Rapid computation of acoustic impulse scattering for rough penetrable surfaces

Chu’s theory for the impulse response of a point source to an isovelocity density contrast wedge [Chu D. Impulse response of density contrast wedge using normal coordinates. J Acoust Soc Am 1989;86:1883–96] enables wedge-assemblage rough surface scattering models to be extended to a broad range of penetrable seafloors, but is computationally intensive since it necessitates finding the multifold roots of a characteristic eigenvalue equation, and summing a power series, for each wedge apex. This present work considers the properties and relationships of the direct, reflected, and diffracted field components of a density contrast wedge. In particular, an analysis of the physical origin and behavior of diffractions associated with specular reflections of the source in the wedge faces leads to a simple extension of the Biot–Tolstoy theory [Biot MA, Tolstoy I. Formulation of wave propagation in infinite media by normal coordinates with an application to diffraction. J Acoust Soc Am 1957;29:381–91] to density contrast wedges with reflectivity ∣R∣ < 1, for wedge angles within the range 150 ≲ θw ≲ 210°, where the diffractions are predominantly associated with a single reflection in each wedge face. This facilitates rapid time domain calculations of acoustic bottom scattering and penetration for complex multilayered seafloors.