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Elastic waves in nonhomogeneous media under 2D conditions: II. Numerical implementation

Authors
Journal
Soil Dynamics and Earthquake Engineering
0267-7261
Publisher
Elsevier
Publication Date
Volume
18
Issue
1
Identifiers
DOI: 10.1016/s0267-7261(98)00039-6
Keywords
  • Dilatation
  • Green'S Function
  • Nonhomogeneous Media
  • Rotation Vector
  • Wave Propagation

Abstract

Abstract The results obtained in the first part of this work for modeling the passage of time harmonic elastic waves through a continuously nonhomogeneous material with depth-dependent elastic moduli and density and under plane strain conditions are now used here to investigate pressure and shear waves travelling in a naturally occurring medium. According to the particular methodology used, we distinguish three basic types of wave speed profiles: (i) one with a periodic structure in the depth coordinate, as generated by the conformal mapping technique; (ii) another which varies as the square root of a linear function in the depth coordinate, as generated by the vector decomposition technique; and finally (iii) one behaving as a linear function of the depth coordinate for the first-order system solution in conjunction with the Fourier transformation. Results are generated for the dilatation and rotation vector in the case of the first two techniques and for the fundamental solution (Green's function) corresponding to the displacement vector in the third case. In all cases, comparisons are carried out with respect to solutions obtained for an equivalent homogeneous medium.

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