In this section I will state the validity condition results of the mathematical analysis that follows in the main body of the paper. A valid acoustic wave equation governing fluid particle motion for a pressure wavefield is
1. It is perfectly rigorous to use (1) in a linear isotropic non-viscous fluid with a constant mass density and a spatially variable bulk modulus such that
2. In ``reasonable'' background models where varies smoothly with respect to pressure wavelength, 1 can be extended to such that
when the following validity condition is satisfied:
Condition (4) is invalid near regions of discontinuities in (e.g., reflecting boundaries), but is valid in regions of smooth-varying spatial properties (e.g., a smoothed migration model).