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1.
Summary . We present a variety of examples, showing systematic fluctuations as a function of angular order of measured eigenfrequencies for given normal modes of the Earth. The data are single station measurements from the GEOSCOPE network. Such fluctuations are attributed to departures from the lowest order asymptotic expression of the geometrical optics approximation. We derive first-order asymptotic expressions for the location parameter for all three components of the Earth's motion, by a method based on the stationary phase approximation and geometric relations on the unit sphere.
We illustrate the sensitivity of the fluctuations to the different parameters involved (source parameters, epicentral distance, laterally heterogeneous earth model) with synthetic examples corresponding to GEOSCOPE observations. Finally, we show the results of first attempts at inversion, which indicate that, when the fluctuations are taken into account, more accurate estimates of the great circle average eigenfrequencies can be obtained, and additional constraints put on the structure in the neighbourhood of the great circle. 相似文献
We illustrate the sensitivity of the fluctuations to the different parameters involved (source parameters, epicentral distance, laterally heterogeneous earth model) with synthetic examples corresponding to GEOSCOPE observations. Finally, we show the results of first attempts at inversion, which indicate that, when the fluctuations are taken into account, more accurate estimates of the great circle average eigenfrequencies can be obtained, and additional constraints put on the structure in the neighbourhood of the great circle. 相似文献
2.
We investigate the importance of wide-band coupling of normal modes due to inner core anisotropy. We compare four different seismic models of inner core anisotropy, which were obtained by others using the splitting of Earth's normal modes. These models have been developed using a self-coupling (SC) approximation, which assumes that coupling between nearby modes through anisotropic inner core structure is negligible. We test the SC approximation by comparing the frequencies and quality factors of 90 inner core sensitive modes, computed for these models using either the SC approximation or full-coupling (FC) among large groups of modes. We find significant shifts in the quality factors and frequencies for some modes. Groups of modes which significantly couple together are constructed for six target modes. These groups are model dependent and in some cases contain large numbers of modes. Synthetic seismograms are calculated to show that the difference between SC and FC is observable on the scale of seismograms and of the same order of magnitude as the difference between synthetic and observed seismograms. Thus, future models of inner core anisotropy should take cross-coupling between large groups of modes into account. 相似文献
3.
Barbara Romanowicz 《Geophysical Journal International》1987,90(1):75-100
Summary. Starting with the first-order formulation of quasi-degenerate splitting theory for the normal modes of a laterally heterogeneous earth, we have obtained an asymptotic expression for the coupling terms corresponding to neighbouring multiplets along the same dispersion branch as the mode considered, valid to order 1/ℓ, where ℓ is the angular order of this mode (ℓ≥ 1).
We show that, to order zero, these coupling terms introduce a small shift in epicentral distance into the expression for the long period seismogram obtained by normal mode summation. This shift depends on the difference between the great circle and the minor arc averages of the local frequency. the coupling terms thus permit us to reconcile results obtained by normal-mode summation and by a propagating wave approach, as far as the dependence on structure of the phase of surface waves is concerned.
To order 1/ℓ, the coupling terms result in a perturbation in the amplitude of the mode considered, which depends on spatial derivatives of the local frequency and thus on the structure in the vicinity of the source station great circle path. We show that this term is equivalent to that which is found using ray perturbation methods for propagating surface waves. We compare and discuss the assumptions underlying both approaches and illustrate, by an example, the potential of the asymptotic normal-mode formulation for improved modelling of lateral heterogeneity in the earth. 相似文献
We show that, to order zero, these coupling terms introduce a small shift in epicentral distance into the expression for the long period seismogram obtained by normal mode summation. This shift depends on the difference between the great circle and the minor arc averages of the local frequency. the coupling terms thus permit us to reconcile results obtained by normal-mode summation and by a propagating wave approach, as far as the dependence on structure of the phase of surface waves is concerned.
To order 1/ℓ, the coupling terms result in a perturbation in the amplitude of the mode considered, which depends on spatial derivatives of the local frequency and thus on the structure in the vicinity of the source station great circle path. We show that this term is equivalent to that which is found using ray perturbation methods for propagating surface waves. We compare and discuss the assumptions underlying both approaches and illustrate, by an example, the potential of the asymptotic normal-mode formulation for improved modelling of lateral heterogeneity in the earth. 相似文献
4.
Michele Caputo 《Geophysical Journal International》1979,59(1):227-230
Summary. The effect of anelasticity on the periods of the Earth's free oscillation (toroidal modes) is examined in the light of several different studies leading to different results. The possibility of discrimination between the different analytic models for the anelasticity of the Earth's interior is discussed. A splitting of the spectral lines caused by Q is also suggested. 相似文献
5.
Anne Sieminski Qinya Liu Jeannot Trampert Jeroen Tromp 《Geophysical Journal International》2007,171(1):368-389
We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by 'banana–doughnut' kernels which exhibit large, path-dependent variations and even sign changes. P -wave traveltimes appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P -wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation traveltime anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation traveltime anomaly, and the second a generalized 'splitting intensity'. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver. 相似文献
6.
Sentinel-1A是欧空局"哥白尼计划"发射的首颗对地观测卫星,其搭载的C波段SAR传感器有效地延续了ERS-1/2和ENVISAT ASAR对地观测任务。简要介绍了Sentinel-1A卫星的特点和轨道参数,并与ERS-1/2和ENVISAT ASAR进行了对比。详细介绍了Sentinel-1A的成像模式(SM,IW,EW,WV)以及每种模式下数据产品(Level-0,Level-1,Level-2)的特征。最后分析了Sentinel-1A数据在不同领域的实际应用,为其在对地观测中的广泛应用提供了参考。 相似文献
7.
High noise levels hamper teleseismic shear wave splitting measurements, which bandpass filtering does not always help. To investigate how robust splitting measurements are to noise, we analysed a set of synthetic records with known splitting parameters and added fixed levels of noise. In the presence of weak anisotropy, single-waveform splitting measurements are unreliable when operating with noisy data sets. A practical rule in terms of S/N ratio and splitting delay time parameters is that splitting is confidently detectable at S/N > 8, regardless of the wave's original polarization orientation. However, for the evidence of weak anisotropy to be detectable and measurable at an S/N value of 4, the backazimuth separation of the phases from the fast polarization direction needs to be higher than 20°. Stacks of individual measurements consistently yield reliable results down to S/N values of 4. Applying stacking to data from DSB (Dublin, Ireland), the fast polarization direction φ and lag time δt are 58° and 0.95 s. This orientation reflects surface trends of deformation in the area, as found elsewhere in the UK. Our result thus reinforces the proposed model that the detected anisotropy in the British Isles originates from lithospheric coherent deformation preserved from the last main tectonic episode. 相似文献
8.
Fabrice R. Fontaine Guilhem Barruol réa Tommasi Götz H. R. Bokelmann 《Geophysical Journal International》2007,170(3):1262-1288
Upper-mantle flow beneath the South Pacific is investigated by analysing shear wave splitting parameters at eight permanent long-period and broad-band seismic stations and 10 broad-band stations deployed in French Polynesia from 2001 to 2005 in the framework of the Polynesian Lithosphere and Upper Mantle Experiment (PLUME). Despite the small number of events and the rather poor backazimuthal coverage due to the geographical distribution of the natural seismicity, upper-mantle seismic anisotropy has been detected at all stations except at Tahiti where two permanent stations with 15 yr of data show an apparent isotropy. The median value of fast polarization azimuths (N67.5°W) is parallel to the present Pacific absolute plate motion direction in French Polynesia (APM: N67°W). This suggests that the observed SKS fast polarization directions result mainly from olivine crystal preferred orientations produced by deformation in the sublithospheric mantle due to viscous entrainment by the moving Pacific Plate and preserved in the lithosphere as the plate cools. However, analysis of individual measurements highlights variations of splitting parameters with event backazimuth that imply an actual upper-mantle structure more complex than a single anisotropic layer with horizontal fast axis. A forward approach shows that a two-layer structure of anisotropy beneath French Polynesia better explains the splitting observations than a single anisotropic layer. Second-order variations in the measurements may also indicate the presence of small-scale lateral heterogeneities. The influence of plumes or fracture zones within the studied area does not appear to dominate the large-scale anisotropy pattern but may explain these second-order splitting variations across the network. 相似文献
9.
Summary. The Lanczos method of separating exponentials is applied to the Fourier transform of seismograms in order to separate the various modes that contribute to the given portion of the seismograms. Phase velocities and amplitudes are obtained as functions of the frequency. When applying the method to artificial seismograms, which are built as an exact superposition of a number of modes, the separation is very accurate. The method was also applied to the surface-wave portion of numerical seismograms for a vertical point force in a layered medium. The phase velocity and amplitude of the fundamental mode are obtained. These functions were taken as the first guess in the Backus—Gilbert generalized inverse procedure and the process converged very rapidly. When a perturbation of the phases and amplitudes is taken as the first guess the process converges to the true model when enough data are available. 相似文献
10.
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
11.
Maureen D. Long Bradford H. Hager Maarten V. de Hoop Rob D. van der Hilst 《Geophysical Journal International》2007,170(2):839-856
We present a series of 2-D numerical models of viscous flow in the mantle wedge induced by a subducting lithospheric plate. We use a kinematically defined slab geometry approximating the subduction of the Philippine Sea plate beneath Eurasia. Through finite element modelling we explore the effects of different rheological and thermal constraints (e.g. a low-viscosity region in the wedge corner, power law versus Newtonian rheology, the inclusion of thermal buoyancy forces and a temperature-dependent viscosity law) on the velocity and finite strain field in the mantle wedge. From the numerical flow models we construct models of anisotropy in the wedge by calculating the evolution of the finite strain ellipse and combining its geometry with appropriate elastic constants for effective transversely isotropic mantle material. We then predict shear wave splitting for stations located above the model domain using expressions derived from anisotropic perturbation theory, and compare the predictions to ∼500 previously published shear wave splitting measurements from seventeen stations of the broad-band F-net array located in southwestern Japan. Although the use of different model parameters can have a substantial effect on the character of the finite strain field, the effect on the average predicted splitting parameters is small. However, the variations with backazimuth and ray parameter of individual splitting intensity measurements at a given station for different models are often different, and rigorous analysis of details in the splitting patterns allows us to discriminate among different rheological models for flow in the mantle wedge. The splitting observed in southwestern Japan agrees well with the predictions of trench-perpendicular flow in the mantle wedge along with B-type olivine fabric dominating in a region from the wedge corner to about 125 km from the trench. 相似文献
12.
Cloud-to-ground (CG) lightning observations for the warm seasons (May-September) of 1989 and 1990 were analyzed for the Great Lakes region in order to assess the diurnal variations in the lightning characteristics. Several parameters, including flash rate, the spatial extent of lightning activity, first stroke peak current, and the percentage of positive flashes, varied markedly over the course of the day. In contrast, other parameters, such as the frequency of lightning periods and the multiplicity of both negative and positive CG flashes, displayed little diurnal variation. A large degree of intraseasonal (i.e., month-to-month) variation was observed in the diurnal patterns for several of the lightning parameters. 相似文献
13.
Summary. In their fundamental paper of 1967, Backus & Gilbert made the following conjecture (p. 265): '… that if we seek uniquely to determine v of the functions ρ, k, μ (with ν = 1, 2, 3) from the mass, moment, and eigen-frequencies of the normal modes, we need 2ν different infinite sequences of eigenfrequencies, each sequence consisting either of all toroìdal modes of a given angular order or all spheroidal modes of a given angular order…' . We show that, at least if attention is not restricted to geophysically realistic solutions, the conjecture is false. The question of its validity remains open when attention is restricted to geophysically realistic solutions. However, as the present result indicates, the fact cannot now be ignored that, even in a quite appropriate geophysical context, an examination of angular-order spectra is not sufficient to determine ρ, k and μ. 相似文献
14.
Toshiro Tanimoto 《Geophysical Journal International》1986,84(1):49-69
Summary. Phase velocity variations obtained in the previous paper are inverted by the Backus–Gilbert method for the velocity structure of the upper mantle. Spheroidal modes and toroidal modes in the period range of 125–260 s are used in the inversion. The data cannot constrain all six parameters in a transversely isotropic medium and we chose to perturb only two parameters, SH and SV velocities. SV velocities are resolved between the depths of about 200 and 400 km and SH velocities between 0 and 200 km. Resolution kernels have half-peak widths of about 200–300 km in depth, becoming broader for deeper target depths. SV velocity kernels show secondary peaks near the surface of the Earth, with widths varying from 50 to 100 km. The deeper the target depths, the wider the secondary peaks near the surface. SH velocity kernels do not possess such secondary peaks. The trade-off between SV and SH velocities is small. SV velocity is essentially determined by spheroidal modes and SH velocity by toroidal modes. Because of the broad width of the resolution kernels, the structure in the resolved region is difficult to detect from our data set; for example the differences in SV velocity structure between 250 and 350 km or the differences in SH velocity between 100 and 200 km are difficult to distinguish. Considering the horizontal resolution of about 2000 km, obtained in the previous paper, averaging kernels for 3-D structure are quite elongated in the horizontal dimension. 相似文献
15.
Summary. The polarizations of shear waves recorded by networks of digital three-component seismometers immediately above small earthquakes near the North Anatolian Fault in Turkey display shear-wave splitting on almost all shear-wave seismograms recorded within the shear-wave window. This splitting is incompatible with source radiation-patterns propagating through simple isotropic structures but is compatible with effective anisotropy of the internal structure of the rock along the ray paths. This paper interprets the phenomena in terms of widespread crack-induced anisotropy. Distributions of stress-induced cracks model many features of the observations, and synthetic polarization diagrams calculated for propagation through simulated cracked rock are similar to the observed patterns. This evidence for widespread crack-induced anisotropy lends strong support to the hypothesis of extensive-dilatancy anisotropy (EDA) suggested by laboratory experiments in subcritical crack-growth. The crucial evidence confirming some form of EDA would be observations of temporal changes in shear-wave splitting as the stress field alters the crack density and crack geometry. There is some weak evidence for such temporal changes at one site, but further analysis of suitable digital three-component seismometer networks in seismic areas is required to confirm EDA. 相似文献
16.
《The Professional geographer》2013,65(3):349-366
Cloud-to-ground (CG) lightning observations for the warm seasons (May-September) of 1989 and 1990 were analyzed for the Great Lakes region in order to assess the diurnal variations in the lightning characteristics. Several parameters, including flash rate, the spatial extent of lightning activity, first stroke peak current, and the percentage of positive flashes, varied markedly over the course of the day. In contrast, other parameters, such as the frequency of lightning periods and the multiplicity of both negative and positive CG flashes, displayed little diurnal variation. A large degree of intraseasonal (i.e., month-to-month) variation was observed in the diurnal patterns for several of the lightning parameters. 相似文献
17.
F. A. Dahlen 《Geophysical Journal International》1974,38(1):143-167
Summary
We consider the problem of inferring information about the lateral heterogeneity of the Earth's physical properties given certain measurements of the eigenfrequency splitting of the elastic-gravitational normal mode multiplets. We show that this problem can be formulated as a series of exactly linear inverse problems; the data which are relevant to at least the first two of these linear inversions can be measured without having to resolve fully the normal mode multiplets. 相似文献
We consider the problem of inferring information about the lateral heterogeneity of the Earth's physical properties given certain measurements of the eigenfrequency splitting of the elastic-gravitational normal mode multiplets. We show that this problem can be formulated as a series of exactly linear inverse problems; the data which are relevant to at least the first two of these linear inversions can be measured without having to resolve fully the normal mode multiplets. 相似文献
18.
There have been several claims that seismic shear waves respond to changes in stress before earthquakes. The companion paper develops a stress-sensitive model (APE) for the behaviour of low-porosity low-permeability crystalline rocks containing pervasive distributions of fluid-filled intergranular microcracks, and this paper uses APE to model the behaviour before earthquakes. Modelling with APE shows that the microgeometry and statistics of distributions of such fluid-filled microcracks respond almost immediately to changes in stress, and that the behaviour can be monitored by analysing seismic shear-wave splitting. The physical reasons for the coupling between shear-wave splitting and differential stress are discussed.
In this paper, we extend the model by using percolation theory to show that large crack densities are limited at the grain-scale level by the percolation threshold at which interacting crack clusters lead to pronounced increases in rock-matrix permeability. In the simplest formulation, the modelling is dimensionless and almost entirely constrained without free parameters. Nevertheless, APE modelling of the evolution of fluid-saturated rocks under stress reproduces the observed fracture criticality and the narrow range of shear-wave azimuthal anisotropy in crustal rocks. It also reproduces the behaviour of temporal variations in shear-wave splitting observed before and after the 1986, M = 6, North Palm Springs earthquake, Southern California, and several other smaller earthquakes.
The agreement of APE modelling with a wide range of observations confirms that fluid-saturated crystalline rocks are stress-sensitive and respond to changes in stress by critical fluid-rock interactions at the microscale level. This means that the effects of changes in stress and other parameters can be numerically modelled and monitored by appropriate observations of seismic shear waves. 相似文献
In this paper, we extend the model by using percolation theory to show that large crack densities are limited at the grain-scale level by the percolation threshold at which interacting crack clusters lead to pronounced increases in rock-matrix permeability. In the simplest formulation, the modelling is dimensionless and almost entirely constrained without free parameters. Nevertheless, APE modelling of the evolution of fluid-saturated rocks under stress reproduces the observed fracture criticality and the narrow range of shear-wave azimuthal anisotropy in crustal rocks. It also reproduces the behaviour of temporal variations in shear-wave splitting observed before and after the 1986, M = 6, North Palm Springs earthquake, Southern California, and several other smaller earthquakes.
The agreement of APE modelling with a wide range of observations confirms that fluid-saturated crystalline rocks are stress-sensitive and respond to changes in stress by critical fluid-rock interactions at the microscale level. This means that the effects of changes in stress and other parameters can be numerically modelled and monitored by appropriate observations of seismic shear waves. 相似文献
19.
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
20.
Selective omission in a road network is a necessary operation for road network generalization. Most existing selective omission approaches involve one or two geometric parameters at a specific scale to determine which roads should be retained or eliminated. This study proposes an approach for determining the empirical threshold for such a parameter. The idea of the proposed approach is to first subdivide a large road network, and then to use appropriate threshold(s) obtained from one or several subdivisions to infer an appropriate threshold for the large one. A series of experiments was carried out to validate the proposed approach. Specifically, the road network data for New Zealand and Hong Kong at different scales (ranging from 1:50,000 to 1:250,000) were used as the experimental data, and subdivided according to different modes (i.e. administrative boundary data, a regular grid of different sizes, different update years, and different road network patterns). Not only geometric parameters, but also structural and hybrid parameters of existing selective omission approaches were involved in the testing. The experimental results show that although the most appropriate thresholds obtained from different subdivisions are not always the same, in most cases, the appropriate threshold ranges often overlap, especially for geometric parameters, and they also overlap with those obtained from the large road network data. This finding is consistent with the use of different subdivision modes, which verifies the effectiveness of the proposed approach. Several issues involving the use of the proposed approach are also addressed. 相似文献