GENERALIZED BREMMER SERIES WITH RATIONAL APPROXIMATION FOR THE SCATTERING OF WAVES IN INHOMOGENEOUS-MEDIA

The Bremmer series solution of the wave equation in generally inhomoge neous media, requires the introduction of pseudodifferential operators . In this paper, sparse matrix representations of these pseudodifferen tial operators are derived. The authors focus on designing sparse matr ices, keeping the accuracy high at the cost of ignoring any critical s cattering-angle phenomena. Such matrix representations follow from rat ional approximations of the vertical slowness and the transverse Lapla ce operator symbols, and of the vertical derivative, as they appear in the parabolic equation method. Sparse matrix representations lead to a fast algorithm. An optimization procedure is followed to minimize th e errors, in the high-frequency limit, for a given discretization rate . The Bremmer series solver consists of three steps: directional decom position into up- and downgoing waves, one-way propagation, and intera ction of the counterpropagating constituents. Each of these steps is r epresented by a sparse matrix equation. The resulting algorithm provid es an improvement of the parabolic equation method, in particular for transient wave phenomena, and extends the latter method, systematicall y, for backscattered waves. (C) 1998 Acoustical Society of America. [S 0001-4966(98)06109-8]