Nonlinearities and Linearities in Internal Gravity Waves of the Atmosphere and Oceans

The spectrum of internal gravity waves in the atmosphere and oceans is sufficiently intense that nonlinear interactions must occur, if these waves are analyzed in Eulerian coordinates as is usually done. As it happens, however, if these waves are analyzed in Lagrangian coordinates the most important nonlinearity can be entirely avoided: it is an Eulerian mathematical construct only, not a physical process. The mathematical basis for this assertion is developed here, and some of its consequences are discussed. Among the latter is a questioning of the validity of standard Eulerian eikonal methods of calculating ray paths and related functions in a multiwave environment, discussed in an appendix.     

Long Nonlinear Surface and Internal Gravity Waves in a Rotating Ocean

Nonlinear dynamics of surface and internal waves in a stratified ocean under the influence of the Earth's rotation is discussed. Attention is focussed upon guided waves long compared to the ocean depth. The effect of rotation on linear processes is reviewed in detail as well as the existing nonlinear models describing weakly and strongly nonlinear dynamics of long waves. The influence of rotation on small-scale waves and two-dimensional effects are also briefly considered. Some estimates of the influence of the Earth's rotation on the parameters of real oceanic waves are presented and related to observational and numerical data.     

圆弧状凹陷地形对平面SH波散射问题闭合形式的解析解

局部不规则地形对地震波散射问题是地震工程学重要的研究课题,其研究成果对于揭示地震动强度以及地震震害程度的空间分布不均匀性的物理机制具有重要的理论价值,而且其定性与定量的结果对于一些大尺度工程(如大跨度桥梁、长输管线等)的抗震设计具有一定的指导意义.该问题的理论研究方法通常有数值法和解析法.数值法包括有限差分法、有限单元法、边界单元法、离散波数法、以及各种混合方法;解析法中应用最为广泛的是波函数展开法.     

Broadband Analytical Solution to the Scattering of Plane SV Waves by Circular Cylindrical Canyons

Based on Fourier-Bessel series expansion of wave functions,an analytical solution to 2-D scattering ofincident plane SV waves by circular cylindrical canyons with variable depthto-width ratios is deduced in this paper. Unlike other analytical solutions,this paper uses the asymptotic behavior of the cylindrical function to directly define the undetermined coefficients of scattered waves,thus,avoiding solving linear equation systems and the related numerical computation problems under high-frequency incident waves,thereby broadening the applicable frequency range of analytical solutions. Through comparison with existing analytical solutions,the correctness of this solution is demonstrated. Finally, the incident plane SV wave scattering effect under circular cylindrical canyons in wider frequency bands is explored.     

风化半圆形河谷对柱面SH波的散射解析解

风化河谷地震效应对建在此类场地上工程结构(如大坝、桥梁)的动力稳定性具有潜在的威胁,为揭示河谷风化层对地面运动的影响,利用波函数展开法推导风化半圆形河谷对线源柱面SH波散射问题的解析解。计算不同震源位置条件下风化半圆形河谷的地表位移反应和地面运动放大因子,分析地面运动的幅值和形态,发现随着震源距离的增大,在河谷附近地震动的放大和衰减的交替更频繁。     

Direct and Inverse Problems in a Variational Concept of Environmental Modeling

A concept of environmental forecasting based on a variational approach is discussed. The basic idea is to augment the existing technology of modeling by a combination of direct and inverse methods. By this means, the scope of environmental studies can be substantially enlarged. In the concept, mathematical models of processes and observation data subject to some uncertainties are considered. The modeling system is derived from a specially formulated weak-constraint variational principle. A set of algorithms for implementing the concept is presented. These are: algorithms for the solution of direct, adjoint, and inverse problems; adjoint sensitivity algorithms; data assimilation procedures; etc. Methods of quantitative estimations of uncertainty are of particular interest since uncertainty functions play a fundamental role for data assimilation, assessment of model quality, and inverse problem solving. A scenario approach is an essential part of the concept. Some methods of orthogonal decomposition of multi-dimensional phase spaces are used to reconstruct the hydrodynamic background fields from available data and to include climatic data into long-term prognostic scenarios. Subspaces with informative bases are constructed to use in deterministic or stochastic-deterministic scenarios for forecasting air quality and risk assessment. The results of implementing example scenarios for the Siberian regions are presented.     

Spectral and Statistical Properties of the Doppler Frequency Shift during Substorms in the F2 Layer

Geomagnetism and Aeronomy - The observational results of the spectral density of the Doppler frequency shift Δfd during intervals of bay-like perturbations in the ionospheric F2 layer are...     

Modeling the Effect of Mesospheric Internal Gravity Waves in the Thermosphere and Ionosphere During the 2009 Sudden Stratospheric Warming

The results of numerical experiments on the modeling of thermospheric and ionospheric disturbances under conditions of sudden stratospheric warming are presented to study the possible mechanisms of such disturbances. Local disturbances caused by a planetary wave with zonal wave number s = 1 and internal gravity waves (IGWs) propagating from the disturbed region in the stratosphere are taken into account as sources of disturbances. It is shown that the inclusion of an additional source of thermospheric disturbances caused by mesospheric variations of atmospheric parameters with IGW periods over the region of sudden stratospheric warming leads to significant changes in the parameters of the thermosphere and ionosphere, including a change in the global structure of the distributions of the gas components of the thermosphere and a shift in maximum concentrations of atomic oxygen to low latitudes of the Southern Hemisphere; there is an increase in the mean values, the diurnal and semidiurnal variations of the ion concentration in the F region of the ionosphere. These features of changes in the parameters of the thermosphere and ionosphere occurred with insignificant disturbances of tidal variations in the thermosphere.     

无限弹性介质中隧道内爆炸动力响应的解析解

基于圆柱形薄壳结构理论,建立爆炸荷载作用下隧道结构的动力平衡方程.采用积分变换法求得Fourier变换域内爆炸荷栽作用下隧道位移场的积分表达式.结合具体算例,采用离散Fourier逆变换的数值计算方法,给出了爆心处隧道位移时程曲线、最大正应力时程曲线及某一时刻隧道位移幅值和最大正应力在x方向的变化曲线.其结果与数值计算结果相一致,验证了方法的可行性.     

Altimetry-Derived Gravity Predictions of Bathymetry by the Gravity-Geologic Method

The gravity-geologic method (GGM) was implemented for 2′ by 2′ bathymetric determinations in a 1.6° longitude-by-1.0° latitude region centered on the eastern end of the Shackleton Fracture Zone in the Drake Passage, Antarctica. The GGM used the Bouguer slab approximation to process satellite altimetry-derived marine free-air gravity anomalies and 6,548 local shipborne bathymetric sounding measurements from the Korea Ocean Research and Development Institute to update the surrounding off-track bathymetry. The limitations of the Bouguer slab for modeling the gravity effects of variable density, rugged bathymetric relief at distances up to several kilometers, were mitigated by establishing ‘tuning’ densities that stabilized the GGM predictions. Tests using two-thirds of the shipborne bathymetric measurements to estimate the remaining third indicated that the tuning densities minimized root-mean-square deviations to about 29 m. The optimum GGM bathymetry model honoring all the ship observations correlated very well with widely available bathymetry models, despite local differences that ranged up to a few kilometers. The great analytical simplicity of GGM facilitates accurately and efficiently updating bathymetry as new gravity and bathymetric sounding data become available. Furthermore, the availability of marine free-air gravity anomaly data ensures that the GGM is more effective than simply extrapolating or interpolating ship bathymetry coverage into unmapped regions.     

Analytical Solutions for Tsunami Waves Generated by Submarine Landslides in Narrow Bays and Channels

Analytical theory of tsunami wave generation by submarine landslides is extended to the case of narrow bays and channels of different geometry, in the shallow-water theory framework. New analytical solutions are obtained. For a number of bottom configurations, the wave field can be found explicitly in the form of the Duhamel integral. It is described by three waves: one forced wave propagating together with the landslide and two free waves propagating in opposite directions. The cases for bays with triangular (V-shaped bay), parabolic (U-shaped bay), and rectangular cross-sections are discussed in detail. The dynamics of the offshore-propagating wave in linearly inclined bays of different cross-section are also studied asymptotically for the resonant moving landslide. Different cases of landslides of increasing and decreasing volume are considered. It is shown that even if the landslide is moving under fully resonant conditions, the amplitude of the propagating tsunami wave may still be bounded, depending on the type of the landslide.     

An Automatic Method of Direct Interpretation of Residual Gravity Anomaly Profiles due to Spheres and Cylinders

We have developed a least-squares minimization approach to determine the depth and the amplitude coefficient of a buried structure from residual gravity anomaly profile. This approach is basically based on application of Werner deconvolution method to gravity formulas due to spheres and cylinders, and solving a set of algebraic linear equations to estimate the two-model parameters. The validity of this new method is demonstrated through studying and analyzing two synthetic gravity anomalies, using simulated data generated from a known model with different random error components and a known statistical distribution. After being theoretically proven, this approach was applied on two real field gravity anomalies from Cuba and Sweden. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable. Moreover, the depth obtained by the proposed approach is found to be in very good agreement with that obtained from drilling information.     

An Overview of Internal Solitary Waves in the South China Sea

Internal solitary waves (ISWs) are the nonlinear large amplitude waves existing in the oceanic pycnocline. They are very active in the northern South China Sea (SCS). With more and more remote sensing data, in situ observational data and the development of the numerical simulation technology, a number of studies on the characteristics, the source site, the generation, and evolution of the ISWs in the SCS are reported. In this paper, earlier studies on the ISWs in the SCS are summarized and some problems worthy of study are put forward.     

Spontaneous Emission of Gravity Waves by Interacting Vortex Dipoles in a Stratified Fluid: Laboratory Experiments

Results from a new series of experiments on the geophysically important issue of spontaneous emission of internal gravity waves during unsteady interactions of vortical structures are presented. Vortex dipoles are a common element of a quasi-two-dimensional turbulent flow. Vortex dipoles perform translational motion and can collide with other vortices. During collision events the flow is unsteady and unbalanced and a further adjustment process associated with these events can therefore result in the spontaneous emission of gravity waves. Our laboratory experiments demonstrate that gravity waves are emitted when two translating vortex dipoles interact (collide) in a layered fluid, in accord with the current theoretical results. The emission was evident both in a two-layer system and in a fluid with a linear distribution of density with depth. The waves were generated during the period of deceleration of the secondary dipoles which constitute a vortex quadrupole emerging immediately after the collision of the primary dipoles.     

基于弹性波频谱特性的沉管隧道灌砂监测方法及应用

灌砂基础加固法在沉管隧道基础处理中应用广泛,然而复杂的施工现场及施工过程中的噪音会对监测产生干扰,故准确的灌砂实时监测方法一直是工程界所关心的重要课题。以多层层状介质中的弹性波传播特性为基础,通过对沉管隧道底板灌砂的全尺寸模型试验进行验证,建立基于弹性波频谱特性的无损监测方法。针对沉管隧道底板的水平层状介质模型,获得下部介质变化前后的弹性波响应波形数据,并对其进行波形频谱分析;同时在数据处理时,设定结构注砂变化前后的主频变化范围为滤波频带,进行滤波,降低施工噪音及复杂施工现场的干扰,从而通过工况变化前后的频谱响应差值进行施工进度实时评价。在理论研究的基础上,通过运用可视化窗口的观测结果与频谱监测结果的对比验证,建立响应频谱能量差与砂盘扩散半径、砂盘填充度的对应关系,采用可视化云图等手段,实时有效地监测基础施工的灌砂进度,为沉管隧道基础灌砂施工提供科学依据。     

Scattering of Seismic Waves by Cracks with the Boundary Integral Method

— We develop a new scheme to compute 2-D SH seismograms for media with many flat cracks, based on the boundary integral method. A dry or traction-free boundary condition is applied to crack surfaces although other kinds of cracks such as wet or fluid-saturated cracks can be treated simply by assigning different boundary conditions. While body forces are distributed for cavities or inclusions to express scattered wave, dislocations (or displacement discontinuities between the top and the bottom surfaces of each crack) are used as fictitious sources along crack surfaces. With these dislocations as unknown coefficients, the scattered wave is expressed by the normal derivative of Green's function along the crack surface, which is called “double-layer potentials” in the boundary integral method, while we used “single-layer potentials” for cavities or inclusions. These unknowns are determined so that boundary conditions or crack surfaces are satisfied in the least-squared sense, for example, traction-free for dry cracks. Seismograms with plane-wave incidence are synthesized for homogeneous media with many cracks. First, we check the accuracy of our scheme for a medium with one long crack. All the predicted phases such as reflected wave, diffraction from a crack tip and shadow behind the crack are simulated quite accurately, under the same criterion as in the case for cavities or inclusions. Next, we compute seismograms for 50 randomly distributed cracks and compare them with those for circular cavities. When cracks are randomly oriented, waveforms and the strength of scattering attenuation are similar to the cavity case in a frequency range higher than k d $\simeq$ 2 where the size of scatterers d (i.e., crack length or cavity diameter) is comparable with the wavelength considered (k is the wavenumber). On the other hand, the scattering attenuation for cracks becomes much smaller in a lower frequency range (k d<2) because only the volume but not detail geometry of scatterers becomes important with wavelength much longer than each scatterer. When all the cracks are oriented in a fixed direction, the scattering attenuation depends strongly on the incident angle to the crack surface as frequency increases (k d>2): scattering becomes weak for cracks oriented parallel to the direction of the incident wave, while it gets close to the cavity case for cracks aligned perpendicular to the incident wave.     

Generalized Solutions of the Inverse Problem and New Technologies for the Quantitative Interpretation of Gravity Anomalies

The approach, fundamentally different from the known ones, to estimating the spatial location of the domain filled with the disturbing masses based on the gravity field measurement data is suggested. The main idea of the approach is, using the set of the probable variants of the interpretation, to construct the distribution of a certain parameter associated with the estimate of probability of detecting the sources of the field in any point of the studied geological medium and then to apply this distribution to each domain eligible for being the true carrier of the anomalous masses. These constructions yield the generalized admissible solutions of the inverse problem with ranking the separate fragments of the model carrier in terms of the probability of detecting anomalous masses in them.     

Attenuation of High Frequency P and S Waves in the Gujarat Region,India

The local earthquake waveforms recorded on broadband seismograph network of Institute of Seismological Research in Gujarat, India have been analyzed to understand the attenuation of high frequency (2–25 Hz) P and S waves in the region. The frequency dependent relationships for quality factors for P (Q _P) and S (Q _S) waves have been obtained using the spectral ratio method for three regions namely, Kachchh, Saurashtra and Mainland Gujarat. The earthquakes recorded at nine stations of Kachchh, five stations of Saurashtra and one station in mainland Gujarat have been used for this analysis. The estimated relations for average Q _P and Q _S are: Q _P = (105 ± 2) f ^{0.82 ± 0.01}, Q _S = (74 ± 2) f ^{1.06 ± 0.01} for Kachchh region; Q _P = (148 ± 2) f ^{0.92 ± 0.01}, Q _S = (149 ± 14) f ^{1.43 ± 0.05} for Saurashtra region and Q _P = (163 ± 7) f ^{0.77 ± 0.03}, Q _S = (118 ± 34) f ^{0.65 ± 0.14} for mainland Gujarat region. The low Q (<200) and high exponent of f (>0.5) as obtained from present analysis indicate the predominant seismic activities in the region. The lowest Q values obtained for the Kachchh region implies that the area is relatively more attenuative and heterogeneous than other two regions. A comparison between Q _S estimated in this study and coda Q (Qc) previously reported by others for Kachchh region shows that Q _C > Q _S for the frequency range of interest showing the enrichment of coda waves and the importance of scattering attenuation to the attenuation of S waves in the Kachchh region infested with faults and fractures. The Q _S/Q _P ratio is found to be less than 1 for Kachchh and Mainland Gujarat regions and close to unity for Saurashtra region. This reflects the difference in the geological composition of rocks in the regions. The frequency dependent relations developed in this study could be used for the estimation of earthquake source parameters as well as for simulating the strong earthquake ground motions in the region.     

楔形空间中圆弧形沉积对平面P波的散射解析解

基于大圆弧假定,利用傅立叶-贝塞尔（Fourier-Bessel）级数波函数展开法,给出了含圆弧形沉积的楔形空间对平面P波的散射解析解。为方便构造地表面引起的散射波场,本文利用2个大圆弧面来模拟地表面,由连续性边界条件建立方程并求解得出该问题的解析解。算例结果表明,楔形空间沉积附近地表的动力响应特征依赖于入射波频率、入射角度、沉积内外介质特性与楔形夹角等因素,且位移放大效应较半空间情况更为显著。