Showing papers on "Half-space published in 1988"

Deformation from Inflation of a Dipping Finite Prolate Spheroid in an Elastic Half‐Space as a Model for Volcanic Stressing

Abstract: Exact analytic expressions are given for the deformation field resulting from inflation of a finite prolate spheroidal cavity in an infinite elastic medium. The field is equivalent to that generated by a parabolic distribution of double forces and centers of dilatation along the spheroid generator. Approximate, but quite accurate, solutions for a dipping spheroid in an elastic half-space are found using the half-space double force and center of dilatation solutions. We compare results of the surface deformation field with those generated by the point source ellipsoidal model of Davis (1986). In the far field both models give identical results. In the near field the finite model must be used to calculate displacements and stresses within the medium. We also test the limits of applicability of the finite model as it approaches the surface by comparing the surface displacement field from a vertical spheroid with that calculated from the finite element method. We find the model gives a satisfactory approximation to the finite element results when the minimum radius of curvature of the upper surface is less than or equal to its depth beneath the free surface. Comparison of surface displacements generated by the point and finite element models gives good agreement, provided this criterion is satisfied. We have used the finite model to invert deformation data from Kilauea volcano, Hawaii. The results, which compare favorably with those obtained from the point ellipsoid model, can be used to estimate the distribution of stresses within the volcano in the near field of the source.

On reflection from a suddenly created plasma half-space: transient solution

Abstract: The reflection by a suddenly created plasma half-space of a time-harmonic plane electromagnetic wave propagating in free space is considered. The problem involves a temporal discontinuity, a spatial discontinuity, and a dispersive medium. The steady-state solution is obtained by considering the basic features of the scattering processes due to each of the discontinuities in terms of analogous transmission-line models. The electric field of the reflected wave consists of two components. One component (called component A) is of the same frequency as the incident wave frequency and is due to the spatial discontinuity. The other component (called component B) is of a different frequency and arises because of the temporal discontinuity. The B component is damped out even if the plasma is only slightly lossy. The damping rate of the B component is calculated. The transient solution is obtained through the use of Laplace transforms. The solution is given in terms of Bessel-like functions. The limiting value of this solution is shown to agree with the steady-state solution. Numerical results illustrating the transient effects are for two typical cases. >

One-dimensional generalized thermoelastic problem for a half space

Abstract: In this paper the theory of generalized thermoelasticity is used to solve a boundary-value problem of an isotropic elastic half-space with its plane boundary held rigidly fixed and subjected to a sudden temperature increase. Approximate small time solution is obtained by using the Laplace transform method. Numerical values of stress and temperature have been obtained. It has been noticed that the displacement is continuous and that there are two discontinuities in both the stress and temperature functions.

Transient surface response of layered isotropic and anisotropic half-spaces with interface cracks: SH case

Abstract: The transient response of the surface of a layered isotropic or anisotropic half-space, with two interface cracks, excited by a plane SH-wave is investigated. The incident field is taken as a bulk wave. The governing equations along with boundary, regularity and continuity conditions across the interface are reduced to a coupled set of singular integral equations. Solutions of these equations are obtained by expanding unknown crack opening displacement (COD) in terms of a complete set of Chebyshev polynomials. As sample problems, the surface response of isotropic as well as anisotropic layered half-spaces with and without crack interactions is computed

Near-source ground motion from a steady state dislocation model in a layered half-space

Abstract: A method to calculate the response on the surface of a multilayered half-space for a fault of finite width and infinite length is presented. The model involves a piecewise-rectilinear and continuous rupture front propagating at a constant rupture velocity along the length of a fault of arbitrary dip angle. The motion produced by this steady state dislocation model corresponds to the passage of the rupture front phase, which is a predominant phase in the near-source region away from the ends of a finite fault. The model gives an efficient way to synthesize a ubiquitous, intermediate frequency, high-amplitude pulse observed in many near-source records. A series of validation tests, using both three- and two-dimensional kinematic fault models, and a limited set of parametric studies clarifying the mechanisms involved in the generation of high amplitudes, are presented. Finally, it is shown that the distribution of peak horizontal velocities in the near-source region calculated by use of a steady state model in a layered medium compare favorably with the regression results of Joyner and Boore (1981).

The electromagnetic response of a heterogeneous layer modeled by two thin sheets in a uniformly conducting half-space

Abstract: Limitations of the thin-sheet method introduced by Price (1949) are pointed out. It is shown that the variety of structures that can be modeled with the thin-sheet technique can be increased by modeling a heterogeneous layer with two thin sheets. One sheet is located on the surface and represents the upper portion of the thickness of the anomalous region, and the second sheet is embedded in the Earth and represents the lower portion of the thickness of the anomalous region. Numerical results are obtained for a representative model using both one and two thin sheets, and the results are compared. Numerical results are obtained for a representative model for both the exact and the approximate dual-thin-sheet model. >

Three‐dimensional scattering of impulsive acoustic waves by a semi‐infinite crack in the plane interface of a half‐space and a layer

Abstract: The three‐dimensional diffraction of a pulsed acoustic wave by a semi‐infinite crack located in the interface of a uniform layer and a half‐space is investigated theoretically. In the analysis the influence of shear stresses in the material structure is neglected. The incident acoustic wave is taken to be generated by an impulsive compressional point source located at the top boundary of the layer. With the aid of the Wiener–Hopf technique and a modified version of the Cagniard–de Hoop technique implemented in an iterative scheme, closed‐form expressions for the particle velocity within any finite time window anywhere at the top boundary of the layer are obtained.

Torsion of rigid circular shaft of varying diameter embedded in an elastic half space

Abstract: The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method (LLIEM), where the problem is formulated by distributions of ficitious fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically. Numerical examples of torsin of rigid conic, cylinder, conical-cylinder embedded in an elastic half space are given and compared with the known result obtained by the others. The exact solution of torsion of rigid half sphere embedded in an elastic half space is also presented.

Fundamental Solutions and Boundary Element for Saturated Porous Halfspace

Abstract: Based on the three-dimensional consolidation theory of Biot, the complete set of fundamental solutions for a saturated porous half-space is derived using McNamee-Gibson displacement functions by the Hankel-Laplace tranform technique. These are half space fundamental solutions for interior vertical and horizontal point loads and interior point source. They will later serve as Green’s functions for the formulation of boundary integral equation for porous half-space solution. Although Green’s functions for saturated porous full space are available, the boundary element based on these functions requires ground surface discretization when it is applied to a half space. Using the half-space fundamental solutions, the exact ground surface condition is automatically included.

The Alekseev–Mikhailenko method applied to P–SV wave propagation in an elastic medium

Abstract: The Alekseev–Mikhailenko method (AMM) is the name given to a series of algorithms that use one or more finite spatial transforms to reduce the dimensionality of a wave-propagation problem to that of one space dimension and time. This reduced equation is then solved using finite-difference techniques, and the space–time solution is recovered by applying inverse finite spatial transform(s). In this paper the elastodynamic wave equation that governs the coupled P–Sv motion in an isotropic, vertically inhomogeneous elastic half space is investigated using the AMM. Two types of impulsive body forces that may be used to excite the medium are examined, as is the problem of obtaining accurate transformed finite-difference analogues at the free surface. The second of these is accomplished by introducing the boundary conditions that the shear and normal stress must vanish here and by incorporating their transforms into the transformed elastodynamic equations. The stability criterion for the explicit finite-differen...

A Dynamic Problem for a Piezoelectric Medium

Abstract: The axisymmetric problem for an elastic dielectric with polarization gradient effects is considered, in which an axisymmetric, time-varying loading is prescribed on the boundary of the half space. Wave propagation in half space is examined in the monochromatic case. Surface waves are discussed, assuming the specific form of loading and the closed form solution is given.

Axisymmetric Elastodynamic Response from a Penny-Shaped Interface Crack in Layered Composites

Abstract: This paper is concerned with the scattering of time harmonic longitudinal wave by a penny-shaped interface crack in layered composites. By Hankel and Abel integral transform, the problem is reduced to a set of singular integral equations which are treated numerically by Jacobi polynomials. The improper integrals in the equations are delt with by contour integral technique so that the accuracy of numerically computing is guaranteed. As an example, the scattering surface displacement field of elastic wave by a penny-shaped interface crack in a layered half space has been investigated in far field case. The theoretical results show that the surface displacements are composed of Rayleigh-Like-Mode waves predominantly. The scattered amplitudes for the first two modes are plotted versus the incident frequency, and it is observed that the multi-resonances occur in a frequency range.

Finite Amplitude Love Waves on an Incompressible Elastic Layered Half Space

Abstract: By employing a singular perturbation expansion the nonlinear modulation of Love waves on a single layered isotropic incompressible hyperelastic half space is investigated. A nonlinear Schrodinger equation is derived to, govern this motion asymptotically. It is shown that the surface solitary wave may exist depending on the nonlinear constitution of the layered half space.