Seismic resonances of spherical acoustic cavities

We study the interaction of a seismic wavefield with a spherical acoustic gas‐ or fluid‐filled cavity. The intention of this study is to clarify whether seismic resonances can be expected, a characteristic feature that may help in detecting cavities in the subsurface. This is important for many applications, in particular the detection of underground nuclear explosions, which are to be prohibited by the Comprehensive Test Ban Treaty. To calculate the full seismic wavefield from an incident plane wave that interacts with the cavity, we considered an analytic formulation of the problem. The wavefield interaction consists of elastic scattering and the wavefield interaction between the acoustic and elastic media. Acoustic resonant modes caused by internal reflections in the acoustic cavity show up as spectral peaks in the frequency domain. The resonant peaks coincide with the eigenfrequencies of the un‐damped system described by the particular acoustic medium bounded in a sphere with stiff walls. The filling of the cavity could thus be determined by the observation of spectral peaks from acoustic resonances. By energy transmission from the internal oscillations back into the elastic domain, the oscillations experience damping, resulting in a frequency shift and a limitation of the resonance amplitudes. In case of a gas‐filled cavity, the impedance contrast is still high, which means low damping of the internal oscillations resulting in very narrow resonances of high amplitude. In synthetic seismograms calculated in the surrounding elastic domain, the acoustic resonances of gas‐filled cavities show up as persisting oscillations. However, due to the weak acoustic–elastic coupling in this case, the amplitudes of the oscillations are very low. Due to a lower impedance contrast, a fluid‐filled cavity has a stronger acoustic–elastic coupling, which results in wide spectral peaks of lower amplitudes. In the synthetic seismograms derived in the surrounding medium of fluid‐filled cavities, acoustic resonances show up as strong but fast decaying reverberations.     

空腔爆炸产生的地震波

本文首先讨论了压力空腔和爆炸中心的等价问题。计算层状介质中的空腔爆炸所产生的位移场时,可先求介质的单位脉冲响应,然后将其与等价的爆炸点源函数做褶积。对于均匀的半空间,自由面位移的暂态解是由三个无量纲的参数所决定的;由此可导出远场位移的精确解。本文也讨论了爆炸点附近的运动。最后还导出多层介质中空腔爆炸所产生的表面位移谱的形式解。     

Peak surface motion due to scattering of plane harmonic P,SV, or Rayleigh waves by a rough cavity embedded in an elastic half-space

Scattering of plane harmonic P, SV, or Rayleigh waves by a two-dimensional rough cavity completely embedded in an isotropic elastic half-space is investigated by using a direct boundary integral equation method. The cavity’s roughness is assumed to be in the form of periodic or random perturbations of arbitrary amplitude superimposed to a smooth elliptical shape. For the randomly corrugated cavities the normal or the uniform probability distribution functions are assumed. Based on multiple random cavity results, the corresponding average surface response is computed. These are compared with the corresponding periodically corrugated and smooth cavity responses. The surface response is evaluated for different cavity shapes and incident waves and for a range of frequencies. The surface motion results are used to determine the peak surface motion frequencies. They depend strongly upon the basic inclusion shape (the principal axes) and the nature of the incident wave. Strong similarity in the peak surface motion frequencies can be observed for the rough and smooth cavity models for both circular and elliptical shapes. In order to quantify the importance of the cavity corrugation upon the surface motion, a roughness influence factor is defined in terms of the rough and smooth cavity surface responses. This factor strongly depends upon the type of the incident wave, the nature of the cavity corrugation, the basic cavity shape, and the frequency. The factor clearly shows the effect of the cavity roughness upon the surface motion.     

An energy-based envelope function for the stochastic simulation of earthquake accelerograms

An energy-based envelope function is developed for use in the stochastic simulation of earthquake ground motion. The envelope function is directly related to the Arias intensity of the ground motion as well to the manner in which this Arias intensity is built-up over time. It is shown that this build-up, represented by a Husid plot, can be very well modelled using a simple lognormal distribution. The proposed envelope makes use of parameters that are commonly available in seismic design situations, either following a deterministic scenario-type analysis or following a more comprehensive probabilistic seismic hazard analysis (PSHA), either in terms of Arias intensity or the more common spectral acceleration. The shape parameters of the envelope function are estimated following the calculation of the analytic envelopes for a large number of records from PEER Next Generation of Attenuation (NGA) database. The envelope may also be used to predict the distribution of peak ground acceleration values corresponding to an earthquake scenario. The distribution thus obtained is remarkably consistent with those of the recent NGA models.     

The influence of the degree of saturation on dynamic response of a cylindrical lined cavity in a nearly saturated medium

In most previous studies on the dynamic response of a long cylindrical cavity subjected to internal transient dynamic loads, the porous medium was usually assumed to be completely saturated by ground water. In practice, however, the full saturation condition does not always exist. In this paper the surrounding soil and the lining of the cavity are respectively treated as a nearly saturated porous medium and an elastic material, and the governing equations for the dynamic problem are derived. A set of exact solutions are obtained in the Laplace transform domain for three types of transient loads, i.e. suddenly applied constant load, gradually applied step load and triangular pulse load. By utilizing a reliable numerical method of inverse Laplace transforms, the time-domain solutions are then presented. The influence of the degree of saturation of the surrounding soil on the dynamic response of the lined cavity is examined for numerical examples.     

The Simulation of Ground Motions Using Envelope Summations

—?The technique of Midorikawa (1993) has been modified to obtain a resultant envelope function at the observation point by placing the rupture causing an earthquake in a layered earth model. The method and its dependency on various modelling parameters are studied in detail. The complete study shows that the generated resultant envelope follows important strong motion characteristics such as directivity and attenuation effects. The simulated resultant envelope is further used for generating synthetic accelerograms by multiplying filtered white noise with the envelope of accelerogram at a particular observation point. Filters through which white noise passes include the effects of geometrical spreading, anelastic attenuation and near-site attenuation at high frequencies.¶Uttarkashi earthquake is among few Indian earthquakes for which strong motion data are available at thirteen different stations. Using the technique presented in this work, envelope function as well as complete acceleration time history during Uttarkashi earthquake has been simulated at these observation points. Comparison of peak acceleration, duration and acceleration response spectra confirms the utility and efficacy of the approach.     

Scattering of shear waves by an elliptical cavity in a radially inhomogeneous isotropic medium

Complex function and general conformal mapping methods are used to investigate the scattering of elastic shear waves by an elliptical cylindrical cavity in a radially inhomogeneous medium. The conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. The medium density depends on the distance from the origin with a power-law variation and the shear elastic modulus is constant. The complex-value displacements and stresses of the inhomogeneous medium are explicitly obtained and the distributions of the dynamic stress for the case of an elliptical cavity are discussed. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Numerical results demonstrate that the wave number, inhomogeneous parameters and different values of aspect ratio have significant influence on the dynamic stress concentration factors around the elliptical cavity.     

Characteristics of S-wave Envelope Broadening in the Changbaishan Tianchi Volcano

High-frequency S-wave seismogram envelopes of microearthquakes broaden with increasing travel distance,a phenomenon known as S-wave envelope broadening. Multiple forward scattering and diffraction for the random inhomogeneities along the seismic ray path are the main causes of S-wave envelope broadening,so the phenomenon of S-wave envelope broadening is used to study the inhomogeneity of the medium. The peak delay time of an S-wave,which is defined as the time lag from the direct S-wave onset to the maximum amplitude arrival of its envelope,is accepted to quantify S-wave envelope broadening. 204 small earthquake records in Changbaishan Tianchi volcano were analyzed by the S-wave envelope broadening algorithm. The results show that S-wave envelope broadening in the Changbaishan Tianchi volcano is obvious,and that the peak delay time of S-wave has a positive correlation with the hypocenter distance and frequency of the S-wave. The relationships between the S-wave peak delay time and the hypocenter distance for different frequency bands were obtained using the statistics method. The results are beneficial to the understanding of the S-wave envelope broadening phenomena and the quantitative research on the inhomogeneities of the crust medium in the Changbaishan Tianchi volcano region.     

对若干地震动包线函数的比较分析

对已经提出的四种经常使用的包线函数模型进行了评价,认为对于评价单峰点包线函数,除了要求形式简单以外,其优劣可以用函数对峰点位置和高峰隆起程度的控制能力作为标准。借助结构动力试验中阻尼比的确定方法,提出用平稳度指数来评价单峰点包线函数平缓程度。据此对四种包线函数的平稳度进行了分析,还对某些包线函数提出了一些改进。通过分析指出如果把“金井清谱”和“Penzien谱”等模型,看作是时间域中包线,这两个模型的调节能力都很强,而且比较方便,其中“Penzien谱”模型可以用来表示具有两个峰点的包线。文中的比较分析结果可以用于地震动包线函数选择和模拟。     

Diffraction of obliquely incident waves by a cylindrical cavity embedded in a layered viscoelastic half-space

The three-dimensional harmonic response in the vicinity of an infinitely long, cylindrical cavity of circular cross-section buried in a layered, viscoelastic half-space is obtained when the half-space is subjected to homogeneous plane waves and surface waves impinging at an oblique angle with respect to the axis of the cavity. The solution is obtained by an indirect boundary integral method based on the use of moving Green's functions for the viscoelastic half-space. Numerical results describing the motion on the ground surface and the motion and stresses on the wall of the cavity are presented for obliquely incident P-, SV-, SH- and Rayleigh waves with different horizontal angles of incidence.     

Ground motion near an expanding preexisting crack

We present a study of the motion of the ground in the near field of a preexisting vertical crack driven by excess tensile stress. Using the discrete wave number method, we make a complete representation of the three components of ground displacement resulting from a small incremental extension of the bottom tip of the crack and analyze the effects of the medium structure on the ground response. The results show the strong impulsive character of the dynamic motion near the source and demonstrate that the first motion is directed everywhere outward. Marked oscillations are observed in the ground response associated with the ringing of the crack faces triggered by the rupture. The displacement is dominantly vertical near the epicenter but becomes predominantly horizontal beyond the immediate source region. The presence of layers has a strong effect on the complexity and duration of the ground response. The static vertical and longitudinal displacements are respectively downward and inward in the epicentral area.     

Earth tides and polar motion

We establish a general theory that describes the rotational motion of a layered, oblate, elastic Earth under the influence of tidal forces when account is taken of the liquid outer core. We obtain a linearized version of the Navier-Stokes equation; within it not only have we retained the Coriolis and centrifugal acceleration terms, but also have included the nutational terms. We also make use of the Euler equation for angular momentum to analytically relate the nutational motion of the rotational axis with the oscillations of the liquid core and obtain a constraint for the nutational amplitude. Consideration of the Poisson equation for density variation completes our analytical model.We primarily discuss the equations of motion for the liquid core and present the solution as the sum of two terms: one being a component of the spheroidal displacement field, the other of the toroidal field. We also formulate the equations valid for the solid mantle when rotational effects are included, and establish the boundary conditions that must hold at the various interfaces in order that a complete integration of the differential system of equations be accomplished.We assume that the outer core consists of an inviscid fluid and ignore the existence of any boundary layer. We do not impose, however, any restriction on the stratification of the fluid. The dynamical coupling between liquid core and solid mantle is represented by a torque which is generated by the forced oscillations within the liquid core; these oscillations are in turn triggered by the diurnal tides.The expected influence of the liquid core/solid mantle boundary on the nutational motion is discussed in view of Poincare's results concerning a liquid core surrounded by a rigid shell. Comparison is finally made of our model with Molodenskii's 1961 theory for a neutral core and the 1976 Shen-Mansinha nutational theory for an unrestricted core.     

基于新《电力设施抗震设计规范》的地震动随机模型参数研究

根据新《电力设施抗震设计规范》(GB50260-2013)对随机地震动功率谱参数的取值进行分析。介绍新《电力设施抗震设计规范》中设计反应谱,推导设计谱到功率谱的转换过程。选取常用的Clough-Penzien修正过滤白噪声模型作为拟合函数,通过功率谱参数拟合,得到不同场地类别、不同抗震设防烈度下的地震动模型参数。该研究成果可为电力工程抗震设计分析提供参考。     

The constants of equivalent systems without feedback for computing the responses of electromagnetic seismographs with several galvanometers

Summary The amplitude and phase responses of electromagnetic seismographs with an arbitrary number of galvanometers, used to increase the dynamic range of the seismograph or to filter perturbing oscillations, are derived. The fundamental parameters of the system, i.e. the partial periods and the partial constants of damping of the seismometer and of the individual galvanometers, together with the coupling terms, are replaced by other constants. These enable the responses of each channel to be computed with the aid of a combination of elementary responses of the systems of the set with zero couplings between the galvanometers and a zero effect of the motion of the galvanometers on the motion of the seismometer. The elementary responses are defined by 2 types of substitute constants: equivalent constants, determined by the roots of the characteristic equation, or by the partial periods, and reduced damping constants. The possibilities of analysing a system with equivalent constants are demonstrated on the case of a seismograph with 2 galvanometers.     

Search for hidden periodicity in magnetometric measurements performed during auroras

A method for detecting discrete equidistant spectra in high-latitude magnetic observations is proposed. The method finds approximate solutions of the classical Schuster problem, which finds a hidden periodicity in observations with considerable noise. The usage of difference signals makes it possible to increase the latitudinal resolution of the magnetometric diagnostics. The equidistant spectra of two different types have been detected based on the proposed method. The spectra of the first type are interpreted as frequencies of coupled compressional-transverse magnetohydrodyncompressionalamic oscillations in the magnetospheric cavity. The origin of the second type of spectra can be related to a rotating source, i.e., a small-scale vortex of magnetospheric convection. Such an interpretation takes into consideration the Doppler frequency shift caused by entrainment of the ionospheric neutral gas by magnetospheric convection. The results confirm the conclusion that discrete auroral frequencies are stable under disturbed conditions.     

Climate response to astronomical forcing

Power spectrum analysis of the oxygen isotopic records of deep-sea cores cannot be directly used for correlation studies with the astronomical forcing functions because of the rapidity of the major deglaciations. The ensuing step change in the isotopic curves, repeated at somewhat irregular intervals, produces, in fact, substantial spectral energy in a wide frequency band that includes the frequencies of the precessional parameters.The isotopic fluctuations within the ramp sections of a composite core curve have been found to be highly correlated with the precessional parameters, indicating a linear response of climate to these parameters and verifying, at the same time, the essential correctness of the time scale adopted.A direct correlation of eccentricity with the major glacial/interglacial cycle is doubtful because some of the eccentricity minima have absolute values of the same order as some of the maxima, while the isotopic amplitude remains essentially constant. In order to test if the major cycle could be related to a terrestrial parameter exhibiting an asymmetric relaxation fluctuation, we have added an asymmetric saw-tooth function to an artificial curve constructed from the precessional parameters on the basis of optimal response amplitude. The curve thus generated reproduces the original isotopic curve with a similarity sufficient to warrant a close search and analysis of the relaxation process.     

中国东北地区及邻区土层场地地震动强度包络函数参数衰减关系研究

利用土层场地数字化强震动记录,研究适用于东北地区及邻区的强震动包络函数参数衰减关系.数据集由2008年后研究区内发生的29次地震事件的水平向和垂直向强震动记录构成.经过基线校正和滤波处理后,结合三段式包络函数模型,应用能量持时计算t1和t2,通过最小二乘法统计回归确定c值,得到了强震动包络函数参数的衰减关系公式.比较水...     

On the electron dynamics in the field of a whistler wave propagating along a magnetic field in a weakly inhomogeneous plasma

The relativistic motion of electrons in the field of a finite amplitude circularly polarized whistler propagating along a constant magnetic field in a plasma with longitudinal inhomogeneity is considered. It is shown that the equations of the particle motion exhibit a constant of the motion despite the spatial dependence of the wave parameters. The existence of the constant allows one to reduce the equations of motion to a canonical form describing one-dimensional oscillations of a particle with the Hamiltonian slowly varying in the process of the oscillations.     

Some methods for the analysis of equipment-structure interaction

We present some numerical methods which simplify the analysis of equipment-structure systems composed of an equipment component which is light with respect to the structure component. We consider completely general forms of equipment-structure interaction. In particular, we consider that an arbitrary number of natural frequencies of the equipment and the structure are nearly equal (or equal) to each other. We show that this coincidence of natural frequencies implies that the equipment-structure system will itself have several closely spaced natural frequencies. The essence of equipment-structure interaction is the formation of beats, with slowly varying amplitude in each degree of freedom, between these natural frequencies-at least in response to a δ-function ground motion. We derive some differential equations, the solutions of which are a slowly varying envelope function (a vector) which yields the above slowly varying amplitudes. It is obtained by numerical integration using some conventional, but modified, methods and using a step size appropriate to capture its slowly varying nature. This envelope function defines the response to a δ-function ground motion. We show how it may be combined with the properties of an arbitrary ground motion (acceleration record or response spectrum) to yield the response to such a ground motion.     

S波包络时间差影响因素的数值分析di

介质非均匀性可引起高频S波包络的展宽．S波包络展宽是定量研究岩石圈中随机速度非均匀性的有力工具．S波的初至与其均方根包络最大振幅的一半之间的时间延迟定义为S波包络时间差,该时间的大小可反映介质非均匀性强弱．采用有限差分算法模拟了2D von Kaacute;rmaacute;n型随机介质中S波包络的展宽现象,统计分析了影响S波包络时间差的主要因素．结果表明,随机介质中S波传播的距离、随机介质速度扰动率及S波频率均可对S波包络时间差产生影响．相比较而言,速度扰动率对S波包络时间差影响程度最大,S波传播距离次之,S波频率影响程度最小．