首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 28 毫秒
1.
We theoretically study the scattering ofP, SV andSH waves by a zonal distribution of cracks, which simulates a fault fracture zone. An investigation is conducted how the geometrical properties of the crack distribution and the frictional characteristics of the crack surface are reflected in the attenuation and dispersion of incident waves, as well as in the amplitudes of the transmitted and reflected waves from the zone. If the crack distribution within the fault zone changes temporally during the preparation process of the expected earthquake, it will be important for earthquake prediction to monitor it, utilizing the scattering-induced wave phenomena.We consider the two-dimensional problem. Aligned cracks with the same length are assumed to be randomly distributed in a zone with a finite width, on which elastic waves are assumed to be incident. The distribution of cracks is assumed to be homogeneous and sparse. The crack surface is assumed to be stress-free, or to undergo viscous friction; the latter case simulates fluid-filled cracks. The opening displacement of the crack is assumed to be negligibly small. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.When the crack surface is stress-free, it is commonly observed for every wave mode (P, SV andSH) that the attenuation coefficientQ –1 peaks aroundka1, the phase velocity is almost independent ofk in the rangeka<1 and it increases monotonically withk in the rangeka>1, wherek is the intrinsicS wavenumber anda is the half length of the crack. The effect of the friction is to shift the peak ofQ –1 and the corner of the phase velocity curve to the low wavenumber range. The high wavenumber asymptote ofQ –1 is proportional tok –1 independently of model parameters and the wave modes. If the seismological observation thatQ –1 ofS waves has a peak at around 0.5 Hz in the earth's crust is combined with our results, the upper limit of crack size within the crust is estimated about 4 km. The information regarding the transmitted and reflected waves, such as the high wavenumber limit of the amplitude of the transmitted wave etc., allows estimation of the strength of the friction.  相似文献   

2.
Multiple scattering from cracks is considered in the two-dimensional plane-strain condition. It is assumed that identical cracks are distributed uniformly in space and that the effective waves propagate normal to the crack surfaces. Then, the apparent dispersion and attenuation are calculated as functions of frequency for three independent modes of wave propagation: SV, P and SH.The calculated results show that, in each case, the attenuation coefficient Q?1 takes a peak value when the wavelength is nearly twice the crack width, while phase velocity has a maximum deviation from the intrinsic value at a frequency lower than the peak frequency for Q?1.  相似文献   

3.
Wave Generation from Explosions in Rock Cavities   总被引：1，自引：0，他引：1  
—?We have developed a measurement method to monitor P- and S-waves generated from laboratory-scale explosions in meter-sized rock samples at a series of stations, as well as invented a device to drill spherical cavities in rock, with diameters up to 10?centimeters. We applied these to experiments in Bedford limestone in which spherical/cylindrical explosives (0.2 to 1.9?g) were centrally placed in 1.2- to 3-cm diameter cavities. Stress waves generated by the explosions were recorded within a radius of 25?cm. The radial stress wave records and post-explosion studies demonstrate that S-waves are generated from explosions in cavities as a result of both wave mode-conversion from the cavity wall and crack propagation in rocks. The experimental results of wave generation from the explosions in spherical and cylindrical cavities demonstrate the cavity geometrical effect on the resulting wave pattern. The P- and S-waves generated by explosions and crack propagation in rocks are analyzed. A simple analytic model for P-wave generation is proposed to explain the differences of P-wave-induced displacement histories between the observed waveforms and those predicted by a step-pressure source. Generally, the qualitative predictions of this model fit the observations. The present results demonstrate the importance of rock cracking and cavities in P- and S-wave generation.  相似文献   

4.
Scattering of an arbitrary elastic wave incident upon a spherically symmetric inclusion is considered and solutions are developed in terms of the spherical vector system of Petrashen, which produces results in terms of displacements rather than displacement potentials and in a form suitable for accurate numerical computations. Analytical expressions for canonical scattering coefficients are obtained for both the cases of incidentP waves and incidentS waves. Calculations of energy flux in the scattered waves lead to elastic optical theorems for bothP andS waves, which relate the scattering cross sections to the amplitude of the scattered fields in the forward direction. The properties of the solutions for a homogeneous elastic sphere, a sphere filled by fluid, and a spherical cavity are illustrated with scattering cross sections that demonstrate important differences between these types of obstacles. A general result is that the frequency dependence of the scattering is defined by the wavelength of the scattered wave rather than the wavelength of the incident wave. This is consistent with the finding that the intensity of thePS scattering is generally much stronger than theSP scattering. When averaged over all scattering angles, the mean intensity of thePS converted waves is2V p 2 /V s 4 times the mean intensity of theSP converted waves, and this ratio is independent of frequency. The exact solutions reduce to simple and easily used expressions in the case of the low frequency (Rayleigh) approximation and the low contrast (Rayleigh-Born) approximation. The case of energy absorbing inclusions can also be obtained by assigning complex values to the elastic parameters, which leads to the result that an increase in attenuation within the inclusion causes an increased scattering cross section with a marked preference for scatteredS waves. The complete generality of the results is demonstrated by showing waves scattered by the earth's core in the time domain, an example of high-frequency scattering that reveals a very complex relationship between geometrical arrivals and diffracted waves.  相似文献   

5.
The presence of subsurface cracks in a halfspace excited by elastic waves may give rise to scattered body and surface waves. For many engineering applications, such as non-destructive testing or oil exploration, the scattered field may yield valuable information to detect cracks and other scatterers. We use the Indirect Boundary Element Method (IBEM) to study the diffraction of P, SV waves with various incidence angles and Rayleigh surface waves. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. Our approach is usually called indirect BEM as the sources' strengths should be obtained as an intermediate step. This indirect formulation can give to the analyst a deep physical insight on the generated diffracted waves because it is closer to the physical reality and can be regarded as a realization of Huygens' Principle. In any event, mathematically it is fully equivalent to the classical Somigliana's representation theorem. In order to gauge accuracy we test our method by comparing with previous results in the literature. Various crack configurations, including multiple cracks, are investigated. Results in frequency and time domains are displayed. Under certain conditions the amplitude spectra of those waves clearly show conspicuous resonance peaks.  相似文献   

6.
Effects of Rock Damage on Seismic Waves Generated by Explosions   总被引：1，自引：0，他引：1  
—?In studying the physical processes involved in the generation of seismic waves by explosions, it is important to understand what happens in the region of high stresses immediately surrounding the explosion. This paper examines one of the processes that takes place in this region, the growth of pre-existing cracks, which is described quantitatively as an increase in rock damage. An equivalent elastic method is used to approximate the stress field surrounding the explosion and a micro-mechanical model of damage is used to calculate the increase in damage. Simulations for a 1?kt explosion reveal that the region of increased damage can be quite large, up to ten times the cavity radius. The damage is initiated on a damage front that propagates outward behind the explosive stress wave with a velocity intermediate between that of P and S waves. Calculations suggest that the amount of increased damage is controlled primarily by the initial damage and the extent of the region of increased damage is controlled primarily by the initial crack radius. The motions that occur on individual cracks when damage increases are converted to seismic moment tensors which are then used to calculate secondary elastic waves which radiate into the far field. It is found that, while the contribution from an individual crack is small, the combined effect of many cracks in a large region of increased damage can generate secondary waves that are comparable in amplitude to the primary waves generated by the explosion. Provided that there is asymmetry in the damage pattern, this process is quite effective in generating S waves, thus providing a quantitative explanation of how S waves can be generated by an explosion. Two types of asymmetry are investigated, a shear pre-stress and a preferred orientation of cracks, and it is found that both produce similar effects.  相似文献   

7.
The simulation of the seismic response of heterogeneous sedimentary basins under incident plane waves is computed using the Indirect Boundary Element Method (IBEM). To deal with these kinds of basins we used approximate analytical expressions for the two-dimensional Greens functions of a medium with constant-gradient wave propagation velocity. On the other hand, for the homogeneous half space underlying the sedimentary basin, the full space Greens functions were used. The response of semi-circular heterogeneous basins under incident SH waves is explored by means of the displacements in the frequency-space diagrams and synthetic seismograms. Moreover, we compared these results with those obtained for other homogeneous semi-circular models. The principal differences among them are pointed out. This simulation provided interesting results that displayed a complex amplification pattern in a rich spectrum of frequencies and locations. The maximum amplitudes levels were found around the edges of the heterogeneous sedimentary basins. In time domain some features characterize the seismic response of the basin which include enhanced generation and trapping of surface waves inside the sediments, and the reduced emission of seismic energy to the hard rock. In the heterogeneous models the lateral reflections of surface waves greatly influence the total displacements at the free surface in comparison with the homogeneous models where the displacements have a shared influence among both vertical and lateral reflections.  相似文献   

8.
Summary Laboratory measurements of rupture and particle velocity are in surprisingly good agreement with seismic values, providing further evidence that stick-slip friction is a suitable mechanism for shallow earthquakes. A simple theory is developed to explain the linear relationship observed between average particle velocity and stress drop for stick-slip events. Both stick-slip ruptures and cracks in brittle material commonly propagate at velocities roughly comparable to theS wave velocity of the material. Rupture normally begins relatively slowly and accelerates to a steady velocity in a few centimeters. Observations suggest that stick-slip ruptures can propagate atS wave speeds or occasionally greater and that cracks in pre-stressed glass can also propagate faster than theS waves. Fracture and thus rupture velocity of intact rock specimens is greatly influenced by the inhomogeneous structure of rock. Fracture may be modeled by coalescence of many cracks rather than growth of a single crack.Lamont-Doherty Geological Observatory Contribution No. 2627.  相似文献   

9.
In this work, we develop the indirect boundary element method (IBEM) to simulate the seismic site response in a realistic, large-scale 3-D sedimentary basin. Most previous applications of boundary element method have used full-space Green’s functions for wave propagation between element points. We use half-space Green’s functions, which include the seismic wavefield interactions at the free surface and require only the boundary elements of the basin interface. In this way, the size of the matrix equation for solution in the IBEM can be reduced to approximately a quarter of that using full-space Green’s functions. The site response modeling of the Granada basin in southern Spain using the IBEM shows that the basin-induced scattering waves were identified as propagating back and forth inside the basin. The scattered waves also generate surface waves that are weakly propagated outside of the basin. The wave propagation inside and outside of the basin shows different patterns. We observe that the scattered wave is locally amplified, and its propagation direction deviates from that of the incident waves propagation direction. Therefore, the computed seismic response in the basin could provide us with good estimates of the seismic motion.  相似文献   

10.
In this paper, we have considered the reflection and refraction of a plane wave at an interface between two half-spaces. The lower half-spaces is composed of highly anisotropic triclinic crystalline material and the upper half-space is homogeneous and isotropic. It has been assumed that due to incidence of a plane quasi-P (qP) wave, three types of waves, namely, quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH), will be generated in the lower half space whereas P and S waves will be generated in the upper half space. The phase velocities of all the quasi waves have been calculated. It has been assumed that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. Some specific relations have been established between directions of motion and propagation, respectively. The expressions for reflection coefficients of qP, qSV, qSH and refracted coefficients of P and SV waves are obtained. Results of reflection and refraction coefficients are presented.  相似文献   

11.
The modelling of elastic waves in fractured media with an explicit finite‐difference scheme causes instability problems on a staggered grid when the medium possesses high‐contrast discontinuities (strong heterogeneities). For the present study we apply the rotated staggered grid. Using this modified grid it is possible to simulate the propagation of elastic waves in a 2D or 3D medium containing cracks, pores or free surfaces without hard‐coded boundary conditions. Therefore it allows an efficient and precise numerical study of effective velocities in fractured structures. We model the propagation of plane waves through a set of different, randomly cracked media. In these numerical experiments we vary the wavelength of the plane waves, the crack porosity and the crack density. The synthetic results are compared with several static theories that predict the effective P‐ and S‐wave velocities in fractured materials in the long wavelength limit. For randomly distributed and randomly orientated, rectilinear, non‐intersecting, thin, dry cracks, the numerical simulations of velocities of P‐, SV‐ and SH‐waves are in excellent agreement with the results of the modified (or differential) self‐consistent theory. On the other hand for intersecting cracks, the critical crack‐density (porosity) concept must be taken into account. To describe the wave velocities in media with intersecting cracks, we propose introducing the critical crack‐density concept into the modified self‐consistent theory. Numerical simulations show that this new formulation predicts effective elastic properties accurately for such a case.  相似文献   

12.
An approximation to plane-wave propagation through a composite material is examined using a physical model with oriented but randomly distributed penny-shaped rubber inclusions within an isotropic epoxy resin matrix. A pulse transmission method is used to determine velocities of shear and compressional waves as a function of angle of incidence and crack density. The experimental and theoretical results of Hudson were compared and limitations within the crack parameters used in this study have been determined. Results from both polarized shear waves (S1, S2) compare favourably with the theory for a composite with up to 7% crack density, but theory and experiment diverge at higher crack densities. On the other hand, compressional-wave velocities at low crack densities (1% and 3%) compare favourably with the theory. It is also shown that the velocity ratio Vp/Vs for two extreme cases, i.e. propagation normal and parallel to the cracks, as a function of crack density and porosity, has a strong directional dependence.  相似文献   

13.
Summary The effects of a uniform external magnetic field on the propagation of waves in a homogeneous, infinitely conducting flat plate with free boundaries have been studied. It has been found that in general all the three types of waves —P, SV andSH waves—are coupled and the influence may be more pronounced in coupling the symmetric and antisymmetric types of motions in every mode.When the magnetic field is parallel to the plane faces and transverse to the direction of wave propagation, the shear wave polarized parallel to the field is purely elastic whereas the coupledP andS V waves are magnetoelastic and exhibit dispersion strikingly similar to the non-magnetic case, provided the electro-magnetic radiation into the surrounding free space is neglected.The results reported in an earlier communication [1]2) are also confirmed.  相似文献   

14.
The propagation of elastic waves in a medium containing many inclusions is considered. Under the assumption that the spatial distribution of inclusions is uniform, a general equation is derived for the determination of the velocity dispersion and attenuation coefficient of the effective waves. A simple example is presented where scatterers are infinitesimally thin cracks. The calculated results show that the attenuation coefficient Q?1 takes a peak value for the wavelength nearly equal to twice the crack length.  相似文献   

15.
Scattering of Seismic Waves by Cracks with the Boundary Integral Method   总被引：3，自引：0，他引：3  
— 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.  相似文献   

16.
—Shear (S) waves differ from compressional (P) waves because of their lower propagation velocities, their lower frequencies and due to the different character of their particle motion. The move-out of travel-time branches of S-wave reflections is different from P waves owing to the difference in the propagation velocities. To distinguish between P and S waves requires broadband-frequency acquisition, long receiver arrays and three-component recording. S-wave generation at the source and P-to-S-wave conversion at crustal interfaces can be very efficient, implying that there is a real danger of misinterpreting signals if only vertical components are used. On the other hand, integrated P- and S-wave studies promise to provide very efficient lithological discriminators in the crystalline crust, in particular concerning the quartz content, and indicators for rock anisotropy, which can be interpreted for the existence of fine layering, the direction of the recent stress regime (alignments of micro-fractures) or for the direction of palaeo-stress (alignments of minerals).  相似文献   

17.
The effect of randomly distributed cracks on the attenuation and dispersion ofSH waves is theoretically studied. If earthquake ruptures are caused by sudden coalescence of preexisting cracks, it will be crucial for earthquake prediction to monitor the temporal variation of the crack distribution. Our aim is to investigate how the property of crack distribution is reflected in the attenuation and dispersion of elastic waves.We introduce the stochastic property, in the mathematical analysis, for the distributions of crack location, crack size and crack orientation. The crack size distribution is assumed to be described by a power law probability density (p(a) a – fora minaa max according to recent seismological and experimental knowledge, wherea is a half crack length and the range 13 is assumed. The distribution of crack location is assumed to be homogeneous for the sake of mathematical simplicity, and a low crack density is assumed. The stochastic property of each crack is assumed to be independent of that of the other cracks. We assume two models, that is, the aligned crack model and the randomly oriented crack model, for the distribution of crack orientation. All cracks are assumed to be aligned in the former model. The orientation of each crack is assumed to be random in the latter model, and the homogeneous distribution is assumed for the crack orientation. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed.We observe the following features common to both the aligned crack model and the randomly oriented crack model. The attenuation coefficientQ –1 decays in proportion tok –1 in the high frequency range and its growth is proportional tok 2 in the low frequency range, wherek is the intrinsic wave number. This asymptotic behavior is parameter-independent, too. The attenuation coefficientQ –1 has a broader peak as increases and/ora min/a max decreases. The nondimensional peak wave numberk p a max at whichQ –1 takes the peak value is almost independent ofa min/a max for =1 and 2 while it considerably depends ona min/a max for =3. The phase velocity is almost independent ofk in the rangeka max<1 and increases monotonically ask increases in the rangeka max>1. While the magnitude ofQ –1 and the phase velocity considerably depend on the orientation of the crack in the aligned crack model, the above feature does not depend on the crack orientation.The accumulation of seismological measurements suggests thatQ –1 ofS waves has a peak at around 0.5 Hz. If this observation is combined with our theoretical results onk p a max, the probable range ofa max of the crack distribution in the earth can be estimated for =1 or 2. If we assume 4 km/sec as theS wave velocity of the matrix medium,a max is estimated to range from 2 to 5 km. We cannot estimatea max in a narrow range for =3.  相似文献   

18.
在油、气储层的勘探和开发中观察到的一个现象是储层岩石中普遍存在孔隙和裂隙.随着近年来孔、裂隙介质弹性波动理论的进展,我们可以将此理论应用于测井技术,以此来指导从声波测井中测量孔、裂隙地层的声学参数.本文计算了孔、裂隙地层里充流体井眼中的多极子声场,分析了声场随裂隙介质的两个主要参数(即裂隙密度和裂隙纵横比)的变化特征.井孔声场的数值计算表明裂隙密度可以大幅度地降低井中声波纵、横波的波速和振幅.随着裂隙密度的增加,在测井频段内也可以看到纵、横波速的频散现象(这种频散在孔隙地层中一般是观察不到的).本文还研究了多极子模式波 (即单极的Stoneley波、伪瑞利波以及偶极的弯曲波)随裂隙参数的变化特征.结果表明,这些模式波的振幅激发和速度频散都受裂隙密度的影响.裂隙密度越高影响越大.此外,裂隙还对模式波的传播造成较大的衰减.相对裂隙密度而言,裂隙纵横比是一个频率控制参数,它控制裂隙对声场影响的频率区间.本文的分析结果对裂缝、孔隙型地层的声波测井具有指导意义.  相似文献   

19.
The formal solutions of displacement field to the problem of elastic wave scattering and diffraction due to an infinitely long rigid cylinder embedded in an infinite elastic medium by an impulsive point source have been obtained in the integral form. The integrals for the reflected and the diffracted waves both in the shadow zone and in the illuminated zone are evaluated asymptotically for the early time motion by the Reisdue-Cagniard method and the Saddle-point-Cagniard method.Numerical results of the diffractedP, S andPS waves at a fixed circum-distance from the surface of the rigid cylinder show noticeably that (1) the energy partition for the diffractedS wave is small in comparison with that for the diffractedP wave, (2) the wave form of the diffractedS wave is broader and more diffused than that of the diffractedP wave, (3) the direction of the radial motions of the diffractedP andS waves varies as a function of the observational point, and (4) the energy partition for the diffractedP wave is much smaller than that for the direct or the reflectedP waves.This paper has been presented at the 46th Annual International Meeting of Society of Exploration Geophysicists in Houston, Texas, Oct. 28, 1976.  相似文献   

20.
弹性层状半空间中沉积谷地对入射平面SH波的放大作用   总被引：6，自引：3，他引：6  
对Wolf理论进行拓展,使之可解决沉积谷地对波的散射问题,进而利用间接边界元法,求解了弹性层状半空间中沉积谷地对入射平面SH波的放大作用问题。通过自由场反应分析,求得假想边界上各点的位移和各单元的应力反应。施加虚拟均布荷载,求得位移和应力的格林函数。根据应力和位移连续边界条件确定虚拟分布荷载,将自由场反应和虚拟分布荷载产生的反应叠加起来,即得到问题的解答。最后,以基岩上单一土层中沉积谷地对入射平面SH波的放大作用为例进行了数值计算分析,结果表明,层状半空间中沉积谷地和均匀半空间中沉积谷地对波的放大作用存在显著差别。文中分析了造成差别的原因,并讨论了覆盖层厚度和刚度对放大作用的影响。  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号