共查询到20条相似文献，搜索用时 15 毫秒
1.
A new nutation series for a more realistic model earth 总被引：1，自引：0，他引：1
J. Schastok 《Geophysical Journal International》1997,130(1):137-150
The frequency-dependent correction coefficients with respect to the forced nutations of a rigid earth are computed using the complex scalar gravitational-motion equations for an earth model with an anelastic mantle. Oceanic loads and tidal currents enter the model via outer boundary conditions. The ellipticity of the core-mantle boundary and the dynamical ellipticity are adjusted to observations. This requires the behaviour inside the model earth to be regarded as non-hydrostatic. Some relevant equations for the evaluation of boundary conditions and some terms in the equations of motion are expanded to second order in ellipticity. The computation of the equipotential-surface ellipticity profile is carried to second order as well. These second-order expansions lead to increased accuracy of the results in general. Moreover, one achieves a better reliability for the integration at frequencies close to a resonance. This allows the integration of the equations of motion at any relevant nutation period without the need for a normal-mode expansion. A complete new nutation series for a realistic model earth is presented. 相似文献
2.
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
3.
Enzo Mantovani 《Geophysical Journal International》1978,53(1):55-60
Summary. Earlier efforts to generate the entire theoretical seismograms, including both body and surface waves for realistic sources buried in a radially heterogeneous anelastic, spherical earth, are extended to include the summation of 16 modes. The comparison between a real seismogram and theoretical time series, relative to different attenuation models in the upper mantle, yields information concerning the anelasticity under the Pacific Ocean. 相似文献
4.
The complex-image method for calculating the magnetic and electric fields produced at the surface of the Earth by the auroral electrojet 总被引：7，自引：0，他引：7
For studying the auroral electrojet and for examining the effects it can produce in power systems on the ground, it is useful to be able to calculate the magnetic and electric fields that the electrojet produces at the surface of the Earth. Including the effects of currents induced in the Earth leads to a set of integral expressions, the numerical computation of which is complicated and demanding of computer resources. An approximate solution can be achieved by representing the induced currents by an image current at a complex depth. We present a simple derivation of the complex-image expressions and use them to calculate the fields produced by the auroral electrojet at the surface of an earth represented by layered conductivity models. Comparison of these results with ones obtained using the exact integral solution show that the errors introduced are insignificant compared to the uncertainties in the parameters used. The complex-image method thus provides a simple, fast and accurate means of calculating the magnetic and electric fields. 相似文献
5.
Investigation of teleseismic P -wave recordings at a temporary network in the Eastern Carpathians, equipped with predominantly short-period sensors, is compared with synthetic modelling of anelastic attenuation of teleseismic waves in the upper mantle. Using the t * approach, we examine variations of amplitude decrease over frequency for teleseismic recordings in the frequency band 0.5–1.5 Hz. The results reveal a consistent pattern of increased t * values in the centre of the network, in the Vrancea region at the bend of the Carpathian Arc, although the magnitude of the observed variation in t * is much higher than expected. Synthetic t * parameter computations for the same event-receiver configurations reproduce the observed pattern in terms of relative variations. However, the amplitude of the synthetic t * values explains only 10–20 per cent of the observed variation in t *. t * is not a direct measure for anelastic attenuation but rather for a combination of anelastic and other attenuating effects such as scattering and amplitude fluctuation related to velocity inhomogeneities. If regional amplitude variations are solely attributed to anelastic attenuation, all other effects are mapped into Q . We discuss the role of anelastic attenuation and other effects in the case of the Eastern Carpathians and conclude that t * is an unsuitable parameter to characterize anelastic attenuation in the Eastern Carpathians. 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.
Expansion of a high-frequency time-harmonic wavefield given on an initial surface into Gaussian beams 总被引：1，自引：0，他引：1
L. Klime&#; 《Geophysical Journal International》1984,79(1):105-118
Summary. Realistic anelastic attenuation laws are usually formulated as convolution operators, but this representation is intractable for time-domain synthetic seismogram methods such as the finite difference method. An approach based on Padé approximants provides a convenient, accurate reformulation of general anelastic laws in differential form. The resulting differential operators form a uniformly convergent sequence of increasing order in the time derivative, and all are shown to be causal, stable and dissi- pative. In the special case of frequency-independent Q , all required coefficients for the operators are obtained in closed form in terms of Legendre polynomials.
Low-order approximants are surprisingly accurate. Finite-difference impulse responses for a plane wave in a constant- Q medium, calculated with the fifth-order convergent, are virtually indistinguishable from the exact solution. The formulation is easily generalized to non-scalar waves. Moreover, this method provides a framework for incorporating amplitude-dependent attenuation into numerical simulations. 相似文献
Low-order approximants are surprisingly accurate. Finite-difference impulse responses for a plane wave in a constant- Q medium, calculated with the fifth-order convergent, are virtually indistinguishable from the exact solution. The formulation is easily generalized to non-scalar waves. Moreover, this method provides a framework for incorporating amplitude-dependent attenuation into numerical simulations. 相似文献
8.
We present an analytical form of the layer propagator matrix for the response of a locally incompressible, layered, linear‐viscoelastic sphere to an external load assuming that the initial density stratification ϱ 0 ( r ) within each layer is parametrized by Darwin's law. From this, we show that the relaxation of a sphere consisting of locally incompressible layers is governed by a discrete set of viscous modes. The explicit dependence of the layer propagator matrix on the Laplace transform variable allows us to determine the amplitudes of the viscous modes analytically. Employing Darwin's parametrization, we construct three simplified earth models with different initial density gradients that are used to compare the effects of the local incompressibility constraint, div ( ϱ 0 u )=0, and the material incompressibility constraint, div u =0, on viscoelastic relaxation. We show that a locally incompressible earth model relaxes faster than a materially incompressible model. This is a consequence of the fact that the perturbations of the initial density are zero during viscoelastic relaxation of a locally incompressible medium, so that there are no internal buoyancy forces associated with the continuous radial density gradients, only the buoyancy forces generated by internal density discontinuities. On the other hand, slowly decaying internal buoyancy forces in a materially incompressible earth model cause it to reach the hydrostatic equilibrium after a considerably longer time than a locally incompressible model. It is important to note that the approximation of local incompressibility provides a solution for a compressible earth model that is superior to the conventional solutions for a compressible earth with homogeneous layers because it is based on an initial state that is consistent with the assumption of compressibility. 相似文献
9.
Summary. We report the results of our continuing efforts to compute theoretical seismograms for direct comparison with the experimental time series obtained with the long-period instruments of the WWSSN. The entire theoretical seismogram — body waves and surface waves — is generated for realistic sources buried in a radially heterogeneous, anelastic, spherical earth. The results described in Paper I (Nakanishi, Schwab & Knopoff) are extended to include the summation of 11 modes; for each, the dispersion, attenuation, and excitation are computed down to a minimum period of 1 s. Examples of the theoretical seismograms, and the comparison with experimental results are presented, The results of this comparison indicate that our first application of combined body- and surface-wave generation will concern the investigation of the intrinsic anelasticity in the upper mantle. The indicated technique for such an investigation is based on body waves simply crossing the region of high attenuation a few times in passing from focus to recording station, while a guided surface wave such as Sa , experiences this anelasticity over the entire propagation path. 相似文献
10.
The Hamiltonian formalism was recently applied by Getino (1995a,b) for the study of the rotation of a non-rigid earth with a heterogeneous and stratified liquid core. That earth model is generalized here by including the effect of the dissipation arising from the mantle-core interaction, using a model similar to that of Sasao, Okubo & Saito (1980), which includes both viscous and electromagnetic coupling. First, a solution for the free nutations is obtained following a classical approach, which in our opinion is more familiar to most of the readers than the Hamiltonian treatment. This solution provides a theoretical basis clear enough to study both the qualitative and quantitative effects of the dissipations considered in the hypotheses. The main qualitative features are, besides the delays, that the free core nutation (FCN) suffers an exponential damping, while the chandler wobble (CW) is not damped at first order, by the dissipation considered. The numerical values obtained for the complex compliances agree with the most recent experimental computations.
Next, the problem is studied under a Hamiltonian formalism, and a solution equivalent to the above is obtained. Besides its interest from a theoretical point of view, this formalism is necessary in order to apply canonical perturbation methods in order to obtain analytical nutation series. 相似文献
Next, the problem is studied under a Hamiltonian formalism, and a solution equivalent to the above is obtained. Besides its interest from a theoretical point of view, this formalism is necessary in order to apply canonical perturbation methods in order to obtain analytical nutation series. 相似文献
11.
Genti Toyokuni Hiroshi Takenaka Masaki Kanao Douglas A. Wiens Andrew Nyblade 《Polar Science》2012,6(2):155-164
We have been developing an accurate and efficient numerical scheme, which uses the finite-difference method (FDM) in spherical coordinates, for the computation of global seismic wave propagation through laterally heterogeneous realistic Earth models. In the field of global seismology, traditional axisymmetric modeling has been used widely as an efficient approach since it can solve the 3-D elastodynamic equation in spherical coordinates on a 2-D cross-section of the Earth, assuming structures to be invariant with respect to the axis through the seismic source. However, it has the severe disadvantages that asymmetric structures about the axis cannot be incorporated and the source mechanisms with arbitrary shear dislocation have not been attempted for a long time. Our scheme is based on the framework of axisymmetric modeling but has been extended to treat asymmetric structures, arbitrary moment-tensor point sources, anelastic attenuation, and the Earth center which is a singularity of wave equations in spherical coordinates. All these types of schemes which solve 3-D wavefields on a 2-D model cross-section are classified as 2.5-D modeling, so we have named our scheme the spherical 2.5-D FDM. In this study, we compare synthetic seismograms calculated using our FDM scheme with three-component observed long-period seismograms including data from stations newly installed in Antarctica in conjunction with the International Polar Year (IPY) 2007–2008. Seismic data from inland Antarctica are expected to reveal images of the Earth's deep interior with enhanced resolution because of the high signal-to-noise ratio and wide extent of this region, in addition to the rarity of sampling paths along the rotation axis of the Earth. We calculate synthetic seismograms through the preliminary reference earth model (PREM) including attenuation using a moment-tensor point source for the November 9, 2009 Fiji earthquake. Our results show quite good agreement between synthetic and observed seismograms, which indicates the accuracy of observations in the Antarctica, as well as the feasibility of the spherical 2.5-D modeling scheme. 相似文献
12.
Fred Pollitz Paramesh Banerjee Kelly Grijalva B. Nagarajan R. Bürgmann 《Geophysical Journal International》2008,173(1):189-204
The 2004 M = 9.2 Sumatra–Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ∼1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress–strain relation; an aspherical perturbation in viscoelastic structure; a 'static' mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra–Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation. 相似文献
13.
Magnetotelluric image of the crust and upper mantle in the backarc of the northwestern Argentinean Andes 总被引：2，自引：0，他引：2
Magnetotelluric data from the backarc of the Central Andes in NW Argentinawere re-examined by employing impedance tensor decomposition and 2-D inversion and modelling techniques. The data in the period range of 50–15 000 s were collected on a profile of 220 km length reaching from the Eastern Cordillera across the Santa Barbara System to the Andean foreland of the Argentinean Chaco.
After a dimensionality analysis, data from most sites were treated as regional 2-D. The exception was the eastern section of the profile, where the magnetotelluric transfer functions for periods ≤ 1000 s reflect a 3-D earth. Application of two tensor decomposition schemes yielded a regional strike direction of N–S, which is the azimuth of the Central Andean mountain chains. Several 2-D models were obtained by pseudo- and full 2-D Occam inversion schemes. Special emphasis was placed on the inversion of phase data to reduce the influence of static shifts in the apparent resistivity data. The smooth inversion models all show a good conductor at depth. A final model was then calculated using a finite element forward algorithm.
The most prominent feature of the resulting model is a conductor which rises from depths of 180 km below the Chaco region to 80 km beneath the Santa Barbara System and the Eastern Cordillera. Its interpretation as a rise of the electrical asthenosphere is supported by seismic attenuation studies. Magnetotelluric results, surface heat-flow distribution in the area, and the electrical properties of crustal and mantle rocks suggest that the upper mantle is predominantly ductile beneath the Eastern Cordillera and the western Santa Barbara System. This generally agrees with anelastic seismic attenuation models of the area and is useful in discriminating between models of Q quality factor distribution. 相似文献
After a dimensionality analysis, data from most sites were treated as regional 2-D. The exception was the eastern section of the profile, where the magnetotelluric transfer functions for periods ≤ 1000 s reflect a 3-D earth. Application of two tensor decomposition schemes yielded a regional strike direction of N–S, which is the azimuth of the Central Andean mountain chains. Several 2-D models were obtained by pseudo- and full 2-D Occam inversion schemes. Special emphasis was placed on the inversion of phase data to reduce the influence of static shifts in the apparent resistivity data. The smooth inversion models all show a good conductor at depth. A final model was then calculated using a finite element forward algorithm.
The most prominent feature of the resulting model is a conductor which rises from depths of 180 km below the Chaco region to 80 km beneath the Santa Barbara System and the Eastern Cordillera. Its interpretation as a rise of the electrical asthenosphere is supported by seismic attenuation studies. Magnetotelluric results, surface heat-flow distribution in the area, and the electrical properties of crustal and mantle rocks suggest that the upper mantle is predominantly ductile beneath the Eastern Cordillera and the western Santa Barbara System. This generally agrees with anelastic seismic attenuation models of the area and is useful in discriminating between models of Q quality factor distribution. 相似文献
14.
15.
We consider the two coupled differential equations of the two radial functions appearing in the displacement components of spheroidal oscillations for a transversely isotropic (TI) medium in spherical coordinates. Elements of the layer matrix have been explicitly written—perhaps for the first time—to extend the use of the Thomson-Haskell matrix method to the derivation of the dispersion function of Rayleigh waves in a transversely isotropic spherical layered earth. Furthermore, an earth-flattening transformation (EFT) is found and effectively used for spheroidal oscillations. The exponential function solutions obtained for each layer give the dispersion function for TI spherical media the same form as that on a flat earth. This has been achieved by assuming that the five elastic parameters involved vary as r p and that the density varies as r p-2 , where p is an arbitrary constant and r is the radial distance. A numerical illustration with p = - 2 shows that, in spite of the inhomogeneity assumed within layers, the results for spherical harmonic degree n , versus time period T , obtained here for the Primary Reference Earth Model (PREM), agree well with those obtained earlier by other authors using numerical integration or variational methods. The results for isotropic media derived here are also in agreement with previous results. The effect of transverse isotropy on phase velocity for the first two modes of Rayleigh waves in the period range 20 to 240 s is calculated and discussed for continental and oceanic models. 相似文献
16.
空间界面理论已显示出强大生命力,但其理论架构还不完善。现有研究基本上是建立在"空间界面确实存在"这一经验判断的前提下进行的,对于其存在性还缺乏理论验证。在提炼空间界面唯象理论的基础上,构建了空间界面的数理模型,并以城乡界面为例,以空间为内生变量,空间中的元素如经济、社会、文化等为外生变量,构建联立方程模型,以河南省108个县域为空间单元,采用三阶段最小二乘法和迭代三阶段最小二乘法进行参数估计,建构了城市系统和乡村系统的函数,并进行了数理推导与求解。研究表明,城市函数与乡村函数存在着交集,且其交集为无穷多个点组成的域面,即存在一个城市与乡村系统空间及其要素相互交织而成的独立系统,进而从理论上证明"城乡界面是存在的"。 相似文献
17.
The short-period seismic phase Sn has been interpreted by Stephens & Isacks as a lid wave' in which the seismic energy is constrained to the uppermost few tens of kilometres of the mantle. We have extended their normal-mode interpretation for structures both with and without low-velocity zones (LVZ) in the upper mantle. We have used spherical, anelastic models of the Earth. For a model of an oceanic mantle with a LVZ, we agree that Sn is a lid wave for sources above 200–250 km, if only the onset of Sn is considered. The later portions of the Sn wave train sample the structure as deeply as the 420-km discontinuity. For deeper foci, the pseudo-lid wave does not appear to be generated; even the onset of Sn samples the deeper mantle structure. For a model of a continental mantle without a LVZ, in general, sources at all depths above the 420-km discontinuity appear to generate teleseismic Sn which samples the entire mantle as deeply as the discontinuity and which travels with a velocity significantly greater than the lid velocity. Thus the velocity of Sn may be an important diagnostic to determine whether or not a LVZ exists in the upper mantle. 相似文献
18.
Wooil Moon 《Geophysical Journal International》1982,69(2):431-458
Summary The linearized equation of motion for the slightly elliptical rotating earth is obtained and using Phinney & Burridge's generalized spherical harmonics, the variational principle is derived for the normal mode oscillations of the Earth. The numerical solutions of two earth models 1066B and B1S6 are searched by minimizing the energy functional for the terrestrial spectral range longer than the lowest order free oscillation. The periods of core modes computed for the earth model B1S6, with stably stratified outer core, ranges from about 4 to 13hr and the periods for the 1066B are much more spread without clustering around the periods of 6 and 12 hr as in B1S6. The results for the earth model 1066B indicate that an outer core can support long-period oscillations even when it is not stably stratified. The Chandler wobble periods obtained are 402.3 day for B1S6 and 402.7 day for 1066B. 相似文献
19.
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
20.
Summary. The forward solution of the general two-dimensional problem of induction in a model earth comprising a uniformly conducting half-space covered by a thin sheet of variable integrated conductivity is obtained. Unlike some previous treatments of similar problems, the method presented here does not require the field to be separated into its normal and anomalous parts. Both the E - and B -polarization modes of induction are considered and in each case the solution is expressed in terms of the horizontal component of the electric field satisfying, on the surface of the conductor, a singular integral equation whose kernel is a well-known analytic function. A recently published solution of the coast effect is included as a special case. The numerical procedure for solving the integral equations is described and some illustrative calculations are presented. 相似文献