Generalization of the phase-screen approximation for the scattering of acoustic waves

With the use of Fourier analysis, we describe the propagation and scattering of acoustic waves in smoothly varying, heterogeneous media. The starting point is the generalized Bremmer coupling series solution-distinguishing multiple up/down scattered constituents - to the wave equation, which requires the introduction of pseudo-differential operators. Then, we introduce a class of approximations to these pseudo-differential operators with the structure of the classical phase-screen method for one-way wave propagation. These approximations induce a fast, iterated, marching algorithm for the evaluation of the Bremmer series. The algorithm consists of multiplications by multiple 'screen' functions in the lateral space domain and generalized 'phase shifts' in the lateral wave number domain; the shuttling between the two domains is accomplished by the fast Fourier transform. Our scheme extends the use of the classical phase-screen method in the following ways: we consider larger medium variations; we enhance the accuracy for wider scattering angles; we introduce (de)composition operators to incorporate any desired source-or receiver-type with the appropriate radiation characteristics; we include the backscattered field with the aid of the generalized Bremmer coupling series. (C) 2000 Elsevier Science B.V. All rights reserved.