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1.
Summary The diffraction of a pressure wave arising from the edge of the floating ice due to an incident wave of the formH[t–(xcos/)+ (ysin/)], whereH(t) is the Heaviside step function, has been studied. The ice sheet has been taken to be moving with a velocity much less than the velocity of sound in the liquid. The problem has been solved using an approximate method of solving Wiener Hopf problems. Finally, the pressure field at a large distance from the edge has been derived in a closed form evaluating the integrals by the saddle point method.  相似文献   

2.
In terms of the general endogeneous evolution of the lithosphere, the continental crystalline crust and the uppermost mantle, formed by regional metamorphic and magmatic processes, show mineral paragenesis stratification, expressed by a regular mineral sequence. The continuous macrolayering of mineral paragenesis through lithospheric depth profile is caused by phase transformations and variations in composition of complex natural systems, and affects the vertical distribution of seismic velocities,V p,V s, and other physical parameters.To evaluate palaeotemperatures (crystallization temperatures of mineral paragenesis), consistentV pandV s (Z) velocity models for the consolidated crust of two regionally separated areas of different geological structures — Precambrian shield (Voronezh Massif) and a young fold-mountain structure in the central part of the Transasian orogeneous belt (Himalaya) — are used as starting data.The velocity models are recalculated into (Z) and (Z) profiles (Z) being the seismic parameter. (Z) the Debye temperature). These, according to Debye theory, allow the determination of variations in entropy, thermodynamic and temperature gradients at the time of crustal generation.For the two regions chosen, palaeotemperature distributions are eventually calculated for the depth intervals given by velocity profiles. Crystallization temperatures calculated from seismic data show good agrrement with the values obtained from mineralogical thermobarometry.  相似文献   

3.
The horizontal and vertical derivative profiles of magnetic anomalies of dykes show some interesting properties. The points of zero derivatives and the points where the derivatives are equal are conjugate point pairs. A method of interpretation of dyke anomalies is suggested, which utilizes the distances between these points.Notation F Magnetic anomaly in total intensity - Z Depth to top of the dyke - 2T Width of the dyke - Geological dip of the dyke - I Effective intensity of magnetisation in the plane of profile - Dip of effective magnetisation vector in the plane of profile - Strike angle of the dyke - i Magnetic dip - Q – - Q f –+arctan (sin coti) - I f   相似文献   

4.
A Markov chain{X t }, which has been useful for modelling in hydrology, can be specified by the Laplace transform (LT) of the conditional p.d.f. ofX t+1 givenX t =x t , which is assumed to be of the exponential formH()exp{-G()x t }. For appropriate choice ofH andG the marginal distribution ofX t is the (univariate) gamma distribution. In this case, the joint p.d.f. ofX t +1,...,X t+n and its LT, are obtained, and this is extended to a seasonal version of the chain. A simple method of generating observations from these multivariate gamma distributions is noted, and the joint LT is applied to the problem of determining moments of weighted sums of such variables.  相似文献   

5.
m m n¶rt;u mamu [7] m aa uu u aa a¶rt;u uu. uau ¶rt; u m¶rt;mu uu u u, a ¶rt;, u mu n nm. ¶rt;um a ama, ma m u¶rt; nm ¶rt; au ¶rt;amma m um. auu mamu ¶rt;um uua aa ¶rt; m unu¶rt;.  相似文献   

6.
Riassunto Si suppone la Terra avvolta da un velo di un fluido perfetto incomprimibile messo in rotazione da un vortice doppio puntiforme. Si calcola l'energia cinetica totale della Terra e del fluido in funzione degli angoli di Eulero , , , che esprimono il moto della Terra rispetto a una terna inerziale, e degli angoli 0, 0 esprimenti il moto del vortice rispetto alla Terra. Si determinano i predetti angoli in funzione del tempo mediante le equazioni di Lagrange; risulta che il moto del vortice è caratterizzato da 0= const., e che la sua influenza sulla polodia è trascurabile.
Summary Supposing the Earth sorrounded by a veil of an incompressible perfect fluid rotationally moved by a point shaped double vortex, the Author calculates the total kinetic energy of the system as a function of the Eulerian angles , , which expres the Earth motion referred to an inertial tern, and of the angles 0, 0 for the vortex motion referred to the Earth. He determines the above said angles as temporal functions by means of the equations of Lagrange. It results that the vortex motion is determined by 0= const., and that its influence on the rate of rotation of the Earth is negligeable.

Comunicazione presentata alla 2a. Assemblea annuale della «Società Italiana di Geofisica e Meteorologia» (Genova, 23–25 Aprile 1954).  相似文献   

7.
Theoretical constraints on the stress-dilation relation for a deforming Coulomb material requirev ifC=0 andv sin-1( m / m ) always, wherev is the dilation angle, is the friction angle,C is cohesion, m is the maximum shear stress, and m is the mean effective stress. Recent laboratory measurements of friction and dilatancy of simulated fault gouge show that small amplitude shear-load cycling causes compaction and consolidation. Comparison of the data with theory indicates that such load cycling produces: (1) increased coefficient of friction (or friction angle), (2) increased cohesion, and (3) increased dilatancy rate (or dilation angle). Under certain conditions of load cycling without significant plastic shear strain accumulation ( p <0.005) we find thatv exceeds both and, in contrast to theory, sin-1( m / m ). This result is interpreted in terms of enhanced cohesion and overconsolidation, which lead to residual stresses within the gouge. An analogy is drawn between these special loading conditions and those extant on natural faults. In particular, our results imply that jostling and minor stress variations associated with microearthquakes may produce strengthening of fault gouge and changes in the fault zone's stress-dilatancy relation. Hence, compaction associated with microseismicity may lead to subsequent dilation of fault gouge, even for faults with large displacement rates and large net offsets (e.g., San Andreas). In regions where such dilation persists over sufficient displacements (on the order of the critical slip distance for seismic faulting) it may tend to inhibit unstable slip.  相似文献   

8.
To study the effects of strong scattering on elastic waves, spatial fluctuation and scattering attenuation ofP waves were examined by laboratory experiments for 2-D models of random media approximately characterized by a triangular correlation function in the range of 2<ka<33, wherek is the wave number anda is the correlation distance of the heterogeneities, i.e., the heterogeneity size. The results obtained are as follows: (1) Forka>10, both the intensity and the correlation distance of the amplitude fluctuation are approximate for any phase of theP-wave train. The correlation distance nearly agrees with the heterogeneity size. These fluctuation properties are quite consistent with the theoretical prediction by the forward-scattering approximation. (2) For 3<ka<6, the fluctuation intensity becomes stronger in later phases of theP-wave train. This shows that scattering is approximately isotropic, and therefore, the scattered energy increases with time within theP-wave train. The correlation distance of the amplitude fluctuation disagrees with the heterogeneity size, and it shows a frequency-dependent property decreasing from 7a to 4a with the increase ofka from 3 to 6. These properties for 3<ka<6 have not yet been predicted theoretically. (3) Forka<3, though the fluctuation is considerably smaller compared with that ofka>10 and 3<ka<6, the fluctuation property is considered similar to that of 3<ka<6. (4) The observed scattering attenuation,Q –1, increases withka forka<3, has a peak aroundka=35, and then decreases withka. (5) When min = 15° and = 0.075, the theoreticalQ –1 curve, predicted by the approximate theory of Wu, roughly matches the observedQ –1 values, where min is the minimum scattering angle measured from the propagation direction of theP waves and is the rms of fractional velocity fluctuation. This suggests that the energy scattered in the range of >15° is lost from theP waves, while the energy scattered in the range of <15° is retained; and that the approximate theory overestimates by about three times the value of the model media used owing to the neglect of multiple scattering. (6) When the size of velocity heterogeneities responsible for forward scattering at 3<ka<6 is estimated from the min value of 15° on the basis of Wu's theory, it nearly agrees with the correlation distance for the initial phase of theP-wave train.  相似文献   

9.
Long-period recordings of dispersive Rayleigh waves along numerous station lines, or profiles, in Europe have for the first time permitted a uniform inversion of these observations based on a new method of phase velocity regionalization.Regional dispersion relations obtained by this method have then been subjected to a complete inversion procedure commonly known as the hedgehog method. The results are presented in a map outlining the thickness of the lower lithosphere (lid) and the shear (S) velocities in both the lid and the asthenosphere channel.A comparison of these results with the minimum compressional (P) wave velocities in the asthenosphere and their corresponding depths provides an estimate of theV p /V s ratio for the asthenosphere in the European area.Contribution No. 314, Institute of Geophysics, ETH-Zürich, Switzerland.  相似文献   

10.
A numerical study has been made of the heat transfer through a fluid layer with recirculating flow. The outer fluid surface was assumed to be spherical, while the inner surface consisted of a sphere concentrically or eccentrically located with respect to the outer spherical surface. The recirculating flow was assumed to be driven by a gas flow creating stress on the fluid's outer surface so that creeping (low Reynolds number) flow developed in its interior. The present study solves the Stokes equation of motion and the convective diffusion equation in bispherical coordinates and presents the streamline and isotherm patterns.Nomenclature a i inner sphere radius - a d outer sphere radius - A 1 defined by equation (5) - A 2 defined by equation (6) - B 1 defined by equation (7) - B 2 defined by equation (8) - c dimensional factor for bispherical coordinates - C constant in equation (4) - d narrowest distance between the two eccentric spheres - E 2 operator defined by equation (1) in spherical coordinates and by equation (21) in bispherical coordinates - G modified vorticity, defined in equation (22) - G * non-dimensional modified vorticity, defined in equation (28) - h metric coefficient of bispherical coordinate system, defined in equation (18) - k w thermal conductivity of water - K 1 defined by equation (9) - K 2 defined by equation (10) - N Re Reynolds number=2a dU/gn - N Pe,h Peclet number=2a dU/ - n integer counter - q heat flux - r radius - r * non-dimensional radius=r/a d - S surface area - t time - t * non-dimensional time=t/a d 2 - T temperature - T o temperature at inner sphere surface - T a temperature at outer sphere surface - T * non-dimensional temperature;=(T–T o)/(Ta–To) - u velocity - u r radial velocity in spherical coordinates - u angular velocity in spherical coordinates - u radial velocity in bispherical coordinates - u angular velocity in bispherical coordinates - U free stream velocity - u r * =u r/U - u * =u /U - u * =u /U - u * =u /U Greek symbols a 1 small displacement - vorticity, defined in equation (17) - * non-dimensional vorticity, defined in equation (27) - radial bispherical coordinates - o bispherical coordinate of inner sphere - a bispherical coordinate of outer sphere - angular coordinate in spherical coordinates - thermal diffusivity - w thermal diffusivity of water - kinematic viscosity - angular bispherical coordinate - spherical coordinate - streamfunction - non-dimensional streamfunction for spherical coordinates, = /(U a d 2 ) - * non-dimensional streamfunction for bispherical coordinates, defined in equation (26)  相似文献   

11.
Summary The influence of the velocity of the movement of the centre of the cycloneV c.c. on the rate of amplitudes' change A/t and periods' change T/t of storm microseisms is investigated. The dependence A/t=k V c.c. and T/t=k 1 V c.c. is obtained. Unmovable depression (V c.c. =0) does not stipulate the change of A/t and T/t.
u V c.c. A/t T/t . A/t=k V c.c. T/t=1 V c.c. . (V c.c. =0) A/t T/t.

Presented as a scientific communication to the IASPEI Assembly in Madrid, Sept. 1969.  相似文献   

12.
Summary A charged particle moves with velocityv in a constant non-uniform magnetic fieldH, spiralling with Larmor radiusR. IfR is small compared with the scale lengthL of the field, the magnetic moment associated with the Larmor motion of the particle is nearly constant. Consequently , the (pitch) angle betweenv andH, varies as arcsinH 1/2. Hence in such adiabatic motion is approximately the same at points on the path whereH has the same value. But the magnetic moment and the pitch angle may differ materially at two such points, each in the region whereR/L is small, if between them the particle traverses a region whereR/L is not small. This region of non-adiabatic motion scatters the pitch angles.Such scattering is investigated for regions of weak field (R large), with and without the presence of a neutral line along whichH=0. Either type of region, it is found, can scatter the pitch angles. This gives support to the theory proposed byAkasofu andChapman to explain why auroral arcs and bands are very thin.The scattering here examined is of interest also in connection with magnetic mirror devices for nuclear energy transformation. It may also have applications to phenomena of solar and stellar atmospheres.  相似文献   

13.
Summary The general problem of Love wave propagation, in a medium with cylindrical anisotropy of hexagonal type, is formulated. The method of seperation of variables is applied to examine the possibility of obtaining formal solutions for different types of inhomogeneities present in the medium. It is found that when the elastic parameters (C 44 and ) are functions of bothv and the equation of motion is not separable. The use of the technique is illustrated, by considering radial inhomogeneity in an anisotropic cylindrical crustal layer, for obtaining the characteristic frequency equation of Love waves in such a medium.  相似文献   

14.
Summary Runcorn's equations, which can be used to compute the stresses caused by convection flows from the outer gravity field, were transformed so that gravity anomalies or geoid heights can be employed as input data.
au aa, m n¶rt;m u n u mmu u anu, a uu nmau, u maua ma, m unam u¶rt; ¶rt; ¶rt;a, aauu u mmu uu mu¶rt;a.
  相似文献   

15.
Summary Approximate expressions for the Hilbert transform of the functionf(t)=exp(- 0 2 t 2/2) cos( 0 t+v) are determined. This function, given a suitable choice of the three parameters 0, and v, approximates a wide class of seismic signals very well. The approximate expressions for the Hilbert transform enable very simple formulae to be given for the elementary seismograms of the individual seismic body waves (in the zero approximation of the ray theory). This accelerates the computation of ray theoretical seismograms considerably.  相似文献   

16.
We estimate (/T) P of the lower mantle at seismic frequencies using two distinct approaches by combining ambient laboratory measurements on lower mantle minerals with seismic data. In the first approach, an upper bound is estimated for |(/T) P | by comparing the shear modulus () profile of PREM with laboratory room-temperature data of extrapolated to high pressures. The second approach employs a seismic tomography constraint ( lnV S / lnV P ) P =1.8–2, which directly relates (/T) P with (K S /T) P . An average (K S /T) P can be obtained by comparing the well-established room-temperature compression data for lower mantle minerals with theK S profile of PREM along several possible adiabats. Both (K S /T) and (/T) depend on silicon content [or (Mg+Fe)/Sil of the model. For various compositions, the two approaches predict rather distinct (/T) P vs. (K S /T) P curves, which intersect at a composition similar to pyrolite with (/T) P =–0.02 to –0.035 and (K S /T) P =–0.015 to –0.020 GPa/K. The pure perovskite model, on the other hand, yields grossly inconsistent results using the two approaches. We conclude that both vertical and lateral variations in seismic velocities are consistent with variation due to pressure, temperature, and phase transformations of a uniform composition. Additional physical properties of a pyrolite lower mantle are further predicted. Lateral temperature variations are predicted to be about 100–250 K, and the ratio of ( lnp/ lnV S ) P around 0.13 and 0.26. All of these parameters increase slightly with depth if the ratio of ( lnV S / lnV P ) P remains constant throughout the lower mantle. These predicted values are in excellent agreement with geodynamic analyses, in which the ratios ( ln / lnV S ) P and ( / lnV S ) P are free parameters arbitrarily adjusted to fit the tomography and geoid data.  相似文献   

17.
Summary The equations of motion for the free oscillations of a heterogeneous spherical earth model are derived. It is found that the lateral variations of density and elastic moduli couple the odd(even) harmonics of the spheroidal oscillations with themselves as well as with the even (odd) harmonics of the torsional oscillations.List of symbols r, , Spherical coordinates;r is the radial distance from earth's center, is the co-latitude, and is the east longitude - r Space vector denoting a point with coordinatesr, , and - Gradient operator - 2 Laplacian operator - ij Kronecker's delta function - I Identity matrix - i   相似文献   

18.
Summary In this paper the generalized thermoelastic longitudinal waves and the temperature field set up due to coupling of the displacement and the temperature fields, with heat wave travelling with certain finite velocity, in an unbounded medium are studied. The thermoelastic displacement potential and the temperature field at any point are obtained in terms of the surface integrals involving the potential, the temperature and their normal derivatives.Notation x i the cartesian coordinate system,i=1,2,3 - n (u i) the displacement vector - (/x i) the del operator - t /t the derivative with respect to time - T o the temperature corresponding to the natural stat of zero stress and strain - T Absolute temperature - c e the specific heat - , Lamé's constants - 0 the density - coefficient of linear thermal expansion - K thermal conductivity coefficient - kk u - 0 the relaxation time  相似文献   

19.
The results of a detailed numerical study of the behaviour of the convective polar ionosphere are presented. The developed theoretical model produces three-dimensional distribution of electron density, electron and ion temperature. The effects of auroral particle precipitation on the density and temperature structures are studied for winter and low solar activity conditions. The high-latitude ionospheric features, such as the tongue of ionization, the main trough the polar ionization peak, the auroral ionization peak, the high-latitude ionization hole, the tongue of electron temperature, the high latitude minima of electron, temperature, and the ion temperature hot spot are obtained from calculations.Numerically obtained results are used for determining the HF propagation paths in the polar ionosphere. The effects of ionospheric irregularities on high frequency ionospheric radio waves are investigated by using a three-dimensional ray-tracing computer program. Ray-path trajectories are presented for different values of the elevation angle of transmission. From our study, it was found that large-scale irregularity structures of the high-latitude ionosphere, in the presence of the earth's magnetic field, significantly affect high frequency radio wave propagation.  相似文献   

20.
To obtain the temperatureT and volumeV (or pressureP) dependence of the Anderson-Grüneisen parameter T , measurements with high sensitivity are required. We show two examples:P, V, T measurements of NaCl done with the piston cylinder and elasticity measurements of MgO using a resonance method. In both cases, the sensitivity of the measurements leads to results that provide information about T (,T), where V/V 0 andV 0 is the volume at zero pressure. We demonstrate that determination of T leads to understanding of the volume and temperature dependence ofq=( ln / lnV) T over a broadV, T range, where is the Grüneisen ratio.  相似文献   

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