Empirical ground-motion relations using moderate earthquakes recorded by Medellín–Aburrá Valley (Colombia) strong-motion networks

We tested attenuation relations obtained for different regions of the world to verify their suitability to predict strong-motion data recorded by Medellín and Aburrá Valley Accelerographic Networks. We used as comparison criteria, the average of the difference between the observed and the predicted data as a function of epicenter distance and its standard deviation. We also used the approach developed by Sherbaum et al. (Bull Seism Soc Am 94:2164–2185, 2004) that provides a method to evaluate the overall goodness-of-fit of ground-motion prediction equations. The predictive models selected use a generic focal depth. We found that this parameter has an important influence in the ground-motion predictions and must be taken into account as an independent variable. We also found important to characterize the local soil amplification to improve the attenuation relations. We found empirical relations for peak horizontal acceleration PGA and velocity PGV based on the Kamiyama and Yanagisawa (Soils Found 26:16–32, 1986) approach. $$\begin{aligned} \log _{10} (PGA)=0.5886M_L -1.0902\log _{10}(R)-0.0035H+C_{st}\pm 0.\text{29} \end{aligned}$$ $$\begin{aligned} \log _{10} (PGV)=0.7255M_L -1.8812\log _{10}(R)-0.0016H+C_{st}\pm 0.36 \end{aligned}$$ where PGA is measured in cm/s $^{2}$ and PGV in cm/s, $M_{L}$ is local magnitude in the range 2.8–6.5, $R$ is epicentral distance up to 290 km, $H$ is focal depth in km and $C_{st}$ is a coefficient that accounts for the site response due to soil conditions of each recording station. The introduction of focal depth and local site conditions as independent variables, minimize the residuals and the dispersion of the predicted data. We conclude that $H$ and $C_{st}$ are sensitive parameters, having a strong influence on the strong-motion predictions. Using the same functional form, we also propose an empirical relation for the root mean square acceleration a $_\mathrm{rms}$ : $$\begin{aligned} \log _{10} \left( {a_{rms} } \right)=0.4797M_L -1.1665\log _{10} (R)-0.00201H+C_{st}\pm 0.40 \end{aligned}$$ where a $_\mathrm{rms}$ is measured in cm/s $^{2}$ , from the S-wave arrival and using a window length equal to the rupture duration. The other variables are the same as those for PGA and PGV. The site correction coefficients $C_{st}$ found for PGA, PGV and a $_\mathrm{rms}$ show a similar trend indicating a good correlation with the soil conditions of the recording sites.     

A semiempirical mathematical model of the secondary pollution of water bodies by soluble iron and manganese forms

A semiempirical mathematical model of iron and manganese migration from bottom sediments into the water mass of water bodies has been proposed based on some basic regularities in the geochemistry of those elements. The entry of dissolved forms of iron and manganese under aeration conditions is assumed negligible. When dissolved-oxygen concentration is <0.5 mg/L, the elements start releasing from bottom sediments, their release rate reaching its maximum under anoxic conditions. The fluxes of dissolved iron and manganese (Me) from bottom sediments into the water mass (J _Me) are governed by the gradients of their concentrations in diffusion water sublayer adjacent to sediment surface and having an average thickness of h = 0.025 cm: \({J_{Me}} = - {D_{Me}}\frac{{{C_{Me\left( {ss} \right)}} - {C_{Me\left( w \right)}}}}{h}\) (D _Me ≈ 1 × 10^–9 m²/s is molecular diffusion coefficient of component Me in solution; C _Me(ss) and C _Me(w) ≈ 0 are Me concentrations on sediment surface, i.e., on the bottom boundary of the diffusion water sublayer, and in the water mass, i.e., on the upper boundary of the diffusion water sublayer). The value of depends on water saturation with dissolved oxygen (\({\eta _{{O_2}}}\)) in accordance with the empiric relationship \({C_{Me\left( {ss} \right)}} = \frac{{C_{_{Me\left( {ss} \right)}}^{\max }}}{{1 + k{\eta _{{O_2}}}}}\) (k is a constant factor equal to 300 for iron and 100 for manganese; C _Me(ss) ^max is the maximal concentration of Me on the bottom boundary of the diffusion water sublayer with C _Fe(ss) ^max ≈ 200 μM (11 mg/L), and C _Mn(ss) ^max ≈ 100 μM (5.5 mg/L).     

Empirical ground-motion models for point- and extended-source crustal earthquake scenarios in Europe and the Middle East

This article presents the latest generation of ground-motion models for the prediction of elastic response (pseudo-) spectral accelerations, as well as peak ground acceleration and velocity, derived using pan-European databases. The models present a number of novelties with respect to previous generations of models (Ambraseys et al. in Earthq Eng Struct Dyn 25:371–400, 1996, Bull Earthq Eng 3:1–53, 2005; Bommer et al. in Bull Earthq Eng 1:171–203, 2003; Akkar and Bommer in Seismol Res Lett 81:195–206, 2010), namely: inclusion of a nonlinear site amplification function that is a function of $\text{ V }_\mathrm{S30}$ and reference peak ground acceleration on rock; extension of the magnitude range of applicability of the model down to $\text{ M }_\mathrm{w}$ 4; extension of the distance range of applicability out to 200 km; extension to shorter and longer periods (down to 0.01 s and up to 4 s); and consistent models for both point-source (epicentral, $\text{ R }_\mathrm{epi}$ , and hypocentral distance, $\text{ R }_\mathrm{hyp}$ ) and finite-fault (distance to the surface projection of the rupture, $\text{ R }_\mathrm{JB}$ ) distance metrics. In addition, data from more than 1.5 times as many earthquakes, compared to previous pan-European models, have been used, leading to regressions based on approximately twice as many records in total. The metadata of these records have been carefully compiled and reappraised in recent European projects. These improvements lead to more robust ground-motion prediction equations than have previously been published for shallow (focal depths less than 30 km) crustal earthquakes in Europe and the Middle East. We conclude with suggestions for the application of the equations to seismic hazard assessments in Europe and the Middle East within a logic-tree framework to capture epistemic uncertainty.     

Stochastic modelling of relative water permeability in vegetative soils with implications on stability of bioengineered slope

Vegetation is known to influence the hydrological state variables, suction \( \left( \psi \right) \) and volumetric water content (\( \theta_{w} \)) of soil. In addition, vegetation induces heterogeneity in the soil porous structure and consequently the relative permeability (\( k_{r} \)) of water under unsaturated conditions. The indirect method of utilising the soil water characteristic curve (SWCC) is commonly adopted for the determination of \( k_{r} \). In such cases, it is essential to address the stochastic behaviour of SWCC, in order to conduct a robust analysis on the \( k_{r} \) of vegetative cover. The main aim of this study is to address the uncertainties associated with \( k_{r} \), using probabilistic analysis, for vegetative covers (i.e., grass and tree species) with bare cover as control treatment. We propose two approaches to accomplish the aforesaid objective. The univariate suction approach predicts the probability distribution functions of \( {\text{k}}_{\text{r}} \), on the basis of identified best probability distribution of suction. The bivariate suction and water content approach deals with the bivariate modelling of the water content and suction (SWCC), in order to capture the randomness in the permeability curves, due to presence of vegetation. For this purpose, the dependence structure of \( \psi \) and \( \theta_{w} \) is established via copula theory, and the \( k_{r} \) curves are predicted with respect to varying levels of \( \psi - \theta_{w} \) correlation. The results showed that the \( k_{r} \) of vegetative covers is substantially lower than that in bare covers. The reduction in \( k_{r} \) with drying is more in tree cover than grassed cover, since tree roots induce higher levels of suction. Moreover, the air entry value of the soil depends on the magnitude of \( \psi - \theta_{w} \) correlation, which in turn, is influenced by the type of vegetation in the soil. \( k_{r} \) is found to be highly uncertain in the desaturation zone of the relative permeability curve. The stochastic behaviour of \( k_{r} \) is found to be most significant in tree covers. Finally, a simplified case study is also presented in order to demonstrate the impact of the uncertainty in \( k_{r} \), on the stability of vegetates slopes. With an increment in the parameter \( \alpha \), factor of safety (FS) is found to decrease. The trend of FS is reverse of this with parameter \( n \). Overall FS is found to vary around 4–5%, for both bare and vegetative slopes.     

Towards fully data driven ground-motion prediction models for Europe

We have used the Artificial Neural Network method (ANN) for the derivation of physically sound, easy-to-handle, predictive ground-motion models from a subset of the Reference database for Seismic ground-motion prediction in Europe (RESORCE). Only shallow earthquakes (depth smaller than 25 km) and recordings corresponding to stations with measured $V_{s30}$ properties have been selected. Five input parameters were selected: the moment magnitude $M_{W}$ , the Joyner–Boore distance $R_{JB}$ , the focal mechanism, the hypocentral depth, and the site proxy $V_{S30}$ . A feed-forward ANN type is used, with one 5-neuron hidden layer, and an output layer grouping all the considered ground motion parameters, i.e., peak ground acceleration (PGA), peak ground velocity (PGV) and 5 %-damped pseudo-spectral acceleration (PSA) at 62 periods from 0.01 to 4 s. A procedure similar to the random-effects approach was developed to provide between and within event standard deviations. The total standard deviation ( $\sigma $ ) varies between 0.298 and 0.378 (log $_{10}$ unit) depending on the period, with between-event and within-event variabilities in the range 0.149–0.190 and 0.258–0.327, respectively. Those values prove comparable to those of conventional GMPEs. Despite the absence of any a priori assumption on the functional dependence, our results exhibit a number of physically sound features: magnitude scaling of the distance dependency, near-fault saturation distance increasing with magnitude, amplification on soft soils and even indications for nonlinear effects in softer soils.     

The role of site effects in the comparison between code provisions and the near field strong motion of the Emilia 2012 earthquakes

A damaging seismic sequence hit a wide area mainly located in the Emilia-Romagna region (Northern Italy) during 2012 with several events of local magnitude \(\hbox {M}_\mathrm{l} \ge 5\) , among which the \(\hbox {M}_\mathrm{l}\) 5.9 May 20 and the \(\hbox {M}_\mathrm{l}\) 5.8 May 29 were the main events. Thanks to the presence of a permanent accelerometric station very close to the epicentre and to the temporary installations performed in the aftermath of the first shock, a large number of strong motion recordings are available, on the basis of which, we compared the recorded signals with the values provided by the current Italian seismic regulations, and we observed several differences with respect to horizontal components when the simplified approach for site conditions (based on Vs30 classes) is used. On the contrary, when using the more accurate approach based on the local seismic response, we generally obtain a much better agreement, at least in the frequency range corresponding to a quarter wavelength comparable with the depth of the available subsoil data. Some unresolved questions still remain, such as the low frequency behaviour ( \(<\) 1 Hz) that could be due either to complex propagation at depth larger than the one presently investigated or to near source effects, and the behaviour of vertical spectra whose recorded/code difference is too large to be explained with the information currently available.     

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).     

Fragility curves for risk-targeted seismic design maps

Seismic design using maps based on “risk-targeting” would lead to an annual probability of attaining or exceeding a certain damage state that is uniform over an entire territory. These maps are based on convolving seismic hazard curves from a standard probabilistic analysis with the derivative of fragility curves expressing the chance for a code-designed structure to attain or exceed a certain damage state given a level of input motion, e.g. peak ground acceleration (PGA). There are few published fragility curves for structures respecting the Eurocodes (ECs, principally EC8 for seismic design) that can be used for the development of risk-targeted design maps for Europe. In this article a set of fragility curves for a regular three-storey reinforced-concrete building designed using EC2 and EC8 for medium ductility and increasing levels of design acceleration \((\hbox {a}_\mathrm{g})\) is developed. These curves show that structures designed using EC8 against PGAs up to about 1 m/s \(^{2}\) have similar fragilities to those that respect only EC2 (although this conclusion may not hold for irregular buildings, other geometries or materials). From these curves, the probability of yielding for a structure subjected to a PGA equal to \(\hbox {a}_\mathrm{g}\) varies between 0.14 ( \(\hbox {a}_\mathrm{g}=0.7\) m/s \(^{2})\) and 0.85 ( \(\hbox {a}_\mathrm{g}=3\) m/s \(^{2})\) whereas the probability of collapse for a structure subjected to a PGA equal to \(\hbox {a}_\mathrm{g}\) varies between 1.7 \(\times 10^{-7}\) ( \(\hbox {a}_\mathrm{g}=0.7\) m/s \(^{2})\) and 1.0 \(\times 10^{-5}\) ( \(\hbox {a}_\mathrm{g}=3\) m/s \(^{2})\) .     

On the seismic response of under-designed caisson foundations

The seismic behaviour of caisson foundations supporting typical bridge piers is analysed with 3D finite elements, with due consideration to soil and interface nonlinearities. Single-degree-of freedom oscillators of varying mass and height, simulating heavily and lightly loaded bridge piers, founded on similar caissons are studied. Four different combinations of the static ( $\text{ FS }_\mathrm{V}$ FS V ) and seismic ( $\text{ FS }_\mathrm{E}$ FS E ) factors of safety are examined: (1) a lightly loaded ( $\text{ FS }_\mathrm{V}= 5$ FS V = 5 ) seismically under-designed ( $\text{ FS }_\mathrm{E} < 1$ FS E < 1 ) caisson, (2) a lightly loaded seismically over-designed ( $\text{ FS }_\mathrm{E} >1$ FS E > 1 ) caisson, (3) a heavily loaded ( $\text{ FS }_\mathrm{V} = 2.5$ FS V = 2.5 ) seismically under-designed ( $\text{ FS }_\mathrm{E} < 1$ FS E < 1 ) caisson and (4) a heavily loaded seismically over-designed caisson. The analysis is performed with use of seismic records appropriately modified so that the effective response periods (due to soil-structure-interaction effects) of the studied systems correspond to the same spectral acceleration, thus allowing their inelastic seismic performance to be compared on a fair basis. Key performance measures of the systems are then contrasted, such as: accelerations, displacements, rotations and settlements. It is shown that the performance of the lightly loaded seismically under-designed caisson is advantageous: not only does it reduce significantly the seismic load to the superstructure, but it also produces minimal residual displacements of the foundation. For heavily loaded foundations, however ( $\text{ FS }_{V} = 2.5$ FS V = 2.5 ), the performance of the two systems (over and under designed) is similar.     

Conditional heavy-tail behavior with applications to precipitation and river flow extremes

This article deals with the right-tail behavior of a response distribution \(F_Y\) conditional on a regressor vector \({\mathbf {X}}={\mathbf {x}}\) restricted to the heavy-tailed case of Pareto-type conditional distributions \(F_Y(y|\ {\mathbf {x}})=P(Y\le y|\ {\mathbf {X}}={\mathbf {x}})\), with heaviness of the right tail characterized by the conditional extreme value index \(\gamma ({\mathbf {x}})>0\). We particularly focus on testing the hypothesis \({\mathscr {H}}_{0,tail}:\ \gamma ({\mathbf {x}})=\gamma _0\) of constant tail behavior for some \(\gamma _0>0\) and all possible \({\mathbf {x}}\). When considering \({\mathbf {x}}\) as a time index, the term trend analysis is commonly used. In the recent past several such trend analyses in extreme value data have been published, mostly focusing on time-varying modeling of location or scale parameters of the response distribution. In many such environmental studies a simple test against trend based on Kendall’s tau statistic is applied. This test is powerful when the center of the conditional distribution \(F_Y(y|{\mathbf {x}})\) changes monotonically in \({\mathbf {x}}\), for instance, in a simple location model \(\mu ({\mathbf {x}})=\mu _0+x\cdot \mu _1\), \({\mathbf {x}}=(1,x)'\), but the test is rather insensitive against monotonic tail behavior, say, \(\gamma ({\mathbf {x}})=\eta _0+x\cdot \eta _1\). This has to be considered, since for many environmental applications the main interest is on the tail rather than the center of a distribution. Our work is motivated by this problem and it is our goal to demonstrate the opportunities and the limits of detecting and estimating non-constant conditional heavy-tail behavior with regard to applications from hydrology. We present and compare four different procedures by simulations and illustrate our findings on real data from hydrology: weekly maxima of hourly precipitation from France and monthly maximal river flows from Germany.     

The TKE dissipation rate in the northern South China Sea

The microstructure measurements taken during the summer seasons of 2009 and 2010 in the northern South China Sea (between 18°N and 22.5°N, and from the Luzon Strait to the eastern shelf of China) were used to estimate the averaged dissipation rate in the upper pycnocline 〈ε _p〉 of the deep basin and on the shelf. Linear correlation between 〈ε _p〉 and the estimates of available potential energy of internal waves, which was found for this data set, indicates an impact of energetic internal waves on spatial structure and temporal variability of 〈ε _p〉. On the shelf stations, the bottom boundary layer depth-integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ reaches 17–19 mW/m², dominating the dissipation in the water column below the surface layer. In the pycnocline, the integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{p}} $ was mostly ～10–30 % of $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ . A weak dependence of bin-averaged dissipation $ \overline{\varepsilon} $ on the Richardson number was noted, according to $ \overline{\varepsilon}={\varepsilon}_0+\frac{\varepsilon_{\mathrm{m}}}{{\left(1+ Ri/R{i}_{\mathrm{cr}}\right)}^{1/2}} $ , where ε ₀ + ε _m is the background value of $ \overline{\varepsilon} $ for weak stratification and Ri _cr?=?0.25, pointing to the combined effects of shear instability of small-scale motions and the influence of larger-scale low frequency internal waves. The latter broadly agrees with the MacKinnon–Gregg scaling for internal-wave-induced turbulence dissipation.     

Characteristics of rain electricity in Nigeria II — Experimental and theoretical relations

Analysis of data, covering four rainy seasons, of rain current, point-discharge current and potential gradient reveal novel relations in the form (i) $$Q_{r + } /Q_{r - } = k_1 (T_{r + } /T_{r - } )^{1.1} $$ for rain charge and duration ratios; and (ii) $$Q_{p - } /Q_{p + } = k_2 (T_{p - } /T_{p + } )^{1.1} $$ for point charge and duration ratios, where thek's are constants; and (iii) $$i_r = - \alpha (i_p - c)$$ for rain and point-discharge current densities, where α has the same value for all types of rain andc is a constant controlled by the rainfall intensityR. For rain not associated with point discharge the relation takes the familiar form $$i_r = - AR(E - \bar E)$$ Theoretical values are obtained for \ga andA on the basis of the Wilson ion-capture theory as worked out in detail by Whipple and Chalmers.     

An analytical method for the evaluation of the in-plan irregularity of non-regularly asymmetric buildings

This paper describes a new method for the evaluation of the static eccentricity $e_{s}$ and the ratio $\Omega _{\uptheta } $ of uncoupled torsional to lateral frequencies in real multi-storey buildings. The above-mentioned parameters greatly affect the lateral-to-torsional coupling of the response of asymmetric systems and thus are of paramount importance in the assessment of the in-plan irregularity of buildings. The proposed method, which is a generalization of that suggested by Calderoni et al. (Earthq Spectra 18(2):219–231, 2002), allows the calculation of the static eccentricity $e_{s}$ and the ratio $\Omega _{\uptheta } $ from the structural response to arbitrary distributions of forces and torsional couples. The effectiveness of the method is validated on some regularly and non-regularly asymmetric buildings characterised by different in-plan irregularity. The analyses demonstrate that the results of the method are rigorous in the case of regularly asymmetric systems and only slightly depend upon the heightwise distribution of the forces in the case of non-regularly asymmetric systems. Finally, the values of the static eccentricity $e_{s}$ and the ratio $\Omega _{\uptheta } $ resulting from the proposed method are compared to those obtained by means of the procedure suggested by Makarios and Anastassiadis in (Struct Des Tall Spec Build 7(1):33–55, 1998a; Struct Des Tall Spec Build 7(1):57–71, 1998b) .     

A copula-based model for air pollution portfolio risk and its efficient simulation

This paper introduces a portfolio approach for quantifying pollution risk in the presence of PM\(_{2.5}\) concentration in cities. The model used is based on a copula dependence structure. For assessing model parameters, we analyze a limited data set of PM\(_{2.5}\) levels of Beijing, Tianjin, Chengde, Hengshui, and Xingtai. This process reveals a better fit for the t-copula dependence structure with generalized hyperbolic marginal distributions for the PM\(_{2.5}\) log-ratios of the cities. Furthermore, we show how to efficiently simulate risk measures clean-air-at-risk and conditional clean-air-at-risk using importance sampling and stratified importance sampling. Our numerical results show that clean-air-at-risk at 0.01 probability level reaches up to \(352\,{\mu \hbox {gm}^{-3}}\) (initial PM\(_{2.5}\) concentrations of cities are assumed to be \(100\,{\mu \hbox {gm}^{-3}}\)) for the constructed sample portfolio, and that the proposed methods are much more efficient than a naive simulation for computing the exceeding probabilities and conditional excesses.     

State of stress in the lithosphere: Inferences from the flow laws of olivine

The experimental flow data for rocks and minerals are reviewed and found to fit a law of the form $$\dot \varepsilon = A'\left[ {sinh (\alpha \sigma )} \right]^n \exp \left[ {{{ - (E * + PV * )} \mathord{\left/ {\vphantom {{ - (E * + PV * )} {RT}}} \right. \kern-\nulldelimiterspace} {RT}}} \right]$$ where \(\dot \varepsilon \) This law reduces to the familiar power-law stress dependency at low stress and to an exponential stress dependency at high stress. Using the material flow law parameters for olivine, stress profiles with depth and strain rate are computed for a representative range of temperature distributions in the lithosphere. The results show that the upper 15 to 25 km of the oceanic lithosphere must behave elastically or fail by fracture and that the remainder deforms by exponential law flow at intermediate depths and by power-law flow in the rest. A model computation of the gravitational sliding of a lithospheric plate using olivine rheology exhibits a very sharp decoupling zone which is a consequence of the combined effects of increasing stress and temperature on the flow law, which is a very sensitive function of both.     

Variation of Seismic Coda Wave Attenuation in the Garhwal Region, Northwestern Himalaya

Seismic coda wave attenuation ( $ Q_{\text{c}}^{ - 1} $ ) characteristics in the Garhwal region, northwestern Himalaya is studied using 113 short-period, vertical component seismic observations from local events with hypocentral distance less than 250?km and magnitude range between 1.0 to 4.0. They are located mainly in the vicinity of the Main Boundary Thrust (MBT) and the Main Central Thrust (MCT), which are well-defined tectonic discontinuities in the Himalayas. Coda wave attenuation ( $ Q_{\text{c}}^{ - 1} $ ) is estimated using the single isotropic scattering method at central frequencies 1.5, 3, 5, 7, 9, 12, 16, 20, 24 and 28?Hz using several starting lapse times and coda window lengths for the analysis. Results show that the ( $ Q_{\text{c}}^{ - 1} $ ) values are frequency dependent in the considered frequency range, and they fit the frequency power law ( $ Q_{\text{c}}^{ - 1} \left( f \right) = Q_{0}^{ - 1} f^{ - n} $ ). The Q ₀ (Q _c at 1?Hz) estimates vary from about 50 for a 10?s lapse time and 10?s window length, to about 350 for a 60?s lapse time and 60?s window length combination. The exponent of the frequency dependence law, n ranges from 1.2 to 0.7; however, it is greater than 0.8, in general, which correlates well with the values obtained in other seismically and tectonically active and highly heterogeneous regions. The attenuation in the Garhwal region is found to be lower than the Q _c ^?1 values obtained for other seismically active regions of the world; however, it is comparable to other regions of India. The spatial variation of coda attenuation indicates that the level of heterogeneity decreases with increasing depth. The variation of coda attenuation has been estimated for different lapse time and window length combinations to observe the effect with depth and it indicates that the upper lithosphere is more active seismically as compared to the lower lithosphere and the heterogeneity decreases with increasing depth.     

Quasi-Static Strain and Stress Fields due to a Moment Tensor in Elastic–Viscoelastic Layered Half-Space

We derived explicit expressions in the time domain for 3-D quasi-static strain and stress fields, due to a point moment tensor source in an elastic surface layer overlying viscoelastic half-space under gravity. The expressions of strain in the elastic surface layer were directly obtained from the expressions of displacement in our previous paper. The conversion of strain into stress is easy, because the stress–strain relation of elastic material is linear. In the viscoelastic substratum, the expressions of strain were obtained by applying the correspondence principle of linear viscoelasticity to the associated elastic solution. The strain–stress conversion is not straightforward, as the stress–strain relation of viscoelastic material is usually given in a differential form. To convert strain into stress, we used an integral form of the stress–strain relation instead of the usual differential form. The expressions give the responses of elastic half-space at \( t = 0 \) , and the responses of an elastic plate floating on non-viscous liquid at \( t = \infty \) . The moment tensor is rationally decomposed into the three independent force systems, corresponding to isotropic expansion, shear faulting and crack opening, and so the expressions include the strain and stress fields for these force systems as special cases. As the first numerical example, we computed the temporal changes in strain and stress fields after the sudden opening of an infinitely long vertical crack cutting the elastic surface layer. Here, we observe that the stress changes caused by the sudden crack opening gradually decay with time and vanish at \( t = \infty \) everywhere. After the completion of stress relaxation, a characteristic pattern of shear strain remains in the viscoelastic substratum. Since the strain and stress fields at \( t = \infty \) can be read as the strain- and stress-rate fields caused by steady crack opening, respectively, this numerical example demonstrates the realization of a steady stress state supported by steady viscous flow in the asthenosphere, associated with steady seafloor spreading at mid-ocean ridges. For the second numerical example, we computed the temporal changes in strain and stress fields after the 2011 Tohoku-oki mega-thrust earthquake, which occurred at the North American-Pacific plate interface. In this numerical example, the stress changes caused by coseismic fault slip vanish at \( t = \infty \) in the viscoelastic substratum, but remain in the elastic surface layer. The coseismic stress changes (and also strain changes) in the elastic surface layer diffuse away from the source region with time, due to gradual stress relaxation in the viscoelastic substratum.     

A Crustal Model for the Eastern Alps Region and a New Moho Map in Southeastern Europe

In the last two decades, south-central Europe and the Eastern Alps have been widely explored by many seismic refraction experiments (e.g., CELEBRATION 2000, ALP 2002, SUDETES 2003). Although quite detailed images are available along linear profiles, a comprehensive, three-dimensional crustal model of the region is still missing. This limitation makes this region a weak spot in continental-wide comprehensive representations of crustal structure. To improve on this situation, we select and collect 37 published active-source seismic lines in this region. After geo-referencing each line, we sample them along vertical profiles—every 50?km or less along the line—and derive P-wave velocities in a stack of homogeneous layers (separated by discontinuities: depth of crystalline basement, top of lower crust, and Moho). We finally merge the information using geostatistical methods, and infer S-wave velocity and density using empirical scaling relations. We present here the resulting crustal model for a region encompassing the Eastern Alps, Dinarides, Pannonian basin, Western Carpathians and Bohemian Massif, covering the region within $45^{\circ}\text{--}51^{\circ}\hbox{N}$ and $11^{\circ} \text{--} 22^{\circ}\hbox{E}$ with a resolution of $0.2^{\circ} \times 0.2^{\circ}.$ We are also able to extend and update the map of Moho depth in a wider region within $35^{\circ}\text{--}51^{\circ}\hbox{N}$ and $12^{\circ}\text{--}45^{\circ}\hbox{E},$ gathering Moho values from the collected seismic lines, other published dataset and using the European plate reference EPcrust as a background. All the digitized profiles and the resulting model are available online.     

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.