Effect of surface stress and irregularity of the interface on the propagation of SH-waves in the magneto-elastic crustal layer based on a solid semi space (original) (raw)
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Latin American Journal of Solids and Structures
The present paper studies the Propagation of SH waves in a double non-homogeneous crustal layers lying over an isotropic homogeneous half-space, where upper layer ((i.e. rigidity and density varying trigonometrically with depth) and intermediate layer (i.e. rigidity and density varying parabolically with depth). The wave velocity equation has been obtained. Closed form solutions have been derived separately for the displacements in two non-homogeneous crustal layers and lower half-space. The dispersion curves are depicted by means of graphs for different values of non-homogeneity parameters and thickness ratio for layers.
Effect of Gravity and Magnetism on Surface Wave Propagation in Heterogeneous Earth Crust
Procedia Engineering, 2016
This paper aims to study the propagation of surface wave in two initially stressed heterogeneous magnetoelastic transversely isotropic media lying over a transversely isotropic half-space under the action of gravity. Heterogeneities of both the layers are caused due to exponential variation in elastic parameters. Dispersion relation is obtained in closed form by using Whittaker's asymptotic expansion. Magnetoelastic coupling parameters, heterogeneity, horizontal compressive initial stress and gravity parameters have remarkable effect on the phase velocity of surface wave. The obtained dispersion relation is found to be in well agreement with the classical Love-wave equation. Comparative study and graphical illustration has been made to exhibit the outcomes.
Crustal Reflection of Plane SH Waves
Journal of Geophysical Research, 1960
An equation has been derived for the amplitude of the free surface displacement due to plane SH waves incident at any angle at the base of a layered crust. Numerical computations have been carried through for the case of a single-layered model of the continental crust. At any given angle of incidence the surface amplitude goes through a series of minima and maxima at periods which, in the single layered case, are harmonically related. At nearly grazing angles of incidence the surface amplitude is relatively small except at periods in the neighborhood of the cutoff periods of the second-and higher-order Love-wave modes.
Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface
Journal of Vibration and Control, 2014
In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.
Acta Geophysica, 2011
This paper stands to investigate the possibility of propagation of SH waves due to a point source in a magnetoelastic monoclinic layer lying over a heterogeneous monoclinic half-space. The heterogeneity is caused by consideration of quadratic variation in rigidity. The methodology employed combines an efficient derivation for Green's functions based on algebraic transformations with the perturbation approach. Dispersion equation has been obtained in the closed form. The dispersion curves are compared for different values of magnetoelastic coupling parameters and inhomogeneity parameters. It is found that as heterogeneity parameters and magnetoelastic coupling parameters increases, the phase velocity increases for both isotropic and monoclinic cases but the increase is more prominent in the monoclinic case. In the isotropic case, when heterogeneity and magnetic field are absent, the dispersion equation is matched with the classical SH wave equation
Acta Mechanica, 2006
A problem of reflection and transmission of a plane SH-wave incident at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space is investigated. Rayleigh's method of approximation is applied to derive the reflection and transmission coefficients for the first and second order approximation of the corrugation. The expressions for reflection and transmission coefficients for the first order approximation of the corrugation are obtained in closed form for a special type of interface, and the energy partition relation is derived. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of elastic properties of the half-spaces and also of the angle of incidence. Numerical examples illustrating the effects of the sandiness, the anisotropy, the corrugation of the interface, the frequency, and the angle of the incidence on the coefficients are presented. Irregularities, such as mountains, basins, mountain roots and salt and ore deposits, affect the reflection and transmission of seismic waves. The interior boundaries of the Earth's media are not planar but are of undulated nature. The roughness or undulation of interfaces do affect the energy partition between the reflected and transmitted waves. The problem of reflection and transmission of waves at irregular interfaces was studied by Asano [1]-[3], Abubakar [4]-[6], Dunkin and Eringen [7], Salvin and Wolf [8], Sumner and Deresiewicz [9], Gupta [10]-[12], Zhang and Shinozuka [13], Tomar and Saini [14], Tomar and Kaur [15] and Kaur et al. [16] among others. Earth is very complex in nature and contains various types of rocks and materials with amazing characteristics such as anisotropy, heterogeneity, sandiness etc. The effect of anisotropy on reflection and transmission of elastic waves at a plane interface between two elastic media was studied by Musgrave [17], Henneke [18], Daley and Hron [19], Saini and Singh [20], Keith and Crampin [21], Rokhlin et al. [22], Mandal [23], Ruger [24], among others.
SUPERFICIAL AMPLIFICATION EFFECTS INDUCED BY SH WAVES IN NONLINEAR ELASTIC LAYERED HALF-SPACE
Rev. Roum. …, 2004
In order to determine the seismic effects in superficial layers of the earth taking into account their nonlinear constitutive behavior, specific wave equations for longitudinal and transversal propagations are deduced. Following approximations schemes previously enounced by the first author, which furnish effective solutions corresponding to a layered half-space as well as correlations between surface effects (displacements and stresses) and the dislocational mechanism of sources located in ground layer, in the present paper the amplification effect for a layered half-space with nonlinear behavior of the surface layer is analyzed. The results are in good agreement with observational data and consist in specific new effects: the existence of very well defined directivity curves and of almost punctual regions with focusing effects, their dependence on focal mechanism, deep rocks structure and wave superposition, the importance of constitutive laws, the nonlinearity of soft surface soils and of multiple wave overlapped simultaneously with increasing fundamental frequency. These facts are pointing out the correlation between nonlinearity and directivity and are encouraging the efforts for a new approach in viscous-plastic and fissional rocks behavior.
Seismic wave in magnetoelastic irregular anisotropic layer
Proceedings of the 6th Wseas International Conference on Computer Engineering and Applications and Proceedings of the 2012 American Conference on Applied Mathematics, 2012
This paper aims to study the propagation of horizontally polarized shear wave (SH wave) in a magnetoelastic anisotropic and irregular layer. The irregular layer is taken as self-reinforced which is sandwiched between two isotropic elastic half-spaces. Irregularity in layer is considered at the lower interface. The perturbation method is used to find the dispersion equation. Effects of size of irregularity and different values of magnetoelastic coupling parameter on dispersion curves have been studied. Variation of phase velocity with wave number has been presented by graphs.
Mechanics Based Design of Structures and Machines, 2020
This paper aims to study the propagation of surface waves in generalized magneto-thermoelastic media under influence of magnetic field and rotation and its applications in Engineering, Geophysics, and Petroleum extracting. The governing equations are considered for generalized thermoelastic problem under magnetic field and rotation and solved to obtain the general solution in x-z plane. The Lame's potential method considering harmonic functions for the physical quantities is used to obtain the secular equation and then the velocity and attenuation coefficient for the types of waves: Stoneley, Love, and Rayleigh. The appropriate boundary conditions at an interface between two dissimilar half-spaces are satisfied with appropriate particular solutions to obtain the frequency equation of the surface wave in the medium. Some special cases as: Stoneley waves, Rayleigh and Love waves also discussed and presented graphically to show the physical meaning of the external parameters effect on the petroleum extracting phenomena and its contributions in KSA vision 2030 in crystal, Iron and steel. A comparison is made with the previous results considering LS model and the absence of rotation that deduces to the previous results as a special case from the present study. Also, if the magnetic field and rotation vanish, the results obtained in the present work are discussed. Experimentally, the results obtained agree with the labs results obtained. The results obtained indicate to a significant impact of the magnetic field and rotation on the waves propagation phenomenon that contributes on the industries and related topics.
Procedia Engineering
The present paper devotes the propagation of SH-wave in an irregular anisotropic self-reinforced layer lying over an initially stressed porous half-space. The various affecting parameter viz. irregularity depth, initial stress and porosity have their prominent effects on the phase velocity of SH-wave. To detect the substantial effect of these affecting parameters on the phase velocity of SH-wave, analytical computation and correspondingly graphical demonstration have been done. The dispersion equation has been established in closed form and found to be in good agreement with the Classical Love wave equation. The comparative study has been made between with reinforcement and without reinforcement structure models. Moreover, as and illustration, the overall effects of reinforcement and without reinforcement consolidated with irregularity and porosity are accentuated through graphs.