric studies are needed.     

The 2014 Earthquake Model of the Middle East: ground motion model and uncertainties

We summarize the main elements of a ground-motion model, as built in three-year effort within the Earthquake Model of the Middle East (EMME) project. Together with the earthquake source, the ground-motion models are used for a probabilistic seismic hazard assessment (PSHA) of a region covering eleven countries: Afghanistan, Armenia, Azerbaijan, Cyprus, Georgia, Iran, Jordan, Lebanon, Pakistan, Syria and Turkey. Given the wide variety of ground-motion predictive models, selecting the appropriate ones for modeling the intrinsic epistemic uncertainty can be challenging. In this respect, we provide a strategy for ground-motion model selection based on data-driven testing and sensitivity analysis. Our testing procedure highlights the models of good performance in terms of both data-driven and non-data-driven testing criteria. The former aims at measuring the match between the ground-motion data and the prediction of each model, whereas the latter aims at identification of discrepancies between the models. The selected set of ground models were directly used in the sensitivity analyses that eventually led to decisions on the final logic tree structure. The strategy described in great details hereafter was successfully applied to shallow active crustal regions, and the final logic tree consists of four models (Akkar and Ça?nan in Bull Seismol Soc Am 100:2978–2995, 2010; Akkar et al. in Bull Earthquake Eng 12(1):359–387, 2014; Chiou and Youngs in Earthq Spectra 24:173–215, 2008; Zhao et al. in Bull Seismol Soc Am 96:898–913, 2006). For other tectonic provinces in the considered region (i.e., subduction), we adopted the predictive models selected within the 2013 Euro-Mediterranean Seismic Hazard Model (Woessner et al. in Bull Earthq Eng 13(12):3553–3596, 2015). Finally, we believe that the framework of selecting and building a regional ground-motion model represents a step forward in ground-motion modeling, particularly for large-scale PSHA models.     

Seismic vulnerability scenarios of Unreinforced Masonry churches in New Zealand

A vulnerability analysis of c.300 unreinforced Masonry churches in New Zealand is presented. The analysis uses a recently developed vulnerability index method (Cattari et al. in Proceedings of the New Zealand Society for Earthquake Engineering NZSEE 2015 conference, Rotorua, New Zealand, 2015a; b; SECED 2015 conference: earthquake risk and engineering towards a Resilient World, Cambridge; Goded et al. in Vulnerability analysis of unreinforced masonry churches (EQC 14/660)—final report, 2016; Lagomarsino et al. in Bull Earthq Eng, 2018), specifically designed for New Zealand churches, based on a widely tested approach for European historical buildings. It consists of a macroseismic approach where the seismic hazard is defined by the intensity and correlated to post seismic damage. The many differences in typologies of New Zealand and European churches, with very simple architectural designs and a majority of one nave churches in New Zealand, justified the need to develop a method specifically created for this country. A statistical analysis of the churches damaged during the 2010–2011 Canterbury earthquake sequence was previously carried out to develop the vulnerability index modifiers for New Zealand churches. This new method has been applied to generate seismic scenarios for each church, based on the most likely seismic event for 500 years return period, using the latest version of New Zealand’s National Seismic Hazard Model. Results show that highly vulnerable churches (e.g. stone churches and/or with a weak structural design) tend to produce higher expected damage even if the intensity level is lower than for less vulnerable churches in areas with slightly higher seismicity. The results of this paper provide a preliminary tool to identify buildings requiring in depth structural analyses. This paper is considered as a first step towards a vulnerability analysis of all the historical buildings in the country, in order to preserve New Zealand’s cultural and historical heritage.     

Neo-deterministic seismic hazard scenarios for India—a preventive tool for disaster mitigation

Current computational resources and physical knowledge of the seismic wave generation and propagation processes allow for reliable numerical and analytical models of waveform generation and propagation. From the simulation of ground motion, it is easy to extract the desired earthquake hazard parameters. Accordingly, a scenario-based approach to seismic hazard assessment has been developed, namely the neo-deterministic seismic hazard assessment (NDSHA), which allows for a wide range of possible seismic sources to be used in the definition of reliable scenarios by means of realistic waveforms modelling. Such reliable and comprehensive characterization of expected earthquake ground motion is essential to improve building codes, particularly for the protection of critical infrastructures and for land use planning. Parvez et al. (Geophys J Int 155:489–508, 2003) published the first ever neo-deterministic seismic hazard map of India by computing synthetic seismograms with input data set consisting of structural models, seismogenic zones, focal mechanisms and earthquake catalogues. As described in Panza et al. (Adv Geophys 53:93–165, 2012), the NDSHA methodology evolved with respect to the original formulation used by Parvez et al. (Geophys J Int 155:489–508, 2003): the computer codes were improved to better fit the need of producing realistic ground shaking maps and ground shaking scenarios, at different scale levels, exploiting the most significant pertinent progresses in data acquisition and modelling. Accordingly, the present study supplies a revised NDSHA map for India. The seismic hazard, expressed in terms of maximum displacement (Dmax), maximum velocity (Vmax) and design ground acceleration (DGA), has been extracted from the synthetic signals and mapped on a regular grid over the studied territory.     

On the stability analysis of sharply stratified shear flows

When the stability of a sharply stratified shear flow is studied, the density profile is usually taken stepwise and a weak stratification between pycnoclines is neglected. As a consequence, in the instability domain of the flow two-sided neutral curves appear such that the waves corresponding to them are neutrally stable, whereas the neighboring waves on either side of the curve are unstable, in contrast with the classical result of Miles (J Fluid Mech 16:209–227, 1963) who proved that in stratified flows unstable oscillations can be only on one side of the neutral curve. In the paper, the contradiction is resolved and changes in the flow stability pattern under transition from a model stepwise to a continuous density profile are analyzed. On this basis, a simple self-consistent algorithm is proposed for studying the stability of sharply stratified shear flows with a continuous density variation and an arbitrary monotonic velocity profile without inflection points. Because our calculations and the algorithm are both based on the method of stability analysis (Churilov J Fluid Mech 539:25–55, 2005; ibid, 617, 301–326, 2008), which differs essentially from usually used, the paper starts with a brief review of the method and results obtained with it.     

Proposal of an empirical site classification method based on target simulated horizontal over vertical spectral ratio

Nowadays, most of the site classifications schemes are based on the predominant period of the site as determined from the average horizontal to vertical spectral ratios of seismic motion or microtremor. However, the difficulty lies in the identification of the predominant period in particular if the observed average response spectral ratio does not present a clear peak but rather a broadband amplification or multiple peaks. In this work, based on the Eurocode-8 (2004) site classification, and assuming bounded random fields for both shear and compression waves-velocities, damping coefficient, natural period and depth of soil profile, one propose a new site-classification approach, based on “target” simulated average \( H/V \) spectral ratios, defined for each soil class. Taking advantage of the relationship of Kawase et al. (Bull Seismol Soc Am 101:2001–2014, 2011), which link the \( H/V \) spectral ratio to the horizontal (\( HTF \)) over the vertical (\( VTF \)) transfer functions, statistics of \( H/V \) spectral ratio via deterministic visco-elastic seismic analysis using the wave propagation theory are computed for the 4 soil classes. The obtained results show that \( H/V \) and \( HTF \) have amplitudes and shapes remarkably different among the four soil classes and exhibit fundamental peaks in the period ranges remarkably similar. Moreover, the “target” simulated average \( H/V \) spectral ratios for the 4 soil classes are in good agreement with the experimental ones obtained by Zhao et al. (Bull Seismol Soc Am 96:914–925, 2006) from the abundant and reliable Japanese strong motions database Kik-net, Ghasemi et al. (Soil Dyn Earthq Eng 29:121–132, 2009) from the Iranian strong motion data, and Di Alessandro et al. (Bull Sesismol Soc Am 106:2, 2011.  https://doi.org/10.1785/0120110084) from the Italian strong motion data. In addition to the 4 EC-8 standard soil classes (A, B, C and D), the superposition of the 4 target \( H/V \) reveals 3 new boundary site classes; AB, BC and CD, for overlapping \( V_{s,30} \) ranges when the predominant peak is not clearly consistent with any of the 4 proposed classes. Finally, one proposes a site classification index based on the ratio between the cross-correlation and the mean quadratic error between the in situ \( H/V \) spectral ratio and the “target” one. In order to test the reliability of the proposed approach, data from 139 sites were used, 132 collected from the Kik-net network database from Japan and 7 from Algeria. The site classification success rate per site class are around 93, 82, 89 and 100% for rock, hard soil, medium soil and soft soil, respectively. Zhao et al. (2006) found an average success for the 4 classes of soil close to 60%, similar to what one found in the present study (63%) without considering the new soil classes, but much smaller if one considers them (86%). In the absence of \( V_{s,30} \) data, the proposed approach can be an alternative to site classification.     

Performance evaluation of WAVEWATCH III model in the Persian Gulf using different wind resources

The third-generation wave model, WAVEWATCH III, was employed to simulate bulk wave parameters in the Persian Gulf using three different wind sources: ERA-Interim, CCMP, and GFS-Analysis. Different formulations for whitecapping term and the energy transfer from wind to wave were used, namely the Tolman and Chalikov (J Phys Oceanogr 26:497–518, 1996), WAM cycle 4 (BJA and WAM4), and Ardhuin et al. (J Phys Oceanogr 40(9):1917–1941, 2010) (TEST405 and TEST451 parameterizations) source term packages. The obtained results from numerical simulations were compared to altimeter-derived significant wave heights and measured wave parameters at two stations in the northern part of the Persian Gulf through statistical indicators and the Taylor diagram. Comparison of the bulk wave parameters with measured values showed underestimation of wave height using all wind sources. However, the performance of the model was best when GFS-Analysis wind data were used. In general, when wind veering from southeast to northwest occurred, and wind speed was high during the rotation, the model underestimation of wave height was severe. Except for the Tolman and Chalikov (J Phys Oceanogr 26:497–518, 1996) source term package, which severely underestimated the bulk wave parameters during stormy condition, the performances of other formulations were practically similar. However, in terms of statistics, the Ardhuin et al. (J Phys Oceanogr 40(9):1917–1941, 2010) source terms with TEST405 parameterization were the most successful formulation in the Persian Gulf when compared to in situ and altimeter-derived observations.     

Numerical modeling of hydrodynamics and sediment transport—an integrated approach

Point measurement-based estimation of bedload transport in the coastal zone is very difficult. The only way to assess the magnitude and direction of bedload transport in larger areas, particularly those characterized by complex bottom topography and hydrodynamics, is to use a holistic approach. This requires modeling of waves, currents, and the critical bed shear stress and bedload transport magnitude, with a due consideration to the realistic bathymetry and distribution of surface sediment types. Such a holistic approach is presented in this paper which describes modeling of bedload transport in the Gulf of Gdańsk. Extreme storm conditions defined based on 138-year NOAA data were assumed. The SWAN model (Booij et al. 1999) was used to define wind–wave fields, whereas wave-induced currents were calculated using the Ko?odko and Gic-Grusza (2015) model, and the magnitude of bedload transport was estimated using the modified Meyer-Peter and Müller (1948) formula. The calculations were performed using a GIS model. The results obtained are innovative. The approach presented appears to be a valuable source of information on bedload transport in the coastal zone.     

The generalized kinetic equation as a model for the nonlinear transfer in third-generation wave models

An alternative model for the nonlinear interaction term S_nl in spectral wave models, the so called generalized kinetic equation (Janssen J Phys Oceanogr 33(4):863–884, 2003; Annenkov and Shrira J Fluid Mech 561:181–207, 2006b; Gramstad and Stiassnie J Fluid Mech 718:280–303, 2013), is discussed and implemented in the third generation wave model WAVEWATCH-III. The generalized kinetic equation includes the effects of near-resonant nonlinear interactions, and is therefore able, in theory, to describe faster nonlinear evolution than the existing forms of S_nl which are based on the standard Hasselmann kinetic equation (Hasselmann J Fluid Mech 12:481–500, 1962). Numerical simulations with WAVEWATCH have been carried out to thoroughly test the performance of the new form of S_nl, and to compare it to the existing models for S_nl in WAVEWATCH; the DIA and WRT. Some differences between the different models for S_nl are observed. As expected, the DIA is shown to perform less well compared to the exact terms in certain situations, in particular for narrow wave spectra. Also for the case of turning wind significant differences between the different models are observed. Nevertheless, different from the case of unidirectional waves where the generalized kinetic equation represents a obvious improvement to the standard forms of S_nl (Gramstad and Stiassnie 2013), the differences seems to be less pronounced for the more realistic cases considered in this paper.     

More statistical tools for maximum possible earthquake magnitude estimation

In this paper, we introduce additional statistical tools for estimating the maximum regional earthquake magnitude, \( m_{\max} \), as complement to those already introduced by Kijko and Singh (Acta Geophys 59(4):674–700, 2011). Four new methods are introduced and investigated, with regard to their applicability and performance. We present an example of application and a comparison that includes the methods introduced earlier by the previous authors. A condition for the existence of the Tate–Pisarenko estimate and a proof of the asymptotic equivalence of the Tate–Pisarenko and Kijko–Sellevoll estimates are presented in the two appendices.     

The French seismic CATalogue (FCAT-17)

In regions that undergo low deformation rates, as is the case for metropolitan France (i.e. the part of France in Europe), the use of historical seismicity, in addition to instrumental data, is necessary when dealing with seismic hazard assessment. This paper presents the strategy adopted to develop a parametric earthquake catalogue using moment magnitude M_w, as the reference magnitude scale to cover both instrumental and historical periods for metropolitan France. Work performed within the framework of the SiHex (SIsmicité de l’HEXagone) (Cara et al. Bull Soc Géol Fr 186:3–19, 2015. doi: 10.2113/qssqfbull.186.1.3) and SIGMA (SeIsmic Ground Motion Assessment; EDF-CEA-AREVA-ENEL) projects, respectively on instrumental and historical earthquakes, have been combined to produce the French seismic CATalogue, version 2017 (FCAT-17). The SiHex catalogue is composed of ~40,000 natural earthquakes, for which the hypocentral location and M_w magnitude are given. In the frame of the SIGMA research program, an integrated study has been realized on historical seismicity from intensity prediction equations (IPE) calibration in M_w detailed in Baumont et al. (submitted) companion paper to their application to earthquakes of the SISFRANCE macroseismic database (BRGM, EDF, IRSN), through a dedicated strategy developed by Traversa et al. (Bull Earthq Eng, 2017. doi: 10.1007/s10518-017-0178-7) companion paper, to compute their M_w magnitude and depth. Macroseismic data and epicentral location and intensity used both in IPE calibration and inversion process, are those of SISFRANCE without any revision. The inversion process allows the main macroseismic field specificities reported by SISFRANCE to be taken into account with an exploration tree approach. It also allows capturing the epistemic uncertainties associated with macroseismic data and to IPEs selection. For events that exhibit a poorly constrained macroseismic field (mainly old, cross border or off-shore earthquakes), joint inversion of M_w and depth is not possible, and depth needs to be fixed to calculate M_w. Regional a priori depths have been defined for this purpose based on analysis of earthquakes with a well constrained macroseismic field where joint inversion of M_w and depth is possible. As a result, 27% of SISFRANCE earthquake seismological parameters have been jointly inverted and for the other 73% M_w has been calculated assuming a priori depths. The FCAT-17 catalogue is composed of the SIGMA historical parametric catalogue (magnitude range between 3.5 up to 7.0), covering from AD463 to 1965, and of the SiHex instrumental one, extending from 1965 to 2009. Historical part of the catalogue results from an automatic inversion of SISFRANCE data. A quality index is estimated for each historical earthquake according to the way the events are processed. All magnitudes are given in M_w which makes this catalogue directly usable as an input for probabilistic or deterministic seismic hazard studies. Uncertainties on magnitudes and depths are provided for historical earthquakes following calculation scheme presented in Traversa et al. (2017). Uncertainties on magnitudes for instrumental events are from Cara et al. (J Seismol 21:551–565, 2017. doi: 10.1007/s10950-016-9617-1).     

The transition from symmetric to baroclinic instability in the Eady model

Here, we explore the transition from symmetric instability to ageostrophic baroclinic instability in the Eady model; an idealised representation of a submesoscale mixed layer front. We revisit the linear stability problem considered by Stone (J Atmos Sci, 23, 390–400, (Stone 1966)), Stone (J Atmos Sci, 27, 721–726, (Stone 1970)), Stone (J Atmos Sci, 29, 419–426, (Stone 1972)) with a particular focus on three-dimensional ‘mixed modes’ (which are neither purely symmetric or baroclinic) and find that these modes can have growth rates within just a few percent of the corresponding two-dimensional growth rate maximum. In addition, we perform very high resolution numerical simulations allowing an exploration of the transition from symmetric to baroclinic instability. Three-dimensional mixed modes represent the largest contribution to the turbulent kinetic energy during the transition period between symmetric and baroclinic instability. In each simulation, we see the development of sharp fronts with associated high rms vertical velocities of up to 30 mm s^?1. Furthermore, we see significant transfer of energy to small scales, demonstrated by time-integrated mixing and energy dissipation by small-scale three-dimensional turbulence totalling about 30 % of the initial kinetic energy in all cases.     

Regional adjustment factors for three NGA-West2 ground-motion prediction equations to be applicable in northern Iran

Ground-motion prediction equations (GMPEs) are essential tools in seismic hazard studies to estimate ground motions generated by potential seismic sources. Global GMPEs which are based on well-compiled global strong-motion databanks, have certain advantages over local GMPEs, including more sophisticated parameters in terms of distance, faulting style, and site classification but cannot guarantee the local/region-specific propagation characteristics of shear wave (e.g., geometric spreading behavior, quality factor) for different seismic regions at larger distances (beyond about 80 km). Here, strong-motion records of northern Iran have been used to estimate the propagation characteristics of shear wave and determine the region-specific adjustment parameters for three of the NGA-West2 GMPEs to be applicable in northern Iran. The dataset consists of 260 three-component records from 28 earthquakes, recorded at 139 stations, with moment magnitudes between 4.9 and 7.4, horizontal distance to the surface projection of the rupture (R _JB) less than 200 km, and average shear-wave velocity over the top 30 m of the subsurface (V _S30) between 155 and 1500 m/s. The paper also presents the ranking results for three of the NGA-West2 GMPEs against strong motions recorded in northern Iran, before and after adjustment for region-dependent attenuation characteristics. The ranking is based on the likelihood and log-likelihood methods (LH and LLH) proposed by Scherbaum et al. (Bull Seismol Soc Am 94: 2164–2185, 2004, Bull Seismol Soc Am 99, 3234–3247, 2009, respectively), the Nash–Sutcliffe model efficiency coefficient (Nash and Sutcliffe, J Hydrol 10:282–290, 1970), and the EDR method of Kale and Akkar (Bull Seismol Soc Am 103:1069–1084, 2012). The best-fitting models over the whole frequency range are the ASK14 and BSSA14 models. Taking into account that the models’ performances were boosted after applying the adjustment factors, at least moderate regional variation of ground motions is highlighted. The regional adjustment based on the Iranian database reveals an upward trend (indicated as high Q factor) for the selected database. Further investigation to determine adjustment factors based on a much richer database of the Iranian strong-motion records is of utmost important for seismic hazard and risk analysis studies in northern Iran, containing major cities including the capital city of Tehran.     

Probabilistic modelling of macroseismic attenuation and forecast of damage scenarios

According to the idea now widespread that macroseismic intensity should be expressed in probabilistic terms, a beta-binomial model has been proposed in the literature to estimate the probability of the intensity at site in the Bayesian framework and a clustering procedure has been adopted to define learning sets of macroseismic fields required to assign prior distributions of the model parameters. This article presents the results concerning the learning sets obtained by exploiting the large Italian macroseismic database DBM1I11 (Locati et al. in DBMI11, the 2011 version of the Italian Macroseismic Database, 2011. http://emidius.mi.ingv.it/DBMI11/) and discusses the problems related to their use in probabilistic modelling of the attenuation in seismic regions of the European countries partners of the UPStrat-MAFA project (2012), namely South Iceland, Portugal, SE Spain and Mt Etna volcano area (Italy). Anisotropy and the presence of offshore earthquakes are some of the problems faced. All the work has been carried out in the framework of the Task B of the project.     

Wave boundary layers in rotating stratified fluid and near-inertial oscillations

Theory of wave boundary layers (WBLs) developed by Reznik (J Mar Res 71: 253–288, 2013, J Fluid Mech 747: 605–634, 2014, J Fluid Mech 833: 512–537, 2017) is extended to a rotating stratified fluid. In this case, the WBLs arise in the field of near-inertial oscillations (NIOs) driven by a tangential wind stress of finite duration. Near-surface Ekman layer is specified in the most general form; tangential stresses are zero at the lower boundary of Ekman layer and viscosity is neglected below the boundary. After the wind ceases, the Ekman pumping at the boundary becomes a linear superposition of inertial oscillations with coefficients dependent on the horizontal coordinates. The solution under the Ekman layer is obtained in the form of expansions in the vertical wave modes. We separate from the solution a part representing NIO and demonstrate development of a WBL near the Ekman layer boundary. With increasing time t, the WBL width decays inversely proportional to \( \sqrt{t} \) and gradients of fields in the WBL grow proportionally to \( \sqrt{t} \); the most part of NIO is concentrated in the WBL. Structure of the WBL depends strongly on its horizontal scale L determined by scale of the wind stress. The shorter the NIO is, the thinner and sharper the WBL is; the short-wave NIO with L smaller than the baroclinic Rossby scale L_R does not penetrate deep into the ocean. On the contrary, for L?≥?L_R, the WBL has a smoother vertical structure; a significant long-wave NIO signal is able to reach the oceanic bottom. An asymptotic theory of the WBL in rotating stratified fluid is suggested.     

Numerical modeling of space-time wave extremes using WAVEWATCH III

A novel implementation of parameters estimating the space-time wave extremes within the spectral wave model WAVEWATCH III (WW3) is presented. The new output parameters, available in WW3 version 5.16, rely on the theoretical model of Fedele (J Phys Oceanogr 42(9):1601-1615, 2012) extended by Benetazzo et al. (J Phys Oceanogr 45(9):2261–2275, 2015) to estimate the maximum second-order nonlinear crest height over a given space-time region. In order to assess the wave height associated to the maximum crest height and the maximum wave height (generally different in a broad-band stormy sea state), the linear quasi-determinism theory of Boccotti (2000) is considered. The new WW3 implementation is tested by simulating sea states and space-time extremes over the Mediterranean Sea (forced by the wind fields produced by the COSMO-ME atmospheric model). Model simulations are compared to space-time wave maxima observed on March 10th, 2014, in the northern Adriatic Sea (Italy), by a stereo camera system installed on-board the “Acqua Alta” oceanographic tower. Results show that modeled space-time extremes are in general agreement with observations. Differences are mostly ascribed to the accuracy of the wind forcing and, to a lesser extent, to the approximations introduced in the space-time extremes parameterizations. Model estimates are expected to be even more accurate over areas larger than the mean wavelength (for instance, the model grid size).     

Impact of Three-Parameter Weibull Models in Probabilistic Assessment of Earthquake Hazards

This paper investigates the suitability of a three-parameter (scale, shape, and location) Weibull distribution in probabilistic assessment of earthquake hazards. The performance is also compared with two other popular models from same Weibull family, namely the two-parameter Weibull model and the inverse Weibull model. A complete and homogeneous earthquake catalog (Yadav et al. in Pure Appl Geophys 167:1331–1342, 2010) of 20 events (M ≥ 7.0), spanning the period 1846 to 1995 from north–east India and its surrounding region (20°–32°N and 87°–100°E), is used to perform this study. The model parameters are initially estimated from graphical plots and later confirmed from statistical estimations such as maximum likelihood estimation (MLE) and method of moments (MoM). The asymptotic variance–covariance matrix for the MLE estimated parameters is further calculated on the basis of the Fisher information matrix (FIM). The model suitability is appraised using different statistical goodness-of-fit tests. For the study area, the estimated conditional probability for an earthquake within a decade comes out to be very high (≥0.90) for an elapsed time of 18 years (i.e., 2013). The study also reveals that the use of location parameter provides more flexibility to the three-parameter Weibull model in comparison to the two-parameter Weibull model. Therefore, it is suggested that three-parameter Weibull model has high importance in empirical modeling of earthquake recurrence and seismic hazard assessment.