共查询到20条相似文献，搜索用时 31 毫秒
1.
Sylvie Kelner Michel Bouchon & Olivier Coutant 《Geophysical Journal International》1999,137(1):197-206
We study the propagation of P waves through media containing open fractures by performing numerical simulations. The important parameter in such problems is the ratio between crack length and incident wavelength. When the wavelength of the incident wavefield is close to or shorter than the crack length, the scattered waves are efficiently excited and the attenuation of the primary waves can be observed on synthetic seismograms. On the other hand, when the incident wavelength is greater than the crack length, we can simulate the anisotropic behaviour of fractured media resulting from the scattering of seismic waves by the cracks through the time delay of the arrival of the transmitted wave. The method of calculation used is a boundary element method in which the Green's functions are computed by the discrete wavenumber method. For simplicity, the 2-D elastodynamic diffraction problem is considered. The rock matrix is supposed to be elastic, isotropic and homogeneous, while the cracks are all empty and have the same length and strike direction. An iterative method of calculation of the diffracted wavefield is developed in the case where a large number of cracks are present in order to reduce the computation time. The attenuation factor Q −1 of the direct waves passing through a fractured zone is measured in several frequency bands. We observe that the attenuation factor Q −1 of the direct P wave peaks around kd = 2, where k is the incident wavenumber and d the crack length, and decreases proportionally to ( kd ) −1 in the high-wavenumber range. In the long-wavelength domain, the velocity of the direct P wave measured for two different crack realizations is very close to the value predicted by Hudson's theory on the overall elastic properties of fractured materials. 相似文献
2.
J. A. Hudson 《Geophysical Journal International》1981,64(1):133-150
Summary. Expressions now exist from which may be calculated the propagation constants of elastic waves travelling through material containing a distribution of cracks. The cracks are randomly distributed in position and may be randomly orientated. The wavelengths involved are assumed to be large compared with the size of the cracks and with their separation distances so that the formulae, based on the mean taken over a statistical ensemble, may reasonably be used to predict the properties of a single sample. The results are valid only for small concentrations of cracks.
Explicit expressions, correct to lowest order in the ratio of the crack size to a wavelength, are derived here for the overall elastic parameters and the overall wave speeds and attenuation of elastic waves in cracked materials where the mean crack is circular, and the cracks are either aligned or randomly orientated. The cracks may be empty or filled with solid or fluid material. These results are achieved on the basis of simply the static solution for an ellipsoidal inclusion under stress.
The extension to different distributions of orientation or to mixtures of different types of crack is quite straightforward. 相似文献
Explicit expressions, correct to lowest order in the ratio of the crack size to a wavelength, are derived here for the overall elastic parameters and the overall wave speeds and attenuation of elastic waves in cracked materials where the mean crack is circular, and the cracks are either aligned or randomly orientated. The cracks may be empty or filled with solid or fluid material. These results are achieved on the basis of simply the static solution for an ellipsoidal inclusion under stress.
The extension to different distributions of orientation or to mixtures of different types of crack is quite straightforward. 相似文献
3.
Effective anisotropic elastic constants for wave propagation through cracked solids 总被引：19，自引：0，他引：19
Stuart Crampin 《Geophysical Journal International》1984,76(1):135-145
Summary. Theoretical developments of Hudson demonstrate how to calculate the variations of velocity and attenuation of seismic waves propagating through solids containing aligned cracks. The analysis can handle a wide variety of crack configurations and crack geometries. Hudson associates the velocity variations with effective elastic constants. In this paper we associate the variation of attenuation with the imaginary parts of complex effective elastic constants. These complex elastic constants permit the simulation of wave propagation through two-phase materials by the calculation of wave propagation through homogeneous anisotropic solids. 相似文献
4.
Seismic body waves in anisotropic media: synthetic seismograms 总被引：5，自引：0，他引：5
Summary. Synthetic seismograms and particle motion diagrams are computed for simple, layered Earth models containing an anisotropic layer. The presence of anisotropy couples the P, SV and SH wave motion so that P waves incident on the anisotropic layer from below produce P, SV and small-amplitude SH waves at the surface both the P velocity and the amplitudes of the converted phases vary with azimuth. Significant SH amplitudes may be generated even when the wavelength of the P wave is much greater than the thickness of the anisotropic layer. Incident SV or SH waves may each generate large amplitudes of both SV and SH motion. This strong coupling is largely independent of the degree of velocity anisotropy of the medium. The arrivals from short-period S waves exhibit S-wave splitting, but arrivals from longer period S waves superpose into a modified waveform. This strong coupling does not allow the arrival of separate phases with pure SV and SH polarization except along directions of symmetry where the motion decouples. 相似文献
5.
Summary. The square-root energy ratios and pulse shapes are presented for P, SV and SH waves transmitted through a layer of orthorhombic olivine between two isotropic half-spaces. Off incident planes of symmetry, incident P waves generate two small amplitude SH waves (one from each interface), whose amplitudes decrease slowly with increasing period. Incident SV (or SH ) waves can generate large amplitude SH (or SV ) waves which decrease rapidly with increasing period. For incident S waves, many pulses not present in isotropic models are generated, often of large relative amplitude, with many of the transmitted S pulses showing evidence of double arrivals, either in the form of S-wave splitting, or a modification of the shape of the input waveform. 相似文献
6.
Angelika-M. Wulff Toshiyuki Hashida Kimio Watanabe & Hideaki Takahashi 《Geophysical Journal International》1999,139(2):395-409
Laboratory measurements of ultrasonic wave propagation in tuffaceous sandstone (Kimachi, Japan) and granite (Iidate, Japan) were performed during increasing fracturing of the samples. The fracturing was achieved by unconfined uniaxial compression up to and beyond the point of macrofracture of the specimen using a constant low strain rate. The observed variation of wave velocity (up to 40 per cent) due to the development of micro- and macrofractures in the rock is interpreted by rock models relating velocity changes to damage and crack density. The calculated density of the newly formed cracks reaches higher values for the sandstone than for the granite. Using the estimated crack densities, the attenuation behaviour is interpreted in terms of different attenuation mechanisms; that is, friction and scattering. Rayleigh scattering as described by the model of Hudson (1981 ) may explain the attenuation qualitatively if the largest plausible crack dimensions are assumed in modelling. 相似文献
7.
Surface-wave propagation in a cracked poroelastic half-space lying under a uniform layer of fluid 总被引：1，自引：0，他引：1
M. D. Sharma 《Geophysical Journal International》1996,127(1):31-39
The effect of cracks on the elastic properties of an isotropic elastic solid is studied when the cracks are saturated with a soft fluid. A polynomial equation in effective Poisson's ratio is obtained, whose coefficients are functions of Poisson's ratio of the uncracked solid, crack density and saturating fluid parameter. Elastic and dynamical constants used in Blot's theory of wave propagation in poroelastic solids are modified for the introduction of cracks. The effects of cracks on the velocities of three types of waves are observed numerically. The frequency equation is derived for the propagation of Rayleigh-type surface waves in a saturated poroelastic half-space lying under a uniform layer of liquid. Dispersion curves for a particular model of oceanic crust containing cracks are plotted. The effects of variations in crack density and saturation on the phase and group velocity are also analysed. 相似文献
8.
Effects of fractures on seismic-wave velocity and attenuation 总被引：1，自引：0，他引：1
The effects of fractures on the seismic velocity and attenuation of a rock are investigated using theoretical results and experimental data. Fractures in a rock mass influence the traveltimes and amplitudes of seismic waves that have propagated through them. The displacement discontinuity model, recently employed in fracture investigations, is modified to describe the effect of fractures on seismic-wave velocity and attenuation. This new model, the modified displacement discontinuity model (MDD), is formulated in a way analogous to transmission-line analysis. The fractures are treated as transmission lines for the passage of seismic waves. The MDD takes into consideration realistic fracture parameters which include the fracture length, the fractional area of a fracture surface in contact, and the nature of the infilling material. A single fracture of varying geometric and material properties is shown to affect dramatically the transmission properties of a propagating waveform, and hence the seismic velocity and attenuation. These effects have been shown to result in a frequency-dependent velocity and attenuation. The sensitivity of the fracture parameters to seismic-wave velocity and attenuation was investigated and interesting results were obtained. Fracture parameters used in designing experimental models consisting of synthetically manufactured cracks were fed into the MDD and a well-known crack model, Hudson's model, for comparison. Velocities as a function of the incident-wave angle were obtained from both numerical models and were compared with the results from the experimental modelling. For P waves, the MDD model results show better agreement with those of the experimental model for all crack densities investigated than those from Hudson's model. 相似文献
9.
F. Luzón F. J. Sánchez-Sesma J. L. Rodríguez-Zúñiga A. M. Posadas J. M. García J. Martin M. D. Romacho M. Navarro 《Geophysical Journal International》1997,129(3):571-578
The diffraction of P, S and Rayleigh waves by 3-D topographies in an elastic half-space is studied using a simplified indirect boundary element method (IBEM). This technique is based on the integral representation of the diffracted elastic fields in terms of single-layer boundary sources. It can be seen as a numerical realization of Huygens principle because diffracted waves are constructed at the boundaries from where they are radiated by means of boundary sources. A Fredholm integral equation of the second kind for such sources is obtained from the stress-free boundary conditions. A simplified discretization scheme for the numerical and analytical integration of the exact Green's functions, which employs circles of various sizes to cover most of the boundary surface, is used.
The incidence of elastic waves on 3-D topographical profiles is studied. We analyse the displacement amplitudes in the frequency, space and time domains. The results show that the vertical walls of a cylindrical cavity are strong diffractors producing emission of energy in all directions. In the case of a mountain and incident P, SV and SH waves the results show a great variability of the surface ground motion. These spatial variations are due to the interference between locally generated diffracted waves. A polarization analysis of the surface displacement at different locations shows that the diffracted waves are mostly surface and creeping waves. 相似文献
The incidence of elastic waves on 3-D topographical profiles is studied. We analyse the displacement amplitudes in the frequency, space and time domains. The results show that the vertical walls of a cylindrical cavity are strong diffractors producing emission of energy in all directions. In the case of a mountain and incident P, SV and SH waves the results show a great variability of the surface ground motion. These spatial variations are due to the interference between locally generated diffracted waves. A polarization analysis of the surface displacement at different locations shows that the diffracted waves are mostly surface and creeping waves. 相似文献
10.
We analysed local earthquake waveforms recorded on a broad-band seismic network in northwestern Himalayas to compute the intrinsic and scattered attenuation parameters from coda waves. Similar to other tectonically active and heterogeneous regions, attenuation-frequency relation for western Himalaya is Q −1 c = (113 ± 7) f (1.01±0.05) where Qc is the coda Q parameter. Intrinsic ( Q −1 i ) and scattering ( Q −1 s ) attenuations was separated using Qc and direct S -wave Q data ( Qd ) . It is observed that estimated Q −1 c is close to Q −1 i and both of them are much larger than Q −1 s suggesting that coda decay is predominantly caused by intrinsic attenuation. At higher frequencies, both the attenuation parameters Qc and, Qd are similar indicating that coda is predominantly composed of back-scattered S waves at these frequencies. 相似文献
11.
Two distinct phases are commonly observed at the initial part of seismograms of large shallow earthquakes: low-frequency and low-amplitude waves following the onset of a P wave ( P 1 ) are interrupted by the arrival of the second impulsive phase P2 enriched with high-frequency components. This observation suggests that a large shallow earthquake involves two qualitatively different stages of rupture at its nucleation.
We propose a theoretical model that can naturally explain the above nucleation behaviour. The model is 2-D and the deformation is assumed to be anti-plane. A key clement in our model is the assumption of a zone in which numbers of pre-existing cracks are densely distributed; this cracked zone is a model for the fault zone. Dynamic crack growth nucleated in such a zone is intensely affected by the crack interactions, which exert two conflicting effects: one tends to accelerate the crack growth, and the other tends to decelerate it. The accelerating and decelerating effects are generally ascribable to coplanar and non-coplanar crack interactions, respectively. We rigorously treat the multiple interactions among the cracks, using the boundary integral equation method (BIEM), and assume the critical stress fracture criterion for the analysis of spontaneous crack propagation.
Our analysis shows that a dynamic rupture nucleated in the cracked zone begins to grow slowly due to the relative predominance of non-coplanar interactions. This process radiates the P1 phase. If the crack continues to grow, coalescence with adjacent coplanar cracks occurs after a short time. Then, coplanar interactions suddenly begin to prevail and crack growth is accelerated; the P2 phase is emitted in this process. It is interpreted that the two distinct phases appear in the process of the transition from non-coplanar to coplanar interaction predominance. 相似文献
We propose a theoretical model that can naturally explain the above nucleation behaviour. The model is 2-D and the deformation is assumed to be anti-plane. A key clement in our model is the assumption of a zone in which numbers of pre-existing cracks are densely distributed; this cracked zone is a model for the fault zone. Dynamic crack growth nucleated in such a zone is intensely affected by the crack interactions, which exert two conflicting effects: one tends to accelerate the crack growth, and the other tends to decelerate it. The accelerating and decelerating effects are generally ascribable to coplanar and non-coplanar crack interactions, respectively. We rigorously treat the multiple interactions among the cracks, using the boundary integral equation method (BIEM), and assume the critical stress fracture criterion for the analysis of spontaneous crack propagation.
Our analysis shows that a dynamic rupture nucleated in the cracked zone begins to grow slowly due to the relative predominance of non-coplanar interactions. This process radiates the P
12.
Thomas M. Hearn Suyun Wang Shunping Pei Zhonghuai Xu James F. Ni Yanxiang Yu 《Geophysical Journal International》2008,174(1):223-234
Amplitude tomography reconstructs seismic attenuation directly from recorded wave amplitudes. We have applied the tomography to amplitude data reported in the 'Annual Bulletin of Chinese Earthquakes' and interpreted the regionally varying crustal attenuation in terms of tectonics. The seismic amplitudes were originally recorded for determining the M L and M S magnitudes. They generally correspond to the maximum amplitudes of the horizontal components of the short-period S waves and intermediate-period Rayleigh waves. Both sets of measurements are sensitive to crustal structure. The peak amplitudes from M L amplitudes spread spherically with significant dispersion and scattering. M S amplitudes show cylindrical spreading with little dispersion. Average crustal Q values for attenuation at 1 Hz are 737 and 505 for M L and M S , respectively, with substantial regional variations. Frequency dependence in the attenuation is also indicated. Regions with the lowest attenuation (high Q values) are beneath the south China Block, Sichuan Basin, Ordos Platform, the Daxinganling and the Korea Craton. These tend to be tectonically inactive regions, which are generally dominated by intrusive and cratonic rocks in the upper crust. Regions with the highest attenuation (low Q values) are beneath Bohai Basin, Yunnan, eastern Songpan-Ganzi Terrain, margins of the Ordos platform and the Qilian Shan. These are predominantly active basins, grabens and fold belts. The continental margin also highly attenuates both S and surface waves. 相似文献
13.
It is pointed out, in the context of the boundary integral equation method (BIEM), that, in the mechanics of 2-D curved in-plane shear cracks, a smooth curve, along which the crack orientation changes continuously, and an abrupt kink, across which it changes discontinuously, are not equivalent to each other. The discrepancy is illustrated by numerical results, and a set of conceptual models is used to demonstrate analytically how the equations that govern the crack mechanics have inherently distinct forms depending on whether the crack orientation changes continuously or abruptly across a bend, as long as one abides by the principles of linear elasticity theory. This has serious implications for the numerical treatment of a curved crack, which can be modelled as a chain of finite elements that are connected either smoothly or at abrupt kinks, the two methods producing different numerical outcomes. No similar paradox arises in the cases of anti-plane shear or open in-plane cracks. 相似文献
14.
Claudio Pecorari 《Geophysical Journal International》1997,129(1):169-175
A new model that accounts for the stress dependence of the phase velocity of elastodynamic waves propagating in a cracked solid under compression is presented. The phase velocities of longitudinal and shear waves are derived from the effective elastic properties of a cracked solid, which are evaluated within the framework of Kachanov's approach. Following Kachanov, the extra-compliance tensor of the cracked solid is related to the crack compliances, which display a marked non-linear behaviour when subjected to a compressive load. Such non-linear behaviour is shown to be derived from the elastic interaction between the contacting crack faces under compression. This work does not address the effect of mutual interaction among cracks and the generation of higher harmonics due to the medium non-linearity. Numerical examples are presented that illustrate the phase velocity changes occurring in a solid with a random distribution of parallel cracks as a function of an external compressive load. A distinctive feature of the acoustoelastic effect in solids with large parallel fractures and in solids with distributions of aligned microcracks is also illustrated. 相似文献
15.
I. N. Gupta R. R. Blandford R. A. Wagner J. A. Burnetti T. W. McElfresh 《Geophysical Journal International》1985,83(2):541-553
Summary. Spectral analysis of P and P coda from NTS explosions recorded at NORSAR shows that magnitudes based on spectral integration of P coda provide a significantly more precise measure of yield than those based on the initial P . Coda amplitudes and spectra are considerably less sensitive to near-source variations than the direct P . A plot of P -coda magnitude, after correcting for the effects of attenuation in the upper mantle and the source spectrum based on knowledge of approximate yield or mb , versus log yield appears to have a slope of unity. This implies that P coda from several stations (with different but known t * values) can be combined to improve the yield determinations further. Single station P coda from Soviet explosions can also be used to determine relative yields that appear to be at least as precise as those from Lg based on a network of stations. 相似文献
16.
L. Knopoff R. G. Mitchel E. G. Kausel † F. Schwab ‡ 《Geophysical Journal International》1979,56(1):211-218
Summary. The Lg phase has been shown previously to be a collection of higher-mode surface waves guided by the continental crust (Knopoff, Schwab & Kausel). A simple scaling between continental and oceanic crustal thicknesses suggests that a search for an oceanic Lg phase should be made in the period range from 1 to 2s. In a search for SH polarized Lg arrivals over oceanic paths, we found that in addition to the fundamental mode, seismo-grams at relatively short ranges in the Pacific showed the presence of only the first higher mode with group velocities on the steep portion of the dispersion curve rather than at the group velocity minimum as expected. Numerical model analysis indicates that, contrary to the continental case, there is no strong confluence of stationary phases of higher-mode crustal waves in the appropriate period range to produce Lg wave packets; this is due to small but significant differences in scaled crustal structures. Further, lateral variations in the thickness of oceanic sediments are sufficient to scatter most of the crustal surface-wave energy within a relatively short distance. Even were this thickness uniform, attenuation in the sediments would be strong enough to absorb the Lg stationary phases in a short distance. 相似文献
17.
A large data set of amplitude measurements of minor and major arc Rayleigh waves in the period range 73–171 s is collected. By comparing these amplitudes with the amplitudes of synthetic waveforms calculated by mode summation, maps of lateral variations in the apparent attenuation structure of the Earth are constructed. An existing formalism for predicting the effects of focusing is employed to calculate amplitude perturbations for the same data set. These perturbations are used to construct 'pseudo‐attenuation' maps and these results are compared with the apparent attenuation maps calculated from the data. It is shown that variations in Rayleigh wave amplitude perturbations in the Earth are dominated by attenuation at long wavelengths (below about degree 8) and by elastic structure at shorter wavelengths. It is also shown that the linear approximation for focusing is successful at predicting Rayleigh wave amplitudes using existing phase velocity maps. These results indicate that future attempts to model the velocity structure of the Earth would be assisted by incorporating amplitude data and by jointly inverting for Q structure. 相似文献
18.
Charles H. Estabrook Michael Weber Rainer Kind 《Geophysical Journal International》1997,130(2):349-364
We investigate large-amplitude phases arriving in the P -wave coda of broad-band seismograms from teleseisms recorded by the Gräfenberg array, the German Regional Seismic Network and the Global Seismic Network. The data set consists of all events m b≤ 5.6 from the Aleutian arc between 1977 and 1992. Earthquakes with large-amplitude coda waves correlate with the presence of oceanic crust in the source region. The amplitudes sometimes approach those of the P wave, much larger than predicted by theory. Modelling indicates that phases in the P -wave coda cannot be P -wave multiples beneath the source and receiver, or underside reflections, which precede PP , from upper-mantle discontinuities. Among the events, seismograms are very similar, where the arrival times of the unusual phases agree approximately with the predicted times of S -to- P conversions from the upper-mantle discontinuities under the source. Because the large-amplitude phases in the P -wave coda have little, if any, dependence on event depth and have predominantly an SV -wave radiation pattern towards the receiver, we suggest that they originate as SV and/or Rayleigh waves and are enhanced by lateral heterogeneity and multipathing from the subducting Aleutian slab. 相似文献
19.
Summary. The Oblique Seismic Experiment (OSE) has been proposed to increase the usefulness of the IPOD crustal borehole as a means of investigating layer 2 of oceanic crust. Specific objectives are: to determine the lateral extent of the structure intersected by the borehole, to analyse the role of cracks in the velocity structure of layer 2, to look for anisotropy which may be caused by large cracks with a preferred orientation and, finally, to measure attenuation in oceanic crust.
The first successful Oblique Seismic Experiment in oceanic crust was carried out in 1977 March in a hole 400 miles north of Puerto Rico. An adequate study of lateral velocity variations was impossible because the hole was not deep enough, the hole was inadequately logged, and the small scale basement topography was not known. In general both P - and S -wave velocity profiles suggest that the crack density decreases with depth in layer 2. Velocities at the bottom of layer 2 are the same as matrix velocities for basalt, implying that crack density may be negligible at this depth. No convincing evidence for anisotropy in either layer 2 or 3 is found from travel time analysis. The hole was not deep enough to measure attenuation from normal incidence shots and amplitudes were not consistent enough to obtain a measure of attenuation from long range shots. 相似文献
The first successful Oblique Seismic Experiment in oceanic crust was carried out in 1977 March in a hole 400 miles north of Puerto Rico. An adequate study of lateral velocity variations was impossible because the hole was not deep enough, the hole was inadequately logged, and the small scale basement topography was not known. In general both P - and S -wave velocity profiles suggest that the crack density decreases with depth in layer 2. Velocities at the bottom of layer 2 are the same as matrix velocities for basalt, implying that crack density may be negligible at this depth. No convincing evidence for anisotropy in either layer 2 or 3 is found from travel time analysis. The hole was not deep enough to measure attenuation from normal incidence shots and amplitudes were not consistent enough to obtain a measure of attenuation from long range shots. 相似文献
20.
Seismic-wave propagation through a cracked solid: polarization as a possible dilatancy diagnostic 总被引：19，自引：0，他引：19
Stuart Crampin 《Geophysical Journal International》1978,53(3):467-496
summary . A new technique is presented for modelling the elastic constants of cracked structures with application to systems with weak concentrations of parallel cracks, and of simple biplanar and triplanar cracks. The velocities and Vp /Vs ratios of these anisotropic structures are used to provide quantitative models for some earthquake precursors. These results indicate the great importance of crack geometry to the behaviour of precursors. The velocities of saturated cracks appear to favour the dilatancy-diffusion model of precursory phenomena. Synthetic seismograms are calculated for propagation through possible dilatancy zones. The seismograms show some characteristic features which may be useful for the investigation of earthquake dilatancy. 相似文献