SUMMARY

Traditional approaches to finite-difference elastic modeling make no distinction between model and wavefield variables. A single differential operator (either in the space or spatial-frequency domain) is used to calculate the spatial derivatives of both the stiffness components and the wavefield components. This lack of distinction can be in part attributed to the way in which most conventional schemes are implemented; the derivatives of the stiffness components are only implicitly computed when the derivatives of the stresses components are evaluated.

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.