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1.
Summary Cauchy theory of initial stress has been applied to investigate the influence of uniform initial stress on the propagation of plane waves in an unbounded elastic medium. It is found that if the initial principal stresses are unequal, the velocity depends on the direction in which the wave propagates, whereas when the initial principal stresses are equal, the velocity is independent of the direction of wave propagation.  相似文献   

2.
Summary Coda waves viz. the tail portion of an earthquake record have been observed and analysed byCarder, Macelwane and others. They showed that the periods of such waves increase with the increase of epicentral distances.Carder observed that these waves have very little transverse component so that these may be considered as of the type of Rayleigh waves. RecentlyOmote showed that the Coda waves contain three periodsT 1,T 2,T 3 of whichT 1 increases with epi-central distances as observed by previous observers. ButT 2,T 3 remain constant for all earthquakes from different epicentral distances.Omote tried to explain this phenomenon by considering that the surface of the earth consists of several layers andT 2,T 3 are free oscillation periods of the surface layers.T 1 period has been explained bySezawa and also byJeffreys which has been shown byGutenberg. The author has attempted to explain the periodsT 2,T 3 by considering passage of cracks at the focal region. The Rayleigh wave character of Coda waves and low velocity of such waves have been explained.  相似文献   

3.
Summary When a high explosive pressure acts on the boundary of a spherical cavity in an elastic medium, the material in a region around the charge behaves plastically and thereafter an elastic wave is propagated. Not only that but the elastic plastic boundary moves also with a certain velocity which is less than the elastic wave velocitySabodash [3]2). In this paper, firstly the case when the elastic plastic boundary moves with a velocityV 0. (V 0<c) has been dealth with. The pressure in the elastic medium on this boundary has been assumed to be constant and equal toP 0. Secondly the case when the elastic plastic boundary moves with an exponentially decaying velocity has been considered. The pressure in the elastic medium on this boundary has also been assumed to be of exponential character.  相似文献   

4.
Summary An irregular wave group (here called pseudospherical), the existence of which is connected with the velocity boundary at which the velocity decreases discontinuously, is investigated. A schlieren modelling device was chosen for a model investigation of this wave since it permits the investigation of wave fields inside the measured models. The model consisted of two layers of transparent gels, the source lay in the layer of higher velocity. The measurements have shown that an irregular wave in the layer of lower velocity exists only in a certain region along the boundary; its wave front has a spherical form and its intensity decreases rapidly with increasing distance of the source from the boundary. The wave always comes only after the regular refracted wave which conforms with the ray theory. These properties correspond to the properties of a wave first described byOtt [1]3) andBrekhovskikh [2]. In the conclusion of the present paper the possibilities of recording pseudospherical waves in seismology are outlined.  相似文献   

5.
Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically.  相似文献   

6.
Abstract

The velocities of the wave patterns relative to the rotating annulus have been measured with either increasing or decreasing positive radial temperature gradients and different rotation rates, with the fluid in thermal equilibrium and in contact with a rigid lid. The pattern velocities are dependent on initial conditions except in the unique areas of the stability diagram, where the velocities observed with either increasing or decreasing ΔT, overlap. The pattern velocities change discontinuously with each wave number transition, with a particularly large discontinuity at the transition from two to one wave. The frequency of the amplitude oscillations of the waves has been measured also. It has been found that the period of the oscillation of the three wave pattern is inversely proportional to the period of the pattern velocity, which means that in this case the ratio of the frequency of amplitude oscillation and the frequency of the pattern revolution is incommensurate.  相似文献   

7.
Acoustic Doppler current profilers (ADCPs) have been used to measure Reynolds stresses in tidally dominated environments where wave action was minimal. In this paper, we examine observations from a microtidal estuary where the effects of wind stress and surface waves dominate the velocity variance. Reynolds stress measurements in this setting require a technique for addressing surface gravity wave contamination. We present here a method of reducing the effect of wave motion on Reynolds stresses by subtracting coincident observations along the axis of the ADCP beam. Linear wave theory is used to account for the attenuation of wave orbital velocities with depth. Using this method, Reynolds stress values are brought in line with those predicted by drag laws at the surface and bottom. The apparent Reynolds stress that is removed by the along-axis subtraction is shown to be largely due to the interaction of a slight tilt (1°) in the ADCP and the wave orbital velocity. During periods of stronger wind and waves, there is evidence of enhanced near-surface turbulence and momentum flux, presumably due to breaking waves. During these events, our calculated Reynolds stress magnitudes still appear reasonable, although the directions are suspect. We develop a diagnostic technique that clearly demarcates this region when it occurs. Coincident density profile measurements are used with the ADCP data to compute gradient Richardson numbers throughout the water column. Enhanced Reynolds stresses appear to correspond to Richardson numbers less than one. Responsible editor: Alejandro Souza  相似文献   

8.
Summary This study presents the focal mechanism solutions of four South American earth-quakes. These solutions have been determined using the sign of the initial motion ofP wave, and the polarization angle ofS wave. A regional study of the strike of the fault plane, the direction of motion, and the regional stress pattern has been made in which the focal mechanism solutions determined byStauder andBollinger were also used.  相似文献   

9.
The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker’s asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot’s gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.  相似文献   

10.
In this paper we solve analytically wave kinematic equations and the wave energy transport equation, for basic long surface gravity wave in the coastal upwelling zone. UsingGent andTaylor's (1978) parameterization of drag coefficient (which includes interaction between long surface waves and the air flow) we find variability of this coefficient due to wave amplification and refraction caused by specific surface water current in the region. The drag coefficient grows towards the shore. The growth is faster for stronger current. When the angle between waves and the current is less than 90° the growth is mainly connected with the waves steepness, but when the angle is larger, it is caused by relative growth of the wave phase velocity.  相似文献   

11.
This work presents a mathematical modelling of Love wave transference through a pre-stress influenced anisotropic medium with heterogeneity between a sandy medium and an initially stressed anisotropic porous medium. Variable separation method has been induced in order to derive the frequency relation. Using appropriate boundary conditions at two interfaces, the dispersion equation has been obtained in its closed form. Possible particular cases are considered, and the corresponding results are consonant with the classical cases. Numerical computations have been employed to demonstrate the role of inhomogeneity factors, initial stresses and porosity, and are depicted by means of graphs which substantiates that those parameters immensely affect the Love wave velocity. In mineral prospecting and exploring technique in earth, the method and the results of this problem may be applicable.  相似文献   

12.
Summary The possibility of propagation of Rayleigh waves in a transversely isotropic medium resting on (i) a rigid base and (ii) a yielding base has been studied in this paper. In the former case the relation between the wave velocity and ratio of wave length to thickness has been found and in the latter case the frequency equation and its possible solutions are obtained.  相似文献   

13.
Summary It has been found that when seismic energy propagates along the surface of the homogeneous crust beside usual Rayleigh waves, it produces certain instability in layers through which it propagates. In the light of this instability, a type of motion corresponding to longitudinal wave will be prominent in horizontal component compared to the vertical component; while transverse wave will be prominent in the vertical component but weak in the horizontal component, a contradiction with the existing knowledge. This has been identified withP F phase. On taking the medium of propagation as slightly heterogeneous which allows existence of low velocity layer, a few larger number of such instabilities have been found. Velocity equation for Rayleigh waves for such media reveals existence of different velocities corresponding to vertical and horizontal components. Table for these velocities has been furnished.  相似文献   

14.
Summary Offshore areas are sometimes found in which seismic record assumes the appearance of a sine wave or a simple combination of sine waves. It is more interesting to note that the dominant frequency on the singing records is the third harmonic of a fundamental whose wave length is four times the water depth. In this paper it has been proved that this peculiar phenomenon happens due to the slope of the sedimentary layer near the observational points. Using the method introduced byCovert (1958) of finding the Green's function for built in bodies, pressure field has been obtained in the water layer for a two dimensional point source in the same medium and it has been proved that due to the slope of the sedimentary layer singing is caused by waves of wave-length equal to four times the water depth.  相似文献   

15.
Numerical solutions of the wave equation for a particular type of non-linear “constant Q” medium were carried out. These solutions were obtained after the transformation of the space derivatives in finite differences; power series of the time are used to express the solutions. The medium is characterized by a not single valued stress-strain relation; the stresses are greater when the absolute values of strain are increasing (passive work), and are less when they are decreasing (active work). A loss of energy follows which is constant for every cycle and independent of frequency. This model represents the simplest type of medium in agreement with the laboratory data on rock samples. For a similar medium the stress’values do not depend only on the instantaneous value of the strain, but also on the previous strain values, i.e. the history of the medium. All these characteristics are not compatible with linearity and require particular types of computing procedures similar to the one shown in this paper. The results of calculations here shown refer both to the propagation of an isolated wave and to the generation of a wave in a spherical hole by change of pressure. They refer particularly to the shape, the amplitude and the width of the isolated wave along the propagation path. The most important results for this type of medium are the following: a) for a plane single isolated wave, the displacement amplitude wave does not change along the propagated distance. The width increases linearly as function of the distance; b) the corresponding particle velocity decreases in amplitude; c) for single isolated spherical waves the displacement amplitude decreases with propagated distance only due to the geometric factor, i.e. inversely proportional to the propagated distance; its width increases in the same way as for plane waves. The comparison between these theoretical results with the field and seismological data show a sufficiently good agreement as far as the value interval of wave width and frequencies is concerned. Less satisfactory is the comparison regarding a linear dependence of the wave width on the distance. This fact happens probably because in the field often long trains of waves and not isolated waves occur. In effect, for trains of waves the behaviour is different than that of an isolated wave; particularly, for the former the frequency variations along the travelled path is less and the displacement variations greater. However, it seems likely that a further similar theoretical research for trains of waves propagating in this type of non-linear medium might be carried out to complete the present research.  相似文献   

16.
Summary The records at Athens of 85 earthquakes with epicenters in several regions on the earth were used to determine group velocities along thirty five paths. The mean crustal thickness along each path has been estimated by comparing the observations withPress's standard curves. A linear relation has been found between the mean crustal thickness and mean elevation along each path. This relation is in agreement with Airy's isostatic hypothesis. Determination of Love wave dispersion along five paths and Rayleigh wave dispersion along two paths in southeastern Europe and northern Asia Minor gave values from 35 to 45 km for the crustal thickness in this region.  相似文献   

17.
Summary Cauchy theory of initial stress has been applied to investigate the problem of SH waves in an initialy stressed elastic plate. The initial stress is assumed to be a uniform tension or compression along the thickness of the plate. It is found that the initial stress influences the velocities of the dispersive modes only but, it has no influence on the velocity of the non-dispersive wave.  相似文献   

18.
Summary The frequency equation is derived for the propagation of Love waves in the earth's crust, composed of transversely isotropic layers and overlying anisotropic and inhomogeneous mantle. The exact boundary value problem is solved for a single layer and extended to multilayered media by generalizing theHaskell's technique. In fact the problem of deriving the frequency equation has been reduced to finding out the solution of the equation of motion subject to the appropriate boundary conditions. To illustrate the method, the author has derived frequency equations of Love waves for linear, exponential and generalized power law variation of vertical shear wave velocity with depth in the half space overlain by transversely isotropic inhomogeneous stratum.  相似文献   

19.
In a previous study published in this journal, the authors developed a comprehensive methodology for modelling the shear wave velocity profile in crustal rock, for purposes of seismic hazard assessment. The derived shear wave velocity profile was used to estimate the amplification and attenuation mechanisms in the transmission of seismic waves. The ability to conduct seismic hazard assessments in regions of low and moderate seismicity is greatly enhanced by this new modelling approach, given that developing a local attenuation model based on curve-fitting strong motion data is generally not feasible under such conditions. This paper reports a follow-up study conducted to evaluate the significance of near-surface attenuation in bedrock (as distinct from attenuation in unconsolidated soft soil sediments). The κ parameter is used to characterize the extent of this attenuation mechanism. Empirical correlations of κ with two forms of near-surface shear wave velocity parameter in crustal rock have been developed, employing information obtained from global sources in conjunction with that from local studies. The resulting development of two simple equations to predict median values of κ as functions of readily available shear wave velocity parameters represents the key outcome of this study. Applications of the proposed empirical approaches to determine κ have been provided, taking Hong Kong and Melbourne as case studies to illustrate different aspects of the proposed methodology. Consistency between the results obtained by the two recommended approaches has thereby been demonstrated.  相似文献   

20.
Summary The basic concept of synoptic statistical methods for construction of prognostic charts was outlined by the author in a previous paper. As a result of these investigations it was found that a high correlation exists between time and space means of contourheights of an isobaric surface (850 mb surface). As it has been shown later byPichler this result may be interpreted by assuming that the geopotential fields obeys a numerical solution of the second order homogenous differential equation for wave propagation (hyperbolic equation) provided the phase velocity is given by . SinceReuter has used for s=666 km and for t=24 hours the conclusion may be drawn that the phase velocity of the wave propagation has an order of magnitude of 5 m/sec. Actually for long waves in the westerlies such a value can be found on an average. The same method can be used for extended forecast procedures if the wave equation is set down for 5 days mean values. Theoretical considerations lead then to a prognostic formula for a 5 days mean chart (8a). This formula can be applied for a sufficient number of grid points in order to construct prognostic charts. The underlying assumption, namely that the mean geopotential field satisfies also a solution of the wave equation turns out to be quite accurate even if only average values of the phase velocity were used for the computation. The usefullness of the method is illustrated for two cases.

Vortrag gehalten am 7. April 1961 auf der 9. Allgemeinversammlung der «Società Italiana di Geofisica e Meteorologia» (Genova, 6.8. April 1961).  相似文献   

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