Propagation of love waves in a medium containing a heterogeneous layer lying over a heterogeneous half space

Summary Propagation and the dispersion equation of love waves for a few generalised models of heterogeneous crust over a heterogeneous mantle have been investigated. Dispersion equations obtained by a few earlier authors have been shown to be the special cases of the above results.     

On the propagation of love waves in a heterogeneous layer lying on a homogeneous medium

Summary The present note is devoted to find out the possibility of propagation of love waves in a heterogeneous layer of finite depth lying on a homogenous semi-infinite elastic medium, the rigidity and density in the upper layer varying as (1–sinz), where is a constant andz is the vertical distance from the interface. The numerical results for the phase velocity for some special Earth models are given.     

Propagation of Love type waves in a non-homogeneous layer lying over a vertically semi-infinite homogeneous isotropic medium

Summary The aim of this paper is to study the propagation of love-type waves in a homogeneous half-space overlain by a heterogeneous crust with various types of heterogenety. Frequency equations are obtained in each of the cases and numerical calculations are done in some cases and the results thus obtained are compared with those done byJeffreys andMitra [3]²).     

Propagation of Rayleigh waves in an axially symmetric heterogeneous layer lying between two homogeneous halfspaces

Summary The propagation of Rayleigh type waves in an axially symmetric inhomogeneous layer lying between two halfspaces is studied. The halfspaces are supposed to be identical in their elastic properties. The variation of the parameters in the layer is assumed to be of the form where is a constant andz is the distance measured from one interface into the layer. With this assumption, the vector wave equation for the layer is separable. The solution is obtained in terms ofWhittaker's functions and the frequency equation of Rayleigh type waves is derived.     

Evolution of localized folding for a thin elastic layer in a softening visco-elastic medium

Long compressed elastic struts on softening elastic foundations have a tendency to buckle locally. The same tendency is demonstrated here for the instantaneous response of elastic struts supported by visco-elastic media. A governing nonlinear partial differential equation is derived to describe the evolution of the localized form in time. Under the assumed constant end-shortening this is found to be approximated by a coupled set of seven ordinary differential (diffusion) equations. As the load drops to zero, the localized buckle pattern evolves towards the form of the single long wave, but remains aperiodic for all time. Three-dimensional plots show how this localized pattern changes over time.     

Response of a randomly inhomogeneous layer overlying a homogeneous half-space to surface harmonic excitation

The paper is concerned with the study of the effect of the randomness of material parameters on mean wave propagation in a semi-infinite viscoelastic medium. The medium considered in this paper is a configuration of a randomly non-homogeneous layer overlying a homogeneous half-space and is loaded harmonically on the top surface. The method used is that of Karal and Keller and is based on the idea of fundamental matrix and Bourret approximation. The integro-differential equation obtained in this paper is solved by the Laplace transform method. By using boundary and continuity conditions the mean wave solution is obtained. Numerical results show that the correlation functions, which introduce long-range interactions, can be the source of the wave amplification.     

Propagation of Love Waves in a certain type of heterogeneous layer

Summary Propagation of Love Waves in a layer in which the velocity first decreases with depth, reaches a miniumm at a certain depth and then increases as the depth further increases in studied in this paper.     

Propagation of Rayleigh waves in a layer lying over a heterogeneous half space

Summary Propagation of Rayleigh waves in a layer lying over a heterogeneous incompressible half space has been studied. The dispersion equations have been derived and displacements due to an infinite line source have also been investigated.     

On love wave dispersion in a homogeneous layer lying over a laterally heterogeneous half-space

A method is proposed for the determination of the dispersion equation of Love waves propagating in a homogeneous layer lying over a laterally inhomogeneous half-space. The proposed method can be made to work only when the lateral inhomogeneities in the lower half-space are finite in nature so that their Fourier transforms are available. As an illustration the dispersion equation of Love waves is obtained for one of such media in which the shear-wave velocity and the rigidity in the lower half-space either increases or decreases along the direction of propagation of waves according as the parameter of heterogeneity is positive or negative.     

Seismic wave propagating in Kelvin-Voigt homogeneous visco-elastic media

The earth media friction attenuates the energy of seismic wave. Obviously, that earth medium is treated as viscoelasticity is more appropriate than as elasticity. Seismic wave in visco-elastic media contains abundant lithology information of the medium. The investiga-tions of the solutions of visco-elastic wave equations, velocities of seismic wave propagating and the at-tenuation of seismic wave in the visco-elastic media are very important for geophysical prospecting tech-nology. Under a sma…     

The disturbance due to a point source in a homogeneous liquid layer over a heterogeneous liquid half-space

Summary The problem of a periodic point source in a homogeneous liquid layer overlying a heterogeneous liquid half-space is discussed. After obtaining the formal solution, the path of integration for the displacement potential of the layer is transformed from the positive real axis to the positive imaginary axis and the Sommerfeld contour and the latter is further distorted to the modified Sommerfeld contour. The residues of the integrand at the poles contained within the Sommerfeld loop constitute the normal mode solution to the problem. The integrands in the expressions for the integrals along the imaginary axis are expanded in a series of negative powers of exponentials and then some of the terms in these expansions are evaluated approximately. This gives various waves reflected from the interface and the integral along the Sommerfeld loop vanishes. The frequency equation is obtained, also by the principle of constructive interference. An expression for the reflection coefficient at an interface of two liquid media, the upper medium being homogeneous and the lower one inhomogeneous, is obtained.     

Propagation of waves in a visco-elastic half-space due to internal sources

Summary The nature of waves and disturbances generated by a time-periodic concentrated force acting inside a visco-elastic half-space has been studied. Interpretations have been given to the various terms in the expressions for the displacement components.     

Disturbances produced in a visco-elastic medium by transient torsional body forces

Summary The disturbances produced in a semi-infinite visco-elastic medium and in a layer of visco-elastic material resting on a rigid foundation by transient torsional body forces have been considered. Formal solutions have been obtained for a general type of body force, and this solution has been used to obtain the displacements for a transient torsional point source in the case of a semiinfinite medium, and for a cylindrical source of finite dimensions and a line source in the case of the layer of visco-elastic material mentioned above. Solutions have also been obtained for a transient shearing stress applied at the free surface of the layer mentioned above.     

Love waves due to a point source in an axially symmetric heterogeneous layer between two homogeneous halfspaces

Summary Acoustic gravity waves, propagating over a spherical earth with an isothermal and windless atmosphere, are considered. The perturbed pressure is expressed as a sum of discrete modes which are shown to be orthogonal. It is found that the excitation for the modes is determined by the specified normal particle velocity over a conical surface enclosing the source. One of the modes excited is shown to have characteristics closely akin to a Lamb wave on a flat earth for an isothermal atmosphere.This work was carried out while the author was a visiting professor at Harvard University.     

Propagation of Rayleigh waves on visco-elastic cylindrical surfaces placed in a magnetic field

Summary This paper studies axial Rayleigh waves in visco-elastic cylinder surrounded by vacuum and for body of same material with a cylindrical cavity. Magneto-elastic equations of motion for wave propagation in the radial and axial direction have been solved to obtain frequency equations.     

Study of the field of a point harmonic source ofSH-waves in a stratified medium and in a medium with a corrugated interface by finite difference methods

Summary The paper presents a numerical solution of the propagation of SH-waves in a stratified and corrugated medium using the finite difference method. There the problem of a suitable choice of mesh is also discussed.     

On disturbances in a visco-elastic medium of Maxwell type in contact with a liquid medium and subjected to a magnetic field

Summary The problem of disturbances in a visco-elastic medium due to Maxwell in contact with a liquid medium — both being perfectly conductive — has been investigated when an impulsive force acts along the plane of the contact. The electro-magnetic equations of Maxwell, equation of elasticity and the stress-strain relations of the material have been used in the investigation.