Waveform Synthesis by Ray Theoretical Methods

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The purpose of these notes is to present in a relatively simple form several techniques to construct synthetic seismograms in the high frequency regime. The simplest and most widely used of the high frequency methods is classical geometrical ray theory, which is the basis of most practical methods for the modeling of seismograms and the inversion of travel times in seismology and applied geophysics. A comprehensive discussion of several aspects of ray theory may be found in the books of Cerveny et al. (1977) and Bleistein (1984), and in the notes by Burridge (1976). Many programs that perform ray tracing have been written in order to calculate travel times and synthetic seismograms based on ray theory. One of the most difficult problems in generating synthetics was the calculation of geometrical spreading. A major advance in this field was made by Popov and Psencik (1978) who proposed a new technique for the calculation of geometrical spreading. This method is usually called dynamic ray tracing. Later work demonstrated that dynamic ray tracing was in fact a subset of what is called paraxial ray theory in optics, i.e., the study of rays propagating in the vicinity of another ray. This method is new to seismology but it has been used in optics for several decades (see, for example, Deschamps, 1972).