ELF wave generation in the ionosphere using pulse modulated HF heating: initial tests of a technique for increasing ELF wave generation efficiency

This paper describes the results of a preliminary study to determine the effective heating and cooling time constants of ionospheric currents in a simulated modulated HF heating, ‘beam painting’ configuration. It has been found that even and odd harmonics of the fundamental ELF wave used to amplitude modulate the HF heater are sourced from different regions of the ionosphere which support significantly different heating and cooling time constants. The fundamental frequency and its odd harmonics are sourced in a region of the ionosphere where the heating and cooling time constants are about equal. The even harmonics on the other hand are sourced from regions of the ionosphere characterised by ratios of cooling to heating time constant greater than ten. It is thought that the even harmonics are sourced in the lower ionosphere (around 65 km) where the currents are much smaller than at the higher altitudes around 78 km where the currents at the fundamental frequency and odd harmonics maximise.     

应用非线性高阶谐波衰减和尾波干涉监测高温作用后水泥制品的损伤演化

非线性高阶谐波和尾波波速变化均能够反映水泥材料内部微结构的应力变化。利用高阶谐波和尾波干涉实验测量系统,对引入高温作用后的3类不同粒径共6块水泥试样进行单轴加载的损伤演化实验,并与无高温作用的完整试样的实验结果进行对比。结果表明,从初始状态到25%抗压强度的过程中,高温作用后的试样的谐波幅值和尾波波速变化出现明显增强的现象（谐波幅值最大增幅约20%）,而无高温作用的完整试样的谐波幅值和尾波波速变化较为平稳（谐波幅值最大增幅约5%）;在达到65%抗压强度的过程中,高温作用后的试样的谐波幅值和尾波波速变化急剧增大（谐波幅值最大增幅约100%）,且粒径较大的试样的增幅高于粒径较小的试样,而无高温作用的完整试样的谐波幅值和尾波波速变化的增幅较小（谐波幅值最大增幅约10%）;当抗压强度超过75%以后,高温作用后的试样的谐波幅值和尾波波速变化急剧衰减（谐波幅值最大衰减幅度约140%）,而无高温作用的完整试样的谐波幅值和尾波波速的最大衰减幅值在40%以内。基于以上观测结果对高温作用后水泥制品损伤演化的物理机制以及这两类监测方法的适用性进行了讨论。     

Harmonic by harmonic removal technique for improving vibroseis data quality

In this paper, an improved method is presented to reduce vibrator harmonic distortion, one harmonic at a time and the method is illustrated with both simulated and field data. This method improves on the previous method that treated all the harmonics at once. The significant contribution in this procedure is a considerable reduction for the harmonics without any alteration for the weakest signals possibly present in positive and negative times. The core of the proposed technique depends on an accurate simulation for all the harmonics one by one existing in the positive and negative times of the data after cross‐correlation with the fundamental sweep and then subtracting the simulated harmonics from the original data using an optimization procedure. The steps and mathematical equations of the procedure are explained in detail in the body of the article in the section titled ‘harmonic by harmonic attenuation procedure’. Accordingly, a well‐developed procedure for enhancing the vibroseis data quality in both down‐ and up‐sweep data is illustrated. The procedure was tested on both synthetic and field data sets.     

REDUCTION OF HARMONIC DISTORTION IN VIBRATORY SOURCE RECORDS*

Due to non-linear effects, the swept frequency signals (sweeps) transmitted into the subsurface by vibrators are contaminated by harmonics. Upon correlation of the recorded seismograms, these harmonics lead to noise trains which are particularly disturbing in the case of down-sweeps. The method described in this paper—which can be regarded as a generalization of Sorkin's approach to the suppression of even order harmonics—allows elimination, from the final vibratory source seismogram, of harmonics of the sweep up to any desired order. It requires that not one single signal but rather a series of M signals is employed where each signal has an initial phase differing from that of the previous one of the series by the phase angle 2πM. Prior to stacking, the seismograms generated with the different signals have to be brought into the form they would have if they had been generated with the same signal. The method seems also to be capable of reducing the correlation noise if sign-bit recording techniques are used.     

Continental elevation influence on the stationary harmonics of the atmospheric motion

Summary The effect of lifting of a latitudinally uniform zonal current of air by the continental elevations, on the stationary harmonics of the atmospheric motion, is investigated. Use of spherical harmonics up to the 15th degree is made within the framework of a simple quasigeostrophic linear theory. The results indicate that such an effect, though significant, cannot alone explain the observations. Some other interesting points regarding some of the assumptions involved (e.g., regarding the Coriolis parameter) are discussed.     

Alternative expressions for gravity gradients in local north-oriented frame and tensor spherical harmonics

The traditional expressions for gravity gradients in local north-oriented frame and tensor spherical harmonics have complicated forms involved with first- and second-order derivatives of spherical harmonics and also singular terms. In this paper we present alternative expressions for these quantities, which are simpler and contain no singular terms. The presented formulas are useful for those disciplines of geosciences which are involved with potential theory, tensor spherical harmonics and second-order derivatives of spherical harmonic series in the local north-oriented frame. A simple numerical test on the solution of the gradiometric boundary value problems presents the correctness of these new expressions and ability of the solutions to continue the gravity gradients from satellite level down to sea level using spherical harmonics.     

A three-dimensional finite-element model of wind effects upon higher harmonics of the internal tide

A non-linear three-dimensional unstructured grid model of the M₂ tide in the shelf edge area off the west coast of Scotland is used to examine the spatial distribution of the M₂ internal tide and its higher harmonics in the region. In addition, the spatial variability of the tidally induced turbulent kinetic energy and associated mixing in the area are considered. Initial calculations involve only tidal forcing, although subsequent calculations are performed with up-welling and down-welling favourable winds to examine how these influence the tidal distribution (particularly the higher harmonics) and mixing in the region. Both short- and long-duration winds are used in these calculations. Tidal calculations show that there is significant small-scale spatial variability particularly in the higher harmonics of the internal tide in the region. In addition, turbulence energy and mixing exhibit appreciable spatial variability in regions of rapidly changing topography, with increased mixing occurring above seamounts. Wind effects significantly change the distribution of the M₂ internal tide and its higher harmonics, with appreciable differences found between up- and down-welling winds and long- and short-duration winds because of differences in mixing and the presence of wind-induced flows. The implications for model validation, particularly in terms of energy transfer to higher harmonics, and mixing are briefly discussed.     

On the sensitivity of computed higher tidal harmonics to mesh size in a finite element model

A finite element model of the Irish and Celtic Sea regions with a range of grid resolutions is used to examine the influence of resolution upon the higher harmonics of the tide in the region. Comparisons are also made with published results from finite difference models of the area, and observations. Calculations using fine near-shore elements with non-zero water depths in coastal regions were found to be more accurate and less time consuming than those using a zero coastal water depth. A detailed examination of the spatial variability of the higher harmonics in near-shore regions of the eastern Irish Sea particularly the Solway and Morecambe Bay showed significant small-scale variability. This together with the variation in higher harmonics in the eastern Irish Sea and adjacent estuaries, clearly shows the need for an unstructured grid model of the region that can include the estuaries. To match the high resolution of the model in near-shore regions accurate high-resolution topography is required.     

Generation and radiation of high power line harmonics

The problems of frequency spectrum generation, radiation, and reception of signals at high power line (PL) harmonics of 50/60 Hz, and high PL harmonics caused by the use of thyristor power controllers in control circuits of large electricity consumers are discussed. The PL for frequencies of 2–8 kHz is considered a sufficiently effective traveling-wave antenna (the so-called Beverage antenna). The response of the spectrometer to a periodic sequence of PL radiation broadband pulses is discussed. The effects of a slow signal frequency drift at high PL harmonics and the occurrence of pulse components with fast frequency drift on the dynamic spectra, which in the literature is often associated with the magnetospheric trigger radiation, are considered.     

Interaction between the electromagnetic and acoustic fields in the marine environment

The possibility of generation of additional acoustic harmonics in the geomagnetic field after the propagation of an acoustic wave in the conducting medium through the region with a variable magnetic field has been considered. Two possible procedures of such a generation have been analyzed: the parametric procedure and the dynamic procedure related to ponderomotive forces. The expressions have been obtained for three acoustic harmonics generated by an oscillating magnetic field.     

On the estimation of a multi-resolution representation of the gravity field based on spherical harmonics and wavelets

The gravitational potential of the Earth is usually modeled by means of a series expansion in terms of spherical harmonics. However, the computation of the series coefficients requires preferably homogeneous distributed global data sets. Since one of the most important features of wavelet functions is the ability to localize both in the spatial and in the frequency domain, regional and local structures may be modeled by means of a spherical wavelet expansion. In general, applying wavelet theory a given input data set is decomposed into a certain number of frequency-dependent detail signals, which can be interpreted as the building blocks of a multi-resolution representation. On the other hand, there is no doubt that the low-frequency part of the geopotential can be modeled appropriately by means of spherical harmonics. Hence, the main idea of this paper is to derive a combined model consisting of an expansion in spherical harmonics for the low-frequency part and an expansion in spherical wavelets for the remaining medium and high-frequency parts of the gravity field. Furthermore, an appropriate parameter estimation procedure is outlined to solve for the unknown model coefficients.     

Break through the limits of vibroseis data quality

The vibroseis method has become the principal data acquisition method in land seismic exploration. It seems that this method has been extended to its limits as the search for energy resources continues. Many practical issues arising from field operations have remained theoretically unexplained, for example, variations in wavelet arrival time, inaccurate wavelet estimation and harmonics in the wavelet itself. The focus of this paper is the proposal of a new model, which is referred to as the vibrator‐coupled ground model, to simulate the filtering effects of a complex coupling system consisting of the coupling between the baseplate and the ground as well as the coupling between the captured ground mass near the vibrator baseplate and the surrounding earth. With this vibrator‐coupled ground model many of the practical issues mentioned above were reasonably addressed. Furthermore, it was demonstrated from experimental tests that both the pilot sweep and the weighted‐sum groundforce, when filtered by the vibrator‐coupled ground model, are proportional to the far‐field particle velocity whereas the unfiltered signals are not. The harmonics on the filtered weighted‐sum groundforce successfully maintain a proportional relationship with the harmonics seen in the far‐field signal.     

行星尺度地磁异常的长期变化

为了综合反映地球表面行星尺度磁异常的展布面积、磁场极值以及磁场分布特征等多种因素及其与磁能的关系，本文用穿过各异常区的“无符号磁通量”为特征参数来表征磁异常区强度.用第八代国际参考地磁场模型(IGRF)，分析了1900年到2000年全球最大的5个磁异常区的长期变化，结果表明，在一百年中，南大西洋(SAT)、大洋洲(AUS)和非洲(AF)3个异常区的磁通量均增加了200MWb以上，欧亚异常(EA)磁通量增加幅度稍小(157MWb)，上述4个异常区磁通量增幅为30%-60%，而北美异常(NAM)的磁通量则减小了50MWb.各异常区面积虽有变化，但最大变化仅为%左右.对磁异常区的西向漂移研究表明，地球表面和核幔界面的西漂明显存在差异：地表磁场有持续而稳定的西向漂移，全球平均西漂速度为0.2°/a；但核幔界面磁场的西向漂移速度要小得多，最大不超过0.1°/a.形成这种差异的原因可能是组成地磁场的不同球谐分量有不同的漂移速度；地表磁场的西漂主要决定于占优势的低阶分量，而核幔界面的西漂则受到高阶分量的重大影响.本文指出，在把地表西漂值用作地核磁流体运动速度的典型值时必须十分谨慎.     

Local Ionospheric Modeling Using the Localized Global Ionospheric Map and Terrestrial GPS

global ionosphere maps are generated on a daily basis at CODE using data from about 200 GPS/GLONASS sites of the IGS and other institutions. The vertical total electron content is modeled in a solargeomagnetic reference frame using a spherical harmonics expansion up to degree and order 15. The spherical Slepian basis is a set of bandlimited functions which have the majority of their energy concentrated by optimization inside an arbitrarily defined region, yet remain orthogonal within the spatial region of interest. Hence, they are suitable for decomposing the spherical harmonic models into the portions that have significant strength only in the selected areas. In this study, the converted spherical harmonics to the Slepian bases were updated by the terrestrial GPS observations by use of the least-squares estimation with weighted parameters for local ionospheric modeling. Validations show that the approach adopted in this study is highly capable of yielding reliable results.     

On the onset of thermal convection in slowly rotating fluid shells

Abstract

The problem of the removal of the degeneracy of the patterns of convective motion in a spherically symmetric fluid shell by the effects of rotation is considered. It is shown that the axisymmetric solution is preferred in sufficiently thick shells where the minimum Rayleigh number corresponds to degree l = 1 of the spherical harmonics. In all cases with l > 1 the solution described by sectional spherical harmonics Y^l _l (θ,φ) is preferred.     

Using quartz grain size and shape analysis to distinguish between aeolian and fluvial deposits in the Dallol Bosso of Niger (West Africa)

Size and Fourier-shape characteristics of quartz sand grains were determined by computerized image analysis in order to distinguish between aeolian and fluvial soil parent materials in the Dallol Bosso in Niger. Factor analysis of grain-size distributions gave four sand end-members that can be related to fluvial transport dynamics operating when the sediments were initially deposited. The medium to fine (and more angular shaped) sand fractions are being reworked by wind. Aeolian deposits were well sorted whereas fluvial deposits were poorly sorted in both size and shape. Although gross-shape characteristics (lower harmonics of Fourier series expansion) indicated a common source rock for all sands, the aeolian sands were well rounded whereas the fluvial sands tended to be more angular (upper harmonics of Fourier series).     

Rossby wave resonance in the presence of a nonlinear critical layer

Abstract

The behavior of Rossby waves on a shear flow in the presence of a nonlinear critical layer is studied, with particular emphasis on the role played by the critical layer in a Rossby wave resonance mechanism. Previous steady analyses are extended to the resonant case and it is found that the forced wave dominates the solution, provided the flow configuration is not resonant for the higher harmonics induced by the critical layer. Numerical simulations for the forced initial value problem show that the solution evolves towards the analysed steady state when conditions are resonant for the forced wave, and demonstrate some of the complications that arise when they are resonant for higher harmonics. In relating the initial value and steady problems, it is argued that the time dependent solution does not require the large mean flow distortion that Haberman (1972) found to be necessary outside the critical layer in the steady case.     

基于快速傅里叶方法的地震前兆振幅谱分析

利用FFT方法,对地电、地磁、形变及重力等前兆时间序列信号进行分析,结果显示,宝昌地震台及乌加河地震台地电两测向日均值时间序列存在3个主要谐波分量,其中周期近一年的分量物理意义明确.FFT方法在精确确定前兆时间序列中的干扰信息周期时具有较好的效果.     

Spherical harmonic analysis of the Navier-Stokes equation in magnetofluid dynamics

The equation of motion (Navier-Stokes equation) for a uniformly rotating, compressible, magnetic, viscous fluid is analyzed in terms of infinite series of spherical surface harmonics. Differential equations are obtained for the radial functions of the poloidal and toroidal harmonics of the velocity, corresponding to those obtained by Bullard and Gellman for the magnetic field from the electromagnetic induction equation. This new analysis opens the way for the dynamical problem of electromagnetic induction in the earth's core to be considered by the spherical harmonic method.     

Application of Fourier series in managing the seasonality of convective and monsoon rainfall

ABSTRACT

This study assesses the performance of Fourier series in representing seasonal variations of the tropical rainfall process in Malaysia. Fourier series are incorporated into a spatial-temporal stochastic model in an attempt to make the model parsimonious and, at the same time, capture the annual variation of rainfall distribution. In view of Malaysia’s main rainfall regime, the model is individually fitted for two regions with distinctive rainfall profiles: one being an urban area receiving rainfall from convective activities whilst the other receives rainfall from monsoonal activities. Since both regions are susceptible to floods, the study focuses on the rainfall process at fine resolution. Fourier series equations are developed to represent the model’s parameters to describe their annual periodicity. The number of significant harmonics for each parameter is determined by inspecting the cumulative fraction of total variance explained by the significant harmonics. Results reveal that the number of significant harmonics assigned for the parameters is slightly higher in the region with monsoonal rains. The overall simulation results show that the proposed model is capable of generating tropical rainfall series from convective and monsoonal activities.

Editor D. Koutsoyiannis Associate editor K. Hamed