Michael G. Brown
RSMAS-AMP, Univ. of Miami, 4600 Rickenbacker Cswy., Miami, FL 33149
The Maslov, or Lagrangian manifold, technique provides a means of constructing a uniform asymptotic solution to the wave equation under conditions in which variables do not separate. This study exploits the assumption that there is a preferred direction of propagation to simplify the presentation of this subject given by Chapman and Drummond [Bull. Seismol. Soc. Am. 72, S277--S317 (1982)]. The one-way assumption does not require that a narrow angle (parabolic) approximation be made. The final one-way wave-field representation is easy to implement numerically, offering several advantages over the Chapman and Drummond formulation. The final wave-field representation correctly describes, in the time domain, direct and multiply turned ray arrivals, wave fields in the vicinity of caustics of arbitrary complexity, edge diffraction and head waves. It is valid in media with strong (nonadiabatic) range dependence. In the one-way formulation, all quantities required to compute the wave field at all depths at a fixed range (the preferred propagation direction) are computed concurrently; the technique is thus particularly well suited to the modeling of wave fields that are sampled using a multielement vertical array. Numerical results, including a comparison with the SLICE89 data set, will be shown. [Work supported by ONR and NSF.]