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.     

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.     

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.     

Asymptotic behavior of an n-species stochastic Gilpin–Ayala cooperative model

An n-species stochastic Gilpin–Ayala cooperative model was investigated in this study. The Lyapunov function and the M-matrix method were applied to study the stability of the solutions. Sufficient conditions for the existence of a global positive solution of the Gilpin–Ayala cooperative model were established. Certain asymptotically stable results of a global positive solution of the cooperative model and its domain of attraction were estimated. That main objective of this study is to provide corrections for errors in some theorems given in the work of Lian et al. (2007). The errors of Theorems 2, 3, 5, and 6 from the published work appeared in the parameters θ _i and p _ii .     

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.     

Seismic performance evaluation of traditional timber <Emphasis Type="Italic">Hımış</Emphasis> frames: capacity spectrum method based assessment

Timber constructions have been widely suggested to be seismically resistant based on post-disaster reconnaissance studies. This observation has, however, remained to a large extent anecdotal due to the lack of experimental work supporting it, especially for certain timber architectural forms, including traditional timber frame “h?m??” structures. To fill this gap, the authors carried out an extensive full-scale testing scheme using frames of various geometrical configurations, tested under reverse-cyclic lateral loading with/without infill (brick and adobe) or cladding (ba?dadi and ?amdolma) (Aktas et al. in Earthq Spectra 30(4):1711–1732, 2014a, b). The tests concluded that h?m?? frames had high energy dissipation capabilities due mostly to nailed connections. Infill/cladding significantly helped improve stiffness and lateral load strength of the frames, and timber type did not seem to make a remarkable impact on the overall behaviour. The current paper, on the other hand, uses test data to calculate capacity/demand ratios based on capacity spectrum method and Eurocode 8 to elaborate more on the performance of “h?m??” structures under seismic loading. The obtained results are discussed to draw important conclusions with regards to how frame geometry and infill/cladding techniques affect the overall performance.     

Quantitative Analysis of Seismicity Before Large Taiwanese Earthquakes Using the G-R Law

Seismicity has been identified as an example of a natural, nonlinear system for which the distribution of frequency and event size follow a power law called the “Gutenberg–Richter (G-R) law.” The parameters of the G-R law, namely b- and a-values, have been widely used in many studies about seismic hazards, earthquake forecasting models, and other related topics. However, the plausibility of the power law model and applicability of parameters were mainly verified by statistical error σ of the b-value, the effectiveness of which is still doubtful. In this research, we used a newly defined p value developed by Clausetet al. (Power-Law Distributions in Empirical Data, SIAM Rev. 51, 661–703, 2009) instead of the statistical error σ of the b-value and verified its effectiveness as a plausibility index of the power-law model. Furthermore, we also verified the effectiveness of K–S statistics as a goodness-of-fit test in estimating the crucial parameter \(M_{\text{c}}\) of the power-law model.     

Decaying grid turbulence experiments in a stratified fluid: flow measurements and statistics

Laboratory experiments of decaying grid stratified turbulence were performed in a two-layer fluid and varying the stratification intensity. Turbulence was generated by towing an array of cylinders in a square vessel and the grid was moved at a constant velocity along the total vertical extent of the tank. In order to investigate the influence of the stratification intensity on the turbulence decay, both 2C-PIV and stereo PIV were used to provide time resolved velocity fields in the horizontal plane and the out-of-plane velocity. As expected, a faster decay of the turbulence level along the vertical axis and the collapse in a quasi-horizontal motion increased with the buoyancy frequency, N. In order to characterise the decay process we investigated the time evolution of the vortex statistics, the turbulence scales and the kinetic energy and enstrophy of the horizontal flow. The exponents recovered in the corresponding scaling laws were compared with the theoretical predictions and with reference values obtained in previous experimental studies. Both the spectral analysis and the evolution of characteristic length scales indicate that, in the examined range of N, the dynamics is substantially independent of the stratification intensity. The results obtained were explained in terms of the scaling analysis of decaying turbulence in strongly stratified fluids introduced by Brethouwer et al. (J Fluid Mech 585:343–368.  https://doi.org/10.1017/S0022112007006854, 2007).     

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.     

Seismic hazard assessment in the megacity of Blida (Algeria) and its surrounding regions using parametric-historic procedure

The region of Blida is characterized by a relatively high seismic activity, pointed especially during the past two centuries. Indeed, it experienced a significant number of destructive earthquakes such as the earthquakes of March 2, 1825 and January 2, 1867, with intensity of X and IX, respectively. This study aims to investigate potential seismic hazard in Blida city and its surrounding regions. For this purpose, a typical seismic catalog was compiled using historical macroseismic events that occurred over a period of a few hundred years, and the recent instrumental seismicity dating back to 1900. The parametric-historic procedure introduced by Kijko and Graham (1998, 1999) was applied to assess seismic hazard in the study region. It is adapted to deal with incomplete catalogs and does not use any subjective delineation of active seismic zones. Because of the lack of recorded strong motion data, three ground prediction models have been considered, as they seem the most adapted to the seismicity of the study region. Results are presented as peak ground acceleration (PGA) seismic hazard maps, showing expected peak accelerations with 10% probability of exceedance in 50-year period. As the most significant result, hot spot regions with high PGA values are mapped. For example, a PGA of 0.44 g has been found in a small geographical area centered on Blida city.     

Limitations of <Emphasis Type="Italic">H</Emphasis>-<Emphasis Type="Italic">κ</Emphasis> stacking: ambiguous results caused by crustal layering

Over the past decade, the H-κ stacking technique of Zhu and Kanamori (J Geophys Res 105:2969–2980, 2000) has become a standard tool to determine the crustal thickness H and the bulk crustal v_P/v_S ratio κ from teleseismic receiver functions. It is obvious that unfavorable noise conditions as well as a complex 3D velocity structure can severely hamper the interpretation of receiver-function data. However, we observe that ambiguities can even arise from a simple 1D layered velocity structure which raises a high potential for misinterpretations. To analyze the feasibility and basic limitations of the H-κ stacking method, we conduct a series of tests based on synthetic data. The impact of different given elementary parameters, related either to the velocity structure or to the data processing, is evaluated in a series of eight individual tests. We deliberately exclude complications such as 3D structural variations and/or noise to show that even a simple 1D velocity structure, involving, e.g., an additional inter-crustal discontinuity, can have significant consequences for the interpretation of the results. However, our modeling suggests that more complex crustal structures may lead to even less reliable results. Additionally, our tests illustrate that time shifts of the maxima in the H-κ domain due to the superposition and merging of individual phases can lead to significantly overestimated v_P/v_S ratios. In general, the depth to the Moho (or other discontinuities of interest) is less significantly affected. Our tests indicate the necessity to accurately check delay times derived from the maxima of the H-κ stacks against corresponding phases in the receiver functions. Repeating the stacking with varied weighting factors and filter ranges can help to reduce the ambiguities and to avoid possible misinterpretation.     

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).     

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.     

Site term from single-station sigma analysis of S-waves in western Turkey

The main aim of this study is to obtain site terms from single-station sigma analysis and to compare them with the site functions resulting from different techniques. The dataset consists of 1764 records from 322 micro- and moderate-size local earthquakes recorded by 29 stations in western Turkey. Median models were derived from S-wave Fourier amplitude spectra for selected 22 frequencies, by utilizing the MLR procedure which performs the maximum likelihood (ML) estimation of mixed models where the fixed effects are treated as random (R) effects with infinite variance. At this stage, b (geometrical spreading coefficient) and Q (quality factor) values were decomposed, simultaneously. The residuals of the median models were examined by utilizing the single-station sigma analysis to obtain the site terms of 29 stations. Sigma for the median models is about 0.422 log10 units and decreases to about 0.308, when the site terms from the single-station sigma analysis were considered (27% reduction). The event-corrected within-event standard deviations for each frequency are rather stable, in the range 0.19–0.23 log10 units with an average value of 0.20 (±?0.01). The site terms from single-station sigma analysis were compared with the site function estimates from the horizontal-to-vertical-spectral-ratio (HVSR) and generalized inversion (INV) techniques by Akyol et al. (2013) and Kurtulmu? and Akyol (2015), respectively. Consistency was observed between the single-station sigma site terms and the INV site transfer functions. The results imply that the single-station sigma analysis could separate the site terms with respect to the median models.     

Earthquake Nucleation on Faults with a Revised Rate- and State-Dependent Friction Law

Recently Nagata et al. (J Geophys Res 117:B02314, 2012) have proposed a new version of rate- and state-dependent friction law (RSF) that seems to have eventually resolved all the previously known discrepancies in the existing RSFs from laboratory observations. The values of a and b, empirical RSF parameters determined by fitting the same laboratory experiments, have been revised to be five times greater and a newly noticed weakening effect by shear stress with a coefficient c has been introduced. By using this revised RSF, we reinvestigated a problem of 2D quasi-static nucleation on faults. A crack-like nucleation-zone expansion known for the ‘aging’ version of RSF is not sustainable with the ‘Nagata’ law, which is understandable as the Nagata law does not produce a slip-weakening distance proportional to the involved strength reduction, an aging law’s feature that contradicts laboratory observations. The later stage of Nagata-law nucleation shows localization of quasi-static slip within a limited spatial extent, but the localization is much milder than that predicted by the ‘slip’ version of RSF. With an appropriate c parameter of the Nagata law, the nucleation size seems to be reduced only by a factor from that of the aging law.     

A novel model and estimation method for the individual random component of earthquake ground-motion relations

In this paper, I introduce a novel approach to modelling the individual random component (also called the intra-event uncertainty) of a ground-motion relation (GMR), as well as a novel approach to estimating the corresponding parameters. In essence, I contend that the individual random component is reproduced adequately by a simple stochastic mechanism of random impulses acting in the horizontal plane, with random directions. The random number of impulses was Poisson distributed. The parameters of the model were estimated according to a proposal by Raschke J Seismol 17(4):1157–1182, (2013a), with the sample of random difference ξ?=?ln(Y ₁ )-ln(Y ₂ ), in which Y ₁ and Y ₂ are the horizontal components of local ground-motion intensity. Any GMR element was eliminated by subtraction, except the individual random components. In the estimation procedure, the distribution of difference ξ was approximated by combining a large Monte Carlo simulated sample and Kernel smoothing. The estimated model satisfactorily fitted the difference ξ of the sample of peak ground accelerations, and the variance of the individual random components was considerably smaller than that of conventional GMRs. In addition, the dependence of variance on the epicentre distance was considered; however, a dependence of variance on the magnitude was not detected. Finally, the influence of the novel model and the corresponding approximations on PSHA was researched. The applied approximations of distribution of the individual random component were satisfactory for the researched example of PSHA.     

Automatic detection of P- and S-wave arrival times: new strategies based on the modified fractal method and basic matching pursuit

In this work, new strategies for automatic identification of P- and S-wave arrival times from digital recorded local seismograms are proposed and analyzed. The database of arrival times previously identified by a human reader was compared with automatic identification techniques based on the Fourier transformation in reduced time (spectrograms), fractal analysis, and the basic matching pursuit algorithm. The first two techniques were used to identify the P-wave arrival times, while the third was used for the identification of the S-wave. For validation, the results were compared with the short-time average over long-time average (STA/LTA) of Rietbrock et al., Geophys Res Lett 39(8), (2012) for the database of aftershocks of the 2010 Maule M _w = 8.8 earthquake. The identifiers proposed in this work exhibit good results that outperform the STA/LTA identifier in many scenarios. The average difference from the reference picks (times obtained by the human reader) in P- and S-wave arrival times is ～ 1 s.     

Probabilistic aftershock hazard analysis,two case studies in West and Northwest Iran

Aftershock hazard maps contain the essential information for search and rescue process, and re-occupation after a main-shock. Accordingly, the main purposes of this article are to study the aftershock decay parameters and to estimate the expected high-frequency ground motions (i.e., Peak Ground Acceleration (PGA)) for recent large earthquakes in the Iranian plateau. For this aim, the Ahar-Varzaghan doublet earthquake (August 11, 2012; M _N =6.5, M _N =6.3), and the Ilam (Murmuri) earthquake (August 18, 2014 ; M _N =6.2) have been selected. The earthquake catalogue has been collected based on the Gardner and Knopoff (Bull Seismol Soc Am 64(5), 1363-1367, 1974) temporal and spatial windowing technique. The magnitude of completeness and the seismicity parameters (a,??b) and the modified Omori law parameters (P,??K,??C) have been determined for these two earthquakes in the 14, 30, and 60 days after the mainshocks. Also, the temporal changes of parameters (a,??b,??P,??K,??C) have been studied. The aftershock hazard maps for the probability of exceedance (33%) have been computed in the time periods of 14, 30, and 60 days after the Ahar-Varzaghan and Ilam (Murmuri) earthquakes. For calculating the expected PGA of aftershocks, the regional and global ground motion prediction equations have been utilized. Amplification factor based on the site classes has also been implied in the calculation of PGA. These aftershock hazard maps show an agreement between the PGAs of large aftershocks and the forecasted PGAs. Also, the significant role of b parameter in the Ilam (Murmuri) probabilistic aftershock hazard maps has been investigated.     

On the possible correlation between the Gutenberg-Richter parameters of the frequency-magnitude relationship

The study of the Gutenberg-Richter (GR) parameters a and b has been very important to describe and characterize the seismicity over the different seismic provinces around the world. As far as we know, the possible correlation between the GR parameters a and b has not received enough attention. Bayrak et al. reported the a and b values for 27 active seismic regions around the boundaries of the main tectonic plates of the world. From these data, we found that there exists a positive correlation between the a and b parameters (R =?0.85, R² =?0.72). On the other hand, we made around 150 computer runs of a spring-block model proposed by Olami et al. (Phys Rev Lett 68(8):1244–1247, 1992). This model roughly emulates the interaction between two fault planes and it reaches a self-organized critical state. With these simulations, we also found that the a and b parameters are positively correlated. Motivated by these results, we propose an analytical demonstration that indeed a and b are positively correlated. In addition, we discuss on other possible applications of the spring-block model to actual seismicity and to frictional experiments made with sandpapers.     

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.