FORWARD MODELING AND DATA INVERSION FOR BEAM PROPAGATION IN A STRATIFIED MEDIUM .1. THEORY

A previously developed matrix Green's function formulation [I. T. Lu and L. B. Felsen, Geophys. J. R. Astron. Soc. 84, 31-42 (1986)] for line-source excited propagation in piecewise-homogeneous stratified media is extended to allow arbitrarily inhomogeneous layers and beam source excitation. This formulation reveals dominant wave processes and allows simultaneous excitation and detection at arbitrarily specified locations. It provides a unified and systematic approach for deriving all alternative representations including mode, ray(beam), spectral integral, ray(beam) mode, collective ray(beam), etc. Both rigorous and practical aspects of the analytic continuation procedures in the complex source point technique are discussed in detail. An efficient beam source localization algorithm, which estimates the beam parameters and the beam location sequentially, is also presented. Numerical results are presented in a companion paper [I. T. Lu and H. Y. Chen, J. Acoust. Soc. Am. 91, 1239-1249 (1992)].