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In this paper we make a comparison between the boundary conditions (BCs) derived by Tiersten and the so-called O(h) BCs for elastic surface waves guided by thin films. By a thin layer we here mean a layer for which the thickness is much smaller than the wavelengths involved. The advantage of the O(h) model is that it starts with the general three-dimensional equation of motion and derives the boundary conditions in a rational manner keeping all terms linear in the layer thickness. The Tiersten model is obtained from the approximate equations for low frequency and flexure of thin plates by neglecting the flexural stiffness. We consider straight-crested surface waves under plane-strain conditions, so-called Rayleigh-type waves (P-SV), and Love waves (SH). It is shown that for the Rayleigh type waves the O(h) BCs gives a much better approximation of the exact case than the Tiersten BCs. Even for the Tiersten model including flexural stiffness, the O(h) BCs yields more accurate results. Concerning Love waves both the Tiersten model and O(h) model reduces to the same dispersion relation which quite well approximates the exact solution.

The scattering of elastic waves in a half-space containing a striplike crack is investigated. As a special case it seems that the crack may be surface breaking. A surface integral equation with the half-space Green tensor is employed. The key point of the method is the expansion of the Green tensor in Fourier representations with the free part of the Green tensor expanded in the crack coordinate system and the half-space part in the half-space coordinate system. The integral equation is discretized by expanding the crack opening displacement in terms of Chebyshew functions having the correct square root behavior along the crack edges. The incident field is emitted from an ultrasonic probe and a recent model for this is employed. The signal response in another (or the same) probe is modeled by a reciprocity argument and the stationary phase approximation is employed to simplify the final answer, which is thus only valid in the far field of the probes (yielding essentially a spherical wave). Numerical results are given and are compared with both other methods and with available experiments.

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