Generalization of the Bremmer coupling series

Source abstract

An operator formalism is developed to expand the acoustic wave field in a multi-dimensionally smoothly varying medium, generated by a source localized in space and time, into a sum of constituents each of which can be interpreted as a wave that has traveled up and down with respect to a direction of preference a definite number of times. This expansion is a generalization of the Bremmer coupling series. The condition of smoothness of the medium relates to the width of the signature of the source in the configuration. Both the existence and the convergence (in the weak sense) of the expansion are discussed. The operator calculus involved leads to a natural generalization of the concept of slowness surface to multi-dimensionally smoothly varying media. The operator associated with the corresponding generalized vertical slowness induces the full one-way wave operator in the type of media under consideration. In addition, a wavefield decomposition operator as well as an interaction operator that couples the decomposed constituents, are derived.