Resonances in the three-body problem with equal masses

Numerical simulations of near-resonant motions occurring in planar rotating systems of three bodies with equal masses are presented for the cases of prograde and retrograde motions of the inner and outer pairs. The ratios n: m of the initial periods of these pairs are within 1 ≤ m ≤ n ≤ 7. It is shown that, as a rule, retrograde are more stable than prograde motions. The k loop structures oriented inwards for prograde and outwards for retrograde motions are revealed. Empirical relations between k and n are found for the main resonances n: 1 and n: 2.     

Proper motions of stars in the region of the Great Nebula in Orion

Six Tautenburg astrograph plates have been used to derive proper motions for 12 740 stars in the region of the Great Nebula in Orion. The Oricat catalog of proper motions and B and R photometry has been compiled, incorporating as well data from other published catalogs. The proper motions presented in different catalogs are compared. The Oricat catalog is useful for studies of features of the structure and kinematics of star clusters and groups.     

Models for convergence, subduction and back-arc development: Plate motions, boundary forces, and horizontal temperature gradients: Implications for the driving mechanism

Largely because of the wide variety of observational constraints which must be satisfied, the search for a viable driving mechanism is perhaps the most perplexing problem related to plate tectonics. The mechanism must be compatible with the rigid behavior of lithospheric plates, and with a wide range of plate sizes, shapes and motions. It must be consistent with complex configurations of plate boundaries and equally complex boundary interactions, such as the destruction of ridges at subduction zones. The mechanism must produce steady-state relative and absolute plate motions which persist for tens of millions of years, but must also account for sudden dramatic changes. Finally, the plate driving mechanism must be consistent with the non-Newtonian properties of olivine and with the fabrics of upper mantle peridotites.Mounting evidence suggests that plate motions result from forces associated with plate boundaries and that the principal resisting force is drag at the base of the lithosphere, particularly beneath continents Several investigators have suggested that gravitational forces acting on thermally-induced, lateral density variations in the upper mantle are the principal driving forces for plate tectonics. If so, plate motions are ultimately controlled by the temperature distribution in the upper mantle, and plate tectonics represents a state of dynamic equilibrium in which plate motions are both the cause and the consequence of temperature and density variations in the mantle. This concept requires that average absolute plate velocities be predictable from the characteristics of individual plates, and that plates tend to move down horizontal temperature gradients.A simple linear relation which includes contributions from ridge push (RP), slab pull (SP), trench suction (TS) and continental drag (CD): (cm/y) = (2.6 ± 0.4) + (4.8 ± 1.8) RP + (14.3 ± 1.7) SP +(3.5 ± 2.5) TS−(5.1 ±0.7) CD predicts plate velocities with an rms error of 0.44 cm/y, and a correlation coefficient of 0.98. That plate velocities can be accurately predicted from their own boundary configurations and proportions of continental lithosphere is strong evidence that plate motions result from negative buoyancy forces associated with plate boundaries.     

Tectonic plate motion and deformation inferred from very long baseline interferometry

We inverted 76 rates of change of baseline lengths measured with very long baseline interferometry (VLBI) during the period 1979–1989 to estimate the parameters of motions of the North American (noam) and Eurasian (eura) plates relative to the Pacific (pcfc) plate. We considered two types of plate motion models, namely, rigid and non-rigid models. In the non-rigid models, we simultaneously determined the non-rigid motions of several stations near plate boundaries due to intraplate deformation. Intraplate deformation in the regions far away from plate boundaries is assumed to be negligible.Among several models considered, a non-rigid model called M2 is found to fit most closely to the observed data. In this model, six stations are assumed to be capable of the non-rigid motion; those are goldvenu, hatcreek, mojave12, ovro 130 and vndnberg, in the southwestern United States and kashima, in Japan. M2 gives parameter sets of 0.827 ± 0.035°/m.y., about 50.5 ± 1.2°N, 78.5 ± 5.3°W and 0.889 ± 0.049°/m.y., about 59.7 ± 1.9°N, 85.1 ± 7.4 °W, representing the noam-pcfc and eura-pcfc relative motions. The plate motion parameters of M2 are nearly identical to those of the newest global-scale plate motion model nuvel-1. The noam-pcfc and eura-pcfc rotation rates of M2 respectively deviate only 0.044°/m.y. and 0.010°/m.y. from those of nuvel-1 (these deviations are only about 6% and 1%, respectively, of the rotation rates themselves). The noam-pcfc and eura-pcfc poles of M2 both lie only 2° from those of nuvel-1 (within a 2σ error ellipse of each pole). nuvel-1 is determined from spreading rates at mid-ocean ridges, azimuths of transform faults and earthquake slip vectors. Since the spreading rates are estimated from marine magnetic anomalies integrated over a geological timescale, nuvel-1 gives the plate motions averaged over this timescale. Thus, we may conclude that there is no appreciable difference between the plate motions averaged over a geological timescale (millions of years) and those in a recent short period ( ~ 10 yr).M2 also gives the horizontal non-rigid motions of VLBI stations in the southwestern United States at rates of 6–9 mm/yr and roughly in opposite direction to the rigid motion of each station associated with plate motion. hatcreek, located near the northern part of the Basin and Range Province (B&R), also shows additional westward motion of about 9 mm/yr, suggesting crustal stretching in the northern B&R. The US VLBI stations show subsidence at rates of about 5–7 mm/yr, except for goldvenu and ovro 130, whose subsidence is negligible. The Japanese VLBI station, kashima, has a horizontal non-rigid motion of about 20 mm/yr in the west-northwest direction, roughly opposite to the direction of the rigid motion. kashima also shows subsidence at a rate of about 12 mm/yr, which is larger than that deduced from geodetic data but consistent with the result from GPS.     

The effect of reservoir length on seismic performance of gravity dams to near- and far-fault ground motions

In this article, the effect of reservoir length on seismic performance of gravity dams to near- and far-fault ground motions is investigated. For this purpose, four finite element models of dam–reservoir–foundation interaction system are prepared by using the Lagrangian approach. In these models, the reservoir length varies from H to 4H (H: the height of dam). The Folsom gravity dam is selected as a numerical application. Two different ground motion records of 1989 Loma Prieta earthquake are used in the analyses. One of ground motions is recorded in near fault; the other is recorded in far fault. Also, the two records have the same peak ground acceleration. The study mainly consists of three parts to assess the effects of reservoir length on the seismic performance of the concrete gravity dam. In the first part, the linear time-history analyses of the four finite element models prepared for the Folsom gravity dam are performed. In the second part, the seismic performance of the dam is evaluated according to demand–capacity ratio and cumulative inelastic duration. Finally, the nonlinear time-history analyses of the finite element models of the dam are carried out by using Drucker–Prager yield criteria for dam concrete. It is seen from the analyses results that the seismic behavior of the concrete gravity dams is considerably affected from the length of the reservoir. The reservoir length of 3H is adequate for concrete gravity dams. The selection of ground motion is on of the important parts of seismic evaluation of gravity dams. Also, the frequency characteristics of the ground motion having the same peak ground acceleration affect the seismic performance of the dam. The near-fault ground motions are generally creates more stress on the dam body than far-fault ground motions. The used performance approach provides a systematic methodology for assessment of the seismic performance and necessity of nonlinear analyses for dam systems.     

Differential tectonic movements in the confluence area of the Huang Shui and Huang He rivers (Yellow River), NE Tibetan Plateau,as inferred from fluvial terrace positions

In the Northeastern Tibetan Plateau (NETP), the courses of the Huang Shui and Huang He near their confluence are characterized by alternating gorges and wide depressions, segmenting the fluvial systems. The river valleys have developed terrace staircases, which are used to infer relative tectonic motions between the segments. The terrace staircases are correlated by means of relative height and optically stimulated luminescence (OSL) dating. At least eight terraces are present, two of which have been dated by OSL (the sixth and the third ones; c. 70 and c. 24 ka, respectively). The correlated longitudinal terrace profiles show no distinct relative tectonic movements within the confluence area, demonstrating that this area behaved as one tectonic block. The correlation of the terrace staircase of this block with areas upstream (Xining area) and downstream (eastern Lanzhou area) indicates relative tectonic movements, which therefore represent different tectonic blocks. The fluvial incision rate since c. 70 ka was much higher in the confluence area than in the blocks upstream and downstream, possibly indicating relative uplift. This relatively strong uplift provided more space for differentiation within the terrace staircase as a result of climatic changes, leading to six terraces formed as a response to minor climatic fluctuations (10³–10⁴ year timescale) since the last interglacial. This may indicate that the stronger the tectonic movement the better the climatic imprint as expressed in the form of terrace development. Over a shorter timescale, two accumulation terraces with thick stacked deposits (>18 m) may indicate relative subsidence in the confluence, occurring sometime between 20 and 70 ka. This indicates changes in relative vertical crustal motions at timescales of tens of thousands of years. We speculate that the inferred tectonic motions are related to transpression movements in the NETP as a result of the collision of the Indian and Asian plates.     

Numerical analysis of block stone displacements in ancient masonry structures: A new method to estimate historic ground motions

An innovative approach is presented, in which the discontinuous deformation analysis (DDA) method is used to estimate historic ground motions by back analysis of unique structural failures in archaeological sites. Two archaeological sites in Israel are investigated using this new approach and results are presented in terms of displacement evolution of selected structural elements in the studied masonry structure. The response of the structure is studied up to the point of incipient failure, in a mechanism similar to the one observed in the field. Structural response is found to be very sensitive to dynamic parameters of the loading function such as amplitude and frequency. Prior to back analysis of case studies, two validations are presented. Both compare the performance of DDA with analytical solutions and present strong agreement between the two. Using comprehensive sensitivity analyses, the most likely peak ground acceleration (PGA) and frequency that must have driven the observed block displacements are found for the two case studies—the Nabatean city of Mamshit and the medieval fortress of Nimrod in southern and northern Israel, respectively. It is found that horizontal peak ground accelerations (HPGA) of 0.5g and 1g were required to generate the observed deformations in Mamshit and Nimrod, respectively. Although these might seem too high, considering structural and topographic amplifications it is concluded that the analyses suggest ground motions of 0.2g at a frequency of 1.5 Hz for Mamshit and up to 0.4g at a frequency of 1 Hz for Nimrod. These values provide constraints on the seismic risk associated with these regions as appears in the local building code using a completely independent approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Strong ground motions from the 2011 off-the Pacific-Coast-of-Tohoku, Japan (Mw?=?9.0) earthquake obtained from a dense nationwide seismic network

The dense recordings of the K-NET and KiK-net nationwide strong motion network of 1,189 accelerometers show clearly the radiation and propagation properties of the strong ground motions associated with the 2011 off-the-Pacific Coast-of-Tohoku, Japan (Mw = 9.0) earthquake. The snapshots of seismic wave propagation reveal strong ground motions from this earthquake that originate from three large slips; the first two slips occurred over the plate interface of off-Miyagi at the southwest and the east of the hypocenter, and the third one just beneath the northern end of Ibaraki over the plate interface or in the crust. Such multiple shocks of this event caused large accelerations (maximum 1–2 G) and prolonged ground shaking lasting several minutes with dominant high-frequency (T < 1 s) signals over the entire area of northern Japan. On the other hand, ground motions of relatively longer–period band (T = 1–2 s), which caused significant damage to wooden-frame houses, were about 1/2–1/3 of those observed near the source area of the destructive 1995 Kobe, Japan (M = 7.3) earthquake. Also, the long-period (T = 6–8 s) ground motion in the Kanto (Tokyo) sedimentary basin was at an almost comparable level of those observed during the recent Mw = 7 inland earthquakes, but not as large as that from the former M = 8 earthquakes. Therefore, the impact of the strong ground motion from the present M = 9 earthquake was not as large as expected from the previously M = 7–8 earthquakes and caused strong motion damage only to short-scale construction and according to instruments inside the buildings, both have a shorter (T < 1 s) natural period.     

How to obtain earthquake ground motions for engineering design

The earthquake ground motions that ultimately are selected for engineering design depend chiefly on the criticality of a site or structure and the engineering analyses that are to be performed. Several key steps are necessary in this selection process: They are (1) a reconnaissance to understand the hazards and obtain preliminary earthquake ground motions; (2) decisions on the application of deterministic or probabilistic methods; (3) selection of appropriate motions for requirements in design; (4) consideration of thresholds at which motions become significant for engineering; and (5) decisions on specifying appropriate earthquake ground motions for sizes of earthquakes, distances from sources, the structures, sites, and testing to be done. This paper presents five tables that show steps for evaluating these factors and for enabling the investigator to specify earthquake ground motions appropriate for engineering design.     

Particle motions in a physical model of shallow angle thrust faulting

A physical model of thrust faulting has been constructed out of elastic foam rubber. The thrust wedge has an angle of 25°., and is forced from the back by a steel-hydraulic system of effectively infinite rigidity, analogous to the force exerted by tectonic plates. The observed particle motions show many features different from those commonly assumed in dislocation models of subduction thrusts. Interface waves associated with fault opening propagate along the thrust plane (from the back) and temporarily decouple the overlying hanging wall plate from the foot wall. Because of the geometry of the reflecting fault boundary, and the free surface (also reflecting), energy is trapped in the wedge and, as a consequence, the particle motions and energy in the hanging wall are much greater than in the foot wall. The interface wave and the energy trapped in the upper plate propagate up the wedge and break out at the toe of the thrust with a spectacular increase in motions. If this model is analogous to the real earth, it suggests that some common assumptions in dislocation modeling may be incorrect. The model may explain apparent missing energy radiated to teleseismic distances, the anomalously low number of empirical Green’s functions needed to model teleseismicp waves, and the evidence of intense shaking on the hanging wall toe of some thrust fault earthquakes. The results support the suggestion that interface waves may explain the lack of high frictional heat generation from thrust faults, and may explain the ‘paradox of large overthrusts’. The results also suggest that the seismic hazard of great subduction thrust earthquakes and continental shallow angle thrust faults might in some cases be seriously underestimated.     

Implications of north pacific plate tectonics in central Alaska: Focal mechanisms of earthquakes

The focal mechanisms for 86 selected earthquakes (3.0 m_b 5.5) located in central Alaska have been investigated from P-wave first motions; the data were gathered by local seismic networks. The results show a depth-dependent characteristic to the fault-plane solutions. For earthquakes having focal depths shallower than 60–70 km, the focal mechanisms indicate either strike-slip or normal faults, while for earthquakes with foci at intermediate depths the focal mechanisms correspond to thrust faults. The nature of the seismicity indicates the hinge line of the Pacific lithospheric plate under the study area to be striking N17°E from Cook Inlet towards interior Alaska. The comparison of the focal mechanisms with the seismicity shows that the strike-slip and normal faults are the predominant processes of stress release along the shallow section of the plate. The earthquakes with intermediate foci systematically occur along the inclined section of the plate. If the gently dipping nodal planes for these earthquakes are chosen as the fault planes, the focal mechanisms correspond to underthrust motions at the foci. In these, the slip vectors are oriented either to the west or north with the resultant being in the N30°W direction. The tension axes for the underthrust solutions are also found to be parallel to the local dip of the plate, indicating that the subducted plate in interior Alaska is undergoing gravitational sinking.     

Proper motions of open star clusters and the rotation rate of the galaxy

The mean proper motions of 167 Galactic open clusters with radial-velocity measurements are computed from the data of the Tycho-2 catalog using kinematic and photometric cluster membership criteria. The resulting catalog is compared to the results of other studies. The new proper motions are used to infer the Galactic rotation rate at the solar circle, which is found to be ω₀=+24.6±0.8 km s^?1 kpc^?1. Analysis of the dependence of the dispersion of ω₀ estimates on heliocentric velocity showed that even the proper motions of clusters with distances r>3 kpc contain enough useful information to be used in kinematic studies demonstrating that the determination of proper motions is quite justified even for very distant clusters.     

Assessing probability of surface manifestation of liquefaction at a given site in a given exposure time using CPTU

This paper is a follow-up to a previous paper on the subject of liquefaction potential index (LPI), a parameter that is often used to characterize the potential for surface manifestation of liquefaction at a given site subjected to a given shaking level (represented by a pair of peak ground surface acceleration a_max and moment magnitude M_w). In the previous paper by Juang and his coworkers, the LPI was re-calibrated for a piezocone penetration test (CPTU) model, and a simplified model based on LPI was created for computing the conditional probability of surface manifestation of liquefaction (P_G). In this paper, the model for this conditional probability P_G is extended into a complete framework for assessing the probability of surface manifestation of liquefaction in a given exposure time at a given site subjected to all possible ground motions at all seismic hazard levels. This new framework is formulated and demonstrated with an example site in 10 different seismic regions in the United States.     

Subduction, back-arc spreading and global mantle flow

The shapes and orientations of Benioff zones beneath island arcs, interpreted as marking the location of subducted lithosphere, provide the best presently available constraints on the global convective flow pattern associated with plate motions. This global flow influences the dynamics of subduction. Subduction zone phenomena therefore provide powerful tests for models of mantle flow. We compute global flow models which, while simple, include those features which are best constrained, namely the observed plate velocities, applied as boundary conditions, and the density contrasts given by thermal models of the lithosphere and subducted slabs. Two viscosity structures are used; for one, flow is confined to the upper mantle, while for the other, flow extends throughout the mantle.Instantaneous flow velocity vectors match observed Benioff zone dips and shapes for the model which allows mantle-wide flow but not for the upper mantle model, which has a highly contorted flow pattern. The effect of trench migration on particle trajectories is calculated; it is not important if subduction velocities are greater than migration rates. Two-dimensional finite element models show that including a coherent high viscosity slab does not change these conclusions. A coherent high viscosity slab extending deep into the upper mantle would significantly slow subduction if flow were confined to the upper mantle. The maximum earthquake magnitude, M_w, for island arcs correlates well with the age of the subducted slab and pressure gradient between the trench and back-arc region for the whole mantle, but not the upper mantle, flow model. The correlations with orientations of Benioff zones and seismic coupling strongly suggest that the global return flow associated with plate motions extends below 700 km. For both models, regions of back-arc spreading have asthenospheric shear pulling the back-arc toward the trench; regions without back-arc spreading have the opposite sense of shear, suggesting global flow strongly influences back-arc spreading.     

Seismic centrifuge modelling of earth dams

Three dynamic centrifuge models were tested to obtain data for safety evaluation of the Jen-Yi-Tan Dam in Taiwan subject to a strong earthquake. In these tests, recorded 1999 Chi-Chi earthquake ground motions were modified and used on the electro-hydraulic shaking table mounted on the 400 g-ton centrifuge at the University of Colorado at Boulder. All tests were conducted under centrifugal acceleration of 150 g, and the input acceleration was scaled accordingly in order to simulate the given earthquake. A rigid container and water as pore fluid were used in the tests. In both Models 2 and 3, no sign of soil liquefaction was observed in the tests although a noticeable amount of settlements were found from the earth dam cross-section profile after testing.     

Seismic performance evaluation of dam-reservoir-foundation systems to near-fault ground motions

Ground motion records obtained in recent major strong earthquakes have provided evidence that ground motions recorded near the near-fault regions differ in many cases from those observed further away from the seismic source. As the forward directivity and fling effect characteristics of the near-fault ground motions, they have the potential to cause more considerable damage to structures during an earthquake. Therefore, understanding the influence of near-fault ground motions on the performance of structures is critical to mitigate damage and perform effective response. This paper presents results of a study aimed at evaluating the effects of near-fault and far-fault ground motions on seismic performance of concrete gravity dams including dam-reservoir-foundation interaction. Koyna gravity dam is selected as a numerical application. Four different near-fault ground motion records with an apparent velocity pulse are used in the analyses. The earthquake ground motions recorded at the same site from other events that the epicenter far away from the site are employed as the far-fault ground motions. The seismic performance evaluation method based on the demand-capacity ratio, the cumulative overstress duration and the spatial extent of overstressed regions is presented. The concrete damaged plasticity model including the strain hardening or softening behavior is employed in nonlinear analyses. Nonlinear seismic damage analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. The results obtained from the analyses show the effects of near-fault ground motions on seismic performance of concrete gravity dams and demonstrate the importance of considering the near-fault ground excitations.     

Structure and kinematics of the ISM near WR 139

The structure and kinematics of the ISM in an extended vicinity of the star WR 139 is analyzed using the results of original Hα interferometric observations together with radio and infrared data. A CO cavity with a size of up to 40′ has been detected around the star at velocities of V _LSR ∼ 2.5–10 km/s; the cavity is bounded to the North by a shell radiating in the optical. Ionized hydrogen emits at the systematic velocities V _LSR ∼ 6–14 km/s toward the CO cavity, and at V _LSR ≃ 4–11 km/s toward the shell. High-velocity motions of ionized hydrogen inside the cavity testify to the probable expansion of gas that has been swept out by the stellar wind of WR 139 at velocities of up to 60–80 km/s.     

Analytical study of ground motion caused by seismic wave propagation across faulted rock masses

Studying seismic wave propagation across rock masses and the induced ground motion is an important topic, which receives considerable attention in design and construction of underground cavern/tunnel constructions and mining activities. The current study investigates wave propagation across a rock mass with one fault and the induced ground motion using a recursive approach. The rocks beside the fault are assumed as viscoelastic media with seismic quality factors, Q_p and Q_s. Two kinds of interactions between stress waves and a discontinuity and between stress waves and a free surface are analyzed, respectively. As the result of the wave superposition, the mathematical expressions for induced ground vibration are deduced. The proposed approach is then compared with the existing analysis for special cases. Finally, parametric studies are carried out, which includes the influences of fault stiffness, incident angle, and frequency of incident waves on the peak particle velocities of the ground motions.     

Framework for assessing probability of exceeding a specified liquefaction-induced settlement at a given site in a given exposure time

This paper presents a framework for assessing the probability of exceeding a specified liquefaction-induced settlement at a given site in a given exposure time. This framework deals not only with the effect of liquefaction (in terms of settlement) but also with probabilistic characterization of all possible ground motions at a given site (in terms of a joint distribution of a_max and M_w). Additionally, a new concept, referred to herein as liquefaction-induced settlement hazard curve, is introduced for assessing the annual rate of settlement exceedance at a given site. This settlement hazard curve concept has the potential to be a very useful tool in the field of geotechnical earthquake engineering. Satisfactory results are obtained in the demonstration examples analyzed with the proposed framework. Whereas the proposed framework is simple and effective, further refinements to this framework, especially on the treatment of epistemic uncertainty, are warranted.     

Earthquake waves in a random medium

Measurements are conducted with small samples in the laboratory and thus for all practical purposes the medium is macroscopically homogeneous. On the other hand, the uncertainties and the irregular changes in situ are macroscopic inhomogeneities. This work is an attempt to account for these stochastic changes in the elastic properties and density in a rational manner. The method used is that of Karal and Keller which is based on the use of the Green's function and neglect of third-order correlations. The resulting integral equations are solved by Laplace transform. The analysis indicates that the energy decay in the mean motion through random mode coupling introduces damping into even a purley'elastic medium and enhances the damping in a significant manner in a hysteretic viscoelastic medium. This consideration is important in relating the damping and dispersion characteristics of wave in situ to those measured in the laboratory. The formulation is extended to multilayer systems through transfer matrices and to arbitrary inputs by Fourier transform. Sample calculations are presented for single and multilayer systems to obtain response spectra and for the response to Gaussian and actual earthquake input motions.