We generalize the streamline approach to transient pressure applications by introducing a "diffusive" time of flight along streamlines. This allows us to define drainage areas or volumes associated with primary recovery and compressible flow under the most general conditions. We then employ developments in seismic tomography and waveform imaging to formulate an efficient approach for integrating transient pressure data into high-resolution reservoir models. The proposed approach exploits an analogy between a propagating wave and a propagating "pressure front" via high-frequency asymptotic solutions to the transient pressure equation. A key advantage of the asymptotic approach is that parameter sensitivities required for solving inverse problems related to production data integration can be obtained analytically using a single streamline simulation. Thus, the approach can be orders of magnitude faster than current techniques that require multiple flow simulations. We demonstrate the power and utility of the approach by applications to both synthetic and field examples. In the field example, the predominant fracture patterns emerging from the inversion are shown to be consistent with outcrop mapping and crosswell seismic imaging.