共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
Susan Friedlander 《Geophysical Journal International》1987,89(2):637-655
Summary. Small amplitude oscillations of a rotating, density-stratified fluid bounded by a spherical shell are examined. No restrictions are placed on the thickness of the shell. The internal mode spectrum is examined in the complete rotation-stratification parameter range including the regime that is appropriate for a plausible stratification distribution in the Earth's fluid core. A mathematical model is derived in terms of an eigenvalue PDE of mixed type. The existence of oscillatory solutions is exhibited in the limits of no rotation and no stratification. The frequency spectrum is extended asymptotically away from these limiting cases. A reduction in the complexity of the PDE for modes oscillating at the inertial frequency is exploited. A variational formulation is constructed in which the stratification parameter is treated as an eigenvalue of the system for fixed wave frequency. The spectral information is again extended asymptotically away from these 'accessible' points. Although the PDE reduces to Laplace's tidal equations (LTE) only under stringent parameter restrictions, it is observed that aspects of the behaviour of low frequency LTE modes are reproduced in the general model. 相似文献
3.
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
4.
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
5.
Raul Madariaga 《Geophysical Journal International》1977,51(3):625-651
We present a theory for the radiation of high-frequency waves by earthquake faults. We model the fault as a planar region in which the stress drops to the kinematic friction during slip. This model is entirely equivalent to a shear crack. For two-dimensional fault models we show that the high frequencies originate from the stress and slip velocity concentrations in the vicinity of the fault's edges. These stress concentrations radiate when the crack expands with accelerated motion. The most efficient generation of high-frequency waves occurs when the rupture velocity changes abruptly. In this case, the displacement spectrum has an ω-2 behaviour at high frequencies. The excitation is proportional to the intensity of the stress concentration near the crack tips and to the change in the focusing factor due to rupture velocity. We extend these two-dimensional results to more general three-dimensional fault models in the case when the rupture velocity changes simultaneously on the rupture front. Results are similar to those described for two-dimensional faults. We apply the theory to the case of a circular fault that grows at constant velocity and stops suddenly. The present theory is in excellent agreement with a numerical solution of the same problem.
Our results provide upper bounds to the high-frequency radiation from more realistic models in which rupture velocity does not change suddenly. The ω-2 is the minimum possible decay at high frequencies for any crack model of the source. 相似文献
Our results provide upper bounds to the high-frequency radiation from more realistic models in which rupture velocity does not change suddenly. The ω
6.
The frequency-domain version of waveform tomography enables the use of distinct frequency components to adequately reconstruct the subsurface velocity field, and thereby dramatically reduces the input data quantity required for the inversion process. It makes waveform tomography a computationally tractable problem for production uses, but its applicability to real seismic data particularly in the petroleum exploration and development scale needs to be examined. As real data are often band limited with missing low frequencies, a good starting model is necessary for waveform tomography, to fill in the gap of low frequencies before the inversion of available frequencies. In the inversion stage, a group of frequencies should be used simultaneously at each iteration, to suppress the effect of data noise in the frequency domain. Meanwhile, a smoothness constraint on the model must be used in the inversion, to cope the effect of data noise, the effect of non-linearity of the problem, and the effect of strong sensitivities of short wavelength model variations. In this paper we use frequency-domain waveform tomography to provide quantitative velocity images of a crosshole target between boreholes 300 m apart. Due to the complexity of the local geology the velocity variations were extreme (between 3000 and 5500 m s−1 ), making the inversion problem highly non-linear. Nevertheless, the waveform tomography results correlate well with borehole logs, and provide realistic geological information that can be tracked between the boreholes with confidence. 相似文献
7.
青海沙利克山祁连圆柏千年树轮宽度序列的变化特征 总被引：6，自引：1，他引：5
利用功率谱、奇异谱和小波分析等方法对在青海沙利克山建立的两条祁连圆柏 (Sabi naprzewalskiiKom )千年树轮宽度序列进行了变化特征的分析 ,发现在低频变化上都存在2 0 0年的最显著周期和百年左右的显著周期 ;各种周期存在不同的演变特征 ,2 0 0年周期在15～ 17世纪最为盛行 ,百年左右的周期变化自 18世纪初以来较为突出。 15世纪下半叶是轮宽序列千年来最突出的低值期 ,它主要体现了 2 0 0年周期的变化 ,而 2 0世纪后期的高值区则主要是百年左右周期变化的作用。轮宽序列的低频变化与太阳活动的长期变化之间存在较好的对应关系 ,说明祁连圆柏年轮宽度序列所指示的气候低频变化可能受太阳活动的影响。 相似文献
8.
The Resolving Power of Gross Earth Data 总被引：22，自引：0，他引：22
A gross Earth datum is a single measurable number describing some property of the whole Earth, such as mass, moment of interia, or the frequency of oscillation of some identified elastic-gravitational normal mode. We show how to determine whether a given finite set of gross Earth data can be used to specify an Earth structure uniquely except for fine-scale detail; and how to determine the shortest length scale which the given data can resolve at any particular depth. We apply the general theory to the linear problem of finding the depth-variation of a frequency-independent local Q from the observed quality factors Q of a finite number of normal modes. We also apply the theory to the non-linear problem of finding density vs depth from the total mass, moment, and normal-mode frequencies, in case the compressional and shear velocities are known. 相似文献
9.
Methodologies for estimating t*(f) from short-period body waves and regional variations of t*(f) in the United States 总被引：1，自引：0，他引：1
Summary. In this paper we discuss some aspects of estimating t * from short-period body waves and present some limits on t* (f) models for the central and south-western United States (CUS and SWUS). We find that for short-period data, with frequencies above 1 or 2 Hz, while the average spectral shape is stable, the smaller details of the spectra are not; thus, only an average t *, and not a frequency-dependent t *, can be derived from such information. Also, amplitudes are extremely variable for short-period data, and thus a great deal of data from many stations and azimuths must be used when amplitudes are included in attenuation studies.
The predictions of three pairs of models for t* (f) in the central and south-western United States are compared with time domain observations of amplitudes and waveforms and frequency domain observations of spectral slopes to put bounds on the attenuation under the different parts of the country. A model with the t * values of the CUS and SWUS converging at low frequencies and differing slightly at high frequencies matches the spectral domain characteristics, but not the time domain amplitudes and waveforms of short-period body waves. A model with t * curves converging at low frequencies, but diverging strongly at high frequencies, matches the time domain observations, but not the spectral shapes. A model with nearly-parallel t* (f) curves for the central and south-western United States satisfies both the time and frequency domain observations.
We conclude that use of both time and frequency domain information is essential in determining t* (f) models. For the central and south-western United States, a model with nearly-parallel t* (f) curves, where Δ t *∼ 0.2 s, satisfies both kinds of data in the 0.3–2 Hz frequency range. 相似文献
The predictions of three pairs of models for t* (f) in the central and south-western United States are compared with time domain observations of amplitudes and waveforms and frequency domain observations of spectral slopes to put bounds on the attenuation under the different parts of the country. A model with the t * values of the CUS and SWUS converging at low frequencies and differing slightly at high frequencies matches the spectral domain characteristics, but not the time domain amplitudes and waveforms of short-period body waves. A model with t * curves converging at low frequencies, but diverging strongly at high frequencies, matches the time domain observations, but not the spectral shapes. A model with nearly-parallel t* (f) curves for the central and south-western United States satisfies both the time and frequency domain observations.
We conclude that use of both time and frequency domain information is essential in determining t* (f) models. For the central and south-western United States, a model with nearly-parallel t* (f) curves, where Δ t *∼ 0.2 s, satisfies both kinds of data in the 0.3–2 Hz frequency range. 相似文献
10.
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
11.
Summary. Use of higher frequencies and a careful selection of the other data acquisition parameters can significantly enhance the resolution obtained in reflection seismic CDP profiling in hard rock terranes. Experiments with a 20–80 Hz non-linear vibroseis sweep near the projected ADCOH site reveal that the wave-field reflected from the upper crust contains frequencies spanning the entire source spectrum even in the presence of a weathered layer of saprolite. Attenuation of higher frequencies and the severe distortion produced by the 'notch' filter for line-frequency necessitate some pre-processing spectral shaping. The operations are linear and yield, as a by-product, an estimate of the average 'Q' for the section - about 250 in the present case. 相似文献
12.
V. Dehant M. Feissel P. Defraigne F. Roosbeek J. Souchay 《Geophysical Journal International》1997,130(2):535-546
The observed time-series of precession/nutation show residuals with respect to an empirical model based on the rigid Earth theoretical nutations and a frequency dependent transfer function with resonances to the Earth's normal modes. These residuals display energy mainly in the frequency domain around 430 and 500 days in the inertial frame. In this frequency band, the energy is possibly related to two normalmode frequencies: the free core nutation (FCN) and the free inner core nutation (FICN). In this paper, we examine the possibility of obtaining this energy from the resonance effect induced by a luni-solar (or planetary) forcing, or by an atmospheric forcing at a frequency very close to these Earth free nutations. The amplification factor due to the resonance is computed from an analytical formula expressed in the case of a simplified three-layer ellipsoidal rotating earth (with an elastic inner core, a liquid outer core and an elastic mantle), as well as the empirical formula based on the analysis of VLBI observations. For the tidal forcing, the theoretical results do not show any resonance at the level of precision we have examined but it is still possible to find one frequency near the FCN or FICN frequencies which could be excited. In contrast, for the atmospheric pressure the level of energy needed could be obtained from the diurnal pressure, depending on the noise level of the Earth's global pressure. We also show that the combination of three waves can explain the observed decrease of energy with time. While the tidal potential amplitudes are too small, a pressure noise level of 0.5 Pa would be sufficient to excite these waves. 相似文献
13.
Shrub encroachment is the advance of woody plants over grasslands. For some shrub species this process is favoured by fire and high precipitation. In northwestern Patagonia spring precipitation is related with the El Niño Southern Oscillation (ENSO). Over the past years, ENSO has shown an increase in both amplitude and frequency. Our study focuses on the population dynamics of the shrub Fabiana imbricata Ruiz & Pav. (Solanaceae) using stochastic models which involve different fire frequencies and variations in spring precipitation. Our results indicate that F. imbricata's population grows at a wide range of fire frequencies, reaching its maximum every 6–10 years. The elasticity analysis show that, as fire frequency diminishes, population growth rate depends almost exclusively on adult survival, recruitment events are rare and the presence of seedlings or juveniles is seldom observed. In this case, the landscape would be formed by mature F. imbricata shrublands, and population persistence would depend on adult survival, seed production and their accumulation in the soil bank. However, in the case of very high fire frequencies, more recurrent recruitment pulses would be observed, with a landscape dominated by young shrublands composed of individuals of different ages and reproductive status. 相似文献
14.
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
15.
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
16.
S. J. Tanner 《Geophysical Journal International》1984,78(1):51-64
Summary. Factors influencing the seismic response characteristics of marine profiling systems are reviewed. The single frequency case is used to illustrate the influence of different frequencies on the response, as well as the towing depths of the source and receiver, and the geometry of a linear receiving array. The more realistic case of band-limited source waveforms is considered, using frequency spectra calculated from theoretically derived airgun signals. The results show that the number and shape of sidelobes of the profiling system response, as well as the filtering characteristics for reflections arising from reflectors in the vertical plane perpendicular to the axis of the receiver array are determined by the depths of the source and receiver and the relative amplitudes of the frequencies in the source waveform. These factors, along with the configuration of the hydrophone elements in the receiver array, determine the frequency and amplitude attenuation of reflections in the vertical plane containing the receiver array.
The filtering characteristics of the system both in and out of the vertical plane containing the receiver array are discussed, with implications for discriminating between off-axis and in-plane reflections. A plan view of the response of the system is constructed in the time domain for various profiling configurations and sources of different frequency content at a given time. This example shows how useful the resulting pictures are for optimizing acquisition parameters in profiling experiments. 相似文献
The filtering characteristics of the system both in and out of the vertical plane containing the receiver array are discussed, with implications for discriminating between off-axis and in-plane reflections. A plan view of the response of the system is constructed in the time domain for various profiling configurations and sources of different frequency content at a given time. This example shows how useful the resulting pictures are for optimizing acquisition parameters in profiling experiments. 相似文献
17.
In the frequency range from millihertz to hundreds of megahertz, many different physical and physico-chemical processes contribute to the electrical polarization of porous water-bearing rocks. This makes the interpretation of their electrical spectra a complicated problem and requires both elaborate theories and model experiments. At high frequencies, the Maxwell–Wagner–Bruggeman–Hanai (MWBH) theory of effective media, which takes into account only bulk properties, shape and partial volume of components, is very appropriate. At low frequencies, surface films, polarization of the electrical double layer (EDL) and clustering of conductive components can produce very strong polarization; corresponding theoretical models are considered in a companion paper ( Chelidze & Gueguen 1999 , hereafter referred to as Paper I). This paper is devoted to the review of experimental data and their comparison with theoretical models.
Experiments on saturated mineral powders and rocks with various surface areas and surface chemistries confirm the existence of significant surface contributions to the electrical spectra of conductivity and polarization of water-bearing rocks and the dominance of this contribution over MWBH values at low frequencies. The effective dielectric constant of porous saturated rocks increases with the surface-to-volume ratio of the system and strongly depends on the surface charge ( ζ potential). At ζ potential, equal to zero, the low-frequency dielectric permittivity (DP) is minimal. The experimental data on relaxation times and the magnitude of the surface polarization of water-bearing porous systems can be satisfactorily explained by theories of film polarization, diffusional polarization generated by deformation of an 'open' electrical double layer (EDL) and percolation. 相似文献
Experiments on saturated mineral powders and rocks with various surface areas and surface chemistries confirm the existence of significant surface contributions to the electrical spectra of conductivity and polarization of water-bearing rocks and the dominance of this contribution over MWBH values at low frequencies. The effective dielectric constant of porous saturated rocks increases with the surface-to-volume ratio of the system and strongly depends on the surface charge ( ζ potential). At ζ potential, equal to zero, the low-frequency dielectric permittivity (DP) is minimal. The experimental data on relaxation times and the magnitude of the surface polarization of water-bearing porous systems can be satisfactorily explained by theories of film polarization, diffusional polarization generated by deformation of an 'open' electrical double layer (EDL) and percolation. 相似文献
18.
To deal with the universal problem of parasitical frequency spectrum in China New Generation Weather Radar transmitter, this paper establishes mathematical models for parasitical signals existing in radar transmitters and analyzes their effects on weather radar performance. Based on an engineering analysis of their possible sources, a step-by-step method to eliminate parasitical spectrum is presented, which is applied to troubleshooting experimental weather radar. Eventually, parasitical spectrum is basically eliminated. As a result, improved spectrum purity and reduced phase noise is achieved. Moreover, accuracy for velocity estimate as well as ground clutter suppression ability of the radar system is enhanced. 相似文献
19.
Reflection coefficients for weak anisotropic media 总被引：1，自引：0，他引：1
Matthias Zillmer Dirk Gajewski Boris M. Kashtan 《Geophysical Journal International》1997,129(2):389-398
The interaction of plane elastic waves with a plane boundary between two anisotropic elastic half-spaces is investigated. The anisotropy dealt with in this study is of a general type. Explicit expressions for energy-related reflection and transmission coefficients are derived. They represent an approximation which is valid for a small deviation of the elastic parameters from isotropy.
Classical perturbation theory is applied on a 6times6 non-symmetric real eigenvalue problem to calculate first-order corrections for the polarization and stress of the plane waves. The explicit solution of the isotropic problem is used as a reference case. Degenerate perturbation theory is used to consider the splitting of the isotropic S -wave into two anisotropic qS-waves. The boundary conditions for two half-spaces in welded contact lead to a 6times6 system of linear equations. A correction to the isotropic solution is calculated by linearization. The resultant coefficients are functions of horizontal slowness, Lamé parameters and densities of the reference media, and of the perturbation of the elasticity tensors from isotropy. 相似文献
Classical perturbation theory is applied on a 6times6 non-symmetric real eigenvalue problem to calculate first-order corrections for the polarization and stress of the plane waves. The explicit solution of the isotropic problem is used as a reference case. Degenerate perturbation theory is used to consider the splitting of the isotropic S -wave into two anisotropic qS-waves. The boundary conditions for two half-spaces in welded contact lead to a 6times6 system of linear equations. A correction to the isotropic solution is calculated by linearization. The resultant coefficients are functions of horizontal slowness, Lamé parameters and densities of the reference media, and of the perturbation of the elasticity tensors from isotropy. 相似文献
20.
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