Rayleigh wave contrast theory

The term in the curly brackets describes the response at x due to the excitation at x, transmitted by the Rayleigh wave mechanism it can therefore be thought of as a kind of Green function. The results described by eqns (7.33) and (7.34) are central to the theory of the contrast from cracks and interfaces that will be presented in Chapter 12. 

Anyone who has successfully used a microscope to image properties to which it is sensitive will sooner or later find himself wanting to be able to measure those properties with the spatial resolution which that microscope affords. Since an acoustic microscope images the elastic properties of a specimen, it must be possible to use it to measure elastic properties both as a measurement technique in its own right and also in order to interpret quantitatively the contrast in images. It emerged from contrast theory that the form of V(z) could be calculated from the reflectance function of a specimen, and also that the periodicity and decay of oscillations in V(z) can be directly related to the velocity and attenuation of Rayleigh waves. Both of these observations can be inverted in order to deduce elastic properties from measured V(z). 

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