SMod2.6 SUMMARYA new method of calculating synthetic seismograms of primary reflections or backscattering for surface reflection surveying is introduced using the De Wolf MFSB approximation and phase-screen one-way propagation. Two versions of algorithm are presented, both of which use the dual domain technique for computational efficiency. One is the direct use of MFSB approximation, in which the step length of calculating the backscattered waves uses the grid spacing, but the step length of forward propagation uses the screen interval which is much greater than the grid spacing. The other version is the screen approximation for both the forward and backward scattered waves and therefore both step lengths can adopt the screen interval, resulting in great computational efficiency. The screen-approximation involves small-angle approximation and may have some effects on largeangle backscattered waves. Numerical examples using both versions of algorithm show good results. Good agreements with finite difference calculation on the second example indicate that even though the screen approximation involves the small-angle approximation, satisfactory results can be obtained for many practical applications with a great computational efficiency. INTRODUCTIONFast modeling methods and algorithms in complex heterogeneous media, especially for 3-D media, are crucial to the development of imaging and inversion methods, interpretations and applications of seismic methods for complex structures. Finite difference and finite element methods, which in principle can model wave propagation in arbitrarily heterogeneous media, are time consuming, even formidable in the case of large 3-D elastic wave problems. In this study we develop a new method based on multiple-forescattering single-backscattering (MFSB) approximation, i.e. the De Wolf approximation for calculating the backscattered field in the configuration of surface reflection surveying. A dual domain formulation is derived for fast implementation of the method. When the scales of heterogeneities are greater than the dominant wavelength, the theory can be further approximated by the thin-slab scattering approximation and the screen scattering approximation. It is shown that the screen approximation can substantially reduce the computation time. Finally two numerical examples are given to demonstrate the validity of the method.

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