Forced vibration of a thin non-homogeneous circular plate having a central hole

Summary This paper deals with the forced vibration produced in a thin non-homogeneous circular plate having a central hole when a periodic force is acting on the internal boundary.     

On twisting of a non-homogeneous circular disk,due to a tangential traction of the boundary of a concentric circular hole

Summary In this note, the stresses and displacements due to tangential traction on the inner boundary of a nonhomogeneous annular circular disk, the outer boundary of the disk being kept fixed have been investigated. Some numerical results are given at the end.     

The effect of couple-stresses in an infinite plate having a circular hole

Summary The investigation of the stress-components in an infinite, plate of isotropic homogeneous material with a circular hole has been made by applying Cosserat's theory of couple-stresses. The plate is acted on by two equal concentrated forces at the diametrically opposite points of the inner boundary.     

On stresses and displacements due to a moving line load over the plane boundary of a heterogeneous elastic half-space

Summary The problem of concentrated line load moving with supersonic speed along the boundary of an isotropic heterogeneous medium has been solved as a plane strain problem. The stresses and displacements in the heterogeneous case considered are found to decay exponentially with distance.     

On the disturbances in a thin elastic circular plate resting on a viscoelastic foundation of Pasternak type

Summary In this paper disturbances due to impulsive as well as transient load in a thin elastic finite circular plate resting on viscoelastic foundation of Pasternak type have been considered separately.     

Numerical modeling of the distribution of horizontal stresses in a moving continental plate

The distribution and time evolution of overlithostatic horizontal stresses in the vertical cross-sections of the model of a solid continent are studied in terms of a 2D numerical model. The continent is moving self-consistently with time-varying mantle flows. Over a period of 50 Ma, the continent, which had been initially located at a distance of about 1500 km from the downward mantle flow (subduction zone), first overlays the region of the marginal sea, then thrusts over the zone of subduction, thus making it inclined and deforming it. It is found that the horizontal tensile stresses observed at the initial stages are succeeded by compressive stresses, especially at the leading edge (up to 40 MPa). This is caused by the change of the dragging action of the subduction zone into the retarding action during the continent crossing over this zone. The dependence of the calculated stresses on the Rayleigh number and on the thickness of the model of the continent is estimated. It is obtained also that the distribution of horizontal stresses along the strike of the continent is rather distinctly indicative of the locations of upward and downward flows in the subcontinental mantle. With the considered values of the model parameters, the tensile stresses in the near-to central regions of the continent may be twice to thrice the tensile stresses at its margins. Hence, in the simplest case of a homogeneous continent, its division will occur in the zone directly above the upward subcontinental flow. Detachment from the continent of the fragments of its edge adjacent to the marginal sea implies that the thickness of the continental plate in that part and/or its strength is considerably lower than in the center of the continent.     

Waves and stresses produced in an elastic medium due to impulsive radial forces and twist on the surface of a spherical cavity

Summary Displacements and stresses produced by impulsive radial pressure and by impulsive twists have been determined. In the former case total flow of energy across a spherical boundary has been obtained.     

On the two dimensional thermo-elastic waves due to the distribution of stresses produced by an impulsive heat nucleus

Summary In this two dimensional thermoelastic problem, the distribution of components of displacement and stress are determined in an infinite elastic solid when the time dependent body force and an impulsive heat nucleus act upon certain region of the solid.     

Changes in the shape of the circumpolar vortex due to heating from above

Summary Based on model considerations it is shown that, under certain assumptions, zonalization of tropospheric circulation may be expected in the region of the auroral oval as a result of heat released at the time energetic electrons penetrate from the Sun into the lower stratosphere.

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On the thermal bending of a thin elastic simply supported rectangular plate resting on an elastic foundation

Pure and Applied Geophysics - Deflection and bending moments of a thin isotropic rectangular plate, having its edges simply supported and maintained at zero temperature, have been investigated in...     

Propagation of an accreting plate boundary: a discussion of new aeromagnetic data in the Gulf of Tadjurah and southern Afar

A detailed aeromagnetic survey of the Republic of Djibouti and immediate surroundings was performed in 1977. This paper summarizes the reduction techniques which are used in order to produce a magnetic anomaly map and discusses the accuracy of this map, which is presented as an insert at a scale of 1/250,000. Two distinct magnetic styles are recognized: linear anomalies with both large amplitude and short wavelength, considered to be typical of oceanic lithosphere, contrast with areas of lower-amplitude longer-wavelength anomalies, which are found mostly in the northern part of the survey. This quiet zone of subdued magnetic style is thought to have undergone major tectonic deformation in the last millions of years. The general morphology of magnetic anomalies is interpreted in terms of a propagating crack model, as proposed by Courtillot [23]. The crack propagates westwards at approximately 3 cm/yr and the crack tip is thought to lie close to Lake Asal, both on the basis of the magnetic data and of other geophysical evidence. The land section of the survey is a central topic of this paper and is interpreted in terms of the crack propagation model in the light of other available geological, geochemical and geophysical data.     

Hilbert transform in the interpretation of magnetic anomalies of various components due to a thin infinite dike

The Hilbert transformH(x) applicable to vertical (Z), horizontal (H), and total (T) magnetic anomalies due to a thin dike of infinite depth extent is derived from the generalised expression of magnetic effectF(x). The depth and dip of the dike is extracted by a simple procedure making use ofF(x) andH(x). A modified version of the amplitude of the analytic signal is given to locate the origin. The abscissa of the point of intersection ofF(x) and the discrete Hilbert transformH(1.x) directly yields the depth to the top. An example for each case is considered theoretically to illustrate the process. Applicability of the method is examined on the vertical component of the well-known magnetic anomaly at Kiirunavaara in northern Sweden, originally described by Von Carlheim Gyllenskjold, as well as on total magnetic anomaly of Bensons Mines, U.S.A.     

On the disturbance due to a point source in an inhomogeneous medium

Summary The problem of a point source in an isotropic, inhomogeneous fluid medium is discussed. It is assumed that the density of the fluid is constant and the acoustic velocity varies with depth asc=c ₀(1 +m z) wherem is a constant andc ₀ is, the velocity at the level of the origin. An approximate expression for the field due to a point source in such a medium is obtained when the medium is infinite as well as when it is semi-infinite. It is found that the results obtained agree with the WKB solution of the problem.     

A model of creep deformation in the lithosphere as a non-isothermal linear viscous circular plate on a Winkler foundation

The lithosphere is known to deform under geologic loads such as those due to surface volcanoes and submerged magma chambers. The lithosphere is modelled here as a linear viscous circular plate supported on the underlying asthenosphere, which in turn is modelled as a Winkler foundation. A two-dimensional steady creep relation is used to derive the governing partial differential equations for deflection, stress and bending moment. The temperature variation through the thickness of the lithosphere is of major importance and is included in the analysis. Solutions to the governing equations are obtained both in general and for an illustrative set of geometric, loading, material and thermal parameters.     

On the disturbance due to a spherical distortional pulse in an elastic medium

Summary Theoretical expressions are derived for the displacement, velocity and stress in the time domain induced by an axially symmetric shearing stress applied at the inner surface of a spherical cavity in a hornogeneous, isotropic, elastic medium of infinite extent. Theoretical seismograms are computed for a step source and for three sources with exponential decay in time. A satisfactory time-dependence of the source can be obtained by combining the step source with one or more exponentially decaying sources.     

Corrugations on the core boundary interfaces due to constitutional supercooling and effects on motion in a predominantly stratified liquid core

With the notion that interface and boundary layer phenomena play an important part in those geophysical processes which, by observation appear to be related to the earth's internal boundaries between the solid and liquid phases of its core and mantle, constitutional supercooling suggests itself as a mechanism capable of generating and maintaining inhomogeneities in concentration and density at the boundaries of the liquid core. The mechanism of constitutional supercooling requires a slow overgrowth of mantle and core, and, it implies that this growth process is associated with a selective partitioning of certain impurities shared in different concentrations by the liquid core and the solid phases of mantle and inner core. It can lead to the formation of regular (quasi-periodic) corrugations of the core-mantle and the inner-outer core boundaries with amplitudes of the order of 1 km. Mass redistributions, off-setting continually regenerated concentration and density inhomogeneities, provide a mechanism for core motion in the form of concentration currents. A regular distribution of corrugations or humps may give rise to (zonal) patterns of closed loops of concentration currents either in layers adjacent to the solid-liquid interfaces, or in loops extending through the entire outer core. The development of regular flow patterns should be enhanced if, referable to one particular constituent of the liquid phase, some parts of the solid-liquid interfaces acted as sources, others as sinks.     

Quasi-static Planar Deformation in a Medium Composed of Elastic and Thermoelastic Solid Half Spaces Due to Seismic Sources in an Elastic Solid

A two-dimensional problem of quasi static deformation of a medium consisting of an elastic half space in welded contact with thermoelastic half space, caused due to seismic sources, is studied. Source is considered to be in the elastic half space. The basic equations, governed by the coupled theory of thermoelasticity, are used to model for thermoelastic half space. The analytical expressions for displacements, strain and stresses in the two half spaces are obtained first for line source and then for dip slip fault. The results for two particular cases, adiabatic conditions and isothermal conditions, are also obtained. Numerical results for displacements, stresses and temperature distribution have also been computed and are shown.     

A fundamental solution due to a periodic point force in the interior of an elastic half-space

The fundamental solution for a periodic point force in the interior of a three-dimensional, homogeneous, isotropic, elastic half-space is derived. The method of synthesis and superposition is employed to obtain the solution in the Laplace transform as well as the frequency domain. These correspond to the dynamic equivalent of Mindlin's static half-space point force solutions. It is reduced, for certain limiting conditions, to the dynamic equivalent of Boussinesq's and Cerruti's problems of a normal and tangential periodic point force respectively, on the boundary of a half-space. Also, static solutions of Mindlin, Boussinesq and Cerruti are recovered for small frequency parameters. Finally, results are presented and compared with other available solutions.     

1983–2003 decaying rate of deflation at Askja caldera: Pressure decrease in an extensive magma plumbing system at a spreading plate boundary

New deformation data from the Askja volcano, Iceland, show that the volcano's caldera has been deflating continuously for over 20 years, and confirm that the rate of subsidence is slowing down. The decay in subsidence rate can be fitted with a function of the form e ^{− t / τ} , where τ is 39 years. Reanalysis of GPS data from 1993–1998 show that these data can be fitted with a model calling for two Mogi point sources, one shallow, and another one much deeper (16.2 km depth). Pressure decrease occurs in both sources. The deeper source is responsible for observed horizontal contraction towards Askja at distances that cannot be explained by the shallower source. Plate spreading of 19 mm/year distributed evenly over about 100-km-wide zone is also favoured by the data.