共查询到20条相似文献，搜索用时 46 毫秒
1.
Susan Friedlander 《Geophysical Journal International》1989,96(2):245-252
Summary. Boundary layer techniques are used to examine the dissipative decay of an internal oscillation that is a member of the inviscid spectrum of normal modes for a rotating fluid shell stratified under a radially directed gravitational field. A formula is derived for the decay factor on the so-called homogeneous spin-down time-scale. Estimates are obtained for the size of the decay factor as a function of wavelength, a function of the frequency and a function of a parameter A which measures the ratio of the stratification strength to the rotation strength. It is shown that all modes decay on the spin-down time-scale. The results are interpreted in the context of a model for the Earth's fluid core. It is observed that the presence of regions of unstable stratification may increase the decay rate for oscillations at frequencies less than twice the rotation frequency. 相似文献
2.
Internal oscillations in the Earth's fluid core 总被引：4，自引：0，他引：4
Susan Friedlander 《Geophysical Journal International》1985,80(2):345-361
3.
Peter Olsen 《Geophysical Journal International》1977,51(1):183-215
This paper investigates possible long-period oscillations of the earth's fluid outer core. Equations describing free oscillations in a stratified, self-gravitating, rotating fluid sphere are developed using a regular perturbation on the equations of hydrodynamics. The resulting system is reduced to a finite set of ordinary differential equations by ignoring the local horizontal component of the earth's angular velocity vector, Ω, and retaining only the vertical component. The angular dependence of the eigensolutions is described by Hough functions, which are solutions to Laplace's tidal equation.
The model considered here consists of a uniform solid elastic mantle and inner core surrounding a stratified, rotating, inviscid fluid outer core. The quantity which describes the core's stratification is the Brunt—Väisälä frequency N , and for particular distributions of this parameter, analytical solutions are presented. The interaction of buoyancy, and rotation results in two types of wave motion, the amplitudes of which are confined predominantly to the outer core: (1) internal gravity waves which exist when N2 > 0, and (2) inertial oscillations which exist when N 2 <4Ω2 . For a model with a stable density stratification similar to that proposed by Higgins & Kennedy (1971), the resulting internal gravity wave eigenperiods are all at least 8 hr, and the fundamental modes have periods of at least 13 hr. A model with an unstable density stratification admits no internal gravity waves but does admit inertial oscillations whose eigenperiods have a lower bound of 12hr. 相似文献
The model considered here consists of a uniform solid elastic mantle and inner core surrounding a stratified, rotating, inviscid fluid outer core. The quantity which describes the core's stratification is the Brunt—Väisälä frequency N , and for particular distributions of this parameter, analytical solutions are presented. The interaction of buoyancy, and rotation results in two types of wave motion, the amplitudes of which are confined predominantly to the outer core: (1) internal gravity waves which exist when N
4.
The concept of a deformation of a simple, non-rotating, spherically symmetric earth model with a fluid outer core, although it is a highly artificial physical situation, provides a useful computational algorithm that allows one lo determine analytically modes of vibration without any Love-number theory. In particular, on these analytically determined modes, we impose regularity conditions at the centre and boundary conditions at the surface, as well as conditions of continuity at the inner-core-outer-core boundary and at the core-mantle boundary. They lead to an eigenvalue equation for the frequency of oscillation. The range of frequencies obtained in this way for different earth models gives an indication of the influence of compressibility and non-homogeneity on the spectrum of eigenfrequencies. 相似文献
5.
Summary. The introduction of Rayleigh friction and Newtonian cooling into the dynamical problem of determining the excitation of the normal modes of oscillation of an earth model with a fluid core by a transient earthquake source is shown to provide a fully satisfactory resolution and a clear physical explanation of the difficulties and paradoxes which have arisen in previous treatments of the corresponding static deformation problem. The source of the previous difficulties is that the dissipation-free limit is associated with an essential singularity in the static response, unless the stratification in the core is neutral. This singularity, in turn, exists because the eigenfrequency spectrum of any earth model with a non-neutrally stratified core has an accumulation point at zero frequency. 相似文献
6.
Summary. We give a systematic formulation and a rigorous justification of a perturbation technique for the computation of the eigenvalues and eigenfunctions of Love waves (and toroidal oscillations by an appropriate change for variables) in an anelastic medium with a constitutive law modelling geophysical media of current interest such as the Kelvin—Voigt Solid, the Maxwell Solid, the Standard Linear Solid, and the Standard Linear Solid with a continuous spectrum of relaxation times. We develop expressions relating the eigenvalues of eigenfunctions for Love waves in a continuously varying vertically stratified anelastic half-space to the corresponding elastic eigenvalues and eigenfunctions. Analytically, our correspondence principle has the form of a regular perturbation expansion in terms of a parameter for both the eigenvalues and eigenfunctions. The identification of ɛ is motivated by the dissipativity principle of viscoelasticity theory. Moreover, we show that our correspondence principle applies respectively only in the high and low frequency range for the Maxwell and Kelvin—Voigt Solids. Outside of the applicable range of frequencies, our correspondence principle yields no useful information. For the family of Standard Linear Solids it is uniformly applicable for all non-zero frequencies.
We also derive an explicit formula to estimate the radius of convergence of our perturbation expansions. This estimate of the radius of convergence for each eigenvalue and eigenfunction is functionally defined by the constitutive model for the anelastic medium. The estimate is frequency dependent and depends on the separation distance between the eigenvalue and the remainder of the spectrum of the corresponding elastic problem. 相似文献
We also derive an explicit formula to estimate the radius of convergence of our perturbation expansions. This estimate of the radius of convergence for each eigenvalue and eigenfunction is functionally defined by the constitutive model for the anelastic medium. The estimate is frequency dependent and depends on the separation distance between the eigenvalue and the remainder of the spectrum of the corresponding elastic problem. 相似文献
7.
C. Sozou 《Geophysical Journal International》1997,130(1):151-156
Laplace's tidal equations for the case of an ocean of constant depth bounded by meridians were considered by two authors at a specific frequency as an eigenvalue problem in the azimuthal wavenumber. A finite spectrum of eigenwavenumbers was found. That eigenvalue problem is re-examined by means of asymptotic techniques and numerical integration of the governing equation of the problem. At low frequencies a formula connecting the frequency and the number of eigensolutions is established. It is shown that at a given frequency the spectrum of eigenwavenumbers is wider than that reported, but (for this type of solution) the meridional boundary conditions are satisfied approximately only for the case of very low frequencies. 相似文献
8.
Summary. The severity of the effect of the Earth's rotation on the transverse motions within the fluid core of the Earth is examined. It is shown that, for any model of the fluid core, the formalism adapted from free oscillation theory is applicable only for periods less than 12 hr. In the limiting case, as the frequency is decreased to 2 cycle day-1 , all modes of response in the fluid are excited to the same order. 相似文献
9.
Roger A. Hansen 《Geophysical Journal International》1982,70(1):155-172
Summary. Recently, time domain methods have been shown to be advantageous in determining the quality of observations of terrestrial eigenvibrations. Complex demodulation has been used in estimating amplitude, period, decay constant Q and phase. Non-linear regression in the frequency domain yields formal uncertainties in each estimate. A crucial problem arises in isolating neighbouring modes of nearly the same frequency and comparable amplitude. Complex demodulation displays can be used to identify interferences such as beating. In such cases, the assumption of stationarity is violated in the regression analysis yielding biased results. Improved resolution has now been obtained by formulating the regression scheme to estimate simultaneously small sets of neighbouring spectral peaks so that stationarity is not violated. Under the assumption of stationarity this procedure becomes optimal in a statistical sense. A general analysis of variance serves to indicate the amount of correlation that exists between estimated parameters of neighbouring modes as well as the relative information that is supplied by each Fourier transform point to the overall system of equations. The covariance matrix indicates that there is no linear correlation between spectral peaks when their frequencies are separated by 5 per cent. There are, however, significant correlations when two frequencies differ by 0.5 per cent. The result is that overtone modes very near in frequency to fundamental modes can, under certain conditions, be resolved with a non-linear regression technique, although parameter uncertainties are underestimated in general. 相似文献
10.
11.
Summary. The response of the Earth to an earthquake is a transient that is effectively zero several days after the event. A recording of the event, of finite duration in time, has a Fourier spectrum that is an entire, or integral, analytic function of frequency. We present a very simple procedure for computing the Fourier spectrum as a function of complex frequency; the analytically continued spectrum. By investigating the properties of the analytically continued spectrum we show how to extract high- Q modes, how to estimate Q either from the amplitude or from the width of a resonance function, and how to improve the resolution of splitting to the theoretical maximum. Examples of these procedures, using observed data, are presented. 相似文献
12.
The free oscillations of an anelastic aspherical earth 总被引：1，自引：0，他引：1
F. A. Dahlen 《Geophysical Journal International》1981,66(1):1-22
Summary. Some century-old results, due to Rayleigh and Routh, have been adapted to investigate the normal mode eigenfrequencies and eigenfunctions of an earth with laterally variable anelasticity and to determine the transient response of such an earth to earthquakes. Using degenerate perturbation theory, the eigenfrequencies are found to first order and the associated eigenfunctions to zeroth order in the small deviations of the Earth away from a spherical perfectly elastic reference earth model. Both the eigenfrequencies and the eigenfunctions are complex and, in addition, the latter are not mutually orthogonal, reflecting the non-Hermitian character of the normal mode eigenvalue problem. The effect of laterally heterogeneous attenuation on the shape of an unresolved multiplet spectrum has been investigated in the surface-wave geometrical-optics limit. Singlet cancellation leads in that limit to the appearance of a single resonance peak whose decay rate or apparent Q −1 depends only on the average attenuation structure underlying the source—receiver great-circle path. 相似文献
13.
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
14.
戈壁风蚀面与植被覆盖面地表性质粗糙度长度的确定 总被引：9，自引：5，他引：4
以Monin-Obukhov相似性理论为基础, 利用量纲分析法分别推导出不同层结稳定度下确定戈壁风蚀面与植被覆盖面空气动力学参数的物理模型, 并利用该模型研究了粗糙度长度与粗糙元性质, 流经近地层流体特征以及大气层结稳定度之间的关系。得出以下结论: 戈壁风蚀面上空气动力学粗糙度长度与砾石粒径、高度、覆盖度、自由风速、摩擦速度以及大气层结稳定度有关; 植被覆盖面空气动力学粗糙度长度取决于植被类型、植被高度、覆盖度、零平面位移高度、自由风速、摩擦速度以及大气层结稳定度。 相似文献
15.
J. B. Minster 《Geophysical Journal International》1978,52(3):479-501
Summary. The transient and impulse responses (Green's function) for onedimensional wave propagation in a standard linear solid are calculated using a Laplace Transform method. The spectrum of relaxation times is chosen so as to model a constant Q medium within an absorption band covering a broad frequency range which may be chosen so as to include the seismic frequencies. The inverse transform may be evaluated asymptotically in the limit of very long propagation times using the saddle point method. For shorter propagation times the method of steepest descent may be modified so as to yield an accurate first motion approximation. The character of the small amplitude precursor to the large amplitude Visible' signal is investigated analytically. It is shown that the signal velocity is intermediate between the high-frequency ('unrelaxed') and the low-frequency ('relaxed') limits of the phase velocity. 相似文献
16.
Summary A uniformly valid linear viscoelastic rheology is described which takes the form of a 'generalized' Burgers' body and which appears capable of reconciling the behaviour of the Earth's mantle across the complete spectrum of geodynamic time-scales. This spectrum is bracketed by the short time-scales of body wave and free oscillation seismology on which anelastic effects are dominant, and the long time-scale of mantle convection on which the Earth behaves viscously. The parameters of the model which control the viscous response are fixed by post-glacial rebound data whereas those which govern the anelasticity are to be determined by fitting the model to observations of seismic Q. The paper is concerned primarily with a discussion of the normal mode spectrum of the Earth as a generalized Burgers' body. Focusing upon the homogeneous model, it includes an initial analysis of the accuracy of first-order perturbation theory as a method of calculating the respective Q s of the elastic gravitational free oscillations. Also considered are the quasi-static modes of relaxation which only exact eigenanalysis can reveal. The importance of these modes is assessed within the context of a discussion of the effect of viscoelasticity upon the efficiency of Chandler wobble excitation. 相似文献
17.
Joint Inversion of Geophysical Data 总被引：6，自引：0，他引：6
《Geophysical Journal International》1975,42(3):977-991
Summary. By jointly inverting several different kinds of geophysical measurements at a site we avoid some of the ambiguity inherent in the individual methods. We show how this can be done for the combination of DC resistivity and magnetotelluric measurements on a layered medium by considering a simple 3-layer model. The combination resolves the resistivity of the thin resistive second layer, even though neither of the two methods can do so alone.
The method is then applied to field data from a shallow sedimentary basin. A blind zone occurs beneath a thick near-surface conductive shale. By a study of the eigenvalue structure of the model it can be seen that resolution in this zone would be slightly enhanced by higher frequency magnetotelluric data, but additional DC data at larger spacing would yield no improvement. 相似文献
The method is then applied to field data from a shallow sedimentary basin. A blind zone occurs beneath a thick near-surface conductive shale. By a study of the eigenvalue structure of the model it can be seen that resolution in this zone would be slightly enhanced by higher frequency magnetotelluric data, but additional DC data at larger spacing would yield no improvement. 相似文献
18.
Z. R. Peng 《Geophysical Journal International》1997,131(3):607-617
This article investigates the effects of a mushy inner core boundary on the eigenperiods of the Slichter modes for a simple, but realistic, earth model (rotating, spherical configuration, elastic inner core and mantle, neutrally stratified, inviscid, compressible liquid core). It is found that the influence of the mushy boundary layer is substantial compared with some other effects, such as those from elasticity of the mantle, non-neutral stratification of the liquid outer core and ellipticity of the Earth and centrifugal potential. The results obtained here may set a lower bound on the eigenperiods of the Slichter modes for a realistic earth model. For example, for a PREM model, the lower bound of the central period of the Slichter modes should be about 5.3 hr. 相似文献
19.
Summary. We present a table of rotational and elliptical splitting parameters for earth model 1066A, including all terms through second order in rotation and first order in ellipticity. An algorithm for calculating the second-order Coriolis splitting by summing over all modes which are coupled to first order is given in detail. Coupling to secular (or zero frequency) modes, as well as the usual seismic modes, can provide significant contributions to these splitting parameters. 相似文献
20.
Multilayer, spherically stratified, self-gravitating relaxation models with a large number of layers (more than 100) can be dealt with analytically. Relaxation processes are studied for both Heaviside surface loads and tidal forcings. Simulations of the relaxation process of a realistic earth model with an incompressible Maxwell rheology show that models containing about 30 to 40 layers have reached continuum limits on all timescales and for all harmonic degrees up to at least 150 whenever an elastic lithosphere is present, irrespective of the viscosity profile in the mantle. In particular, fine-graded stratification of the shallow layers proves to be important for high harmonic degrees in these models. The models produce correct long-time (fluid) limits. It is shown that differences in the transient behaviour of the various models are due to the applied volume-averaging procedure of the rheological parameters. Our earlier proposed hypothesis that purported shortcomings in the fundamental physics of (discrete) normal-mode theory are artificial consequences of numerical inaccuracies, theoretical misinterpretations and the use of incomplete sets of normal modes is reinforced by the results presented. We show explicitly that the models produce both continuous behaviour resulting from continuous rheological stratifications and discrete behaviour resulting from sharp density contrasts, as at the outer surface and the core-mantle boundary. The differences between volume-averaged models and fixed-boundary contrast models are outlined. Reducing many-layer models with a volume-averaging procedure before employing a normal mode analysis is both economical and highly accurate on all timescales and for all spherical harmonic degrees. The procedure minimizes the chances of missing contributing modes, while using models with more layers will not result in any substantial increase of accuracy. 相似文献