Sharp boundary inversion in crosswell travel-time tomography

The reconstruction of seismic images of the medium from crosswell travel-time data is a typical example of the ill-posed inverse problem. In order to obtain a stable solution and to replace an ill-posed problem by a well-posed one, a stabilizing functional (stabilizer) has to be introduced. The role of this functional is to select the desired stable solution from a class of solutions with specific physical and/or geometrical properties. One of these properties is the existence of sharp boundaries separating rocks with different petrophysical parameters, e.g., oil- and water-saturated reservoirs. In this paper, we develop a new tomographic method based on application of a minimum support stabilizer to the crosswell travel-time inverse problem. This stabilizer makes it possible to produce clear and focused images of geological targets with sharp boundaries. We demonstrate that the minimum support stabilizer allows a correct recovery of not only the shape but also the velocity value of the target. We also point out that this stabilizer provides good results even with a low ray density, when the traditional minimum norm stabilizer fails.