Martin D. Verweij
Lab. of Electromagnetic Res., Dept. of Elec. Eng., Delft Univ. of Technol., P. O. Box 5031, 2600 GA Delft, The Netherlands
A method is presented for the determination of the space-time domain acoustic wave field, and in particular the space-time domain Green's function, in homogeneous, isotropic equivalent fluid media that represent materials with a complicated viscoelastic behavior. The viscoelastic properties are modeled with the aid of arbitrarily intricate compliance memory functions, and the inertia behavior of the media is allowed to show memory effects as well. The presented integral transformation-type method consists of the transform domain Neumann series solution or WKBJ iterative solution, and the Cagniard--De Hoop method of inverse transformation. Analysis of the terms of the Newmann series solution yields a recurrence scheme that can ideally be evaluated using symbolic manipulation. Application of the Cagniard--De Hoop method results in an analytical transformation back to the space-time domain, which makes the method computationally fast. After explaining the theory, numerical results for several lossy media with an almost constant-Q behavior, like many types of rock, are presented. It is shown that it is sufficient to take into account only a few terms of the Newmann series solution to obtain accurate results, even for media with high losses.