Anisotropic viscoelastic models with singular memory

The physical background of singular memory models and in particular the Cole–Cole model is discussed. Three models of anisotropic linear viscoelasticity with frequency-dependent stiffness coefficients are considered. The models are constructed in such a way that anisotropic properties are separated from anelastic effects. Two of these models represent finite-speed wave propagation with singularities at the wavefronts (the exponential relaxation model) and without singularities at the wavefronts (the Cole–Cole model), while a third model called the fractional model is related to the constant Q with unbounded propagation speed. The Cole–Cole and fractional models belong to the class of singular memory models studied earlier because of their applications in polymer rheology, poroelasticity, poroacoustics, seismic wave propagation and other applications. Well-posedness of initial boundary value problems with mixed Dirichlet–Neumann boundary conditions is established for the three models. Regularity properties of the three models are examined.     

Explosion quakes at Stromboli (Italy)

This paper reports the results of two seismic experiments aimed at determining the wave field of explosion quakes at Stromboli Island (Mediterranean Sea, Southern Italy). The typical Strombolian activity mostly consists of explosive phenomena causing pyroclastic, materials to be emitted together with jets of volcanic gases from one or more craters. Stromboli is an active volcano characterized by persistent seismic activity consisting of explosion quakes that are seismic events associated with the explosive volcanic phenomena. Explosion quakes are short lived seismic events occurring intermittently whose amplitude tends to decrease with distance from the vent. A distinctive feature of explosion quakes is the presence on seismograms of two, often clearly distinct, seismic phases. The first, low-frequency seismic phase (<2 Hz) is in fact usually followed by a high-frequency seismic phase (>3–4 Hz) after one second or more. The first seismic phase of explosion quakes has been shown to be characterized by a nearly radial linear polarization and by an apparent propagation velocity estimated at 600–800 m/s. The second phase is characterized by a more chaotic motion and a lower apparent propagation velocity of 150–450 m/s. The wavefield associated with the first low-frequency seismic phase appears to be generated by a resonating P-wave seismic source accompanying gas explosion and emission of pyroclastic materials. The wavefield associated with the second high-frequency seismic phase of explosion quakes appears to be mainly composed of scattered and converted waves due to the critical topography of the volcano.     

A new approximation of the velocity-depth distribution and its application to the computation of seismic wave fields

Summary A new approximation of the velocity-depth distribution in a vertically inhomogeneous medium is suggested. This approximation guarantees the continuity of velocity and of its first and second derivatives and does not generate false low-velocity zones. It is very suitable for the computations of seismic wave fields in vertically inhomogeneous media by ray methods and its modifications, as it removes many false anomalies from the travel-time and amplitude-distance curves of seismic body waves. The ray integrals can be evaluated in a closed form; the resulting formulae for rays, travel times and geometrical spreading are very simple. They do not contain any transcendental functions (such asln (x) orsin ^–1, (x)) like other approximations; only the evaluation of one square root and of certain simple arithmetic expressions for each layer is required. From a computational point of view, the evaluation of ray integrals and of geometrical spreading is only slightly slower than for a system of homogeneous parallel layers and even faster than for a piece-wise linear approximation.     

Evidence for periodic seismicity in the inner Aegean seismic zone

The most complete and reliable data of strong (M _s6.5), shallow (h<70 km) earthquakes which occurred in the inner Aegean seismic zone have been utilized to describe its seismicity time variation during 1800–1986 by two independent statistical models. The first is a sequentially stationary model of seismicity rates which shows that intervals of low seismicity rate, lasting for some 37 years, alternate with high rate intervals of 8–12 years duration. The second model is a statistical model according which seismic energy released within 5-year time windows approximates a harmonic curve within a period of about 50 years. This model is in agreement with the notion that the time series of strong earthquake occurrences in the inner Aegean seismic zone consists of a random (shocks withM _s=6.5–6.8) and a nonrandom component (M _s6.9). Maxima and minima of the harmonic curve coincide with the high and low rate intervals, respectively. A model of regional stationary accumulation of thermal stresses along certain seismic belts and their cyclic relaxation may explain this periodicity.     

Frictional Behavior of Steel-PTFE Interfaces for Seismic Isolation

The widespread use of sliding bearings for the seismic isolation of structures requires detailed knowledge of their behavior and improved modeling capability under seismic conditions. The paper summarizes the results of a large experimental investigation on steel–PTFE interfaces, aimed at evaluating the effects of sliding velocity, contact pressure, air temperature and state of lubrication on the mechanical behavior of steel-PTFE sliding bearings. Based on the experimental outcomes, two different mathematical models have been calibrated, which are capable of accounting for the investigated parameters in the evaluation of the sliding friction coefficient. The first model is basically an extension of the model proposed by Constantinou et al. (1990)Journal of Earthquake Engineering, 116(2), 455–472, while the second model is derived from the one proposed by Changet al. (1990)Journal of Engineering Mechanics, 116, 2749–2763. Expressions of the model parameters as a function of bearing pressure and air temperature are presented for lubricated and non-lubricated sliding surfaces. Predicted and experimental results are finally compared.     

An isolation system for limited seismic gaps in near‐fault zones

The ability of a recently proposed seismic isolation system, with inherent self‐stopping mechanism, to mitigate or even eliminate seismic pounding of adjacent structures is investigated under severe near‐fault earthquakes. The isolation system is referred to as roll‐in‐cage (RNC) isolator. It is a rolling‐based isolator that provides in one unit the necessary functions of vertical rigid support, horizontal flexibility with enhanced stability, hysteretic energy dissipation, and resistance to minor vibration loads. In addition, the RNC isolator is distinguished by a self‐stopping (buffer) mechanism to limit the bearing displacement under excitations stronger than a design earthquake or at limited seismic gaps, and a linear gravity‐based self‐recentering mechanism to prevent permanent bearing displacement without causing vertical fluctuation of the isolated structure. A previously developed multifeature SAP2000 model of the RNC isolator is improved in this paper to account for the inherent buffer mechanism's damping. Then, the effectiveness of the isolator's buffer mechanism in limiting peak bearing displacements is studied together with its possibly arising negative influence on the isolation efficiency. After that, the study investigates how to alleviate or even eliminate those possibly arising drawbacks, due to the developed RNC isolator's inner pounding as a result of its buffer activation, to achieve efficient seismic isolation with no direct structure‐to‐structure pounding, considering limited seismic gaps with adjacent structures and near‐fault earthquakes. The results show that the RNC isolator could be an efficient solution for aseismic design in near‐fault zones considering limited seismic gaps. Earthquake Engineering and Structural Dynamics. Copyright © 2014 John Wiley & Sons, Ltd.     

Scaling of peak ground motions from digital recordings of small earthquakes at Campi Flegrei,southern Italy

The dependence of peak ground acceleration and velocity on seismic moment is studied for a set of small earthquakes (0.7<M _L<3.2) recorded digitally at distances of a few km in the Campi Flegrei volcanic area near Naples, Italy, during the ground uplift episode of 1982–1984. Numerical simulations, using the -square spectral model with constant stress drop and ane ^–kf high frequency decay, fit well both the velocity and acceleration data for an averagek=0.015. The observed ground motions in the 1–24 Hz frequency band appear to consist of radiation from simple sources modified only slightly by attenuation effects. Moreover, the scaling of peak values agrees closely with those determined in nonvolcanic areas, once the difference in stress drop is taken into account.     

Effects of rainfall on soil–structure system frequency: Examples based on poroelasticity and a comparison with full-scale measurements

In this paper, a simple two-dimensional soil–structure interaction model, based on Biot's theory of wave propagation in fluid saturated porous media, is used to explain the observed increase of the apparent frequencies of Millikan library in Pasadena, California, during heavy rainfall and recovery within days after the rain. These variations have been measured for small amplitude response (to microtremors and wind excitation), for which Biot's linear theory is valid. The postulated hypothesis is that the observed increases in frequency are due to the water saturation of the soil. The theoretical model used to explore this hypothesis consists of a shear wall supported by a circular foundation embedded in a poroelastic half-space. This rigid foundation model may be appropriate only for the NS response of Millikan library. This paper presents results for the foundation stiffness, and for the system response for model parameters similar to those for Millikan library (located on alluvium with shear wave velocity of about 300 m/s). The foundation impedance matrix, foundation input motion and system response are compared for dry and fully saturated half-space, with permeable and impermeable foundation. The results show that for embedded foundations, the effects of saturation on the horizontal foundation stiffness are as significant as for the vertical stiffness, contrary to what has been known for surface foundations investigated by other authors. Further, the results suggest a 1–2% increase in system frequency of the first two modes of vibration, depending on the drainage condition along the foundation–soil interface. Such increases agree qualitatively with the observations.     

System identification estimation of soil properties at the Lotung site

Dynamic properties of the soils at the Lotung test site, Lotung, Taiwan, are estimated from seismic vertical array measurements (input–output data sets) using both time-invariant and time-variant parametric modeling methods (system identification). Soil properties are directly mapped from model parameters to an equivalent lumped mass model of the soil interval. Shear stiffness and damping ratios were calculated for 8 events with M_L ranging from 4.5 to 7.0. Shear stiffness ranged between 0.5 and 6 MN/m, inversely proportional to PGA. The equivalent viscous damping ratio varied from 2 to 30% of critical damping, proportional to PGA. Degradation of soil behavior, while less pronounced with increasing depth, consistently occurs above a peak input acceleration of 0.07 g. Although “non-linear” behavior is evident above 0.17 g, Event 7 (0.21 g) is accurately predicted using a linear constant parameter model estimated from the smaller Event 8 aftershock ground motions.     

2-D Crustal Velocity Structure Along Hirapur-Mandla Profile in Central India: An Update

The 2-D crustal velocity model along the Hirapur-Mandla DSS profile across the Narmada-Son lineament in central India (Murty et al., 1998) has been updated based on the analysis of some short and discontinuous seismic wide-angle reflection phases. Three layers, with seismic velocities of 6.5–6.7, 6.35–6.40 and 6.8 km s^–1, and upper boundaries located approximately at 8, 17 and 22 km depth respectively, have been identified between the basement (velocity 5.9 km s^–1) and the uppermost mantle (velocity 7.8 km s^–1). The layer with 6.5–6.7 km s^–1 velocity is thin and is less than 2-km deep between the Narmada north (at Katangi) and south (at Jabalpur) faults. The upper crust shows a horst feature between these faults, which indicates that the Narmada zone acts as a ridge between two pockets of mafic intrusion in the upper crust. The Moho boundary, at 40–44 km depth and the intra-crustal layers exhibit an upwarp suggesting that the Narmada faults have deep origins, involving deep-seated tectonics. A smaller intrusive thickness between the Narmada faults, as compared to those beyond these faults, suggests that the intrusive activities on the two sides are independent. This further suggests that the two Narmada faults may have been active at different geological times. The seismic model is constrained by 2-D gravity modeling. The gravity highs on either side of the Narmada zone are due to the effect of the high velocity/high density mafic intrusion at upper crustal level.     

Tomographic Study of the Adriatic Plate

Two well-known methodologies have been used, for the first time, to derive a detailed and reliable lithospheric model of the Adriatic Plate, consistent with the thus far available data: non linear inversion of phase and group velocity dispersion curve obtained from surface-wave tomography, and body-waves tomography. To carry out the body-waves tomography, about 16500 P phases and 2000 S phases from 1219 seismic events, 73 seismic stations located at the border of the investigated region and a vertically heterogeneous starting model derived from the nonlinear inversion of average dispersion measurements, are used. The 3-D velocity model of the upper lithosphere, obtained from the combined analysis, shows a rather clear structural anomaly on the northeastern side, where the crust is thicker, and an uprising of the top of the lid in the northern part of the plate with a very thin, if any, transition zone from crust to mantle.Acknowledgement We are grateful to Bruno Alessandrini and Luisa Filippi (National Seismic Service, Rome – Italy) for providing the computer code SIMULPS and for their very useful advice on the local earthquakes tomography method. This work has been supported by the Italian project MURST-COFIN prot. 2001048324-001 (2001).     

Seismic soil–structure interaction of massive flexible strip-foundations embedded in layered soils by hybrid BEM–FEM

A study on the seismic response of massive flexible strip-foundations embedded in layered soils and subjected to seismic excitation is presented. Emphasis is placed on the investigation of the system response with the aid of a boundary element–finite element formulation proper for the treatment of such soil–structure interaction problems. In the formulation, the boundary element method (BEM) is employed to overcome the difficulties that arise from modeling the infinite soil domain, and the finite element method (FEM) is applied to model the embedded massive flexible strip-foundation. The numerical solution for the soil–foundation system is obtained by coupling the FEM with the BEM through compatibility and equilibrium conditions at the soil–foundation and soil layer interfaces. A parametric study is conducted to investigate the effects of foundation stiffness and embedment on the seismic response.     

Combined geothermal-geophysical models of the earth's crust and upper mantle for the European continent

An attempt is made to obtain a combined geophysical model along two regional profiles: Black Sea— White Sea and Russian Platform—French Central Massif. The process of the model construction had the following stages: 1. The relation between seismic velocity (V_p, km/s) and density (σ, g/cm³) in crustal rocks was determined from seismic profiles and observed gravity fields employing the trial and error method. 2. Relations between heat production HP (μW/m³), velocity and density were established from heat flow data and crustal models of old platforms where the mantle heat flow HF_M is supposed to be constant. The HF_M value was also determined to 11 ± 5 mW/m². 3. A petrological model of the old platform crust is proposed from the velocity-density models and the observed heat flow. It includes 10–12 km of acid rocks, 15–20 km of basic/metamorphic rocks and 7–10 km of basic ones. 4. Calculation of the crustal gravity effects; its substraction from the observed field gave the mantle gravity anomalies. Extensively negative anomalies have been found in the southern part of Eastern Europe (50–70 mgal) and in Western Europe (up to 200 mgal). They correlate with high heat flow and lower velocity in the uppermost mantle. 5. A polymorphic advection mechanism for deep tectonic processes was proposed as a thermal model of the upper mantle. Deep matter in active regions is assumed to be transported (advected) upwards under the crust and in its place the relatively cold material of the uppermost mantle descends. The resulting temperature distribution depends on the type of endogeneous regime, on the age and size of geostructure. Polymorphic transitions were also taken into account.     

Mining-related and tectonic seismicity in the East Mountain area Wasatch Plateau,Utah, U.S.A.

As part of a larger multi-institutional seismic monitoring experiment during June–August 1984 in the eastern Wasatch Plateau, Utah, data from a subarray of 20 portable seismographs were used to investigate seismicity in the East Mountain area, an area of active underground coal mining and intense microseismicity. Eight stations of the subarray were concentrated on top of East Mountain, about 600 m above mine level, at an average spacing of 2 to 3 km. The primary objective was the accurate resolution of hypocenters and focal mechanisms for seismic events originating at submine levels. Data from high-resolution seismic reflection profiles and drill-hole sonic logs yielded a detailed velocity model. This model features a strong velocity gradient in the uppermost 1 km, which has a significant effect on takeoff angles for first-arrivingP-waves from shallow seismic events. Two hundred epicenters located with a precision of ±500 m cluster within an area about 5 km in diameter and show an evident spatial association with four sites of longwall mining during the study period. A special set of foci rigorously tested for focal-depth reliability indicates submine seismicity predominating within 500 m of mine level and extending at least to 1 km, and perhaps to 2 km, below mine level. Continuous monitoring for a 61-day period (June 15–August 15) bracketed a 16-day mining shutdown (July 7–22) during which significant seismicity, comparable to that observed before the shutdown, was observed. Ten focal mechanisms for seismic events originating at or down to 2 km below mine level nearly all imply reverse faulting, consistent with previous results and the inferred tectonic stress field. Enigmatic events recorded with all dilatational first motions can be fit with double-couple normal-faulting solutions if they in fact occurabove mine level, perhaps reflecting overburden subsidence. If these events are constrained to occur at mine level, their first-motion distributions are incompatible with a double-couple source mechanism.     

Subduction zone seismicity and the thermo-mechanical evolution of downgoing lithosphere

In this paper we discuss characteristic features of subduction zone seismicity at depths between about 100 km and 700 km, with emphasis on the role of temperature and rheology in controlling the deformation of, and the seismic energy release in downgoing lithosphere. This is done in two steps. After a brief review of earlier developments, we first show that the depth distribution of hypocentres at depths between 100 km and 700 km in subducted lithosphere can be explained by a model in which seismic activity is confined to those parts of the slab which have temperatures below a depth-dependent critical valueT _cr.Second, the variation of seismic energy release (frequency of events, magnitude) with depth is addressed by inferring a rheological evolution from the slab's thermal evolution and by combining this with models for the system of forces acting on the subducting lithosphere. It is found that considerable stress concentration occurs in a reheating slab in the depth range of 400 to 650–700 km: the slab weakens, but the stress level strongly increases. On the basis of this stress concentration a model is formulated for earthquake generation within subducting slabs. The model predicts a maximum depth of seismic activity in the depth range of 635 to 760 km and, for deep earthquake zones, a relative maximum in seismic energy release near the maximum depth of earthquakes. From our modelling it follows that, whereas such a maximum is indeed likely to develop in deep earthquake zones, zones with a maximum depth around 300 km (such as the Aleutians) are expected to exhibit a smooth decay in seismic energy release with depth. This is in excellent agreement with observational data. In conclusion, the incoroporation of both depth-dependent forces and depth-dependent rheology provides new insight into the generation of intermediate and deep earthquakes and into the variation of seismic activity with depth.Our results imply that no barrier to slab penetration at a depth of 650–700 km is required to explain the maximum depth of seismic activity and the pattern of seismic energy release in deep earthquake zones.     

Body-wave wave-form modelling and source parameters for the indochina border earthquakes

Wave-form modelling of body waves has been done to study the seismic source parameters of three earthquakes which occurred on October 21, 1964 (M _b =5.9), September 26, 1966 (M _b =5.8) and March 14, 1967 (M _b =5.8). These events occurred in the Indochina border region where a low-angle thrust fault accommodates motion between the underthrusting Indian plate and overlying Himalaya. The focal depths of all these earthquakes are between 12–37 km. The total range in dip for the three events is 5°–20°. TheT axes are NE-SW directed whereas the strikes of the northward dipping nodal planes are generally parallel to the local structural trend. The total source durations have been found to vary between 5–6 seconds. The average values of seismic moment, fault radius and dislocation are 1.0–11.0×10²⁵ dyne-cm, 7.7–8.4km and 9.4–47.4 cm, respectively whereas stress drop, apparent stress and strain energy are found to be 16–76 bars, 8.2–37.9 bars and 0.1–1.7×10²¹ ergs, respectively. These earthquakes possibly resulted due to the tension caused by the bending of the lithospheric plate into a region of former subduction which is now a zone of thrusting and crustal shortening.     

Response spectrum predictions for potential near-field and far-field earthquakes affecting Hong Kong: rock sites

To realistically assess the seismic risk relating to built infrastructures in Hong Kong and in the neighbouring coastal cities of southern Guangdong province, it is necessary to predict ground shaking induced by different earthquake scenarios with good accuracy. A companion paper has described the modelling of the spatial and temporal distribution of the diffused seismic activities in the region, based on the newly-developed ‘Expanding Circular Disc’ (ECD) method. Representative Magnitude–Distance (M–R) combinations for both near-field and far-field earthquakes (in relation to Hong Kong) have been derived using the ECD method. The present paper describes the modelling of the response spectrum on rock sites associated with the predicted M–R combinations, using the Component Attenuation Model (CAM) that was also developed recently by the authors, based on stochastic simulations of the seismological model. The significant effects of soil resonance on the response spectrum are described in a separate publication.The accuracy of CAM in modelling ground motion properties on rock sites has been tested here by comparisons with (i) strong motions recorded in Taiwan and South China from the 1999 ‘Chi-Chi’ earthquake in Taiwan (M=7.6), (ii) motions recorded in South China from another earthquake occurring in the southern Taiwan Strait in the same year (M=5.1), and (iii) historical seismic intensity data obtained within South China. The overall capability of CAM in modelling both near-field and far-field attenuation has been shown to be unmatched by existing empirical models. Results of the comparison studies confirm the accuracy of CAM, particularly within an epicentral distance of 300–400 km.This study shows that the developed serviceability response spectra (i.e. at short return periods) are controlled mainly by the earthquake recurrence behaviour of major distant seismic sources. In contrast, the ultimate response spectra (i.e. at long return periods) relate to events with magnitudes close to the maximum credible earthquake (MCE) limit, the effect of which may also be represented by the Characteristic Response Spectrum (CRS). Both types of earthquake scenario can be significantly affected by the regional crustal properties. The proposed response spectrum envelopes have been compared with previously developed recommendations, and a critical review has been conducted. The intrinsic advantages of the ECD–CAM modelling approach have been highlighted, emphasising its directness and transparency when compared with the more complex process required to implement traditional Probabilistic Seismic Hazard Assessment (PSHA).     

Historical 1942 Ecuador and 1942 Peru subduction earthquakes and earthquake cycles along Colombia-Ecuador and Peru subduction segments

Two large shallow earthquakes occurred in 1942 along the South American subduction zone inclose proximity to subducting oceanic ridges: The 14 May event occurred near the subducting Carnegie ridge off the coast of Ecuador, and the 24 August event occurred off the coast of southwestern Peru near the southern flank of the subducting Nazca ridge. Source parameters for these for these two historic events have been determined using long-periodP waveforms,P-wave first motions, intensities and local tsunami data.We have analyzed theP waves for these two earthquakes to constrain the focal mechanism, depth, source complexity and seismic moment. Modeling of theP waveform for both events yields a range of acceptable focal mechanisms and depths, all of which are consistent with underthrusting of the Nazca plate beneath the South American plate. The source time function for the 1942 Ecuador event has one simple pulse of moment release with a duration of 22 suconds, suggesting that most of the moment release occurred near the epicenter. The seismic moment determined from theP waves is 6–8×10²⁰N·m, corresponding ot a moment magnitude of 7.8–7.9. The reported location of the maximum intensities (IX) for this event is south of the main shock epicenter. The relocated aftershcks are in an area that is approximately 200 km by 90 km (elongated parallel to the trench) with the majority of aftershocks north of the epicenter. In contrast, the 1942 Peru event has a much longer duration and higher degree of complexity than the Ecuador earthquake, suggesting a heterogeneous rupture. Seismic moment is released in three distinct pulses over approximately 74 seconds; the largest moment release occurs 32 seconds after rupture initiation. the seismic moment as determined from theP waves for the 1942 Peru event is 10–25×10²⁰N·m, corresponding to a moment magnitude of 7.9–8.2. Aftershock locations reported by the ISS occur over a broad area surrounding the main shock. The reported locations of the maximum intensities (IX) are concentrated south of the epicenter, suggesting that at least part of the rupture was to the south.We have also examined great historic earthquakes along the Colombia-Ecuador and Peru segments of the South American subduction zone. We find that the size and rupture length of the underthrusting earthquakes vary between successive earthquake cycles. This suggests that the segmentation of the plate boundary as defined by earthquakes this century is not constant.     

Investigation of seismic behavior of fluid–rectangular tank–soil/foundation systems in frequency domain

Main purpose of this study is to evaluate the dynamic behavior of fluid–rectangular tank–soil/foundation system with a simple and fast seismic analysis procedure. In this procedure, interaction effects are presented by Housner's two mass approximations for fluid and the cone model for soil/foundation system. This approach can determine; displacement at the height of the impulsive mass, the sloshing displacement and base forces for the soil/foundation system conditions including embedment and incompressible soil cases. Models and equations for proposed method were briefly explained for different tank–soil/foundation system combinations. By means of changing soil/foundation conditions, some comparisons are made on base forces and sloshing responses for the cases of embedment and no embedment. The results showed that the displacements and base shear forces generally decreased, with decreasing soil stiffness. However, embedment, wall flexibility, and soil–structure interaction (SSI) did not considerably affect the sloshing displacement.