Geophys. zyxwvutsr J. R. astr. SOC. zyxwvut (1985) zyxwvu 83, 307-317 Synthetic SH seismograms in a laterally varying medium by the discrete wavenumber method Michel Campillo and Michel Bouchon Laboratoirede ctophysique Interne et Tectonophysique, IRICM, llniversitt Scientifique et Medicale de Grenoble, BP 68, 38402 zyxwvut Saint Martin zyxwvu d’ Hkres Cedex. France Accepted 1985 March 6. Received 1985 February 8; in original form 1984 August 6 Summary. We present a new method to calculate the SH wavefield produced by a seismic source in a half-space with an irregular buried interface. The diffractiog interface is represented by a distribution of body forces. The Green’s functions needed to solve the boundary conditions are evaluated using the discrete wavenumber method. Our approach relies on the introduc- tion of a periodicity in the source-medium configuration and on the discreti- zation of the interface at regular spacing. The technique developed is applicable to boundaries of arbitrary shapes and is valid at all frequencies. Some examples of calculation in simple configurations are presented showing the capabilities of the method. Key words: seismology, synthetic seismograms, diffraction, vertical seismic profiles. Introduction The discrete wavenumber method (Bouchon zyxwv & Aki 1977; Bouchon 1981) is a powerful technique of simulation of wave propagation in a viscoelastic flat-layered medium. Our aim is to develop the generalization of this method to a laterally heterogeneous medium. This problem is of crucial interest for geophysical prospecting purposes as well as for the interpre- tation of earthquake data. In the last decade seismologists have devoted a lot of work to these studies. A large number of techniques have been used including finite differences (Boore 1972; Kelly et al. 1976; Virieux 1985), finite elements (Smith 1974) and frequency- wavenumber methods (Aki & Larner 1970). High-frequency asymptotic ray theory has also been applied following different formulations (Cerveny, Molotkov & PlenEik 1977; Hong & Helmberger 1978, MacMechan & Mooney 1980; Haines 1983) including the Gaussian beam method (Cerveny 1983; Cerveny & PSenEik 1984; Novak & Aki 1985). Finally, boundary integral equations have been used to compute the complete response of an irregular free surface (e.g. Sanchez-Sesma & Esquivel 1979; Sanchez-Sesma 1983) or of an irregular buried interface (Dravinski 1983). In this paper we present a method of representation of the scattered wavefields by distri- buting sources along the diffracting interface (Huyghens’s principle). We follow the approach Downloaded from https://academic.oup.com/gji/article/83/1/307/570413 by guest on 07 February 2022