弹性随机介质模型的特征频率

为研究弹性随机介质模型中的波场特征,本文使用弹性波动方程正演模拟了平面波在二维弹性随机介质模型中的传播.通过大量正演模拟,我们首先发现若使用不同频率的瑞克子波作为震源函数,计算散射波场的能量相对值ΔE,则对每一个固定的随机介质模型,ΔE都会在某一个与模型对应的震源频率f*处达到最大值.本文由此提出了随机介质模型的特征频率这一新的概念.本文充分说明了特征频率的客观存在性;给出了相应的计算方法;进一步全面研究了随机介质中的各种模型特征（如自相关长度、背景速度、扰动标准差以及模型尺寸等）与模型的特征频率之间的关系;并得到了若干结论和相应的经验关系表达式.     

Harmonic wave propagation through viscoelastic heterogeneous media exhibiting mild stochasticity — II. Applications

The results obtained in Part I (Soil Dynam. Earth. Engng, 1996, 15, 119-27) of this work for modelling harmonic wave propagation through viscoelastic heterogeneous media that exhibit a small random fluctuation of their material properties about mean values are now used here to investigate SH wave propagation in two naturally occurring media, namely sandstone and topsoil. These results are in the form of depth dependent, deterministic mean values and non-isotropic covariances for both the wave speed profile in the medium and for the fundamental solution in terms of displacement due to a unit point source. The results are also compared against conventional Monte Carlo simulations.     

随机弹性介质中地震波散射衰减分析(英文)

地震波衰减一直是许多学科研究的热点,因为可以反映介质的特性。导致地震波衰减的因素很多,如:传播过程中由于能量扩散导致的几何衰减,固体岩石内部晶粒间相对滑移导致的摩擦衰减,岩石结构不均匀引起的地震波散射衰减。本文主要从统计的观点出发,通过多次数值模拟的方法研究纵波散射在随机弹性介质中所引发的衰减。首先用随机理论建立了二维空间随机弹性介质模型,然后用错格伪谱法的数值方法模拟了波在随机介质中的传播,再通过波场中虚拟检波器的记录,用谱比法估计了弹性波在随机介质中的散射衰减。不同非均匀程度随机弹性介质中的数值结果表明:介质不均匀程度越高,散射衰减越大;在散射体尺寸小于波长的前提下,不同散射体尺寸的计算结果说明:散射体尺寸越大,弹性波衰减越明显。最后提出了一种不均匀孔隙介质中流体流动衰减的方法。通过对随机孔隙介质中地震波的总衰减和散射衰减分别进行了计算,并定量得出了随机孔隙介质中流体流动衰减,结果表明:在实际地震频段下,当介质不均匀尺度101米量级时,散射衰减比流体流动衰减要大,散射衰减是地震波在实际不均匀岩石孔隙介质中衰减的主要原因。     

OnP F and other phases in the early part of seismogram

Summary It has been found that when seismic energy propagates along the surface of the homogeneous crust beside usual Rayleigh waves, it produces certain instability in layers through which it propagates. In the light of this instability, a type of motion corresponding to longitudinal wave will be prominent in horizontal component compared to the vertical component; while transverse wave will be prominent in the vertical component but weak in the horizontal component, a contradiction with the existing knowledge. This has been identified withP _F phase. On taking the medium of propagation as slightly heterogeneous which allows existence of low velocity layer, a few larger number of such instabilities have been found. Velocity equation for Rayleigh waves for such media reveals existence of different velocities corresponding to vertical and horizontal components. Table for these velocities has been furnished.     

Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations

The perfectly matched layer (PML) is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second-order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite-element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.     

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.     

On love waves in heterogeneous media

Summary Love waves in a half space with one homogeneous elastic layer overlying a semiinfinite medium having elastic properties varying with depth has been considered. The frequency equation for small wave lengths has been obtained, considering general variation, and has been shown to involve the first three derivatives of the rigidity of the heterogeneous medium at its interface with the homogeneous layer.     

ANISOTROPIC Q AND VELOCITY DISPERSION OF FINELY LAYERED MEDIA1

When a seismic signal propagates through a finely layered medium, there is anisotropy if the wavelengths are long enough compared to the layer thicknesses. It is well known that in this situation, the medium is equivalent to a transversely isotropic material. In addition to anisotropy, the layers may show intrinsic anelastic behaviour. Under these circumstances, the layered medium exhibits Q anisotropy and anisotropic velocity dispersion. The present work investigates the anelastic effect in the long-wavelength approximation. Backus's theory and the standard linear solid rheology are used as models to obtain the directional properties of anelasticity corresponding to the quasi-compressional mode qP, the quasi-shear mode qSV, and the pure shear mode SH, respectively. The medium is described by a complex and frequency-dependent stiffness matrix. The complex and phase velocities for homogeneous viscoelastic waves are calculated from the Christoffel equation, while the wave-fronts (energy velocities) and quality factor surfaces are obtained from energy considerations by invoking Poynting's theorem. We consider two-constituent stationary layered media, and study the wave characteristics for different material compositions and proportions. Analyses on sequences of sandstone-limestone and shale-limestone with different degrees of anisotropy indicate that the quality factors of the shear modes are more anisotropic than the corresponding phase velocities, cusps of the qSV mode are more pronounced for low frequencies and midrange proportions, and in general, attenuation is higher in the direction perpendicular to layering or close to it, provided that the material with lower velocity is the more dissipative. A numerical simulation experiment verifies the attenuation properties of finely layered media through comparison of elastic and anelastic snapshots.     

The discrete wave number formulation of boundary integral equations and boundary element methods: A review with applications to the simulation of seismic wave propagation in complex geological structures

We review the application of the discrete wave number method to problems of scattering of seismic waves formulated in terms of boundary integral equation and boundary element methods. The approach is based on the representation of the diffracting surfaces and interfaces of the medium by surface distributions of sources or by boundary source elements, the radiation from which is equivalent to the scattered wave field produced by the diffracting boundaries. The Green's functions are evaluated by the discrete wave number method, and the boundary conditions yield a linear system of equations. The inversion of this system allows the calculation of the full wave field in the medium. We investigate the accuracy of the method and we present applications to the simulation of surface seismic surveys, to the diffraction of elastic waves by fractures, to regional crustal wave propagation and to topographic scattering.     

Response of a randomly inhomogeneous layer overlying a homogeneous half-space to surface harmonic excitation

The paper is concerned with the study of the effect of the randomness of material parameters on mean wave propagation in a semi-infinite viscoelastic medium. The medium considered in this paper is a configuration of a randomly non-homogeneous layer overlying a homogeneous half-space and is loaded harmonically on the top surface. The method used is that of Karal and Keller and is based on the idea of fundamental matrix and Bourret approximation. The integro-differential equation obtained in this paper is solved by the Laplace transform method. By using boundary and continuity conditions the mean wave solution is obtained. Numerical results show that the correlation functions, which introduce long-range interactions, can be the source of the wave amplification.     

A multi‐azimuth seismic refraction study for a horizontal transverse isotropic medium: physical modelling results

To investigate the characteristics of the anisotropic stratum, a multi‐azimuth seismic refraction technique is proposed in this study since the travel time anomaly of the refraction wave induced by this anisotropic stratum will be large for a far offset receiver. To simplify the problem, a two‐layer (isotropy–horizontal transverse isotropy) model is considered. A new travel time equation of the refracted P‐wave propagation in this two‐layer model is derived, which is the function of the phase and group velocities of the horizontal transverse isotropic stratum. In addition, the measured refraction wave velocity in the physical model experiment is the group velocity. The isotropic intercept time equation of a refraction wave can be directly used to estimate the thickness of the top (isotropic) layer of the two‐layer model because the contrast between the phase and group velocities of the horizontal transverse isotropic medium is seldom greater than 10% in the Earth. If the contrast between the phase and group velocities of an anisotropic medium is small, the approximated travel time equation of a refraction wave is obtained. This equation is only dependent on the group velocity of the horizontal transverse isotropic stratum. The elastic constants A₁₁, A₁₃, and A₃₃ and the Thomsen anisotropic parameter ε of the horizontal transverse isotropic stratum can be estimated using this multi‐azimuth seismic refraction technique. Furthermore, under a condition of weak anisotropy, the Thomsen anisotropic parameter δ of the horizontal transverse isotropic stratum can be estimated by this technique as well.     

随机介质非均匀地质体尺度研究(英文)

为了定量地反映复杂非均匀介质非均匀地质体的尺度大小,本文利用统计学方法建立了能够很好地描述复杂非均匀介质特征的随机介质模型,模型参量自相关长度描述了非均匀介质横向和纵向上非均匀体的平均尺度。基于所建立的随机介质模型通过速度的横向变化和速度标准差分别探讨了自相关长度与非均匀体尺度之间的关系。对速度横向变化的研究表明:随机介质内速度具有一定均值和方差并呈随机扰动特征;随着模型自相关长度的增大,非均匀体尺度也随之增大。通过速度标准差的研究得出自相关长度与非均匀体尺度之间关系的拟合公式,利用此公式可以定量地获取非均匀体尺度的实际大小。     

深层地震勘探的地震波传传播理论研究前景

深层地震勘探为地震波传播理论研究提出了新的挑战和机遇。深层地震勘探的主要难点是上覆层的影响甚大，使后续的处理有隔靴挠痒之感，必须应用波场延拓消除上覆层影响。深层波速的高速性和横向不均匀性决定了大角散射和弹性波处理方法的重要性。本文具体评述了深层地震勘探的主要方法对策，深入探讨了波场延拓的李群方法和弹性反演的某些问题，目的在于为深化深层地震提供新的研究手段和方法。     

非均匀弹性介质地震波动模拟的Fourier变换方法

一、前言 地震模型技术是应用地震法研究地下储油地层分布的基础工作,它可以用来研究地,震波的传播以及各种波的特性,可以通过修改地质模型,反复进行正演,实现对实际地震剖面的最优逼近,以实现地震反问题。本文在文献[1]的基础上,应用Fourier变换方法研究了用非均匀弹性介质波动方程正演问题的解来模拟地震波的传播,探索了该方法对非均匀弹性介质地震模型的有效性及实用性。     

Effect of Corrugation and Reinforcement on the Dispersion of SH-wave Propagation in Corrugated Poroelastic Layer Lying over a Fibre-reinforced Half-space

The presence of porosity and reinforcement in a medium is an important factor affecting seismic wave propagation and plays vital role in many geophysical prospects. Also, the presence of salt and ore deposits, mountains, basins, mountain roots, etc. is responsible for the existence of corrugated boundary surfaces of constituent layers. Such facts brought motivation for the present paper which deals with the propagation of SH-wave in a heterogeneous fluid-saturated poroelastic layer with corrugated boundaries lying over an initially stressed fibre-reinforced elastic halfspace. Closed form of dispersion relation has been obtained and is found in well agreement to classical Love wave equation for isotropic case. The effect of corrugation, wave number, undulation, position parameter, horizontal compressive/tensile initial stress and heterogeneity on phase velocity has been analysed through numerical computation and graphical illustration. Moreover, comparative study exploring the effect of presence and absence of reinforcement in half-space on dispersion curve is the major highlight of the current study.     

Response of fixed offshore structures in random sea

An integrated model is developed for the short-term and long-term dynamic response of an offshore structure subjected to random wave excitation. A discrete linear, elastic model of the upper structure is coupled with an iterative linear quasi-three-dimensional finite element model for the pile-soil medium, and the system is subjected to stochastic storms described by mean rate of arrival, joint probability distribution of storm duration and average intensity, and a random process that describes the variations of a statistical wave height measure during each storm. Sarpkaya's 1977 experimental information is used to specify values for C_M and C_D, in Morison's equation, consistent with the flow and response characteristics. Soil (clay) degradation, due to cyclic excitation, is followed during the passage of a storm. The indicator of soil degradation is taken to be the value of the horizontal foundation stiffness and the stiffness degradation is modelled by a homogeneous Markov process.     

Separation of equation of motion of love waves in curvilinearly anisotropic inhomogeneous medium

Summary The general problem of Love wave propagation, in a medium with cylindrical anisotropy of hexagonal type, is formulated. The method of seperation of variables is applied to examine the possibility of obtaining formal solutions for different types of inhomogeneities present in the medium. It is found that when the elastic parameters (C ₄₄ and ) are functions of bothv and the equation of motion is not separable. The use of the technique is illustrated, by considering radial inhomogeneity in an anisotropic cylindrical crustal layer, for obtaining the characteristic frequency equation of Love waves in such a medium.     

Non-homogeneous elastic waves in soils: Notes on the vector decomposition technique

Geological media are invariably non-homogeneous, which complicates considerably the analysis of seismically induced wave propagation phenomena. Thus, closed-form solutions in the form of Green's functions are difficult to construct, but are quite valuable in their own right and often play the role of kernels in boundary integral equation formulations that are used for the solution of complex boundary-value problems of engineering importance. In this work, we examine in some detail the types of wave-like equations that result from vector decomposition of the equations of motion for the infinitely extending non-homogeneous continuum, which would be a first step for evaluating Green's functions. Specifically, an eigenvalue analysis is first performed, followed by computations using the finite difference method for a specific example involving a soil layer with quadratically varying material parameters. The aforementioned wave-like equations, defined in terms of dilatational and rotational strains, are originally coupled. Their uncoupling involves use of algebraic transformations, which are in turn valid for certain restricted categories of non-homogeneous materials. Numerical solution of these equations clearly shows attenuation patterns and phase changes that are manifested as the incoming wave disturbance is continuously scattered by non-constant material stiffness values encountered along the propagation path.     

双变参数标量纵波方程正演模拟方法

常见弹性波动理论的建立是基于介质均匀这一基本假设,实际介质的非均匀性非常普遍.为研究连续介质中波的传播特征,本文从弹性力学中建立弹性波动方程的三个基本方程出发,考虑连续介质弹性参数的空变特征,建立非均匀介质的弹性波动方程,利用Alkhalifah声学近似思想建立位移表征的纵波波动方程,利用本征值问题求解方法建立标量波频率-波数域传播算子,从而建立描述纵波传播的标量波方程,其中波函数为纵波位移的散度,不同于均匀介质标量波方程的波函数为位移势.随后推导含PML边界波动方程差分格式并建立不同模型数值模拟进行数值试算,与均匀假设标量波方程和变密度方程对比证明本方法的准确性和稳定性.