Reflection Rayleigh wave

Figure 4.7. Internal reflection of a shock wave from a free surface, (a) Reflection of a shock wave from a free surface causes a reflected rarefaction wave. As indicated in (b), this increases the velocity of the shocked material from u, to Uf. The path upon shocking is Rayleigh line 0-1, whereas unloading occurs along release isentrope curve I -O, (c) Release isentrope path in P- V plane is indicated.

Fig. 7.3. Ray model of an acoustic lens with negative defocus aa is an arbitrary ray, which is reflected at such an angle that is misses the transducer (or else hits the transducer obliquely and therefore contributes little to the signal because of phase cancellation across the wavefront) bb is the axial ray, which goes straight down and returns along the same path cc is the symmetrical Rayleigh propagated wave, which returns to the transducer normally and so also contributes to the signal. The wavy arrow indicates the Rayleigh wave.

In transmission microscopy of specimens with properties not too different from those of water, Rayleigh waves may safely be disregarded. But in reflection microscopy of specimens of higher stiffness, Rayleigh waves generally play a dominant role. This is recognized explicitly in the ray theory treatment. 

If the field incident on the surface of the specimen is described by pinc( )> and Pinc(kx) is its Fourier transform, then the reflected field at the surface can be found by taking the inverse Fourier transform of the product of PiBC kx) and R(kx). Lower case denotes real-space fields, upper case spatial frequency (or reciprocal-space) fields. A time dependence exp(iwt), corresponding to a frequency w/27r, is implicit throughout. If the reflected field is separated into the geometrical part Rq x) and the leaky Rayleigh wave part Pr(x),... 

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). 

The experimental observation that Rayleigh wave scattering plays a dominant role in the contrast suggests that the reflection coefficient should be separated into the geometrical and Rayleigh parts in the way described in 7.2.1 ... 

When a crack is present eqn (12.4) must be extended to include a total of four terms. Let the crack be situated at the origin, and let it be characterized by coefficients of reflection Rr and transmission TR for Rayleigh waves. Consider first the response at a point x < 0 to the left of the crack. The contributions are ... 

These two equations give the reflected field at the surface due to the Rayleigh wave interaction for any incident field. 

Dong, R. and Adler, L. (1984). Measurements of reflection and transmission coefficients of Rayleigh waves from cracks. /. Acoust. Soc. Am. 76,1761-3. [264]... 

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