When the model parameters are a smooth function of the spatial variables, the same high-order, long operator can be used for both model and field derivatives, but when sharp boundaries are present, a short operator should be used for the derivatives of the model parameters. This approach, referred to as the dual-operator method, was implemented in a modified staggered grid within the framework of the equivalent media theory. For a simple model that includes a liquid layer the dual-operator method generated less dispersive more accurate results then the traditional finite-difference method. In particular, the angle-dependent plane-wave response obtained with the dual-operator method was more accurate than the one obtained with traditional finite-differences and at least as accurate as the one obtained with the propagator-matrix method.

11/18/1997