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1.
Summary An extension of the Love-Larmor theory to a low-loss unelastic earth model, leads to the surprisingly simple approximation
   
where τs= 447.4 sidereal day is the static wobble period, τR= 306 sidereal day is the rigid-earth wobble period and τw= 433 sidereal day is the observed Chandler period. Q W, Q μ are the respective average Q values of the wobble and the Earth's mantle at τW. The known numerical factor F is only slightly dependent on the Earth structure.  相似文献   

2.
Summary. A new asymptotic formula is obtained for the spectrum of an isolated normal mode multiplet nSl or nTl , with n ≪ l , on a laterally heterogeneous Earth. The principal feature of this formula is that it is uniformly valid on the Earth's surface, including near the epicentre and its antipode. The formal conditions for its validity are that | δm / m 0|≪ 1 and s max≪ l ≪ s min| δm / m 0|–1, where | δm / m 0| is the relative magnitude of the lateral heterogeneity, and s min and s max are the minimum and maximum significant degrees in its spherical harmonic expansion. As well as providing a basis for the geographical interpretation of near-epicentral or near-antipodal long-period recordings, the new formula also unifies the asymptotic theory and adds insight into the phenomena which govern the details of multiplet spectra in general.  相似文献   

3.
Approaches to Modelling the Surface Albedo of a High Arctic Glacier   总被引：1，自引：0，他引：1  
Broadband surface albedo measurements, made during the summer melt season at three weather stations on John Evans Glacier (79°40 ' N, 74°00 ' W), varied strongly with the solar zenith angle ( θ z ). Tests were carried out to assess the impact of diurnal variations in surface albedo on seasonal net shortwave radiation ( K * ) totals. Removing the diurnal signal from albedo measurements by daily averaging of hourly measurements, or by applying midday measurements to all hours of the day, changed K * by up to 16%. Ignoring measurements made at θ z & 75°, to account for measurement (cosine) error at high θ z , decreased K * by between 5 and 18%. Given the sensitivity of K * to diurnal patterns in surface albedo, experiments were carried out with two albedo models. One model accounted for albedo variations with θ z and one did not. The model driven by θ z , when implemented within a surface energy balance model for John Evans Glacier, produced better melt estimates. This suggests that diurnal variations in surface albedo should be accounted for in energy balance models of glacier melt.  相似文献   

4.
Summary. We investigate one-dimensional waves in a standard linear solid for geophysically relevant ranges of the parameters. The critical parameters are shown to be T*= tu/Qm where t u is the travel time and Qm the quality factor in the absorption band, and τ−1 m , the high-frequency cut-off of the relaxation spectrum. The visual onset time, rise time, peak time, and peak amplitude are studied as functions of T* and τ m. For very small τ m , this model is shown to be very similar to previously proposed attenuation models. As τ m grows past a critical value which depends on T* , the character of the attenuated pulse changes. Seismological implications of this model may be inferred by comparing body wave travel times with a'one second'earth model derived from long-period observations and corrected for attenuation effects assuming a frequency independent Q over the seismic band. From such a comparison we speculate that there may be a gap in the relaxation spectrum of the Earth's mantle for relaxation times shorter than about one second. However, observational constraints from the attenuation of body waves suggest that such a gap might in fact occur at higher frequencies. Such a hypothesis would imply a frequency dependence of Q in the Earth's mantle for short-period body waves.  相似文献   

5.
Within the mushroom-shaped head of a cylindrical mantle plume melting occurs, the melt segregates from the matrix, and the matrix deforms and spreads laterally. These processes have been studied with a model of two-phase flow with melting. After characteristics of the solution near the axis of symmetry of the plume were found, a set of asymptotic relations for the variables along the symmetry axis was derived from McKenzie's equations for conservation of mass, momentum and energy of a two-phase system. The distribution of porosity along the plume axis and the vertical and radial segregation velocity of the melt in the vicinity of the axis of symmetry were obtained as functions of depth. Our analytic results show that within the head of a cylindrical mantle plume the contribution of the deformation of the matrix to the total non-hydrostatic pressure gradient cannot be neglected, and melt convergence or divergence is controlled by the radial scale of the upward velocity profile at the depth of the beginning of melting.  相似文献   

6.
Summary. This note presents an exact analytical formula for determining the magnitude of coseismic surface volume change (δ V ) of earthquake faults in a half-space. For a Poisson solid, the formula is remarkably simple; δ V = M zz |8μ, where M zz is one of the moment tensor elements of the source. Maximum δ V values derive from dip slip on faults plunging 45°. For these events, surface volume changes of 0.0001 and 4.3 km3 can be expected for magnitude 5 and 8 earthquakes respectively. All of the coseismic surface volume change is recovered in the interseismic period through relaxation of the Earth and rebound of the surface. A useful rule of thumb for estimating the magnitude of vertical rebound in 45° dip slip events is δ h p=Δ s /24, where Δ s is the coseismic slip on the fault.  相似文献   

7.
Summary. The potential function ø for a magnetic body of susceptibility μ in a medium of susceptibility μ* satisfies the integral equation
Here Φ* is the potential function for the region without the heterogeneity and R is the distance from the point of observation to the point on the surface, s , of the body. δΦ /δn is the normal derivative, in the direction of the outward normal. The equation allows for the effects of demagnetization. For numerical purposes the surfaces can be divided into N facets over which δΦ/δ n is a constant. The unknown quantities δΦ/δnj can be found from the system of equations defined by:
The prime on the summation sign denotes that the summation does not include the i th element. The magnetic field in the direction of the unit vector P( P 1, P 2, P3 ) is given by:   相似文献   

8.
Summary. A combination of analytic solutions and numerical computations has been used to obtain the low-frequency, far-field P - and S -wave radiation patterns from Heaviside-loaded ellipsoid cavities of fixed volume and varying eccentricity (including the sphere and the finite cylinder) in an unbounded elastic solid. Results show that as the spherical cavity becomes a prolate ellipsoid, S -waves are radiated with strength proportional to the increasing aspect ratio ( A R) (major axis/minor axis). With large aspect ratios ( A R > 10) both P - and S -wave radiation strengths approach asymptotically a limit for which the maximum P -wave amplitude is twice as large as the maximum S -wave amplitude, irrespective of Poisson's ratio.
A representation of the radiation pattern is obtained whose mathematical form can be interpreted as due to the action of a centre of dilatation plus a vector linear dipole, both appropriately weighted. the weights are nonlinear functions of A R. On the basis of numerical results, we have obtained an approximate formula that relates those weights to A R. the radiation patterns thus obtained are in excellent agreement with the experimental results reported by Gupta & Kisslinger. the results may be of some importance to the investigation of explosions in non-spherical cavities and in the study of the origin and mechanisms of volcanic (explosive) earthquakes.  相似文献   

9.
Summary. One method to determine the depths of sources of anomalies in the Earth's gravity field is to plot log [(2 n + 1) σ n ] versus n where σ n is the n th term in the amplitude spectrum of the Earth's gravitational potential. This procedure assumes that the amplitude spectrum of the anomalous density variations does not vary with n. Such an assumption may not apply to the Earth.  相似文献   

10.
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11.
The deformation at the core–mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core–mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field ( J 2) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 1018 Pa s, the postseismic J 2 variation in the next years is expected to leave a detectable signal in geodetic observations.  相似文献   

12.
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13.
The traveltime perturbation equations for the quasi-compressional and the two quasi-shear waves propagating in a factorized anisotropic inhomogeneous (FAI) media are derived. The concept of FAI media simplifies considerably these equations. In the FAI medium, the density normalized elastic parameters a ijkl ( X i ) can be described by the relation a ijkl ( X i) = f 2( x i ) A ijkl, where A ijkl are constants, independent of coordinates x i and f 2( x i) is a continuous smooth function of x i . The types of anisotropy ( A ijkl ) and inhomogeneity [ f ( x i)] are not restricted. The traveltime perturbations of individual seismic body waves ( q P , qS 1 and qS 2) propagating in the FAI medium depend, of course, both on the structural pertubations [δ f 2( x i)] and on the anisotropy perturbations (δ A ijkl ), but both these effects are fully separated. The perturbation equations for the time delay between the two qS -waves propagating in the FAI medium are simplified even more. If the unperturbed (background) medium is isotropic, the perturbation of the time delay does not depend on the structural perturbations (δ f 2( x i) at all. This striking result, valid of course only in the framework of first-order perturbation theory, will simplify considerably the interpretation of the time delay between the two split qS -waves in inhomogeneous anisotropic media. Numerical examples are presented.  相似文献   

14.
Summary. The inverse gravity potential problem consists in the determination of the form and the density of the body by its exterior gravity potential. We describe two similar classes of bodies for which this problem has a unique constructive solution.
(1) The first class contains the cylindrical bodies with finite length, arbitrary form of section and ρ( R , ø, z) =ρ1( z )ρ2( R , ø) density distribution, where z is the cylindrical coordinate; R , ø are the polar coordinates in a section plane. This class is important for prospecting geophysics in that it allows us to determine in a unique and constructive way, the function ρ1( R , ø), the length, form and orientation of the cylinder if we know the function ρ1( z ) and the exterior potential. The classical moment problem of functions is the basis for the solution of this problem.
(2) The analogous problem for the class of the spherical cylinders, or bodies bounded by arbitrary similar sections of two different concentric spheres and the radial lateral surface, appears when bodies of planetary size are studied. (An example of these bodies would be the Moon mascons.) The density distribution of these cylinders is ρ(τ, θ, ø) =ρ1(τ)ρ2(θ, ø) where τ, θ, ø are the spherical coordinates. The function ρ1(θ, ø), length and form of spherical sections can be uniquely determined by exterior potential if we know the function ρ1(τ). We propose a new constructive method for harmonic continuation of the gravity potential into the region containing the perturbing masses for the solution of the problem.  相似文献   

15.
The sea lochs (fjords) of north-west Scotland are located in a region of Europe particularly well situated to monitor changes in westerly air streams. The moisture transported in these air streams has a profound effect on regional precipitation, freshwater run-off and, in turn, sea loch circulation. The gentle slope of the regional salinity:δ18O mixing-line, defined as 0.18 ‰ per salinity unit, suggests that the temperature: δ18O relationship may be readily resolved in these coastal waters. Deep-water renewal events, both observed and predicted from empirical models, in the bottom-waters of Loch Etive provide an opportunity to assess the temperature, salinity and δ18O relationship. Predicted changes in δ18Ocalcite as a function of changing salinity (ΔS) and changing temperature (ΔT) during deep-water renewal events suggest that >80% fall above analytical detection limits. The theoretical likelihood of recording such renewal events in the "palaeoclimate" record appears to be promising, but temperature and salinity change during renewal events may have either sign. Scottish fjords, because of the relatively small impact which salinity has on δ18Owater, may provide useful study sites in palaeoclimate research, particularly where palaeotemperature is the primary record of interest.  相似文献   

16.
Magnetic susceptibility ( χ ) variations and the behaviour of the ratio of susceptibility to saturation magnetization ( χ/J s ) along the loess/palaeosol section at Koriten (NE Bulgaria) are used to deduce climatic changes during the Pleistocene in southeastern Europe. A good correlation of susceptibility variations with the astronomically tuned oxygen isotope record from ODP site 677 enables us to propose a more precise dating of the upper part of the Bulgarian loess complex. Close correspondence between susceptibility and δ 1 8 O records demonstrates the global significance of the palaeoclimatic signal recorded, although differences in relative amplitudes of χ and χ/J s and δ 1 8 O create difficulties in making quantitative estimates of the climatic humidity in the past. The role of local factors affecting the palaeoclimatic mineral magnetic record deduced from the profile studied in Bulgaria is discussed.  相似文献   

17.
Summary. A method is outlined to determine the dynamic behaviour of a phase boundary in the Earth when non-uniform time-varying pressure and temperature conditions are assumed at the Earth's surface. An integral equation describing the phase boundary motion is derived and it is solved under a linearizing assumption. The solution is obtained in the form of a double integral transform. Short and long time-expansions of the solution can be obtained from series expansion and integration of the Laplace transform along a branch cut. The method is illustrated by considering a stepwise change in surface pressure conditions.
For short times, the solution exhibits the same type of time dependence (i.e. the first-order term is in t 1/2) as the one obtained in the one-dimensional case (i.e. uniform pressure perturbation at the Earth's surface).
For long times, it is shown that the time dependence of the phase boundary motion is almost identical to the one derived for the one- dimensional case if the wavenumber k L of the surface excitation is such that κ k 2Lτ≤ 1 (where τ is the relaxation time associated with the one-dimensional phase boundary motion and κ is the thermal diffusivity). If κ k 2Lτ > 1, then the relaxation time for the phase boundary motion in two dimensions is of the order of κ−1 k −2L.
When considering parameters that would be appropriate for a basalt to eclogite phase transition at Moho depth, the latter situation is met only when the load wavelength is smaller than 35 km.  相似文献   

18.
In this paper, approximately 100 VLBI/SLR/GPS velocities map European strain rates from <0.09 × 10−8 to >9.0 × 10−8 yr−1 with regional uncertainties of 20 to 40 per cent. Kostrov's formula translates these strain-rate values into regional geodetic moment rates M¯˙ geodetic . Two other moment rates, M¯˙ seismic , extracted from a 100-year historical catalogue and M¯˙ plate , taken from plate-tectonic models, contrast the geodetic rates. In Mediterranean Europe, the ratios of M¯˙ seismic to M¯˙ geodetic are between 0.50 and 0.71. In Turkey the ratio falls to 0.22. Although aseismic deformation may contribute to the earthquake deficit ( M¯˙ seismic values less than M¯˙ geodetic ), the evidence is not compelling because the magnitudes of the observed shortfalls coincide with the random variations expected in a 100-year catalogue. If the lack of aseismic deformation inferred from the 100-year catalogue holds true for longer periods, then much of Europe's strain budget would have to be accommodated by more frequent or larger earthquakes than have been experienced this century to raise the ratios of M¯˙ seismic to M¯˙ geodetic to unity. Improved geological fault data bases, longer historical earthquake catalogues, and densification of the continent's space geodetic network will clarify the roles of aseismic deformation versus statistical quiescence.  相似文献   

19.
Summary. Titanomagnetites of composition Fe2.4-δAlδTi0.6O4 and Fe2.6-δAlδTi0–4O4(δ=0, 0.1 and 0.2 in both cases) were prepared in the monodomain state by pulverization of sintered synthetic material. In low fields, the thermoremanence (TRM) was found to be linear with inducing field and of high enough intensity to account for typical natural remanent magnetizations of fresh submarine basalts. The higher field TRM acquisition curves follow the Néel model curve for an assemblage of non-interacting identical particles in a general way only, the differences being due to interactions, or the range of particle blocking temperatures and volumes or other features of the samples not included in the model. The unblocking temperatures of low field TRM lie in a narrow range below the Curie point. The low field TRM is very resistant to alternating field demagnetization and provides a very striking illustration of the strength of the TRM mechanism in preserving a stable record of a weak magnetic field. The result of a Lowrie-Fuller test on the material is consistent with the monodomain state.  相似文献   

20.
Summary. Palaeomagnetic investigations were carried out on nine lava flows around the Dhar region, which constitute the northern part of the Deccan traps. The stability of remanent magnetism of these specimens was analysed by an alternating magnetic field, thermal demagnetization and memory tests. Six flows exhibited characteristic components of magnetization, with a mean direction of D =143°, I =+46° ( K = 107.1, α95=5.5°). This gives a VGP located at 29° N, 67° W (δp=4.5°, δm= 7.0°). The lower site with normal magnetization and the upper five sites with reverse magnetization indicate a geomagnetic field reversal during the initial phases of Deccan volcanism in the Early Tertiary period. A rapid northward migration of about 18° in latitude and a simultaneous anticlockwise rotation of 37° is calculated for the subcontinent.  相似文献   

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