Inversion of pressure observations: an integral formulation

It is possible to express the inverse problem for flow in an integral form. The integral formulation affords some insight concerning the recovery of subsurface flow properties. In particular, we find that rapid or high frequency variations in head are primarily sensitive to the specific storage. Conversely, slow or low frequency variations are most strongly influenced by hydraulic conductivity. The nonlinearity of the inverse problem is due to the presence of product terms in which the head field, or its gradient, multiplies a term dependent on flow properties. Thus, in their discrete form, the equations describing the inverse problem are algebraic. The integral formulation provides an alternative approach to linearizing the inverse problem, the Born approximation. We apply the methodology to data from a set of crosswell pressure tests conducted at the Raymond field site. We are able to image two fracture zones within the granitic subsurface. The location of these zones agrees with results from crosswell seismic tomography and borehole logging.