Using an asymptotic methodology, including an expansion in inverse powers of {radical}{omega}, where {omega} is the frequency, we derive a solution for flow in a medium with pressure dependent properties. The solution is valid for a heterogeneous medium with smoothly varying properties. That is, the scale length of the heterogeneity must be significantly larger then the scale length over which the pressure increases from it initial value to its peak value. The resulting asymptotic expression is similar in form to the solution for pressure in a medium in which the flow properties are not functions of pressure. Both the expression for pseudo-phase, which is related to the 'travel time' of the transient pressure disturbance, and the expression for pressure amplitude contain modifications due to the pressure dependence of the medium. We apply the method to synthetic and observed pressure variations in a deforming medium. In the synthetic test we model one-dimensional propagation in a pressure-dependent medium. Comparisons with both an analytic self-similar solution and the results of a numerical simulation indicate general agreement. Furthermore, we are able to match pressure variations observed during a pulse test at the Coaraze Laboratory site in France
