Boundary-reflected waves and ultrasonic coda waves in rock physics experiments

Ultrasonic coda waves are widely used to study high-frequency scattering. However, ultrasonic coda waves are strongly affected by interference from by boundary-reflected waves. To understand the effect of boundary-reflected waves, we performed ultrasonic experiments using aluminum and shale samples, and the rotating staggered-mesh finite-difference method to simulate the wavefield. We analyzed the wavefield characteristics at the different receiving points and the interference characteristics of the boundary-reflected waves with the ultrasonic coda wave, and the effect of sample geometry on the ultrasonic coda waves. The increase in the aspect ratio of the samples delays the interference effect of the laterally reflected waves and reduces the effect on the ultrasonic coda waves. The main waves interfering with the ultrasonic coda waves are laterally reflected PP-, PS-, PPP-, and PPS-waves. The scattering and attenuation of the high-frequency energy in actual rocks can weaken the interference of laterally reflected waves with the ultrasonic coda waves.     

Internal waves in llyn Tegid

Summary The paper deals with the formation of internal waves of periods of about 12 hours, 24 hours, and in one case 48 hours on Lake Tegid (Bala) in North Wales. It was possible to isolate these waves by means of a numerical filter, applied to the outputs of 30 thermistors place below each other on a chain suspended from a buoy. The wave characteristics are very closely related to those of the wind and a high correlation can be found in most cases with the internal waves lagging behind the corresponding filtered components in the wind stress by about a third of a period.The movement of the waves round the lake was investigated by using two buoys, one of which was moved round the lake perimeter and then after using the filter, obtaining the phase difference between the two for the various components. The results indicated a clockwise movement which is contrary to what one would expect of simple Kelvin waves. The effect can be caused, however, by the interference of several waves of approximately the same frequency but of different mode and wavelength.The filter was also used to examine the vertical profile of the water movement. The profiles indicated, as expected, that there is a mixture of many modes present but some of these can be identified by comparison with the theoretical mode profiles.     

Nonlinear waves in rotating magnetohydrodynamics

We consider an electrically conducting fluid in rotating cylindrical coordinates in which the Elsasser and magnetic Reynolds numbers are assumed to be large while the Rossby number is assumed to vanish in an appropriate limit. This may be taken as a simple model for the Earth's outer core. Fully nonlinear waves dominated by the nonlinear Lorentz forces are studied using the method of geometric optics (essentially WKB). These waves are assumed to be of the form of an asymptotic series expanded about ambient magnetic and velocity fields which vanish on the equatorial plane. They take the form of short wave, slowly varying wave trains. The first-order approximation is sinusoidal and basically the same as in the linear problem, with a dispersion relation modified by the appearance of mean terms. These mean terms, as well the undetermined amplitude functions, are found by suppressing secular terms in a “fast” variable in the second-order approximation. The interaction of the mean terms with the dispersion relation is the primary cause of behaviors which differ from the linear case. In particular, new singularities appear in the wave amplitude functions and an initial value problem results in a singularity in one of the mean terms which propagates through the fluid. The singularities corresponding to the linear ones are shown to develop when the corresponding waves propagate toward the equatorial plane.     

Surface waves in restricted Hadamard materials

Summary The propagation of waves of small amplitude in an elastic medium composed of Hadamard material, satisfying also the Ordered Forces condition and the Strong Ellipticity condition, and subjected to a large homogeneous biaxial stress, is investigated in detail. Consideration is given to the existence and general properties of Rayleigh waves on the surface of a semi-infinite medium, and to the propagation of plate waves in a medium of finite thickness.     

Multiple scattering of seismic waves in fractured media: Velocity and effective attenuation of the coherent components ofP waves andS waves

We show that the multiple scattering by small fractures of seismic waves with wavelengths long compared to the fracture size and fracture spacing is indistinguishable from multiple-scattering effects produced by regular porosity, except for an orientation factor due to fracture alignment. The fractures reduce theP-wave andS-wave velocities and produce an effective attenuation of the coherent component of the seismic waves. The attenuation corresponds to 1000/Q of about unity for a Gaussian spectrum of fractures, and it varies with frequencyf asf ³. For a Kolmogorov spectrum of fractures of spectral index the attenuation is an order of magnitude or so larger and varies with frequency asf ^3-v The precise degree of attenuation depends upon the matrix properties, the fracture porosity, the degree of fracture anisotropy, the type of fluid filling the fractures, and the incidence angle of the wave.For fracture porosities less than about 15% theP-wave andS-wave velocities are decreased by the order of 5–10% with a lesser dependence on the type of fluid filling the fractures (gas, oil, or brine) and with a dependence on both the degree of anisotropy and the incident angle made by the wave. The tendency of fractures to occur perpendicularly to bedding suggests that the best way to measure seismically fractured rock behavior in situ is by using the travel-time delay and reflection amplitude. As both the offset and the azimuth of receivers vary from a shot, the travel-time delay and reflection amplitude should both show an elliptical pattern of behavior—the travel-time delay in response to the varying seismic speed, and the reflection amplitude in response to angular variations in the multiple scattering. Observations of attenuation at several frequencies should permit (a) determination of the spectrum of fractures (Gaussian versus Kolmogorovian) and (b) determination of the contribution of viscous damping to the effective attenuation.     

Migrating sand waves

A simple mathematical model is described, which reproduces the major features of sand waves' appearance and growth and in particular predicts their migration speed. The model is based on the linear stability analysis of the flat configuration of the sea bottom subject to tidal currents. Attention is focused on the prediction of the complex growth rate that bottom perturbations undergo because of both oscillatory fluid motions and residual currents. While the real part _r of controls the amplification or decay of the amplitude of the bedforms, the imaginary part _i is related to their migration speed. Previous works on the migration of the sand waves (Németh etal. 2002) consider a forcing tide made up by the M2 constituent (oscillatory period equal to 12 h) plus the residual current Z0 and predict always a downcurrent migration of the bedforms. However, field cases exist of upcurrent-migrating sand waves (downcurrent/upcurrent-migrating sand waves mean bedforms moving in the direction of the steady residual tidal current or in the opposite direction, respectively). The inclusion of a tide constituent characterized by a period of 6 h (M4) is the main novelty of the present work, which allows for the prediction of the migration of sand waves against the residual current Z0. Indeed, the M4 tide constituent, as does also the residual current Z0, breaks the symmetry of the problem forced only by the M2 tide constituent, and induces sand-wave migration. The model proposed by Besio etal. (2003a) forms the basis for the present analysis. Previous works on the subject (Gerkema 2000; Hulscher 1996a,b; Komarova and Hulscher 2000) are thus improved by using a new solution procedure (Besio etal. 2003a) which allows for a more accurate evaluation of the growth rate for arbitrary values of the parameter r, which is the ratio between the horizontal tidal excursion and the perturbation wavelength. Responsible Editor: Jens Kappenberg     

Propagation of Rayleigh waves in soils

Summary Propagation of Rayleigh type waves in soils is considered in this paper. It is a well known fact that soils do not behave like an ordinary isotropic elastic medium where the ratio of Young's modulus to the modulus of rigidity is much less than that in sandy soils. Considering the velocity of Rayleigh type wave as less than that of distortional wave (which is an observed fact) a probable value of this ratio is determined, and also assuming the value of this ratio based on some experimental data, the velocity of wave propagation in the medium is deduced.     

Response of pile foundations to rayleigh waves and obliquely incident body waves

The paper presents results of a study on the harmonic response of piles and pile groups embedded in a halfspace to various forms of seismic waves. These include the Rayleigh wave as well as obliquely incident P, SV and SH waves. The pertinent mixed boundary value problems of pile-soil-pile interaction are solved by a numerical model of the boundary integral nature. All modes of foundation vibrations, i.e. translational, rocking and torsional, are included in the model. The results presented are used to highlight the salient features of the seismic response of piles. In addition, the influence of certain pile-soil parameters, such as pile rigidity and pile spacing, on the seismic behaviour of pile foundations is investigated.     

Ponderomotive effects in magnetospheric hydromagnetic waves

The ponderomotive force (PMF) is a ubiquitous nonlinear wave effect arising in plasma physics when applied wave fields or plasma parameters have significant spatial gradients. Some basic properties of the PMF are described as they relate to ULF hydromagnetic waves in the magnetosphere. Examples are given of recent results obtained using both analytical and numerical techniques for waves from the lowest frequencies (determined by the dimensions of the magnetosphere) up to the vicinity of the ion cyclotron frequency. These results include the possibilities that the PMF may transport plasma over large distances in the magnetosphere, and that the PMF may energize magnetospheric ions significantly. In particular the PMF may play a role in transporting and energizing O⁺ ions from the ionosphere into the body of the magnetosphere. The PMF can also generate nonlinear coupling between the slow magnetosonic mode and the other hydromagnetic modes. This should lead to limitation of density enhancements and, notably in the case of standing Alfvén waves, to spatial harmonic generation, secularly growing frequency shifts, and saturation of driven wave fields. Some implications of these results for the magnetosphere are discussed.Based on an invited review given in IAGA Symposium 3.07, Nonlinear and Kinetic Effects in ULF Waves, at the IUGG XXI General Assembly, Boulder, Colorado, July 2-14, 1995.     

太湖波浪数值模拟

在太湖实际波浪观测的基础上,采用率定验证后的第三代动谱平衡方程,考虑实际水底地形、波浪折射、浅化、反射、破碎、湖流等条件下,对太湖波浪进行数值模拟,研究太湖波浪的主要影响因素.结果表明:SWAN模型可以较好地模拟风作用下太湖风浪的生成和传播过程,模型在太湖应用是合适的;波高、波长、波周期等波浪参数在太湖的分布与风速、风向、水深等因素密切相关;在相同风向、不同风速情况下,太湖波浪发展至稳定状态的时间不一样;在不同风向,相同风速持续作用下,有效波高达到稳定的时间差不多,变化趋势也比较相同.说明波浪的发展不光取决于风速的大小,还同风的持续吹的时间和风区长度有关.     

Magnetohydrodynamic waves in the erath's liquid core

Summary The possibility of generation of magnetohydrodynamic waves in a rotating spherical system under the efect of small disturbances of the medium velocity is investigated. The initial stationary state of the system has been chosen with a view to known geophysical facts, and the effect of the solid inner core is considered. It is proved that two types of waves with distinctly different frequencies can be generated in the liquid region. The behaviour of longperiod magnetic waves is also studied in detail, and it is proved that the direction in which they propagate at a certain point depends on the position of this point in the meridional plane and on the configuration of the initial magnetic field. The phase velocities of the longperiod magnetic waves, propagating towards the west, have been computed within a selected network of points and the region in which they are generated has been defined. It is proved that the phase velocities of these waves are compatible with the observed velocity of the westward drift of the geomagnetic dipole.     

On progressive internal waves in non-uniform depths

Summary An expansion technique is used to investigate effects of finite amplitude on three-dimensional progressive internal waves in continuously stratified fluid of variable depth. The results are illustrated for the case of uniform density gradients. Reflection is neglected in the perturbation scheme. In two dimensions, damping of long progressive waves is considered through energy dissipation in the bottom boundary layer.     

Nonlinear wave propagation on a sphere: Interaction between Rossby waves and gravity waves; stability of the Rossby waves

Abstract

An analytical spectral model of the barotropic divergent equations on a sphere is developed using the potential-stream function formulation and the normal modes as basic functions. Explicit expressions of the coefficients of nonlinear interaction are obtained in the asymptotic case of a slowly rotating sphere, i.e. when the normal modes can be expressed as single spherical harmonics.     

Thermo-elastic Rayleigh waves in transversely isotropic solids

Summary The frequency equation of the thermo-elastic Rayleigh waves in a semi-infinite transversely isotropic solid has been obtained. The form of the frequency equation for small values of the reduced frequency has also been deduced, and it is found that, as in the isotropic medium, the velocity does not depend on the frequency. But unlike the isotropic case, the velocity depends upon the thermal constants as well.     

Magneto-acoustic-gravity waves in the horizontal magnetic field

Abstract

In this paper we consider the propagation of magneto-acoustic-gravity waves in a compressible, conducting isothermal atmosphere permeated by a uniform horizontal magnetic field. The singular levels, arising in a horizontal magnetic field, are considered in their most general form. Exact analytical solutions for a number of particular cases of wave propagation are obtained. The wave transformation is analyzed for all these cases using the solutions obtained.

Based on the theory of wave propagation across a magnetic field, low-frequency wave trapping in a chromospheric resonator is explained, and some properties of running penumbral waves are discussed.     

Studies on seismic waves

The development of seismic wave study in China in the past four years is reviewed. The discussion is divided into several aspects, including seismic wave propagation in laterally homogeneous media, laterally heterogeneous media, anisotropic and porous media, surface wave and seismic wave inversion, and seismic wave study in prospecting and logging problems. Important projects in the current studies on seismic wave is suggested as the development of high efficient numerical methods, and applying them to the studies of excitation and propagation of seismic waves in complex media and strong ground motion, which will form a foundation for refined earthquake hazard analysis and prediction.