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I consider the validity conditions for the variable velocity acoustic wave
equation (1). This equation is sometimes used in
geophysical applications
of seismic wave propagation, imaging and inversion, without regard to the
specific assumptions underlying its derivation or the validity of its use
as a practical approximation. To gain some insight into these validity
conditions, I carry out the necessary mathematical analysis to
further illuminate the subject. To apply my results to seismic data,
one has to assume that the Earth is a linear isotropic non-viscous fluid,
which it clearly is not. I therefore hope to extend this analysis in a future
work using the elastodynamic wave equation. In the meantime, my results
may be useful in as much as treating seismic waves as uncoupled acoustic
(scalar) waves has been useful to the geophysical community in the past.

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Stanford Exploration Project

11/18/1997