Removal of guided waves from seismic data in laterally varying media

A major source of unwanted signals in seismic data recorded for geophysical exploration is the presence of guided waves which are scattered near the surface of the earth. These waves do not contain information on the structure of the deeper subsurface and should therefore be removed. In this paper we derive a method for removing this type of waves based on a modal expansion. The problem of finding an appropriate scatterer distribution is formulated as a minimization problem. We apply the method to simulated data and watertank data, and find that the scattered guided waves are strongly attenuated and that the reflections of interest (from deeper layers) are not affected.     

Reflection and transmission of seismic waves at the boundaries of porous media

The mode conversions which occur during the reflection and transmission of seismic waves at the boundaries of porous media are analysed. It is shown how the energy partitioned to the various modes depends on the incident angle and on the physical properties of the fluid and solid components on each side of the boundary. The boundary conditions used here predict the occurrence of bright and dark spots as are currently observed in seismic studies of heavy oil reservoirs. They also give rise to a class of pseudo interface waves which propagate in a direction almost parallel to the surface and which become true interface waves in the limiting case where the porous media degenerate to elastic solids. When thermomechanical coupling is an important attenaution mechanism in one of the media it is also observed to have a substantial effect on the mode conversions which occur at the boundary.     

The decoupling of seismic waves

A decoupling algorithm is applied to the two-point boundary value problem which arises in calculating reflection matrices. The solution of this two-point boundary value problem using Thomson-Haskell propagator matrices is known to be unstable at high frequency in the presence of evanescent waves. The decoupling algorithm described here eliminates the instability. The algorithm makes it possible to decouple the upgoing waves from the downgoing waves and to advance each in the direction in which it decays. The difficulty with the Thomson-Haskell propagator method has been eliminated in other ways. The decoupling algorithm retains most of the algebraic simplicity of the propagator matrix method.     

Spherical blast waves in multicomponent media

The solution of the problem of propagation of a wave in soils is presented for the case when the wave is produced by the detonation of a spherical charge of some explosive material (EM). The solution is obtained on a computer by the method of characteristics. The soils are regarded as multicomponent media consisting of solid particles, water, and air in conformity with the model proposed in [1, 2]. The dependence of the pressure, velocity of the particles, and the density in the wave front on the distance is determined; the variation of these parameters with time at fixed points of the medium is also determined. The results are compared with the results of tests [1, 2]. Their close agreement for different contents of the components indicates the applicability of the multicomponent model to soils. The limits of applicability of the model are determined. The propagation of a plane wave under the same conditions was investigated in [3].     

Linear waves in saturated porous media

The peculiarity of linear and nonlinear wave propagation in porous media saturated with liquid or gas has been investigated by the methods of multiphase media mechanics. It has been shown that for the analysis and interpretation of experimental data, it is expedient to build models taking into account the nonstationary powers of interaction between the solid and liquid phases and the viscouselastic behaviour of the porous media skeleton. Inertia and inertia-viscous powers principally influence wave attentuation in porous media. Two interphase mechanisms of momentum transfer (two stress tensors — in the solid phase and liquid) lead to two types of waves. Attenuation is determined not only by interphase friction, but also by dissipation resulting from intergrain friction in the solid phase, the influence of which multiplexly exceeds the liquid viscosity influence. The real decrement of attenuation may exceed the sphere restricted by the limiting curves corresponding to the frozen and equilibrium schemes of intergrain deformation. The attenuation of momentum perturbation has been studied. The method of discrete Fourier transform has been used. The analysis of experimental data contained in the literature and their comparison with the results of calculations has been carried out.     

Modelling of fibre pull-out in cracked fibre reinforced composites with linear elastic fracture mechanics

A method of finite element modelling the fracture mechanics of a fibre reinforced cement composite is presented. It embodies the use of beam elements with negative extensional stiffness. The method compares favourably with experimental work. Whilst fibre reinforced cement composites are used in this work, the techniques used are applicable to any type of fibre composite material.     

Precursors for waves in random media

We consider scattering of a pulse propagating through a three-dimensional random media and study the shape of the pulse in the parabolic approximation. We show that, similarly to the one-dimensional O’Doherty–Anstey theory, the pulse undergoes a deterministic broadening. Its amplitude decays only algebraically and not exponentially in time, due to the signal low/midrange frequency component. We also argue that the parabolic approximation captures the front evolution (but not the signal away from the front) correctly even in the fully three-dimensional situation.     

Decaying surface waves in inhomogeneous media

Two problems on plane decaying surface waves in an inhomogeneous medium are under consideration: the problem where the waves similar to Rayleigh waves propagate in an isotropic elastic half-space that borders with a layer of an ideal incompressible fluid and the problem where the waves similar to Love waves propagate in a semi-infinite saturated porous medium that borders with a layer of an isotropic elastic medium.     

Guided electromagnetic waves in anisotropic media

Summary The propagation of guided waves in anisotropic media has recently become of interest in two fields, viz. in the interpretation of ferromagnetic resonance experiments and in the construction of microwave fourpoles which violate the reciprocity relation. In both cases we are faced with the solution of Maxwell's equations in a volume which is enclosed by perfectly conducting walls and which is completely or partially filled with a medium whose magnetic permeability is described by a second order tensor. An account is given here of some work, both theoretical and experimental, on this subject. Chapter I is an introduction, containing a short survey of the theory of guided waves in isotropic media and of the problems arising in anisotropic media, together with a historical synopsis. Chapter II gives a general formulation of the theory of guided waves in anisotropic media, comprising the existing theories, and also deals with some new applications. In Chapter III a cavity technique for measuring Faraday rotations is described which has several advantages over older techniques. In Chapter IV experimental results obtained for the series of Ferroxcubes IVA, B, C, D, E are collected. Chapter V finally deals with the physical interpretation of these results. In particular the experimental data are compared with Rado's theory of the permeability tensor in non-saturated ferromagnetics.     

爆炸地震波模拟研究

基于能够描述爆炸地震波的非平稳随机过程模型进行爆炸地震波的模拟研究。基于爆炸地震能量守恒以及经验关系,提出了能够考虑装药量和爆距影响的爆炸地震波功率谱密度和幅值包络线模型,并且利用实测的爆炸试验数据,对模型参数进行标定,给出单点、两点（微差）和多点（微差）爆炸地震波实用模拟方法。结果表明模拟得到的爆炸地震波时程能够很好地再现爆炸地震波的一些特性。     

Stability of rarefaction waves in viscous media

We study the time-asymptotic behavior of weak rarefaction waves of systems of conservation laws describing one-dimensional viscous media, with strictly hyperbolic flux functions. Our main result is to show that solutions of perturbed rarefaction data converge to an approximate, Burgers rarefaction wave, for initial perturbations w ₀ with small mass and localized as w ₀(x)= The proof proceeds by iteration of a pointwise ansatz for the error, using integral representations of its various components, based on Green's functions. We estimate the Green's functions by careful use of the Hopf-Cole transformation, combined with a refined parametrix method. As a consequence of our method, we also obtain rates of decay and detailed pointwise estimates for the error.This pointwise method has been used successfully in studying stability of shock and constant-state solutions. New features in the rarefaction case are time-varying coefficients in the linearized equations and error waves of unbounded mass (log (t)). These diffusion waves have amplitude (t ^-1/2logt) in linear degenerate transversal fields and (t ^-1/2logt) in genuinely nonlinear transversal fields, a distinction which is critical in the stability proof.     

Shock waves in saturated thermoelastic porous media

The objective of this paper is to develop and present the macroscopic motion equations for the fluid and the solid matrix, in the case of a saturated porous medium, in the form of coupled, nonlinear wave equations for the fluid and solid velocities. The nonlinearity in the equations enables the generation of shock waves. The complete set of equations required for determining phase velocities in the case of a thermoelastic solid matrix, includes also the energy balance equation for the porous medium as a whole, as well as mass balance equations for the two phase. In the special case of a rigid solid matrix, the wave after an abrupt change in pressure propagates only through the fluid.