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1.
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 SphThese 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   

2.
Summary An extension of the Love-Larmor theory to a low-loss unelastic earth model, leads to the surprisingly simple approximation
   
where τs= 447.4 sidereal day is the static wobble period, τR= 306 sidereal day is the rigid-earth wobble period and τw= 433 sidereal day is the observed Chandler period. Q W, Q μ are the respective average Q values of the wobble and the Earth's mantle at τW. The known numerical factor F is only slightly dependent on the Earth structure.  相似文献   

3.
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 Q c 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   

4.
Seismic sources with observable glut moments of spatial degree two   总被引：1，自引：0，他引：1  
Let ζΛ and r Λ. be the hypocentral position and time of an extended indigenous seismic source. Backus showed that the force moment tensors of the source, Γ( m +1, n )(ζΛ, r Λ), determine and are determined by the motion which the source produces. For small m + n , only the long-period motion is relevant. The glut moment tensor Λ( m,n ) (ζΛ, r Λ.) can be calculated uniquely from γ( m +1, n )(ζΛ r Λ) only if m = 0 or m = 1. The tensor G =Λ(2,0)(ζΛ) gives the spatial variance tensor WΛ of the source, and WΛ. roughly describes the size, shape and orientation of the source region. Therefore the failure of the observed F =Γ(3,0)(ζΛ) to determine G uniquely is of seismological interest. In the present paper we show that F determines G uniquely if we assume the source to be a simple straight line source (SSLS) or an ideal fault in an isotropic medium with isotropic prestress (IFIMIP). We give tests on F which determine whether it can come from a SSLS, from an IFIMIP or from a simple plane surface source (SPSS). If we assume the source to be a SPSS then knowing F and the fault plane determines G to within an unknown scalar multiple of a certain tensor tangent to the fault plane. Moreover F determines the fault plane uniquely unless F can come from a SSLS. If it can, then F determines this virtual source line uniquely, and F permits the fault plane to be any plane containing the virtual source line.  相似文献   

5.
Summary. Normal mode theory, extended to the slightly laterally heterogeneous earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love wave (200–500 s) for the Earth's lateral heterogeneity at l = 2 and a spherically symmétric anelasticity ( Q μ) structure. The data are from the Global Digital Seismograph Network (GDSN). The l =2 pattern is very similar to the results of other studies that used either different méthods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analysed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5 per cent in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range cannot constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.
The calculated modal Q values for the obtained Q μ model fall within the error bars of the observations. The result demonstrates the discrepancy of Rayleigh wave Q and Love wave Q and indicates that care must be taken when both Rayleigh and Love wave data, including amplitude information, are inverted simultaneously.
Anomalous amplitude inversions of G2 and G3, for example, are observed for some source-receiver pairs. This is due to multipathing effects. One example near the epicentral region, which is modelled by the obtained l = 2 heterogeneity, is shown.  相似文献   

6.
Fundamental-mode Rayleigh and Love waves generated by several earthquakes situated along great-circle paths between pairs of seismograph stations have been analysed to obtain coefficients of attenuation, group velocities, phase velocities, and specific quality factors in the period range 18–80s in two regions of the South American continent. One set of paths crosses the shield region which lies on the eastern coast and another set traverses the mountainous region inland. the average attenuation coefficient values are clearly higher in the tectonically active western region throughout the entire period range than in the eastern or shield region.
Inversion of the attenuation data yielded shear wave internal friction ( Q -1β) models as a function of depth in the crust and upper mantle in both regions. A low- Q zone below the lithosphere is prominent in both regions. the results show that substantial variations of Q β occur in the two regions of South America. the Qβ values were found to be inversely related to the heat flow values or to the temperature.  相似文献   

7.
This paper presents a method to invert underside-reflection ( P d P or S d S arrivals) data for lateral depth variations of upper-mantle discontinuities, combining traveltime and amplitude data. The method greatly improves the resolution of small-scale undulations obtained by existing imaging methods and does not suffer from the long-wavelength biases that are likely to be present in currently available models. Existing inversion methods account for the large size of the Fresnel zone of underside reflections, but not for its complexity, arising from the mini-max traveltime nature of PP- and SS -related waves. This neglect results in long-wavelength artefacts from small-scale undulations of the discontinuities, obscuring true long-wavelength depth variations. The inversion method presented in this paper uses a complex-valued sensitivity kernel, derived from the representation of underside reflections through a Kirchhoff integral formulation. The sensitivity kernel accounts for the varying sensitivity of the waveforms to discontinuity structure over the Fresnel zone. The method is applied to a large, synthetic data set. The data set consists of P d P amplitudes and traveltimes. The results show that the new inversion method resolves depth variations on a lateral scale that is smaller than the size of the Fresnel zone of individual underside reflections (but larger than the dominant wavelength), retaining the resolution of large-scale variations. The results presented here suggest that the discontinuity depth variations induced by slab penetration of the 670 discontinuity could be resolved by current broad-band P 670 P data sets.  相似文献   

8.
Shock-compressed MgO radiates thermally at temperatures between 2900 and 3700 K in the 170–200 GPa pressure range. A simple energy-transport model of the shocked-MgO-targets distinguishes between different shock-induced radiation sources in these targets and provides estimates of spectral absorption-coefficients, α ΛMgO, for shocked MgO (e.g. at 203 GPa, α ΛMgO˜ 630, 7500, 4200 and 3800 m−1, at 450, 600, 750 and 900 nm, respectively). The experimentally inferred temperatures of the shock-compressed states of MgO are consistent with temperatures calculated for MgO assuming that (1) it deforms as an elastic fluid, (2) has a Dulong-Petit value for specific heat at constant volume in its shocked state, and (3) undergoes no phase transformation below 200 GPa.  相似文献   

9.
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   

10.
We explore the inner dynamics of daily geoelectrical time series measured in a seismic area of the southern Apennine chain (southern Italy). Autoregressive models and the Higuchi fractal method are applied to extract maximum quantitative information about the time dynamics from these geoelectrical signals. First, the predictability of the geoelectrical measurements is investigated using autoregressive models. The procedure is based on two forecasting approaches: the global and the local autoregressive approximations. The first views the data as a realization of a linear stochastic process, whereas the second considers the data points as a realization of a deterministic process, which may be non-linear. Comparison of the predictive skills of the two techniques allows discrimination between low-dimensional chaos and stochastic dynamics. Our findings suggest that the physical systems governing electrical phenomena are characterized by a very large number of degrees of freedom and can be described only with statistical laws. Second, we investigate the stochastic properties of the same geoelectrical signals, searching for scaling laws in the power spectrum. The spectrum fits a power law P (  f )∝  f  −α , with the scaling exponent α a typical fingerprint of fractional Brownian processes. In this analysis we apply the Higuchi method, which gives a linear relationship between the fractal dimension D Σ and the spectral power law scaling index α : D Σ=(3− α )/2. This analysis highlights the stochastic nature of geoelectrical signals recorded in this seismic area of southern Italy.  相似文献   

11.
Observation of Coriolis coupled modes below 1 mHz   总被引：3，自引：0，他引：3  
We present observations of spectral energy at toroidal mode frequencies in vertical seismic recordings of the 1998 Balleny Islands earthquake. Since toroidal modes on a spherically symmetric, nonrotating Earth have horizontally polarized particle motion these observations call for an explanation. We first rule out local and instrumental effects as being responsible for the verticalcomponent signal of the toroidal modes 0 T 3 (0.59 mHz) and 0 T 4 (0.77 mHz). The global effects that we consider are general heterogeneous mantle structure, ellipticity of figure and rotation. We find that rotation through Coriolis coupling of loworder spheroidal and toroidal oscillations is the dominant mechanism.  相似文献   

12.
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   

13.
Summary. The inverse gravity potential problem consists in the determination of the form and the density of the body by its exterior gravity potential. We describe two similar classes of bodies for which this problem has a unique constructive solution.
(1) The first class contains the cylindrical bodies with finite length, arbitrary form of section and ρ( R , ø, z) =ρ1( z )ρ2( R , ø) density distribution, where z is the cylindrical coordinate; R , ø are the polar coordinates in a section plane. This class is important for prospecting geophysics in that it allows us to determine in a unique and constructive way, the function ρ1( R , ø), the length, form and orientation of the cylinder if we know the function ρ1( z ) and the exterior potential. The classical moment problem of functions is the basis for the solution of this problem.
(2) The analogous problem for the class of the spherical cylinders, or bodies bounded by arbitrary similar sections of two different concentric spheres and the radial lateral surface, appears when bodies of planetary size are studied. (An example of these bodies would be the Moon mascons.) The density distribution of these cylinders is ρ(τ, θ, ø) =ρ1(τ)ρ2(θ, ø) where τ, θ, ø are the spherical coordinates. The function ρ1(θ, ø), length and form of spherical sections can be uniquely determined by exterior potential if we know the function ρ1(τ). We propose a new constructive method for harmonic continuation of the gravity potential into the region containing the perturbing masses for the solution of the problem.  相似文献   

14.
We have studied the response of normal modes to perturbations in inner-core shear velocity and attenuation, using fully coupled mode synthetics. Our results indicate that (i) mode pairs   n S l – n ±1 S l   are strongly coupled by anelasticity, (ii) this coupling causes shear velocity perturbations to strongly affect the Q values of modes through exchange of inner-core characteristics, (iii) there is no evidence for a weakly attenuating inner core in shear, and (iv) the discrepancy between attenuation models returned from normal modes and body waves is small. These results suggest that inversions for inner-core attenuation and shear velocity should be performed simultaneously and should take account of the strong cross-coupling due to attenuation.  相似文献   

15.
Summary. Advantages of using the mode in analysis of palaeomagnetic vectors are discussed, and a computer technique is described for contouring and precisely locating the modes of vector distributions that may be highly skewed. In contrast to conventional determinations of the mode, unit vectors from a given data set are treated not as discrete points, but as identical Fisherian probability density functions defined (at an angle θ from the unit vector) by: p = exp [ sk (cos θ– 1)], where kis the estimate of the Fisherian concentration parameter, and s is an arbitrarily assigned 'smoothing parameter'. A grid, representing the cumulative probability distribution of the total sample of vectors, is contoured to provide a graphical display of the distribution around the most probable value, the mode. By repeatedly contouring the same sample of vectors with successively larger values of s, and by treating the mode as a vector with length given by the total probability value at the mode, 'progressive modal diagrams' can be constructed, to aid in determining the stable position of the mode of skewed distributions. In addition, a new statistic β95 is suggested as an error estimator for the mode. The statistic β95 is derived from the largest subset of the total sample that has a mean identical with the mode of the total sample; this statistic is defined as the Fisherian half-angle of the cone of 95 per cent confidence for the mean of this subset.  相似文献   

16.
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   

17.
We derive asymptotic formulae for the toroidal and spheroidal eigenfrequencies of a SNREI earth model with two discontinuities, by considering the constructive interference of propagating SH and P-SV body waves. For a model with a smooth solid inner core, fluid outer core and mantle, there are four SH and 10 P-SV ray parameters regimes, each of which must be examined separately. The asymptotic eigenfrequency equations in each of these regimes depend only on the intercept times of the propagating wave types and the reflection and transmission coefficients of the waves at the free surface and the two discontinuities. If the classical geometrical plane-wave reflection and transmission coefficients are used, the final eigenfrequency equations are all real. In general, the asymptotic eigenfrequencies agree extremely well with the exact numerical eigenfrequencies; to illustrate this, we present comparisons for a crustless version of earth model 1066A.  相似文献   

18.
We modify the receiver-functions stacking technique known as velocity spectrum stacking (VSS) so as to estimate combinations of velocity model ( VP and VS ) and depth that stack the Ps conversion from upper-mantle discontinuities most coherently. We find that by estimating the differences in the depths to the 660 and 410 km discontinuities using velocities that maximize the stacked amplitudes of P410s and P660s phases we can estimate the thickness of the transition zone more accurately than the depths to either of these discontinuities. We present two examples indicating that the transition zone beneath Obninsk, Russia, is 252±6 km thick and that beneath Pasadena, California, is only 220±6 km thick.  相似文献   

19.
Summary. A new asymptotic formula is obtained for the spectrum of an isolated normal mode multiplet nSl or nTl , with n ≪ l , on a laterally heterogeneous Earth. The principal feature of this formula is that it is uniformly valid on the Earth's surface, including near the epicentre and its antipode. The formal conditions for its validity are that | δm / m 0|≪ 1 and s max≪ l ≪ s min| δm / m 0|–1, where | δm / m 0| is the relative magnitude of the lateral heterogeneity, and s min and s max are the minimum and maximum significant degrees in its spherical harmonic expansion. As well as providing a basis for the geographical interpretation of near-epicentral or near-antipodal long-period recordings, the new formula also unifies the asymptotic theory and adds insight into the phenomena which govern the details of multiplet spectra in general.  相似文献   

20.
Summary. A technique based on ray asymptotics has been developed to propagate complex spectra of elastic normal mode surface waves in a waveguide with material and geometrical properties varying smoothly in the lateral directions. In the technique, the original problem defined in the unstretched coordinates has been transformed into an eiconal equation as well as into a certain number of transport equations defined in stretched coordinates.
The solution of the eiconal equation is equal to the solution of the eigenproblem of the eiconal operator A0. Due to the self-adjointness of A0, in each of the relevant local inner product spaces, LIPS, the solution of the eigenproblem, A0ψ= v ψ results in the set { v t} of real local eigenvalues and in the orthonormal system {ψt} of local eigenvectors.
As the Hamiltonian function of an initial value problem, each eigenvalues gives birth to a bicharacteristic curve as well as to the related ray. The introduction of the rays induces connections between the vertical cross-sections of the waveguide.
Finally, for each asymptotic order j , the LIPS-valued transport equations are reduced to a set of matricial propagation equations in the local spectral amplitude vectors, LSAVs. Consequently, a knowledge of the initial conditions at a vertical cross-section makes it possible to propagate the LSAVs along the rays of the relevant modes. However, to complete the propagation one needs, in addition to the initial values, information about certain additional quantities, non-diagonal terms of order j , diagonal terms of orders lower than j and the auxiliary boundary terms of orders from 1 to j . The treatment has been completed by the propagation of the modal phases along the relevant rays.  相似文献   

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