Abstract A critical review is presented of recent progress in classical diffraction theory. Both scalar and electromagnetic problems are discussed. The report may serve as an introduction to general diffraction theory although the main emphasis is on diffraction by plane obstacles. Various modifications of the Kirchhoff and Kottler theories are presented. Diffraction by obstacles small compared with the wavelength is discussed in some detail. Other topics included are: variational formulation of diffraction problems, the Wiener—Hopf technique of solving integral equations of diffraction theory, the rigorous formulation of Babinet’s principle, the nature of field singularities at sharp edges, the application of Mathieu functions and spheroidal wave functions to diffraction theory. Reference is made to more than 500 papers published since 1940.

Abstract We present an improved method for modeling 3D acoustic wavefields scattered at smooth curved interfaces. The approach is based on a high-frequency approximation of surface integral propagators and a correct description of their boundary values in terms of transmission operators. The main improvement is a uniform local approximation of these operators in the form of effective reflection and transmission coefficients. We show that the effective coefficients represent a generalization of the plane-wave coefficients widely used in conventional seismic modeling, even for the case of curved reflectors, nonplanar wave fronts, and finite frequencies. The proposed method is capable of producing complex wave phenomenas, such as caustics, edge diffractions, and head waves. Seismograms modeled for even simple models reveal significant errors implicit in the plane-wave approximation. Comparison of modeling based on effective coefficients with the analytic solution reveals errors less than 4% in peak amplitude at seismic frequencies.