Application of wavelet transformation to determine wavelengths and phase velocities of gravity waves observed by lidar measurements

During the last two decades, important advances have been made in the investigation of gravity waves. However, more efforts are needed to study certain aspects of gravity waves. In the real atmosphere, gravity waves occur with different properties at different altitudes and, most often, simultaneously. In this case, when there is more than one dominant wave, the determination of gravity wave characteristics, such as the vertical wavelength and the phase velocity, is difficult. The interpretation of temperature perturbation plots versus the altitude and time as well as the application of the Fourier spectral analysis can produce errors.Exact knowledge of the wave characteristics is important both for determination of other characteristics, for example, the horizontal wave components, and for study of wave climatology. The wavelet analysis of vertical temperature profiles allows one to examine the wave's location in space. Up to now, gravity waves have been studied mainly by continuous wavelet transformation to determine dominant waves. We apply wavelet analysis to a time series of temperature profiles, observed by the ALOMAR ozone lidar at Andoya, Norway, and by the U. Bonn lidar system at ESRANGE, Sweden, both for determination of the dominant waves and for specifying the vertical wavelengths and the vertical component of the phase velocities. For this purpose, the wavelet amplitude spectra and the wavelet phase spectra are filtered and Hovmöller diagrams for dominant wavelengths are constructed. The advantage of this type of diagrams is that they give clear evidence for the localization of the dominant waves in space and time and for the development of their phase fronts.     

Stochastic finite-fault simulation of ground motion from the August 11, 2012, <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript> 6.4 Ahar earthquake,northwestern Iran

In this study, the 11 August 2012 M _w 6.4 Ahar earthquake is investigated using the ground motion simulation based on the stochastic finite-fault model. The earthquake occurred in northwestern Iran and causing extensive damage in the city of Ahar and surrounding areas. A network consisting of 58 acceleration stations recorded the earthquake within 8–217 km of the epicenter. Strong ground motion records from six significant well-recorded stations close to the epicenter have been simulated. These stations are installed in areas which experienced significant structural damage and humanity loss during the earthquake. The simulation is carried out using the dynamic corner frequency model of rupture propagation by extended fault simulation program (EXSIM). For this purpose, the propagation features of shear-wave including \( {Q}_s \) value, kappa value \( {k}_0 \), and soil amplification coefficients at each site are required. The kappa values are obtained from the slope of smoothed amplitude of Fourier spectra of acceleration at higher frequencies. The determined kappa values for vertical and horizontal components are 0.02 and 0.05 s, respectively. Furthermore, an anelastic attenuation parameter is derived from energy decay of a seismic wave by using continuous wavelet transform (CWT) for each station. The average frequency-dependent relation estimated for the region is \( Q=\left(122\pm 38\right){f}^{\left(1.40\pm 0.16\right)}. \) Moreover, the horizontal to vertical spectral ratio \( H/V \) is applied to estimate the site effects at stations. Spectral analysis of the data indicates that the best match between the observed and simulated spectra occurs for an average stress drop of 70 bars. Finally, the simulated and observed results are compared with pseudo acceleration spectra and peak ground motions. The comparison of time series spectra shows good agreement between the observed and the simulated waveforms at frequencies of engineering interest.     

南北地震带川滇甘陕地区竖向与水平向加速度反应谱比的统计分析

本文收集了从南北地震带川滇甘陕地区263个有详细场地资料的强震台站获得的802组强震动记录,按照场地、震级和震中距等因素统计分析了竖向与水平向加速度反应谱比的形状以及不同场地、震级和震中距下不同周期段内的谱比平均值,并与建筑抗震规范GB50011—2010规定的0.65进行了比较。结果表明:竖向与水平向加速度反应谱比受场地、震级和震中距等因素的影响; Ⅰ类和Ⅱ类场地在全周期段的谱比均值基本上大于0.65;无论何种分组情况谱比均值在0.1—1.0 s周期范围内基本低于定值0.65,周期大于1.0 s的谱比均值基本上远高于0.65。因此对于大部分抗震规范直接把竖向地震作用取为水平向地震作用的0.65倍,有待商榷。本文建议根据水平向反应谱的标定方式来确定现有竖向强震动记录的竖向地震作用。      

基于强震动记录确定的场地卓越周期

本文介绍了3种根据场地强震动记录获取场地卓越周期的方法: ① 地表记录的傅里叶谱分析法; ② 地表水平/垂直傅里叶谱比法; ③ 地表/地下傅里叶谱比法. 基于日本强震动观测台网KiK-net中两个基岩台站和两个Ⅲ类场地台站获取的数百条强震动记录, 分别使用上述3种方法确定场地的卓越周期, 并对比分析各种方法的优缺点及其适用情况. 结果表明: 对于基岩场地, 由于记录信息复杂, 局部场地条件对地震动影响较小, 地震动自身特性突出, 导致3种方法所得到的结果均比较分散; 对于土层场地, 场地条件影响比较显著, 3种方法基本都可以得到一个较为准确的数值; 但对于某些场地, 地表水平/垂直傅里叶谱比法所得结果存在不确定性, 相比之下, 地表/地下傅里叶谱比法则能给出一个更为准确的场地卓越周期值.      

Decaying grid turbulence experiments in a stratified fluid: flow measurements and statistics

Laboratory experiments of decaying grid stratified turbulence were performed in a two-layer fluid and varying the stratification intensity. Turbulence was generated by towing an array of cylinders in a square vessel and the grid was moved at a constant velocity along the total vertical extent of the tank. In order to investigate the influence of the stratification intensity on the turbulence decay, both 2C-PIV and stereo PIV were used to provide time resolved velocity fields in the horizontal plane and the out-of-plane velocity. As expected, a faster decay of the turbulence level along the vertical axis and the collapse in a quasi-horizontal motion increased with the buoyancy frequency, N. In order to characterise the decay process we investigated the time evolution of the vortex statistics, the turbulence scales and the kinetic energy and enstrophy of the horizontal flow. The exponents recovered in the corresponding scaling laws were compared with the theoretical predictions and with reference values obtained in previous experimental studies. Both the spectral analysis and the evolution of characteristic length scales indicate that, in the examined range of N, the dynamics is substantially independent of the stratification intensity. The results obtained were explained in terms of the scaling analysis of decaying turbulence in strongly stratified fluids introduced by Brethouwer et al. (J Fluid Mech 585:343–368.  https://doi.org/10.1017/S0022112007006854, 2007).     

Spectral amplitudes of strong earthquake accelerations recorded in buildings

Fourier spectrum amplitudes of horizontal and vertical earthquake accelerations recorded at the foundation levels of 57 buildings in the Los Angeles metropolitan area have been used to study the dependence of spectral amplitudes on the building foundation sizes. Comparison of these amplitudes with those predicted by empirical models for scaling ‘free field’ Fourier amplitude spectra does not indicate any significant dependence of the spectral amplitudes on the size of the foundation. Third degree polynomials have been employed to smooth the spectra of the accelerations recorded inside the buildings and their coefficients have been examined as functions of the foundation plan dimensions. These results also indicate no significant dependence of the spectral amplitudes on the foundation dimensions. A qualitative analysis of the spectral amplitudes for possible effects caused by the phenomena associated with soil-structure interaction indicates that the Fourier spectra of the recorded accelerations may experience some amplification as the relative ‘density’ of the foundation-structure system increases.     

Wave response of the ionosphere to the partial solar eclipse of August 1, 2008

Quasi-periodic variations in the Doppler shift of the HF range frequency at a vertical path and critical frequency of the F ₂ layer caused by wave disturbances in the ionosphere on the day of the partial (the magnitude was about 0.42) solar eclipse and on background days are analyzed. For the spectral analysis, the window Fourier transform, adaptive Fourier transform, and wavelet analysis were jointly used. It is shown that on the day of the eclipse and the background day, spectral characteristics of wave disturbances within the 150–200 km height range differed substantially. The changes in the spectral composition began approximately 30–35 min after the solar eclipse beginning and lasted more than 1.5 h.     

Spectral analysis of plasma drift measurements from the AE-E satellite: evidence of an inertial subrange in equatorial spread F

Plasma drift data from the AE-E satellite are spectrally analyzed to investigate the characteristics of the flow in the topside equatorial F region ionosphere during strong spread F conditions. Plasma flow around rapidly rising depletions is thought to exhibit behavior similar to two-dimensional Kolmogorov turbulence, but only on flux tubes with sufficiently small integrated ion–neutral collision frequencies. We find that one-dimensional spectra computed from vertical plasma drift measurements made in such depletions on such flux tubes tend to display a −5/3 spectral index over scale sizes from about 1 to $\text{100}\text{km}$, suggesting the operation of an inverse energy cascade. This universal spectral form is evidence of an inertial regime of the underlying ionospheric interchange instability.     

Ground motion prediction equations for horizontal and vertical components of acceleration in Northern Iran

Recent studies have shown that the vertical component of ground motion can be quite destructive on a variety of structural systems. Development of response spectrum for design of buildings subjected to vertical component of earthquake needs ground motion prediction equations (GMPEs). The existing GMPEs for northern Iranian plateau are proposed for the horizontal component of earthquake, and there is not any specified GMPE for the vertical component of earthquake in this region. Determination of GMPEs is mostly based on regression analyses on earthquake parameters such as magnitude, site class, distance, and spectral amplitudes. In this study, 325 three-component records of 55 earthquakes with magnitude ranging from M _w 4.1 to M _w 7.3 are used for estimation on the regression coefficients. Records with distances less than 300 km are selected for analyses in the database. The regression analyses on earthquake parameters results in determination of GMPEs for peak ground acceleration and spectral acceleration for both horizontal and vertical components of the ground motion. The correlation between the models for vertical and horizontal GMPEs is studied in details. These models are later compared with some other available GMPEs. According to the result of this investigation, the proposed GMPEs are in agreement with the other relationships that were developed based on the local and regional data.     

Radiative properties of cirrus clouds in NOAA 4 VTPR channels: Some explorations of cloud scenes from satellites

A one-dimensional spectral infrared radiative transfer model has been developed for atmospheres containing cirrus clouds and absorbing gases above, below and within the cloud. The transfer model takes into consideration the inhomogeneity of the cloudy atmosphere, the gaseous absorption in scattering cloud layers and the wavenumber dependence of radiative transfer. In addition, the cirrus cloud is further divided into a number of sub-layers to account for the non-isothermal and inhomogeneous cloud characteristics. Single-scattering properties for ice crystals are calculated assuming ice cylinders 200 and 60 m in lenght and width, respectively, randomly oriented in a horizontal plane. The spectral infrared transfer program is applied to VTPR channels of the NOAA 4 satellite to simulate upward radiances in cirrus cloud conditions.Comparisons between satellite observed and theoretically simulated upward radiances are carried out for selected cirrus cloud cases. Incorporating atmospheric profiles obtained from radiosonde and the observed cloud information into the spectral transfer program, we show a systematic agreement between observed and computed upward radiances. Systematic reduction patterns of the upward radiance caused by the increase of the cloud ice content are clearly demonstrated for VTPR channels employing tropical and midlatitude atmospheric profiles. Having the quantitative relationships between upward radiances and ice contents, procedures are described for the inference of the cloud ice content and cloud amount. The proposed method has been successfully applied to the three cirrus cloud cases.     

Time-frequency tools of signal processing for EISCAT data analysis

We demonstrate the usefulness of some signal-processing tools for the EISCAT data analysis. These tools are somewhat less classical than the familiar periodogram, squared modulus of the Fourier transform, and therefore not as commonly used in our community. The first is a stationary analysis, Thomsons estimate of the power spectrum. The other two belong to time-frequency analysis: the short-time Fourier transform with the spectrogram, and the wavelet analysis via the scalogram. Because of the highly non-stationary character of our geophysical signals, the latter two tools are better suited for this analysis. Their results are compared with both a synthetic signal and EISCAT ion-velocity measurements. We show that they help to discriminate patterns such as gravity waves from noise.     

汶川地震远场地震动场地相关性与分析方法评价

为考查远场地震动的场地相关性并评价一些场地特性分析方法的适用性,采用不同方法对汶川地震山东省12个远场台站的强震记录进行了分析.选取台站分别位于按建筑抗震设计规范(CBC)场地划分中的Ⅰ—Ⅲ类场地上.地震动记录的分析方法包括傅里叶幅值谱法,地震反应谱法,水平与竖向谱比率法,参考点谱比率法,以及尾波分析等.结果表明,按傅里叶幅值谱法,地震反应谱法,水平与竖向谱比法计算得到的卓越周期均远大于台站场地的卓越周期,不同方法得到的结果之间也有较大差别,且主要反映长周期地震动的卓越频率;参考点谱比率法的结果未反映地震动的卓越周期,也与场地的卓越周期差别较大;对完整记录尾波分析所得的结果比较接近场地的卓越周期.希望本文能为考虑远场地震作用时设计谱的建立,以及场地特性估计时地震动分析方法的选取提供参考依据.     

Spherical Harmonic Analysis of Gravitational Curvatures and Its Implications for Future Satellite Missions

In this study we assume that a gravitational curvature tensor, i.e. a tensor of third-order directional derivatives of the Earth’s gravitational potential, is observable at satellite altitudes. Such a tensor is composed of ten different components, i.e. gravitational curvatures, which may be combined into vertical–vertical–vertical, vertical–vertical–horizontal, vertical–horizontal–horizontal and horizontal–horizontal-horizontal gravitational curvatures. Firstly, we study spectral properties of the gravitational curvatures. Secondly, we derive new quadrature formulas for the spherical harmonic analysis of the four gravitational curvatures and provide their corresponding analytical error models. Thirdly, requirements for an instrument that would eventually observe gravitational curvatures by differential accelerometry are investigated. The results reveal that measuring third-order directional derivatives of the gravitational potential imposes very high requirements on the accuracy of deployed accelerometers which are beyond the limits of currently available sensors. For example, for orbital parameters and performance similar to those of the GOCE mission, observing third-order directional derivatives requires accelerometers with the noise level of \({\sim}10^{-17}\,\hbox {m}\,\hbox {s}^{-2}\) Hz\(^{-1/2}\).     

An analysis of heat-, momentum-transports,and spectra for clear air turbulence in mid-stratosphere

Summary An analysis of the clear air turbulence in the mid-stratosphere indicates that the turbulence is characterized by an anisotropic field of turbulence with an intense lateral component of the turbulence, associated with strong thermally stable stratification. The Richardson number in the region of turbulence is generally smaller than , the Taylor's criterion for a stratified shear flow.The cospectra for the momentum transport by the streamwise, lateral, and vertical components of the velocity show similarity in their distribution, decreasing with increasing wavenumber. The cospectra for the heat transport by the streamwise, lateral, and vertical components of the velocity show similarity in the high and medium wavenumber ranges, but not in the low wavenumber range of the spectra.The power spectra of the temperature and wind speed are very similar, and are approximately proportional to the power of the wavenumber. The power spectra of the streamwise and lateral components of the velocity are approximately proportional to the –2 power of the wavenumber, whereas the spectrum of the vertical component of the velocity is approximately proportional to the –1 power of the wavenumber.sponsored by the National Science Foundation.     

A study of response spectra for different geological conditions in Gujarat,India

In this study, the effect of ground geology on the acceleration response spectra is studied at 32 sites in Gujarat, India. The sites are grouped into Proterozoic, Mesozoic, Tertiary and Quaternary. The normalized acceleration response spectra at 5% damping of 407 strong ground motions (horizontal and vertical components) recorded at these sites varying in magnitude from 3.0 to 5.7 are determined. The study shows that the shape of the acceleration response spectra is influenced by the regional geology and local site conditions. The peak of maximum horizontal spectral amplification is between 0.03 and 0.05 s in Proterozoic formations, 0.06 and 0.10 s in Mesozoic formations, 0.06 and 0.08 s in Tertiary and 0.12 s in Quaternary formations. The maximum vertical spectral acceleration is at 0.025 s in Proterozoic, 0.07 s in Mesozoic, 0.05 s in Tertiary and 0.10 s in Quaternary formations. The average acceleration amplification factor in all the geological formations is between 2.5 and 3.0 both in horizontal and vertical components. It has been observed that acceleration response spectra at sites having same geological formations are also influenced by local site conditions. The study shows that the acceleration response spectrum in the current Indian code applicable for the entire country underestimates the seismic forces at hard-rock sites and overestimates at soft-soil sites. Using recorded strong motion data with Mw ranging from 3.5 to 5.7, an attenuation relationship is developed at six periods to predict geometric mean of horizontal spectral amplitudes for rock and soil sites. The spectral amplitudes predicted with the attenuation relationship match well with the observed one within statistical limits for hypocentral distances less than 200 km.     

Temperature and heat flux spectra in the turbulent buoyancy subrange

The physical nature of motions with scales intermediate between approximately isotropic turbulence and quasi-linear internal gravity waves is not understood at the present time. Such motions play an important role in the energetics of small scales processes, both in the ocean and in the atmosphere, and in vertical transport of heat and constituents. This scale range is currently interpreted either as a saturated gravity waves field or as a buoyancy range of turbulence.We first discuss some distinctive predictions of the classical (Lumley, Phillips) buoyancy range theory, recently improved (Weinstock, Dalaudier and Sidi) to describe potential energy associated with temperature fluctuations. This theory predicts the existence of a spectral gap in the temperature spectra and of an upward mass flux (downward buoyancy and heat fluxes), strongly increasing towards large scales. These predictions are contrasted with an alternate theory, assuming energetically insignificant buoyancy flux, proposed by Holloway.Then we present experimental evidences of such characteristic features obtained in the lower stratosphere with an instrumented balloon. Spectra of temperature, vertical velocity, and cospectra of both, obtained in homogeneous, weakly turbulent regions, are compared with theoretical predictions. These results are strongly consistent with the improved classical buoyancy range theory and support the existence of a significant downward heat flux in the buoyancy range.The theoretical implications of the understanding of this scale range are discussed. Many experimental evidences consistently show the need for an anisotropic theory of the buoyancy range of turbulence.     

Earthquake Induced Site Effect in the Algiers–Boumerdes Region: Relation Between Spectral Ratios Higher Peaks and Observed Damage During the May 21st M w 6.8 Boumerdes Earthquake (Algeria)

The Algiers–Boumerdes regions were hit by an M _w 6.8 destructive earthquake on May 21, 2003. The accelerometric and seismometric networks successfully recorded the main shock and many aftershocks at some locations where the damage was most extensive. A microtremor measurement was performed in the same locations; some of them are localized on the Mitidja basin. In this paper, we propose to analyze earthquake-induced site effect derived from horizontal to vertical spectral ratio from ambient noise (noise horizontal to vertical—NHV), or from very weak, weak, moderate and strong ( peak ground acceleration—PGA >10 % g) seismic motions (EHV), and transfer function evaluation from soil velocity profile data at four sites. H/V spectral ratios are computed by using both Fourier and response spectra. Compared to the transfer function, the obtained results show that in the case of soft soils, NHV as well as EHV give a good estimation of the soil's fundamental frequency, whereas the NHV underestimate the H/V amplitude and the EHV amplitude increase with the seismic motion intensity. In the case of firm soils, whereas the NHV gives flat curves synonymous for a rock site or a bump, the EHV is more appropriate as seen by identifying clear peaks with non negligible amplitude. In the case of soft sites as well as in the case of firm sites, strong peaks at frequencies higher than the fundamental one are found from EHV curves. Those peaks would not be found when looking at NHV ratios alone, are evidenced by the computed transfer function as well as by an analytical formulation, and are in agreement with the observed distribution of damage during the M _w 6.8 2003 Boumerdes earthquake. Finally, the same analysis is performed by using response spectra rather than Fourier spectra and leads to the same conclusions. Moreover, the calculation of the response spectra is more easily compared with the smoothing operation of the Fourier spectra.     

Preliminary empirical model for scaling fourier amplitude spectra of strong ground acceleration in terms of modified mercalli intensity and recording site conditions

This paper presents an empirical model for scaling Fourier amplitude spectra of ground acceleration during strong earthquake shaking in terms of the reported Modified Mercalli Intensity (MMI) and the simplified characteristics of the geologic environment at the recording station. This analysis shows that (i) for the intermediate and high-frequency motions the spectral amplitudes approximately double for every level of the MMI; that (ii) the uncertainties associated with estimation of Fourier spectral amplitudes in terms of MMI are not greater than the uncertainties associated with similar estimation in terms of earthquake magnitude and epicentral distance; that (iii) the high frequency spectral amplitudes tend to be greater on basement rock sites relative to alluvium sites, with this trend being reversed for the low-frequency spectral amplitudes; and that (iv) the spectral amplitudes of very high-frequency vertical shaking are equal to or higher than the corresponding spectral amplitudes for horizontal shaking.     

应用小波变换提取张北地震的震磁效应

以1998年1月10日的张北地震为例,应用小波变换及傅里叶分析,分析震中附近的6个地磁台站在地震前后共6个月的地磁场三分量分钟值采样数据.发现各个地磁台站记录的地磁场Z分量在张北地震前三个月内出现不同程度的异常现象,这种现象的出现频率随着离发震时间越近而越来越高,出现的地点由南向北迁移.地磁场H和D分量没有此类异常出现.用这6个地磁台出现异常时同一频率所对应的振幅值绘出等值曲线,得到的图形是稳定的四象限分布,震中基本上位于0～3nT的等值线上.结果表明小波分析是提取地震磁效应的有效工具,同时也证实了地震磁效应的客观存在.     

Modal analysis of a DAM–Foundation system based on an FE–BE method in the time domain

A modal analysis procedure based on an FE–BE method in the time domain is first formulated and then applied to a dam–foundation system. In the application, horizontal and vertical impulsive responses are calculated for the system having six different impedance ratios. Modal characteristics such as natural frequencies, damping ratios and mode shapes are evaluated from the Fourier spectra of the responses. The proposed procedure allows analysis of not only the underdamped but also the overdamped modes. According to the analysis, the radiation damping pertinent to the vertical vibration is half of that pertinent to the horizontal vibration and the interaction effect on the modes is not negligibly small when the impedance ratio exceeds 0·3.