On pressure waves in the coastal region

Summary Several authors have tried to explain the different aspects of pressure waves in water including the phenomenon of «Singing» by assuming another fluid layer below the water column. In this note an attempt has been made to determine the thickness of such a layer.     

浅层地震反射资料的多阶振型面波反演

浅层地震反射波法和面波方法是两种相互独立发展的地震勘探方法,在各自的数据采集和处理中,对方都是作为干扰信号而存在. 本文利用浅层地震反射资料中被视为干扰的面波信号,通过成熟的多道面波勘探技术处理浅层地震反射资料,在频率-波数域中提取多阶振型面波的频散曲线,并基于该曲线反演浅地表S波速度结构. 这种方法充分开发利用了已有数据,无需单独的面波数据采集系统,同时为解释浅层地震反射资料提供了额外的信息约束. 结果表明:浅层地震反射资料中可提取出可靠的多阶振型面波频散曲线,并能给出稳定的反演结果,同时,面波反演的多解性可以通过高阶振型反演得以进一步约束;低速层的存在是观测频散曲线出现振型跳跃或呈“之”字形回折的必要条件而非充分条件.      

On solitary waves generated by a moving pressure field

Summary The waves generated by a steadily moving two-dimensional pressure distribution are examined using non-linear shallow water theory. The applied pressure is zero ahead of the disturbance, that is in the downstream direction, and is a constantP ₀ in the upstream direction, these regions being joined smoothly by a cubic function.We consider here only the case of supercritical flow in both regions, the solution representing an asymmetric solitary wave travelling with the disturbance. The wave profiles are determined by an iterative method previously employed for non-linear waves. Wave amplitudes and profiles, and the wave drag, associated with each system are computed for various values ofP ₀/Q g h, whereh is the undisturbed depth of water ahead of the wave.The solution obtained reduces to the classical solitary wave of finite amplitude when the applied pressure is everywhere zero.

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Résumé Nous avons calculé les expressions des profils d'ondes solitaires produites par une pression, qui se propagent sur la surface d'une couche d'eau peu profonde avec une vitesseU plus grande que (g h)^1/2. La pression appliquée est nulle en avant de l'onde, elle est une constanteP ₀ en arrière, et entre ces deux régions elle est representée par une fonction cubique. Les profils sont calculés par une methode iterative déjà employée pour des ondes non-linéaires. L'amplitude, le profil et la force ont été evalués pour diverses valeurs deP ₀/Q g h, ouh est la profondeur en avant de l'onde.

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Division of Numerical and Applied Mathematics, National Physical Laboratory.     

A Hamiltonian approach to asymptotic seismic reflection and diffraction modelling

A model-independent Hamiltonian formulation of paraxial and diffracted ray-tracing equations is presented. It is applied to asymptotic Green's function computations. The medium can have an arbitrary number of interfaces, possibly intersecting at diffracting edges and vertices. Continuously varying model parameters and anisotropy are allowed. The algorithm for elastic waves, involving accuracy control and amplitude computation, is implemented in a platform-independent object-orientated C++ package. Numerical tests and modelling examples are presented.     

The reflection of water waves by shear currents

The refraction and reflection of linear water waves entering a following jet-type current is considered. A short-wave asymptotic solution is presented and the reflection coefficient found. This varies continuously from zero when the waves are normal to the current to unity when they are very oblique to it. The trapping of waves by an opposing current is also considered.     

Phase fluctuations of radio waves experiencing total reflection from a randomly inhomogeneous plasma layer

We examine the problem of small-angle scattering of radio waves experiencing total reflection from a randomly inhomogeneous layer of plasma. We consider the waves to be normally incident on the layer. To take into account the scattering peculiarities in the neighborhood of the reflection point, we introduce an analytical transformation for the eikonal equation solution derived by the perturbation method. This transformation permits calculations of radio-wave phase fluctuations for any monotonous profile of the regular dielectric permittivity of the plasma in the layer. Using this approach, we have derived analytical formulas for the variance and two-dimensional spatial spectrum of phase fluctuations, depending on the three-dimensional power spectrum of plasma fluctuations. We have also estimated a contribution of reflection point fluctuations to the phase fluctuations and determined the limits of applicability of the derived formulas. The presented analytical transformation of the eikonal equation solution can be used to calculate other statistical moments of the radio wave phase in many problems of solar–terrestrial physics where scattering and reflection of radio waves by plasma formations are important.     

On the stable growth of segregated ice in freezing soil under negligible overburden pressure

The stable growth condition of a segregated ice layer is studied by the use of the principle of mass and heat conservation. This condition evidently depends upon the properties of a thin transitional zone, which is believed to exist between the boundary of an ice layer and a 0[°C] isotherm. All probable models of the transitional zone are classified and the conditions for each model is derived. The effect of the small amount of soil minerals contained in an ice layer is also studied.     

黏弹各向异性介质中波的反射与透射问题分析

黏弹各向异性介质中传播不均匀波,其反射、透射模式不仅与介质分界面两侧速度对比有关,还与品质因子Q的对比有关. 用伪谱技术模拟黏弹各向异性介质分界面上波的反射、透射,并与弹性各向异性介质、黏弹各向同性介质和弹性各向同性介质的模拟结果做比较. 计算平面波的反射、透射系数,分析介质的黏弹性和各向异性对反射、透射系数的影响. 数值模拟了一个三层介质模型中的波场,分析两个分界面上产生的反射波的特征. 黏弹各向异性介质中,qS波比qP波衰减程度大.     

宽角反射地震波走时模拟的双重网格法

在研究地壳结构的人工源宽角反射地震资料解释中,常规宽角反射波走时和射线路径计算大都假定地壳模型为层状块状均匀介质.为了逼近实际地壳结构模型,要求模型尺度较大,为了提高地震资料解释的可靠性,须减小模型离散单元的尺寸,但同时计算量大大增加,使资料解释的效率较低.为此,本文尝试同时提高宽角反射地震资料解释效率和可靠性的方法,即使用双重网格计算宽角反射地震波走时和射线路径的最小走时树方法.双重网格法在均匀介质内部仅计算大网格节点,在速度变化点、震源点和检波点区域,同时计算小网格节点;在界面边界点使用比介质内部节点更大的子波传播区域.模型计算结果表明,对于大尺度的层状块状均匀介质模型,在保证精度的条件下,本文所提出的双重网格射线追踪方法的计算效率比单网格方法显著提高.     

各向异性TI介质qP反射波走时层析成像

地震走时层析成像是反演地层各向异性参数分布的有效方法, 但是关于地震各向异性介质走时层析成像的研究并不多, 其技术远远没有达到成熟的阶段.在野外数据采集时, 地表反射波观测方式相对井间和垂直地震剖面观测方式的成本更低, 利用qP反射波走时反演各向异性参数具有更加广泛的实用价值.本文实现的TI介质地震走时层析成像方法结合了TI介质反射波射线追踪算法、走时扰动方程和非线性共轭梯度算法, 它可以对任意强度的TI介质模型进行反演, 文中尝试利用qP反射波走时重建TI介质模型的参数图像.利用qP反射波对层状介质模型和块状异常体模型进行走时反演, 由于qP波相速度对弹性模量参数和Thomsen参数的偏微分不同, 所以可以分别反演弹性模量参数和Thomsen参数.数值模拟结果表明:利用qP反射波可以反演出TI介质模型的弹性模量参数与Thomsen参数, 不同模型的走时迭代反演达到了较好的收敛效果, 与各向同性介质走时反演结果相比较, 各向异性介质走时反演结果具有较好的识别能力.     

Long-term observations of the group structure of surface waves in ice

Ocean Dynamics - Several years of surface wave observations in the Chukchi Sea reveal wave groups are a common feature in open water and ice-covered conditions. The strength of the groupiness, here...     

Generation of waves by advected pressure fluctuations

Abstract

Because of the dispersion of surface gravity waves, the rate at which advected pressure fluctuations generate wave energy is independent of the coherence time of the pressure fluctuations provided that this time is long compared with the period of the waves. Phillips' (1957) analysis is correct insofar as it concerns wave components exactly “resonant” with the advected pressure fluctuations, but it does not deal adequately with the “bandwidth” of the resonance.     

On waves generated by a moving pressure field,II: Cnoidal wave effects

Summary In a recent paperHunt andTanner [3]²) investigated the waves generated by a steadily moving two-dimensional pressure distribution, which was zero ahead of the disturbance and a constantp ₀, tehind it, these regions being joined smoothly by a cubic function. Only those solutions with supercritical flow in both regions were considered, these were found to lead to an asymmetric solitary wave.This result is now extended to take account of the possibility of subcritical flow in either or both the regions, that is when there is a cnoidal wave train either behind and or ahead of the main solitary wave crest.The wave profiles are determined by the iterative method employed in the previous paper. This together with the wave drag associated with each system is computed for various values ofp ₀/U ², where is the fluid density andU a typical velocity.     

Scattering and reflection of SH waves around a slope on an elastic wedged space

The scattering and reflection of SH waves by a slope on an elastic wedged space is investigated. A series solution is obtained by using the wave function expansion method. The slope on a wedged space is divided into two subregions by an artificial, auxiliary circular arc. The wave fields with unknown complex coefficients within each sub-region are derived. Applying Graf addition theorem, the scattered waves in the sub-regions are expressed in a global coordinate system. Fourier transform is adopted to derive a consistent form of standing waves in the inner region using the orthogonality of the cosine functions. The boundary-valued problem is solved by stress and displacement continuity along the artificial, auxiliary arc to obtain the unknown complex coefficients. Parametric studies are next performed to investigate how the topography from the slope on the wedged space will affect the scattering and diffraction, and hence the amplification and de-amplification of the SH waves. Numerical results show that the surface motions on the slope of the wedged space is influenced greatly by the topography. Amplification of the surface motions near the slope vertex is significant. The corresponding phases along the wedged space surfaces are consistent with the direction that the SH waves are propagating.     

粘弹性介质P波反射透射系数近似及对比分析

随着油气勘探的发展,勘探的重点已逐渐转向岩性油气藏、隐蔽油气藏.理想弹性介质有时并不能解释许多复杂的实际问题.因此,本文是在粘弹性介质精确Zoeppritz方程的基础上,根据介质的分解理论,将均匀各向同性介质当作背景,将弹性参数的变化和粘弹性参数(品质因子和衰减角)均看成扰动,推导出了P波入射到粘弹性界面的反射透射系数近似公式,并利用四类AVO典型界面模型对反射系数近似公式进行分析与比较,一方面验证粘弹性近似式的正确性,另一方面进一步得到粘弹性介质地震波反射特征,为以后粘弹性近似式的应用提供了理论指导.