Transient acoustic wave fields in continuously layered fluids with attenuation

Abstract

The space-time domain acoustic wave field in an isotropic, lossy, continuously layered fluid is analyzed using a method that employs a combination of higher-order WKBJ asymptotics and the Cagniard–De Hoop method of inversion. The loss behavior of the fluid is described with the aid of general temporal compliance and inertia memory functions. The continuous layering of the medium manifests itself in the acoustic wave speed, the density of mass, and both memory functions, which are independent, continuous functions of the vertical coordinate. After the application of forward transformations, higher-order WKBJ asymptotic representations of the transform domain solution are derived. The coefficients that occur in these representations satisfy a recurrence scheme, which is well suited for implementation in a symbolic manipulation program. The transform domain WKBJ asymptotic representations are analytically transformed back to the space-time domain with the aid of the Cagniard–De Hoop method. Numerical results for several configurations with an intricate loss behavior are presented.