An asymptotic formulation of the inverse problem for flow reveals that the inversion may be partitioned into two complementary subproblems. In the first problem the arrival time associated with the peak slope of the transient curve is directly related to reservoir properties. The second inverse problem is similar to current methods for interpreting flow data; the transient head amplitudes are related to reservoir storage and conductivity. The first subproblem, the arrival time inversion, involves much less computation than does amplitude matching. Furthermore, it appears to be more robust with respect to the starting model. Therefore the solution to the arrival time inversion provides a starting model for amplitude matching. The methodology is particularly suited to the analysis of observations from well tests. We apply the approach to observations from two interference tests conducted at the Borehole Test Facility in Oklahoma. Using the transient pressure measurements, we image a shallow conductive fracture. The existence and location of the fracture has been verified by both geophysical and borehole data. In particular, core from a slant well contains an open, vertical fracture which coincides with our conductive feature.