scholarly journals Calculation of surface motions of a layered half-space

1970 ◽  
Vol 60 (5) ◽  
pp. 1625-1651 ◽  
Author(s):  
N. C. Tsai ◽  
G. W. Housner
Keyword(s):  
Approximate Method ◽  
Half Space ◽  
Transient Response ◽  
Computing Time ◽  
Plane Waves ◽  
New Method ◽  
Satisfactory Accuracy ◽  
Time Required ◽  
Elastic Layers ◽  
Layered Half Space

Abstract A new method is presented for computing the transient response of a set of horizontally stratified, linearly elastic layers overlying a uniform half-space and excited by vertically incident, transient plane waves. In addition, a simple approximate method of satisfactory accuracy is developed that reduces the computing time required. Calculated responses are compared with motions recorded under Union Bay in Seattle to evaluate the agreement between recorded and calculated motions.

Exact Transient Response of an Elastic Half Space Loaded Over a Rectangular Region of Its Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 516-522 ◽  
Author(s):  
F. R. Norwood
Keyword(s):  
Half Space ◽  
Real Axis ◽  
Transient Response ◽  
Plane Waves ◽  
Elastic Half Space ◽  
Impulsive Loading ◽  
Rectangular Region ◽  
The Real ◽  
Algebraic Expressions ◽  
Straight Lines

The response of an elastic half space to a normal impulsive loading over one half and also over one quarter of its bounding surface is considered. By a simple superposition the solution is obtained for a half space loaded on a finite rectangular region. In each case the solution was found to be a superposition of plane waves directly under the load, plus waves emanating from bounding straight lines and the corners of the loaded region. The solution was found by Cagniard’s technique and by extending the real transformation of de Hoop to double Fourier integrals with singularities on the real axis of the transform variables. Velocities in the interior of the half space are given for arbitrary values of Poisson’s ratio in terms of single integrals and algebraic expressions.

Elastic Wave Scattering From an Interface Crack in a Layered Half Space Submerged in Water: Part I: Applied Tractions at the Liquid-Solid Interface

1986 ◽  
Vol 53 (2) ◽  
pp. 326-332 ◽  
Author(s):  
S. M. Gracewski ◽  
D. B. Bogy
Keyword(s):  
Elastic Wave ◽  
Integral Equations ◽  
Half Space ◽  
Interface Crack ◽  
Wave Scattering ◽  
Plane Waves ◽  
Crack Tip ◽  
Solid Interface ◽  
Elastic Wave Scattering ◽  
Layered Half Space

In Part I of this two-part paper, the analytical solution of time harmonic elastic wave scattering by an interface crack in a layered half space submerged in water is presented. The solution of the problem leads to a set of coupled singular integral equations for the jump in displacements across the crack. The kernels of these integrals are represented in terms of the Green’s functions for the structure without a crack. Analysis of the integral equations yields the form of the singularities of the unknown functions at the crack tip. These singularities are taken into account to arrive at an algebraic approximation for the integral equations that can then be solved numerically. Numerical results in the form of crack tip stress intensity factors are presented for the cases in which the incident disturbance is a harmonic uniform normal or shearing traction applied at the liquid-solid interface. These results are compared with a previously published solution for this problem in the absence of the liquid. In Part II, which immediately follows Part I in the same journal issue, the more realistic disturbances of plane waves and bounded beams incident from the liquid are considered.

The Method of Generalized Ray-Revisited

2000 ◽  
Vol 16 (1) ◽  
pp. 37-44
Author(s):  
Franz Ziegler ◽  
Piotr Borejko
Keyword(s):  
Wave Propagation ◽  
Parallel Computing ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Plane Waves ◽  
Solution Technique ◽  
New Developments ◽  
Infinite Space ◽  
Layered Half Space

ABSTRACTBased on a landmark paper by Pao and Gajewski, some novel developments of the method of generalized ray integrals are discussed. The expansion of the dynamic Green's function of the infinite space into plane waves allows benchmark 3-D solutions in the layered half-space and even enters the background formulation of elastic-viscoplastic wave propagation. New developments of software of combined symbolic-numerical manipulation and parallel computing make the method a competitive solution technique.

Elastic Wave Scattering From an Interface Crack in a Layered Half Space Submerged in Water: Part II: Incident Plane Waves and Bounded Beams

1986 ◽  
Vol 53 (2) ◽  
pp. 333-338 ◽  
Author(s):  
S. M. Gracewski ◽  
D. B. Bogy
Keyword(s):  
Elastic Wave ◽  
Half Space ◽  
Interface Crack ◽  
Wave Scattering ◽  
Ultrasonic Transducer ◽  
Plane Waves ◽  
Incident Beam ◽  
Numerical Results ◽  
Elastic Wave Scattering ◽  
Layered Half Space

This is Part II of a two part paper which analyzes time harmonic elastic wave scattering by an interface crack in a layered half space submerged in water. The analytic solution was derived in Part I. Also numerical results for uniform harmonic normal or shear traction applied to the liquid-solid interface were presented. These were compared with previously published results as a check on the computer program used to obtain the numerical results. Here in Part II, additional numerical results are presented. Plane waves incident from the liquid onto the solid structure are first considered to gain insight into the response characteristics of the structure. The solution for an incident beam of Gaussian profile is then presented since this profile approximates the output of an ultrasonic transducer.

Wave Scattering of Plane P, SV, and SH Waves by a 3D Alluvial Basin in a Multilayered Half-Space

2020 ◽  
Vol 110 (2) ◽  
pp. 576-595 ◽  
Author(s):  
Zhenning Ba ◽  
Ying Wang ◽  
Jianwen Liang ◽  
Vincent W. Lee
Keyword(s):  
Half Space ◽  
Incident Angle ◽  
Plane Waves ◽  
Single Layer ◽  
Fundamental Solutions ◽  
New Method ◽  
General Applicability ◽  
Sh Waves ◽  
Sedimentary Sequences ◽  
Homogeneous Half Space

ABSTRACT A special indirect boundary element method (IBEM) is proposed to investigate the waves scattering of plane P, SV, and SH waves by a 3D alluvial basin embedded in a multilayered half-space. The new IBEM, which uses half-space Green’s functions for uniformly distributed loads acting on an inclined plane as its fundamental solutions, has the merits of (1) excellent capability of dealing with the stratification of the basin and the external half-space, (2) without the problem of singularity due to fictitious distributed loads being directly applied on the real boundaries, and (3) good adaptability to complex models with trapezoidal or triangular elements being used to discretize the boundaries. The validity and accuracy of the new method are verified by comparing its results with those in the literature. To illustrate the general applicability and efficiency of the new method further, 3D alluvial basins of varying shapes, depths, and sedimentary sequences embedded in a single layer overlying a homogeneous half-space are numerically studied. Numerical results show that the basin’s shape, depth, and sedimentary sequence all have significant impact on the ground seismic responses; the incident angle also has noticeable effects on the surface motion, and these effects are more prominent at the observation points along the incident direction of the plane waves; for the case of layered model, the displacement spectral amplification is affected by the eigenmodes of the vibrations of the layers, both inside and outside the basin.

An efficient method for computing Green's functions for a layered half-space with sources and receivers at close depths (part 2)

1995 ◽  
Vol 85 (4) ◽  
pp. 1080-1093
Author(s):  
Yoshiaki Hisada
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Efficient Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
New Method ◽  
Direct Wave ◽  
Transmitted Waves ◽  
Dipole Sources ◽  
Layered Half Space

Abstract In this study, we improve Hisada's (1994) method to efficiently compute Green's functions for viscoelastic layered half-spaces with sources and receivers located at equal or nearly equal depths. Compared with Hisada (1994), we can significantly reduce the range of wavenumber integration especially for the case that sources and receivers are close to the free surface or to boundaries of the source layer. This can be done by deriving analytical asymptotic solutions for both the direct wave and the reflected/transmitted waves from the boundaries, which are neglected in Hisada (1994). We demonstrate the validity and efficiency of our new method for several cases. The FORTRAN codes for this method for both point and dipole sources are open to academic use through anonymous FTP.

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