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We present some results of the theory of high-frequency radiation by seismic sources. The emphasis will be placed on the kinematics of high-frequency waves, especially the stopping phases produced when the rupture encounters barriers of general shape. These results will be obtained from the representation theorem in which we replace the Green function by its asymptotic approximation at high frequencies, i.e. what is usually called the far-field approximation. This yields an expression akin to the Kirchhoff diffraction integral used in the modelling of reflection profiles and in seismic migration. The results obtained by this method are valid at distances from the fault which are longer than the dominant wavelength of the radiation. By a detailed analysis of the asymptotic method we find the wavefront discontinuities produced by rupture velocity jumps (barriers) or slip discontinuities (asperities) on the fault. Some examples of comparison between synthetics calculated with the new methods and those obtained by complete near-field synthesis will be presented. Among the examples we will consider is the circular fault, a model proposed by Bouchon for the Coyote Lake earthquake.
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