Introduction

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.