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1.
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
2.
The vertical velocity, , and the diabatic heating were computed at 800, 600, 400 and 200 mb surfaces using the Omega equation. The highest contribution to is from the diabatic heating produced by condensation associated with the precipitations appearing to be the main source of diabatic heating. The net radiative cooling and the thermal advection in the upper troposphere over the warm anticyclone result in diabatic cooling over the eastern part of the Bay of Bengal and adjoining northern and eastern regions.List of Symbols Used
C
p
Heat capacity at constant pressure
-
f
Coriolis parameter
-
g
Acceleration due to gravity
-
P
Atmospheric pressure
-
Q
Diabatic heating rate per unit mass
-
R
Gas constant of air
-
S
Static stability parameter
-
t
Time
-
U, V
Zonal and meridional wind components
-
Specific volume
-
Relative vorticity
-
Absolute vorticity
-
Potential temperature
-
Geopotential
-
Vertical velocity (dP/dt)
- 1
Adiabatic vertical velocity
- 2
Vertical velocity due to certain forcing
- 3
Diabatic vertical velocity
-
Isobaric gradient operator
- 2
Laplacian operator
-
J(A, B)
Jacobian operator 相似文献
3.
Prof. K. Ledersteger 《Pure and Applied Geophysics》1959,44(1):1-19
Zusammenfassung Die Gleichgewichtsfiguren lassen sich gänzlich unabhängig vom Dichtegesetz durch die Eingeschaft charakterisieren, daß der Absolutbetrag des Formparametersf0 ein Minimum sein muß. Diese merkwürdige Eigenschaft liefert eine Gleichung zwischen der geometrischen Abplattung und den beidenStokesschen Konstanten und , mit deren Hilfe aus den 4 Lösungen desHelmertschen Gleichungssystems für eine bestimmte Masse die 3 Gleichgewichtsfiguren ausgesiebt werden können. Jede beliebige heterogene sphäroidische Gleichgewichtsfigur ist entweder durch die Masse und die Gestalt ihrer freien Oberfläche oder durch die Masse und drei physikalische Parameter gänzlich eindeurig bestimmt; sie hat ein streng individuelles Dichtegesttz. Aus der dreifach unendlichen Mannigfaltigkeit der Gleichgewichtsfiguren können linear Reihen herausgegriffen werden, indem man entweder zwei physikalische Parameter festhält oder indem man die Figuren aufsucht, welche eine gegebene Fläche zur gemeinsamen äußeren Niveaufläche besitzen oder die Reihe jener Gleichgewichtsfiguren, die sich aus der Schar der äußeren Niveauflähen einer gegebenen Gleichgewichtsfigur bilden läßt.Obwohl das HauptträgheitsmomentC keineStockessche Konstante ist, kann das durch ,W
0 undC eindeutig definierte Normalsphäroid der Erde hypothesenfrei bestimmt werden, weil in der Reihe (,K) auch die Trägheitsmomente und damit die dynamische Abplattung konstant ist. Damit kann die empirisch bekannte dynamische Abplattung mittels des Rückganges auf die homogene Ausgangsfigur der Reihe (,K) durch die statische Abplattung ersetzt werden. Allerdings muß der Ableitung des Normalsphäroides an Stelle der primär unbekannten Werte für die Erdmasse und den Potentialwert des Geoides die Äquatorschwere und die Äquatorachse zugrunde gelegt werden.Abschließend werden noch die drei linearen Reihen (,W
0), (,K) und (W
0,K) diskutiert, welche sich im Normalsphäroid schneiden müssen. Auch kann in dem mit den Achsena, undh
m
gebildeten Koordinatensystem die Hüllfläche der Gleichgewichtsfiguren angegeben werden; sie ist durch den Formparameterf=–3a2/2 gekennzeichnet.
Summary The figures of equilibrium independant from the law of density in their interior can be characterized by the remarkable property that the absolute value of the «shape-parameter» must be a minimum. This gives an equation between the flattening and the twoStokes constant and , by which the 3 figures of equilibrium can be selected from the 4 solutions ofHelmert's equations for a given mass. Each inhomogeneous spheroidical figure of equilibrium is determined unequivocally by the mass and the shape of its free surface or by the mass and three physical parameters; the law of density is strictly individual. From the threefold infinite multiplicity of the figures of equilibrium linear series are to find out with two fixed physical parameters or you can compute a series of figures with a common level surface or the series built by all level surface of a given figure of equilibrium.Though the moments of inertia are notStokes constants the normal spheroid of earth unequivocally defined by ,W 0 andC can be determined without hypotheses, because in the series (,K) also the moments of inertia and the mechanical ellipticity are constant. Therefore the empirically known mechanical ellipticity can be substituted by the static flattening returning to the homogenous figure in the beginning of the series. Of course the determination of the normal spheroid of earth demands the knowledge of gravity in equator and of the equator-axis instead of the unknown mass of earch series (,W 0), (,K) and (K,W 0), which intersect in the normal spheroid, are discussed. Also the boundary surface of the figures of equilibrium in the Cartesian system of the coordinatesa, andh m is discussed; this surface is determined byf=–3a2/2.相似文献
4.
Zusammenfassung Aus der schon früher bewiesenen Eindeutigkeit des Dichtegesetzes der sphäroidischen Gleichgewichtsfiguren ergibt sich die Möglichkeit, aus einer gegebenen Gleichgewichtsfigur durch «Entblätterung» eine unendliche Reihe neuer Gleichgewichtsfiguren derselben Rotationsgeschwindigkeit mit ständig abnehmender Größe und Masse zu bilden. Auf diese Weise kann man jede beliebige innere Niveaufläche der ursprünglichen Figur bloßlegen und aus der von ihr umschlossenen TeilmasseE, der Rotationsgeschwindigkeit , der Äquatorachsea und der Äquatorachsea
h
des homogenen Ausgangsellipsoides der zugehörigen Figurenreihe (,C) die Abplattung berechnen und gewinnt so die Abplattungsfunktion im Innern einer Gleichgewichtsfigur gänzlich unabhängig von derClairautschen Differentialgleichung. Die Methode der Entblätterung ist auch auf höherparametrige Gleichgewichtsfiguren mit unstetigem Dichtegesetz anwendbar; sie liefert für dasWiechertsche Modell die Kernoberfläche in einer Tiefe von 3864.75 km und einen Dichtesprung von 17.84.
Summary In a previous paper I have shown, that the law of density of the spheroidal figures of equilibrium is strictly individual. This makes it possible from a given figure of equilibrium by the so called method of «stripping of leaves» to gain an infinite series of new figures of equilibrium with permanently decreasing size and mass. In this manner any inner level surface of the given figure can be laid bare and its flattening can be calculated from the enclosed part of massE, the rotation velocity , the equator axisa and from the equator axisa h of theMacLaurin ellipsoid in the beginning of the series (,C) belonging to the seeked figure. So the function of flattening in the interior of any equilibrium figure is gained totally independant fromClairaut's differential equation. The method of «stripping of leaves» also can be used for figures of equilibrium with more than one form-parameter and with discontinual density distribution. It yields forWiechert's model the surface of the core in a depth of 3864.75 km and a discontinuity of 17.84 in density.相似文献
5.
A recurrence procedure is outlined for constructing asymptotic series for surface wave field in a half-space with weak lateral heterogeneity. Both horizontal variations of the elastic parameters and of the wave field are assumed small on the distances comparable with the wavelength. This is equivalent to the condition that the frequency is large. The Surface Wave Asymptotic Ray Theory (SWART) is an analog of the asymptotic ray theory (ART) for body waves. However the case of surface waves presents additional difficulty: the rate of amplitude variation is different in vertical and horizontal directions. In vertical direction it is proportional to the large parameter . To overcome this difficulty the transformation equalizing vertical and horizontal coordinated is suggested, Z = z. In the coordinates x,y,Z the wave field is represented as an asymptotic series in inverse powers of . The amplitudes of successive terms of the series are determined from a recurrent system of equations. Attention is paid to similarity and difference of the procedures for constructing the ray series in SWART and ART. Applications of SWART to interpretation of seismological observations are discussed. 相似文献
6.
In a previous paper (Makropoulos andBurton, 1983) the seismic risk of the circum-Pacific belt was examined using a whole process technique reduced to three representative parameters related to the physical release of strain energy, these are:M
1, the annual modal magnitude determined using the Gutenberg-Richter relationship;M
2, the magnitude equivalent to the total strain energy release rate per annum, andM
3, the upper bound magnitude equivalent to the maximum strain energy release in a region.The risk analysis is extended here using the part process statistical model of Gumbel's IIIrd asymptotic distribution of extreme values. The circum-Pacific is chosen being a complete earthquake data set, and the stability postulate on which asymptotic distributions of extremes are deduced to give similar results to those obtained from whole process or exact distributions of extremes is successfully checked. Additionally, when Gumbel III asymptotic distribution curve fitting is compared with Gumbel I using reduced chi-squared it is seen to be preferable in all cases and it also allows extensions to an upper-bounded range of magnitude occurrences. Examining the regional seismicity generates several seismic risk results, for example, the annual mode for all regions is greater thanm(1)=7.0, with the maximum being in the Japan, Kurile, Kamchatka region atm(1)=7.6. Overall, the most hazardous areas are situated in this northwestern region and also diagonally opposite in the southeastern circum-Pacific. Relationships are established between the Gumbel III parameters and quantitiesm
1(1),X
2 and , quantities notionally similar toM
1,M
2 andM
3 although is shown to be systematically larger thanM; thereby giving a physical link through strain energy release to seismic risk statistics. Inall regions of the circum-Pacific similar results are obtained forM
1,M
2 andM
3 and the notionally corresponding statistical quantitiesm
1(1),X
2 and , demonstrating that the relationships obtained are valid over a wide range of seismotectonic enviroments. 相似文献
7.
M. Dunst 《Pure and Applied Geophysics》1975,113(1):535-548
Summary Investigating the jetstream formation in the upper troposphere, it becomes evident that two-dimensional transfer processes are, to a high degree, responsible for the accumulation of kinetic energy and momentum in those upper tropospheric regions. To shed light on these processes a series of barotropic model experiments has been carried out using a special dynamic procedure for vortex generation. In a large, rotating, cylindrical vessel (filled with water, rotation rate 0) three smaller cylinders have been fitted eccentrically. Their rotation relative to the vessel (rotation rate
i
,i=1, 2, 3) produces a sharply limited narrow region around each of them, where a nearly two-dimensional relative motion can be observed. Beyond this region — we call it friction zone — there is no motion. Now if we impose some perturbation on this steady mean flow (e.g. by setting
i
= 0) the zonal current breaks down into a definite number of vortices which show a random distribution. The dynamic behaviour of these nearly two-dimensional vortices can then be studied.The main results are: I) After the sudden breakdown of the friction zones the most intensive eddies, which are cyclonic, drift more or less directly towards the centre to be organized there into a larger vortex. This development is strongly influenced by the -effect and the ratio =
i
/0, which controls the supply of rotational energy. II) If there exists a steady zonal basic current, the vortices will be more and more deformed when approaching and penetrating the zonal flow until they are wholly incorporated. 相似文献
8.
By using Molodensky and Sasao (1995a) and Molodensky and Groten (1998) an approach of expansion in powers of the small parameter =(+)/ (where + and are the frequencies of nutational motion in space and in a mantle-fixed reference frame, respectively, is tidal frequency) a theory of diurnal Earth tides and nutation for a realistic model of the Earth with an inhomogeneous, viscous liquid core and an anelastic mantle is constructed. It is shown that our approach is self-consistent for semi-annual, annual, and principal nutational components (when ||1/180). By comparing the results of modern VLBI-nutational data and the results of our calculations, we have found the region of possible values of the parameters which describe the anelastic properties of the Earth's lower mantle and the viscosity of the liquid core. It is shown that modern VLBI-data are about six orders of magnitude more sensitive to the liquid core viscosity than modern seismic data or Earth free oscillations data. 相似文献
9.
The VLF-wave frequency modulation efficiency as a function of magnetosphere plasma parameters under the weak pitch-angle diffusion regime is studied. The study is based on the VLF growth-rate modulation both in the magnetosphere equatorial plane and after integrating along the magnetic field line. It is shown that for the typical quiet magnetosphere plasma parameters the relative shift of the maximum intensity frequency m/m is approximately equal to relative disturbance of the magnetic field in the magnetosphere equatorial plane, but may exceed it when both electron temperature anisotropy and the parameter are small; here is the total-to-warm electron content ratio and is the electron parallel beta. It is also shown that relative shift of the maximum intensity frequency m/m after integrating along the field line is not less than 50% from its value at the equatorial plane, which allows the use of the equatorial-plasma-parameter data to estimate the VLF frequency modulation on the ground. The upper cut-off frequency modulation is considered as well. The calculated theoretical sonagrams show that this frequency modulation may be related to the non-dispersive and to the inverted-V structures of QP hiss. 相似文献
10.
Calibrating functions for determination of P-wave spectral magnitudes calculated by Duda and Yanovskaya (1994) on the basis of the IASP91 velocity model and the PREM Q-model are verified empirically. For this purpose IRIS broadband records for 120 earthquakes are used, each earthquake having been recorded at about 100 stations. The discrepancies indicate that anelastic absorption assumed in PREM is too high. New calibrating functions are calculated on the basis of the AK135 velocity and anelasticity models (Kennet et al., 1995; Montagner and Kennet, 1996), in which Q in the mantle is higher than in PREM. The verification of the new calibrating functions based on the same observations yields magnitude figures less depending on the epicentral distance. In addition the parameter 2in the Liu-Anderson Q(T) model is estimated, proceeding from the assumption that on the average the radiated spectra comply with the 2-model. The value of 2 was assumed to be 0.1 s in the analysis and its use resulted in the verification of the 2-model for the source spectrum. 相似文献
11.
Summary On the basis of investigating 10 storms (1965–1967) good correlation was found between the density of the solar wind energy (2=1/2mNv2) and the intensity of the main phase of the geomagnetic storms, expressed in terms of the maximum decrease of the horizontal intensity (B=H/cos). The relation between 2, or Nv2, and B could then be used to determine the quantities and 0 ( is the factor expressing the increase in energy density in the magnetosphere, 0 is the energy density of the particles in a quiet magnetosphere). A comparison with the directly observed distribution of the energy density of the particles in the magnetosphere indicates that the computed value of 0 seems to be realistic. The magnitude of the factor will have to be checked again. 相似文献
12.
Dr. H. P. Schmitz 《Pure and Applied Geophysics》1949,15(3-4):215-219
Zusammenfassung Mittels der Differentialgleichungen für den Rotor und die Divergenz horizontaler turbulenter Luftbewegung und der Kontinuitätsgleichung wird näherungsweise die Vertikalbewegung in Abhängigkeit von den Druckänderungen bestimmt, deren zeitliche Variation als vertikal abnehmende periodische Schwankung (unter Berücksichtigung verschiedener Frequenzen ) angenommen wird. In allen durchgerechneten Fällen hängt die Vertikalgeschwindigkeit der Troposphäre in hohem (mit variierendem) Masse von der Reibung ab. Bei vielen, insbesondere den kleineren Frequenzen vorkommender Grösse besteht die Vertikalbewegung der unteren Troposphäre überwiegend aus dem Teil, der ohne Turbulenzreibung nicht entstehen würde. Auf diesem Wege kann die Bodenreibung die Vertikalbewegung und mittels dieser die Luftströmungen und Druckänderungen in allen Höhen massgeblich beeinflussen.
Summary By means of the differential equations of curl and divergence of horizontal turbulent motion of air and the equation of continuity an approaching vertical motion is determined in dependance of pressure changes the temporal variation of which is supposed as a vertically decreasing oscillation (with regard to different frequencies ). In all calculated cases the vertical motion of the troposphere is modified by friction in a high degree (varying with ). With many, especially the smaller frequencies of realized magnitude vertical velocity of the lower troposphere consists prevailingly of that part which would not arise without additional stress components of turbulent motion. In this way friction at the earth's surface is able to influence essentially the vertical motion and by it the air currents and pressure changes in all levels.相似文献
13.
Chris Marone 《Pure and Applied Geophysics》1991,137(4):409-419
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
14.
Summary Drawing on papers [4, 5] a semi-quantitative model of filtration and resonance of a linearly polarized HM-wave has been constructed in a horizontally stratified Earth atmosphere. The wave is filtered in a system of 3 homogeneous layers, limited by two halfspaces. Attenuation of the wave is only assumed in the lower layer, i.e. in the ionosphere. A relation has been derived for the amplitude coupling factor HT/HF expressing the absolute ratio of the amplitude of the wave after transmission through the system of layers and the amplitude of the wave, incident at the system of layers. The mechanism of geomagnetic pulsations is illustrated on the principle of the resonance of a HM-wave in the Earth's magnetosphere. The magnetosphere has been replaced by the said system of layers, and the dependence of HT/HF=f() on the parameters of the system of layers has been studied using a computer. 相似文献
15.
A new dissipation model based on memory mechanism 总被引：5，自引：0，他引：5
Summary The model of dissipation based on memory introduced by Caputo is generalized and checked with experimental dissipation curves of various materials.List of symbols
unidimensional stress
-
unidimensional strain
-
Q
–1
specific dissipation function
-
c(t)
creep compliance
-
m(t)
relaxation modulus
-
c
0
instantaneous compliance
-
m
equilibrium modulus
- (t)
creep function
-
relaxation function
- ()
spectral distribution of retardation times
-
spectral distribution of relaxation times
-
c
*()
complex compliance
-
m
*()
complex modulus
- tang
loss-tangent 相似文献
16.
Summary The secular positive acceleration of the Earth's rotation has been computed on the basis of the observed secular decrease of the second zonal harmonic[5]. It corresponds to the observed secular deceleration of the Earth's rotation which should be greater because of oceanic tides.
¶rt; u a¶rt;a u m aauu [5], u ¶rt;a num u au. m mmmu a¶rt;a u mu au u, m.. n¶rt; n m uu , ¶rt; m n auu nuua.相似文献
17.
Low frequency electrostatic waves are studied in magnetized plasmas with an electron temperature which varies with position in a direction perpendicular to the magnetic field. For wave frequencies below the ion cyclotron frequency, the waves need not follow any definite dispersion relation. Instead a band of phase velocities is allowed, with a range of variation depending on the maximum and minimum values of the electron temperature. Simple model equations are obtained for the general case which can be solved to give the spatial variation of a harmonically time varying potential. A simple analytical model for the phenomenon is presented and the results are supported by numerical simulations carried out in a 2.5-dimensional particle-in-cell numerical simulation. We find that when the electron temperature is striated along B0 and low frequency waves (ci) are excited in this environment, then the intensity of these low frequency waves will be striated in a manner following the electron temperature striations. High frequency ion acoustic waves (ci) will on the other hand have a spatially more uniform intensity distribution. 相似文献
18.
Non-linear - dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of - solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo waves amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunders minimum. 相似文献
19.
Summary Two alternative methods are presented of determining the secular changes of the geoid in the Fennoscandian uplift region. Both are based on the Airy-Heiskanen hypothesis of isostatic compensation. The first alternative is the usual Stokes integration of changes of free-air anomalies in the given region. Another alternative was derived, which is based on calculating the gravitational potential of the surface uplift layer and of the same layer at the depth of compensation. The calculated changes of the shape of the geoid were then compared with the results of Bjerhammar's geophysical interpretation of the expansion of the Earth's gravity potential (regional depression of the geoid in the Fennoscandian uplift region). Regression analysis indicates a strong correlation between the two quantities (r=0.88). The time required to level this depression of the geoid is estimated. A relation was derived for improving the accuracy of the observed values of Fennoscandian uplifts, which takes into account the elastic reaction of the Earth's body to the change of gravitational potential and perturbations, caused by the secular decrease of the depth of the northern part of the Baltic Sea.
¶rt;ma ¶rt;a auama m¶rt;a n¶rt;u uuu¶rt;a amu n¶rt;a a¶rt;uu. a u¶rt;m uunm uamu nauu u-aa. auam — umuau ma uu aau ¶rt; ¶rt; ¶rt;a amu. ¶rt; m auam, a a uuuaumau nmuaa nm n¶rt;a, u a au nauu. am u uu u¶rt;a auam mamau aaa nuu umnmauu au nmuaa u mmu u (ua ¶rt;nuuu¶rt;a amu a¶rt;uauu). u aau aam a u au u uu (r=0,88). uam , ¶rt;u ¶rt; auau a ¶rt;nuuu¶rt;a. ¶rt; mu ¶rt; mu u au n¶rt; a¶rt;uauu, a n au u a uuaumau nmuaa u u, mau u uu amu amu .相似文献
20.
Riassunto Il lavoro riguarda una serie di misure su campioni di 5 tipi diversi di rocce italiane aventi lo scopo di determinare la rispettiva conducibilità termica. Dopo la descrizione dell'apparecchiatura usata, vengono esposti i risultati ottenuti, analizzando in dettaglio l'influenza della scistosità. In base alle misure fatte su campioni di ardesia questa influenza può esprimersi con la formola:k
=k
90+m cos , dove è l'angolo fra la direzione del flusso termico ed il piano di stratificazione, mentrem è una costante caratteristica della scistosità.
Lavoro eseguito con un contributo del Consiglio Nazionale delle Ricerche (Comitato per la Geologia). 相似文献
Summary Experiments made for obtain the thermal conductivity of different kinds of italian rocks are described and discussed. The effect of schistosity was derived for slate rocks and it can be represented with the formula:k =k 90+m cos , where is the angle between the direction of thermal flux and the plain of stratification, whereasm is a constant characterizing the schistosity.
Lavoro eseguito con un contributo del Consiglio Nazionale delle Ricerche (Comitato per la Geologia). 相似文献