Artificial ground motion compatible with specified peak velocity and target spectrum

In this paper, a method, which synthesizes the artificial ground motion compatible with the specified peak velocity as well as the target acceleration response spectrum, was proposed. In this method, firstly, an initial acceleration time history α8^（0） （t）, which satisfies the prescribed peak ground acceleration, the target spectral acceleration ST（ω, ζ）,and the specified intensity envelope, is generated by the traditional method that generates the requency domain; secondly,α8^（0） （t）is further modulated by superimposing narrow-band time histories upon it in the time domain to make its peak velocity, approach the target peak ground velocity, and at the same time to improve its fitting precision to the target spectrum. Numerical examples show that this algorithm boasts high calculation precisions.     

Formulae for errors for initial displacement and velocity problems using the Newmark method

A standard test of the Newmark method in structural dynamics is its application to the determination of the response of a damped or undamped single-degree-of-freedom system to a prescribed initial displacement or velocity. In this paper formulae for the error, Δ_j, in the response, after applying the Newmark method for j time-steps each of duration Δt, are proposed and their acceptable accuracy is demonstrated.     

A numerical study of comparison of two one-state-variable,rate- and state-dependent friction evolution laws

The two one-state-variable, rate- and state-dependent friction laws, i.e., the slip and slowness laws, are compared on the basis of dynamical behavior of a one-degree-of-freedom spring-slider model through numerical simulations. Results show that two (normalized) model parameters, i.e., Δ (the normalized characteristic slip distance) and β?α (the difference in two normalized parameters of friction laws), control the solutions. From given values of Δ, β, and α, for the slowness laws, the solution exists and the unique non-zero fixed point is stable when Δ>(β?α), yet not when Δ < (β?α). For the slip law, the solution exists for large ranges of model parameters and the number and stability of the non-zero fixed points change from one case to another. Results suggest that the slip law is more appropriate for controlling earthquake dynamics than the slowness law.     

Experimental simulations of gas-driven eruptions: kinetics of bubble growth and effect of geometry

 Simulated gas-driven eruptions using CO₂–water-polymer systems are reported. Eruptions are initiated by rapidly decompressing CO₂–saturated water containing up to 1.0 wt.% CO₂. Both cylindrical test cells and a flask test cell were used to examine the effect of magma chamber/conduit geometry on eruption dynamics. Bubble-growth kinetics are examined quantitatively in experiments using cylindrical test cells. Uninhibited bubble growth can be roughly expressed as dr/dt≈λD(β-1)/(γt ^1/3) for a CO₂–water-polymer system at 0–22  °C and with viscosities up to 5 Pa·s, where r is the radius of bubbles, λ and D are the Ostwald solubility coefficient and diffusivity of the gas in the liquid, β is the degree of saturation (decompression ratio), and γ characterizes how the boundary layer thickness increases with time and is roughly 1.0×10^–5 m/s^1/3 in this system. Unlike the radius of cylindrical test cells, which does not affect the eruption threshold and dynamics, the shape of the test cells (flask vs cylindrical) affects the dynamics but not the threshold of eruptions. For cylindrical test cells, the front motion is characterized by constant acceleration with both Δh (the height increase) and ΔV (the volume increase) being proportional to t ²; for the flask test cell, however, neither Δh nor ΔV is proportional to t ² as the conduit radius varies. Test-cell geometry also affects foam stability. In the flask test cell, as it moves from the wider base chamber into the narrower conduit, the bubbly flow becomes fragmented, affecting the eruption dynamics. The fragmentation may be caused by a sudden increase in acceleration induced by conduit-shape change, or by the presence of obstacles to the bubbly flow. This result may help explain the range in vesicularities of pumice and reticulite. Received: 16 May 1997 / Accepted: 11 October 1997     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Numerical simulations of transport of non-ergodic solute plumes in heterogeneous aquifers

Transport of non-ergodic solute plumes by steady-state groundwater flow with a uniform mean velocity, μ, were simulated with Monte Carlo approach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an exponential covariance. The ensemble averages of the second spatial moments of the plume about its center of mass, <S _{i i} (t)>, and the plume centroid covariance, R _{i i} (t) (i=1,2), were simulated for the variance of Y=log T, σ _Y ²=0.1, 0.5 and 1.0 and line sources normal or parallel to μ of three dimensionless lengths, 1, 5, and 10. For σ _Y ²=0.1, all simulated <S _{i i} (t)>−S _{i i} (0) and R _{i i} (t) agree well with the first-order theoretical values, where S _{i i} (0) are the initial values of S _{i i} (t). For σ _Y ²=0.5 and 1.0 and the line sources normal to μ, the simulated longitudinal moments, <S ₁₁(t)>−S ₁₁(0) and R ₁₁(t), agree well with the first-order theoretical results but the simulated transverse moments <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) are significantly larger than the first-order values. For the same two larger values of σ _Y ² but the line sources parallel to μ, the simulated <S ₁₁(t)>−S ₁₁(0) are larger than but the simulated R ₁₁ are smaller than the first-order values, and both simulated <S ₂₂(t)>−S ₂₂(0) and R ₂₂(t) stay larger than the first-order values. For a fixed value of σ _Y ², the summations of <S _{i i} (t)>−S _{i i} (0) and R _{i i} , i.e., X _{i i} (i=1,2), remain almost the same no matter what kind of source simulated. The simulated X ₁₁ are in good agreement with the first-order theory but the simulated X ₂₂ are significantly larger than the first-order values. The simulated X ₂₂, however, are in excellent agreement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that the transverse moments may be significantly underestimated if less accurate hydraulic head solutions are used and that the decreasing of <S ₂₂(t)>−S ₂₂(0) with time or a negative effective dispersivity, defined as , may happen in the case of a line source parallel to μ where σ _Y ² is small.     

Control strategy for variable damping element considering near‐future excitation influence

A control strategy is proposed for variable damping elements (VDEs) used together with auxiliary stiffness elements (ASEs) that compose a time‐varying non‐linear Maxwell (NMW) element, considering near‐future excitation influence. The strategy first composes a state equation for the structural dynamics and the mechanical balance in the NMW elements. Next, it establishes a cost function for estimating future responses by the weighted quadratic norms of the state vector, the controlled force and the VDEs' damping coefficients. Then, the Euler equations for the optimum values are introduced, and also approximated by the first‐order terms under the autoregressive (AR) model of excitation information. Thus, at each moment t_k, the strategy conducts the following steps: (1) identify the obtained seismic excitation information to an AR model, and convert it to a state equation; and (2) determine VDEs' damping coefficients under the initial conditions at t_k and the final state at t_k+L, using the first‐order approximation of the Euler equations. The control effects are examined by numerical experiments. Copyright © 2000 John Wiley & Sons, Ltd.     

Note on the scalar dynamo model

Abstract

Bayly (1993) introduced and investigated the equation (? _t + v·▽-η ▽²)S = RS as a scalar analogue of the magnetic induction equation. Here, S(r, t) is a scalar function and the flow field v(r, t) and “stretching” function R(r, t) are given independently. This equation is much easier to handle than the corresponding vector equation and, although not of much relevance to the (vector) kinematic dynamo problem, it helps to study some features of the fast dynamo problem. In this note the scalar equation is considered for linear flow and a harmonic potential as stretching function. The steady equation separates into one-dimensional equations, which can be completely solved and therefore allow one to monitor the behaviour of the spectrum in the limit of vanishing diffusivity. For more general homogeneous flows a scaling argument is given which ensures fast dynamo action for certain powers of the harmonic potential. Our results stress the singular behaviour of eigenfunctions in the limit of vanishing diffusivity and the importance of stagnation points in the flow for fast dynamo action.     

Variations in the amplitude of the chandler wobble

It is shown that within the framework of the Kolmogorov model the “energy” of the pole E(t) = x ₁² + x ₂² can be interpreted as a Markovian process. The exact analytical expression has been obtained for the density of the conditional probability of the quantity E(t) and the problem of the first passage time of the process E(t) has been analyzed. It was shown that the available data on the swing of the function E(t) are not at variance with the Kolmogorov model and a short-period drop of the amplitude of the Chandler wobble in the early 20th century fits this model at Q = 50–200 too; values of Q > 350 are less reasonable.     

IR band of O<Subscript>2</Subscript> at 1.27 μm as the tracer of O<Subscript>3</Subscript> in the mesosphere and lower thermosphere: Correction of the method

The problem of systematic overestimation (20–50%) of the retrieved ozone concentrations in the altitude range of 60–80 km in the TIMED–SABER satellite experiment in the daytime has been solved. The reason for overestimation is the neglect of the electronic vibrational kinetics of photolysis products of ozone and molecular oxygen O₂(b¹Σ_g ⁺, ν) and O₂(a¹Δ_g, ν). The IR emission band of O₂(a¹Δ_g, ν = 0) at 1.27 μm can be correctly used in remote sensing in order to obtain the ozone altitude profile in the altitude range of 50–88 km only with the use of a complete model of electronic vibrational kinetics of O₂ and O₃ photolysis products (YM2011) in the Earth’s mesosphere and lower thermosphere. Alternative ozone tracers have been considered, and an optimum tracer in the altitude range of 50–100 km such as O₂(b¹Σ_g ⁺, ν = 1) molecule emissions has been proposed.     

Possible early Neoproterozoic magmatism associated with slab window in the Pingshui segment of the Jiangshan-Shaoxing suture zone: Evidence from zircon LA-ICP-MS U-Pb geochronology and geochemistry

We report here geochemical data, U-Pb zircon ages, and Hf isotopes for the high-Mg diorites (HMDs), Nb-enriched basaltic porphyrys (NEBPs) and plagiogranites (PLAGs) in the Pingshui segment of the Jiangshan-Shaoxing suture zone. The HMDs are characterized by high Mg^# (>60), high Na and LREE contents, depletion of HREE and HFSE, and pronounced positive ε_Nd(t) values of 7.0 to 7.7, similar to some adakitic high-Mg andesites. The NEBPs are relatively Na-rich (Na₂O/K₂O>6) and display high abundances of P₂O₅ (∼1.00%), TiO₂ (∼3.08%) and HFSE (e.g., Nb=9.53–10.27 ppm). Their Nd isotopic compositions (ε_Nd(t)=6.8–8.0) are comparable to those of the HMDs. The PLAGs are metaluminous (A/CNK=0.84–0.89) and sodic (Na₂O/K₂O>10). Their depletion in HFSE (e.g., Nb, Ta) is consistent with “SSZ-type” plagiogranite. Zircon LA-ICP-MS U-Pb dating yields an age of 932±7 Ma for the HMD, 916±6 Ma for the NEBP, and 902±5 Ma for the PLAG, respectively, indicating that they were products of early Neoproterozoic magmatism. The PLAGs exhibit relatively high zircon Hf isotopes and positive ε_Hf(t) values of 11.0 to 16.2, consistent with their Nd isotopic data (ε_Nd(t)=7.5–8.4). Such features are similar to those of oceanic plagiogranites in ophiolites and distinct from those of crust-derived granites. The PLAGs were most likely derived from partial melting of subducted oceanic crust in an active continental margin. Considering these results in the context of the regional geology, we suggest that a slab window in the subducting oceanic crust between the Yangtze Block and Cathaysia Block was possibly the principal cause for the unique arc magmatism in the area. The upwelling asthenosphere below the slab window may have provided significant thermodynamic conditions. Supported by China Geological Survey (Grant No. 1212010610611) and the Ministry of Land and Resources (Grant No. 200811015)     

Internal waves in a randomly stratified fluid

Abstract

We discuss the propagation of internal waves in a rotating stratified unbounded fluid with randomly varying stability frequency, N. The first order smoothing approximation is used to derive the dispersion relation for the mean wave field when N is of the form N ² = N _o ²(1 + ?μ), where μ is a centered stationary random function of either depth (z) or time (t), N _o = constant and O < ?² ≦ 1. Expressions are then derived for the change in phase speed and growth rate due to the random fluctuations μ; in particular, attention is focused on the behaviour of these expressions for short and long correlation lengths (case μ = μ(z)) and times (case μ = μ(t)). For the case μ = μ(z), which represents a model for the temperature and salinity fine-structure in the ocean, the appropriate statistics of the fluctuations observed at station P (50°N, 145°W) have been incorporated into the theory to estimate the actual importance of the effects due to these random fluctuations. It is found that the phase speed of the mean wave decreases significantly if (i) the wavelength is short compared to g/N_o ² or (ii) the wave number vector is essentially horizontal and the wave frequency is very close to N _o. Also, the random fluctuations cause a significant growth (decay) in the amplitude of a wave propagating upwards (downwards) through a depth of a few kilometers. However, in the direction of energy propagation, the kinetic energy is conserved. Finally, it is shown that the average effect of the depth dependent fluctuations at station P is to slightly decrease the stability frequency and the magnitude of the group velocity.     

Non-Gaussian probability distributions of solar wind fluctuations

The probability distributions of field differences x()=x(t+)-x(t), where the variable x(t) may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag , ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD) turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.     

The GPS-gravimetry boundary value problem

Boundary value problem (BVP) plays a funda-mental role in physical geodesy that aims at determin-ing the earth’s shape and its external gravity field. TheMolodensky BVP and the Stokes BVP are typical inphysical geodesy, and the gravity anomaly is a kind ofbasic data. With the wide use of GPS, measurementaccuracy of the earth’s surface can reach one centime-ter, while that of the gravity measurement can reachμgals. Hence, it is necessary to establish a new kind ofBVP which can satisfy…     

Prediction of rockburst probability given seismic energy and factors defined by the expert method of hazard evaluation (MRG)

In this paper we suggest that conditional estimator/predictor of rockburst probability (and rockburst hazard, P ^T (t)) can be approximated with the formula P ^T (t) = P ₁(θ ₁)…P _N (θ _N )·P _dyn ^T (t), where P _dyn ^T (t) is a time-dependent probability of rockburst given only the predicted seismic energy parameters, while P _i (θ _i ) are amplifying coefficients due to local geologic and mining conditions, as defined by the Expert Method of (rockburst) Hazard Evaluation (MRG) known in the Polish mining industry. All the elements of the formula are (approximately) calculable (on-line) and the resulting P ^T value satisfies inequalities 0 ≤ P ^T (t) ≤ 1. As a result, the hazard space (0–1) can be always divided into smaller subspaces (e.g., 0–10⁻⁵, 10⁻⁵–10⁻⁴, 10⁻⁴–10⁻³, 10⁻³–1), possibly named with symbols (e.g., A, B, C, D, …) called “hazard states” — which saves the prediction users from worrying of probabilities. The estimator P ^T can be interpreted as a formal statement of (reformulated) Comprehensive Method of Rockburst State of Hazard Evaluation, well known in Polish mining industry. The estimator P ^T is natural, logically consistent and physically interpretable. Due to full formalization, it can be easily generalized, incorporating relevant information from other sources/methods.     

Yield and overflow from a finite stochastic reservoir

The paper discusses the overflow (spillage) and yield rates and the total overflow and total yield over a specified time from a finite discrete stochastic reservoir, in which the yieldY _t during the working interval (t,t+1) is a function of the storageZ _t at timet, the inflow sequence {X _t } being IID.The distribution vector of the spillage rate at timet is a telescoped version of the distribution of a certain Markovian variable whose transition matrix is derived. Formulae are given for the distribution of the total spillageW _h given suitable initial conditions, forh=1,2,3; and a simple expression derived forE(W _h ).     

Exploring the effect of different time resolutions to calculate the rainfall erosivity factor R in Calabria,southern Italy

The rainfall erosivity factor R of the Universal Soil Loss Equation is a good indicator of the potential of a storm to erode soil, as it quantifies the raindrop impact effect on the soil based on storm intensity. The R‐factor is defined as the average annual value of rainfall erosion index, EI, calculated by cumulating the EI values obtained for individual storms for at least 22 years. By definition, calculation of EI is based on rainfall measurements at short time intervals over which the intensity is essentially constant, i.e. using so‐called breakpoint data. Because of the scarcity of breakpoint rainfall data, many authors have used different time resolutions (Δt = 5, 10, 15, 30, and 60 min) to deduce EI in different areas of the world. This procedure affects the real value of EI because it is strongly dependent on Δt. In this contribution, after a general overview of similar studies carried out in different countries, the relationship between EI and Δt is explored in Calabria, southern Italy. The use of 17 139 storm events collected from 65 rainfall stations allowed the calculation of EI for different time intervals ranging from 5 to 60 min. The overall results confirm that calculation of EI is dependent on time resolution and a conversion factor able to provide its value for the required Δt is necessary. Based on these results, a parametric equation that gives EI as a function of Δt is proposed, and a regional map of the scale parameter a that represents the conversion factor for converting fixed‐interval values of (EI₃₀)_Δt to values of (EI₃₀)₁₅ is provided in order to calculate R anywhere in the region using rainfall data of 60 min. Copyright © 2015 John Wiley & Sons, Ltd.     

Petrogenesis of Shangyu gabbro-diorites in western Shandong: Geochronological and geochemical evidence

Chronology and geochemistry of the Shangyu gabbro-diorite in western Shandong were studied to understand their petrogenesis and the nature of the Mesozoic lithospheric mantle. The Shangyu intru-sion is mainly composed of a suite of gabbro-diorite. Zircons from the intrusion display eu-hedral-subhedral in shape and have high Th/U ratios (1.23―2.87), implying their magmatic origin. LA-ICP-MS zircon U-Pb dating results for two samples indicate that they were formed in the Early Cre-taceous, yielding weighted mean 206Pb/238U ages of 129±1Ma and 134±2Ma, respectively. Except for early cumulate such as sample QT-19, their SiO2 and MgO contents range from 50.12% to 56.37% and from 3.52% to 6.37%, respectively. Moreover, the gabbro-diorites are characterized by high Mg# (0.54―0.63), enrichment in Na (Na2O/K2O ratios more than 1), Cr (73×10-6―217×10-6) and Ni (34×10-6―241×10-6), and intensive enrichments in light rare earth elements (LREEs) and large ion lithophile elements (LILEs) and depletion in high field strength elements (HFSEs). Their initial 87Sr/86Sr ratios and ε Nd(t) values range from 0.70962 to 0.71081 and from-16.60 to-13.04, respectively. Taken together with the Early Creta-ceous high-Mg diorites and the mantle xenoliths from the Tietonggou and Jinling as well as basalts from the Fangcheng and Feixian, it is suggested that the primary magma for the Shangyu gab-bro-diorites should be derived from the enriched lithospheric mantle intensively modified by conti-nental crust. The Sr-Nd-Pb isotopic compositions for the Early Cretaceous high-Mg diorites in western Shandong display a trend of spatial variations, i.e., initial 87Sr/86Sr, 207Pb/204Pb and 208Pb/204Pb ratios de-creasing and ε Nd(t) values increasing from southeast to northwest in western Shandong, which is con-sistent with the tectonic model that the Yangtze Craton subducted beneath the North China Craton oriented in north-west direction in the Early Mesozoic.     

Observation of the shadow of O3 on the D Layer in the lonospheric VLF guide over the atlantic ocean

Abstract

Detailed studies have been made of the sudden increase of the phase velocity of radio waves observed at sunrise in the 10 kH band, when optical path and terminator are crossing together at a small angle along the 12,000 km line between the ground based station of Caen (France) and the Loran transmitter at Trelew (Argentina). Assuming that the increase of electron density in the lower part of the E layer at twilight is mainly due to electron detachment of O^? ₂ by collision with newly created O(³P) and O₂(¹Δg), we analyse the specific contributions of the hard and soft components of the Hartley band and the far end of Schumann-Runge band to the amount of these constituents by action on molecular O₂ and O₃ between 80 and 90 kilometers. Using an exponential distribution of O₃ supposed to be responsible for the U.V. screening above 60 km, we discuss preliminary results of daily measurements of the mean total mass of O₃ in the mesosphere between 49°N and 45°S, by the end of every December night (in 1975 and 1976).     

Conditional spectrum‐based ground motion record selection using average spectral acceleration

The use of a seismic intensity measure (IM) is paramount in decoupling seismic hazard and structural response estimation when assessing the performance of structures. For this to be valid, the IM needs to be sufficient;that is, the engineering demand parameter (EDP) response should be independent of other ground motion characteristics when conditioned on the IM. Whenever non‐trivial dependence is found, such as in the case of the IM being the first‐mode spectral acceleration, ground motion selection must be employed to generate sets of ground motion records that are consistent vis‐à‐vis the hazard conditioned on the IM. Conditional spectrum record selection is such a method for choosing records that are consistent with the site‐dependent spectral shape conditioned on the first‐mode spectral acceleration. Based on a single structural period, however the result may be suboptimal, or insufficient, for EDPs influenced by different period values, for example, peak interstory drifts or peak floor accelerations at different floors, potentially requiring different record suites for each. Recently, the log‐average spectral acceleration over a period range, AvgSA, has emerged as an improved scalar IM for building response estimation whose hazard can be evaluated using existing ground motion prediction equations. Herein, we present a recasting of conditional spectrum record selection that is based on AvgSA over a period range as the conditioning IM. This procedure ensures increased efficiency and sufficiency in simultaneously estimating multiple EDPs by means of a single IM. Copyright © 2017 John Wiley & Sons, Ltd.