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

The results obtained in the first part of this work for modeling the passag e of time harmonic elastic waves through a continuously nonhomogeneous mate rial with depth-dependent elastic moduli and density and under plane strain conditions are now used here to investigate pressure and shear waves trave lling in a naturally occurring medium. According to the particular methodol ogy used, we distinguish three basic types of wave speed profiles: (i) one with a periodic structure in the depth coordinate, as generated by the conf ormal mapping technique; (ii) another which varies as the square root of a linear function in the depth coordinate, as generated by the vector decompo sition technique; and finally (iii) one behaving as a linear function of th e depth coordinate for the first-order system solution in conjunction with the Fourier transformation. Results are generated for the dilatation and ro tation vector in the case of the first two techniques and for the fundament al solution (Green's function) corresponding to the displacement vector in the third case. In all cases, comparisons are carried out with respect to s olutions obtained for an equivalent homogeneous medium. (C) 1998 Elsevier S cience Ltd. All rights reserved.