共查询到20条相似文献，搜索用时 46 毫秒
1.
Summary. A generalized ray theory for transient SH -waves in a wedge-shaped layer over an elastic half-space is developed in this paper. The ray integrals for multiply reflected waves in the layer are derived in terms of two systems of coordinates and two sets of local wavenumbers, one along the free surface and the other along the sloped interface. All local wavenumbers are then transformed to a common wavenumber in all ray integrals which are evaluated by the Cagniard method. Results for the first motion approximation are in agreement with previous investigations. 相似文献
2.
The phase velocity and the attenuation coefficient of compressional seismic waves, propagating in poroelastic, fluid-saturated, laminated sediments, are computed analytically from first principles. The wavefield is found to be strongly affected by the medium heterogeneity. Impedance fluctuations lead to poroelastic scattering; variations of the layer compressibilities cause inter-layer flow (a 1-D macroscopic local flow). These effects result in significant attenuation and dispersion of the seismic wavefield, even in the surface seismic frequency range, 10–100 Hz. The various attenuation mechanisms are found to be approximately additive, dominated by inter-layer flow at very low frequencies. Elastic scattering is important over a broad frequency range from seismic to sonic frequencies. Biot's global flow (the relative displacement of solid frame and fluid) contributes mainly in the range of ultrasonic frequencies. From the seismic frequency range up to ultrasonic frequencies, attenuation due to heterogeneity is strongly enhanced compared to homogeneous Biot models. Simple analytical expressions for the P -wave phase velocity and attenuation coefficient are presented as functions of frequency and of statistical medium parameters (correlation lengths, variances). These results automatically include different asymptotic approximations, such as poroelastic Backus averaging in the quasi-static and the no-flow limits, geometrical optics, and intermediate frequency ranges. 相似文献
3.
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
4.
Summary. A method of synthetic seismogram computation for teleseismic SV -waves is developed in order to treat quantitatively SV -waves in problems of body wave source inversion and source—receiver structure studies. The method employs WKBJ theory for a generalized ray in a vertically inhomogeneous half-space and the propagator matrix technique for waves in near-surface homogeneous layers. Wavenumber integration is done along the real axis of the wavenumber plane and anelasticity is included by using complex velocity in all regions of the earth model. The near-surface source structure is taken into account in the computation for the case of the shallow source by allowing a point source to be located in the homogeneous layers. Source and receiver area structures are also allowed to differ. A general moment tensor point source is considered. 相似文献
5.
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
6.
Antonio García-Jerez Francisco Luzón Manuel Navarro 《Geophysical Journal International》2008,173(3):844-858
A method for the computation of phase velocities of surface waves from microtremor waveforms is shown. The technique starts from simultaneous three-component records obtained in a circular array without a central station. Then, Fourier spectra of vertical, radial and tangential components of motion are calculated for each station and considered as complex-valuated functions of the azimuthal coordinate. A couple of intermediate real physical quantities, B and C , can be defined from the 0- and ±1-order coefficients of the Fourier series expansion of such functions. Finally, phase velocities of Rayleigh and Love waves can be retrieved from B and C by solving respective one-unknown equations. The basic assumption is the possibility of expanding the wavefield as a sum of plane surface waves with Rayleigh and Love wavenumbers being univocal functions of the circular frequency. The method is tested in synthetic ambient noise wavefields confirming its reliability and robustness for passive seismic surveying. 相似文献
7.
J. Gagnepain-Beyneix 《Geophysical Journal International》1987,89(2):681-704
Summary. Spectral attenuation of coda waves has been studied in the range 2–40 Hz from local events recorded in the western Pyrenean range from 1980 to 1982. Q c was obtained using a single scattering model of S -waves for different segments of the coda. An increase of Q c with lapse time was found and attributed to a rapid increase of Q β with depth.
Three groups of events were selected from distinct focal areas. Two data sets are mainly composed of aftershocks of moderate earthquakes of magnitude 5.1 and 4.8, respectively. No moderate earthquake occurred in the third area in the few years preceding or following the selected events. Use of stations close to epicentres allowed sampling of the coda at very short lapse times and then study of small, distinct scattering volumes. Noticeable differences were found between the three studied areas and attributed to spatial rather than temporal variations.
The Qc frequency dependence was studied according to Q c = qf α . α is found to range from 0.7 to 1.1 and q from 30 to 140. These values are in agreement with those found in other tectonic areas. It is shown that scattering is the dominant attenuation process below 10Hz. 相似文献
Three groups of events were selected from distinct focal areas. Two data sets are mainly composed of aftershocks of moderate earthquakes of magnitude 5.1 and 4.8, respectively. No moderate earthquake occurred in the third area in the few years preceding or following the selected events. Use of stations close to epicentres allowed sampling of the coda at very short lapse times and then study of small, distinct scattering volumes. Noticeable differences were found between the three studied areas and attributed to spatial rather than temporal variations.
The Q
8.
B. L. N. Kennett 《Geophysical Journal International》1984,79(1):235-255
Summary. The propagation of surface waves in a laterally varying medium can be described by representing the wavetrain as a superposition of modal contributions for a reference structure. As the guided waves propagate through a heterogeneous zone the modal coefficients needed to describe the wavetrain vary with position, leading to interconversions between modes and reflection into backward travelling modes. The evolution of the modal terms may be described by a set of first-order differential equations which allow for coupling to both forward and backward travelling waves; the coefficients in these equations depend on the differences between the actual structure and the reference structure. This system is established using the orthogonality properties of the modal eigenfunctions and is valid for SH -waves, P - SV -waves and full anisotropy.
The reflected and transmitted wavefields for a region of heterogeneity can be related to the incident wave by introducing reflection and transmission matrices which connect the modal coefficients in these fields to those in the incident wavetrain. By considering a sequence of models with increasing width of heterogeneity we are able to derive a set of Ricatti equations for the reflection and transmission matrices which may be solved by initial value techniques. This avoids an awkward two-point boundary value problem for a large number of coupled equations. The method is demonstrated for 1 Hz Lg - and Sn -waves in a multilayered model for which there are 19 coupled modes.
The method is applicable to three-dimensional heterogeneity, and we are able to show that the interconversion between Love and Rayleigh waves, in the presence of gradients in seismic properties transverse to the propagation path, leads to a net rate of increase of the transverse components of the seismogram at the expense of the other components. 相似文献
The reflected and transmitted wavefields for a region of heterogeneity can be related to the incident wave by introducing reflection and transmission matrices which connect the modal coefficients in these fields to those in the incident wavetrain. By considering a sequence of models with increasing width of heterogeneity we are able to derive a set of Ricatti equations for the reflection and transmission matrices which may be solved by initial value techniques. This avoids an awkward two-point boundary value problem for a large number of coupled equations. The method is demonstrated for 1 Hz Lg - and Sn -waves in a multilayered model for which there are 19 coupled modes.
The method is applicable to three-dimensional heterogeneity, and we are able to show that the interconversion between Love and Rayleigh waves, in the presence of gradients in seismic properties transverse to the propagation path, leads to a net rate of increase of the transverse components of the seismogram at the expense of the other components. 相似文献
9.
Summary. The long wavelength radiation patterns of P - and S -waves are determined for an elastic prestressed earth model. The prestress is treated as a perturbation of an isotropic medium. Non-zero first-order corrections are found to the eigenvalues and eigenvectors of the deviatoric seismic moment tensor. The radiation pattern given by a purely tangential dislocation is equivalent to a double couple contaminated by a dipolar term linear in the perturbation. 相似文献
10.
Toshikazu Odaka 《Geophysical Journal International》1984,76(2):497-513
Summary. A ray-theoretical approach is successfully employed for obtaining the relations between the intrinsic dissipation factors of P - and S -waves, Q α and Q β , and the apparent dissipation factors of toroidal and spheroidal oscillations, Q Tor and Q Sph These are given in quite simple forms and are expressed, to zero-order approximatiom which neglects the effect of reflection of waves at an interface and/or at a free surface), as where α and β are the P - and S -wave velocities and the integrals are evaluated long the surface to surface P - and S -rays.
Some numerical comparisons support the validity of these formulae for higher modes of toroidal and radial oscillations of a realistic earth model.
A first-order approximation reveals that the existence of a discontinuity in an earth induces a systematic fluctuation in normal-mode Q values for any given phase velocity as a function of frequency (or radial mode number). 相似文献
Some numerical comparisons support the validity of these formulae for higher modes of toroidal and radial oscillations of a realistic earth model.
A first-order approximation reveals that the existence of a discontinuity in an earth induces a systematic fluctuation in normal-mode Q values for any given phase velocity as a function of frequency (or radial mode number). 相似文献
11.
F. A. Dahlen 《Geophysical Journal International》1979,59(1):19-42
Summary. Exact spectra of a normal mode multiplet n Sl or n Tl on a non-rotating ellipsoidal earth are composed of l + 1 lines. Asymptotically, in the limit of large l , such spectra appear, however, as a single line or peak broadened by attenuation alone. The location within the multiplet of this single peak depends only upon the angle of inclination of the source-receiver great circle path to the axis of ellipsoidal symmetry. The appearance of a single peak is produced by the cancellation of nearby singlets. To assess the utility of the single peak approximation, exact and asymptotic synthetic spectra have been compared directly for a number of multiplets and for a variety of source-receiver configurations. Except in the immediate vicinity of the source and its antipode, the approximation appears to be satisfactory on an ellipsoidal earth down to about l ∼ 10. Additional studies will be required to determine the limits of validity on a laterally heterogeneous earth. 相似文献
12.
A numerical method is presented for calculating complete theoretical seismograms, under the assumption that the earth models have velocity, density and attenuation profiles which are arbitrary piece-wise continuous functions of depth only. Solutions for the stress-displacement vectors in the medium are expanded in terms of orthogonal cylindrical functions. Our method for solving the resulting two-point boundary value problems differs from that of other investigators in three ways. First, collocation is used in traditionally troublesome situations, e.g. for highly evanescent waves, at turning points, and in regions having large gradient in material properties. Second, in some situations (high frequencies and small gradients) P and S -waves decouple and we use a different solution method for each wave type, instead of trying to force a single method to find all solutions. For example, above the P - and S -waves turning points an approximate fundamental matrix may be used for each wave type. At the P -wave turning point, the fundamental matrix may be used for the S -wave components but collocation is used for the P -wave. Between the P - and S -wave turning points collocation is used for the evanescent P -wave and the fundamental matrix is used for the S -wave. At the S -wave turning point and below, collocation is used for both. Third, the computational algorithm chooses the appropriate solution method and depth domain upon which it is employed based upon a specified error tolerance and the known inaccuracies of the various approximations employed. Once solutions of the boundary value problems are obtained, a Fourier—Bessel transform is then applied to get back into the space-time domain. 相似文献
13.
Summary. The seismic structure has been measured to a depth of about 3 km along a 30 km seismic profile in east central Ireland. This profile is unusual in that it is the S -wave velocity—depth structure that has been measured to a degree of precision more normally associated with P -wave results. One reason for this is that the sources used were quarry blasts which generated strong S -waves and short-period surface waves but rather weak P -waves.
The results show a layer of Carboniferous limestone with shear velocity 2.65 km−1 s overlying a layer with a velocity of 3.06 km s−1 . This second layer was interpreted as Lower Palaeozoic strata (Silurian/Ordovician) since this velocity was evident in an inlier seen at the surface at the northern end of the line. A third refraction horizon, shear velocity 3.45 km s−1 and displaying a basinal structure, was also recognized. This may be Cambrian or Precambrian basement. 相似文献
The results show a layer of Carboniferous limestone with shear velocity 2.65 km
14.
J. B. Minster 《Geophysical Journal International》1978,52(3):503-524
Summary. We investigate one-dimensional waves in a standard linear solid for geophysically relevant ranges of the parameters. The critical parameters are shown to be T*= tu /Qm where t u is the travel time and Qm the quality factor in the absorption band, and τ−1 m , the high-frequency cut-off of the relaxation spectrum. The visual onset time, rise time, peak time, and peak amplitude are studied as functions of T* and τ m . For very small τ m , this model is shown to be very similar to previously proposed attenuation models. As τ m grows past a critical value which depends on T* , the character of the attenuated pulse changes. Seismological implications of this model may be inferred by comparing body wave travel times with a'one second'earth model derived from long-period observations and corrected for attenuation effects assuming a frequency independent Q over the seismic band. From such a comparison we speculate that there may be a gap in the relaxation spectrum of the Earth's mantle for relaxation times shorter than about one second. However, observational constraints from the attenuation of body waves suggest that such a gap might in fact occur at higher frequencies. Such a hypothesis would imply a frequency dependence of Q in the Earth's mantle for short-period body waves. 相似文献
15.
We have developed an inversion formuialion for velocity and attenuation structure using seismic attributes, including envelope amplitude, instantaneous frequency and arrival times of selected seismic phases. We refer to this approach as AFT inversion for amplitude, (instantaneous) frequency and time. Complex trace analysis is used to extract the different seismic attributes. The instantaneous frequency data are converted to t * using a matching procedure that approximately removes the effects of the source spectra. To invert for structure, ray-perturbation methods are used to compute the sensitivity of the seismic attributes to variations in the model. An iterative inversion procedure is then performed from smooth to less smooth models that progressively incorporates the shorter-wavelength components of the model. To illustrate the method, seismic attributes are extracted from seismic-refraction data of the Ouachita PASSCAL experiment and used to invert for shallow crustal velocity and attenuation structure. Although amplitude data are sensitive to model roughness, the inverted velocity and attenuation models were required by the data to maintain a relatively smooth character. The amplitude and t * data were needed, along with the traveltimes, at each step of the inversion in order to fit all the seismic attributes at the final iteration. 相似文献
16.
Ru-Shan Wu 《Geophysical Journal International》1985,82(1):57-80
Summary. In order to separate the scattering effect from the intrinsic attenuation, we need a multiple scattering model for seismic wave propagation in random heterogeneous media. In this paper, we apply radiative transfer theory to seismic wave propagation and formulate in the frequency domain the energy density distribution in space for a point source. We consider the cases of isotropic scattering and strong forward scattering. Some numerical examples are shown. It is seen that the energy density–distance curves have quite different shapes depending on the values of medium seismic albedo B 0 =ηs /(ηs +ηa ) where ηs is the scattering coefficient and ηa is the absorption coefficient of the medium. For a high albedo ( B > 0.5) medium, the energy–distance curve is of arch shape and the position of the peak is a function of the extinction coefficient of the medium ηe =ηs +ηa . Therefore it is possible to separate the scattering effect and the absorption based on the measured energy density distribution curves. 相似文献
17.
Zoltan A. Der Thomas W. McElfresh Anne O'Donnell 《Geophysical Journal International》1982,69(1):67-99
Summary. Studies of teleseismic P -and S -wave amplitudes and spectra in the 0.5–4 Hz band show large variations in the attenuative properties of the upper mantle under the United States. The data indicate that attenuation is greatest under the south-western United States including, but not confined to, the Basin and Range province. The lowest attenuation prevails under the north central shield regions. The north-eastern part of the country, consisting of New England and possibly including a larger area along the eastern seaboard, is characterized by moderate attenuation in the mantle.
The level of the high-frequency energy in short-period seismic waves and the differences between Q values derived from short-and long-period data indicate that Q is frequency dependent. The form of frequency dependence of t * compatible with the data in the 0.5–4 Hz range does not allow a rapid decrease of t * with increasing frequency. Rather it supports a gradual decrease covering the broader 0.1–4 Hz range. The curves of t * versus frequency, for shield-to-shield and mixed shield-to-western United States type paths are parallel with an average difference of 0.2 s in t * in the short-period band, but may diverge towards the long-period band. For both curves t *p is below 1 s. For shield-to-shield paths t *p must be below 0.5 s at 1 Hz. 相似文献
The level of the high-frequency energy in short-period seismic waves and the differences between Q values derived from short-and long-period data indicate that Q is frequency dependent. The form of frequency dependence of t * compatible with the data in the 0.5–4 Hz range does not allow a rapid decrease of t * with increasing frequency. Rather it supports a gradual decrease covering the broader 0.1–4 Hz range. The curves of t * versus frequency, for shield-to-shield and mixed shield-to-western United States type paths are parallel with an average difference of 0.2 s in t * in the short-period band, but may diverge towards the long-period band. For both curves t *
18.
Danny J. Harvey 《Geophysical Journal International》1981,66(1):37-69
Summary. A normal mode superposition approach is used to synthesize complete seismic codas for flat layered earth models and the P-SV phases. Only modes which have real eigenwavenumbers are used so that the search for eigenvalues in the complex wavenumber plane is confined to the real axis. In order to synthesize early P -wave arrivals by summing a number of'trapped'modes, an anomalously high velocity cap layer is added to the bottom of the structure so that most of the seismic energy is contained in the upper layers as high-order surface waves. Causality arguments are used to define time windows for which the resulting synthetic seismograms are close approximations to the exact solutions without the cap layer. The traditional Thomson—Haskell matrix approach to computing the normal modes is reformulated so that numerical problems encountered at high frequencies are avoided and numerical results of the locked mode approximation are given. 相似文献
19.
Summary. The paper gives the results of a study of the anisotropy of seismic wave velocities within the Ashkhabad test field in Central Asia. The anisotropy was studied by analysing variations in the values of apparent velocities of first arrivals for epicentral distances ranging from 30 to 130 km and by analysing the delays (Δ ts1 -s2 ) between the arrival times of shear waves with different polarizations.
The velocities of P -waves vary with azimuth from 5.3 to 6.27 km s-1 and the velocities of S -waves vary from 3.15 to 3.5 km s-1 .
The delay times Δ tS1 - S2 depend on the direction of the propagation. The character of the variation of the propagation velocity of the longitudinal wave, the presence of two differently polarized shear waves S 1 and S 2 propagating at different velocities, and the character of the distribution of Δ tS1 - S2 on the stereogram suggest that the symmetry of the anisotropic medium is close to hexagonal with a nearly horizontal symmetry axis coinciding with the direction of maximal velocity. The azimuth of the symmetry axis of the medium is 140° and coincides with the direction of geological faults. 相似文献
The velocities of P -waves vary with azimuth from 5.3 to 6.27 km s
The delay times Δ t
20.
Summary. We report the initial results of our attempts to obtain theoretical seismograms for direct comparison with the experimental time series obtained with the long-period instruments of the WWSSN. The entire theoretical seismogram, including both body waves and surface waves, can be generated for a spherical, anelastic earth by simple inverse Fourier transformation of the sum of the propagating fundamental and higher-mode surface waves. The key to success in reproducing the WWSSN records involves the number of modes, and the minimum period used in these computations; here we use eight modes and a minimum period of 2 s. Efficient computational algorithms make it possible to handle up to 2000 frequency points for each mode; approximately 200 layers are used to model the radial heterogeneity of the earth; attenuation is treated exactly. Examples are given of the SH theoretical seismograms resulting from dislocation sources buried at various depths in the Earth. 相似文献