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) |

**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) |

**2.** In ``reasonable'' background models where varies smoothly
with respect to pressure wavelength, **1** can be extended to
such that

(3) |

when the following validity condition is satisfied:

(4) |

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).

11/18/1997