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- W1977888958 abstract "In many applications the parabolic equation method would be ideal were it not for the limitation to narrow angles. Recently, Fishman and McCoy [J. Math. Phys. 25, 285–296 (1984)] used the theory of pseudo-differential operators to derive an integral equation for H, the square root of the operator B = ω2/c2(z) + ρ(z)∂z[ρ−1(z)∂z], thereby obtaining an exact, arbitrary-angle PE theory. Numerical construction of the operator H = B remains an area of great interest because the integral equation for H is not easily solved. We show that the operator H can be numerically constructed to any desired accuracy by well-known methods of computational linear algebra. The key to this construction is that, whenever the sound-speed profile is real, the operator B is self-adjoint with respect to the inner product 〈,〉 where 〈φ,ψ〉 = ∫ dz ρ−1(z) φ̄(z)ψ(z). This means that the matrix of B can be diagonalized, hence, H =B and exp(iΔxH) are straighforward to compute. [Work supported by ONR.]" @default.
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- W1977888958 date "1986-05-01" @default.
- W1977888958 modified "2023-09-24" @default.
- W1977888958 title "Notes on wide angle PE" @default.
- W1977888958 doi "https://doi.org/10.1121/1.2023151" @default.
- W1977888958 hasPublicationYear "1986" @default.
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