Sharp boundary inversion in crosswell travel-time tomography

Abs tract The reconstruction of seismic images of the medium from cross we ll travel-time data is a typic al examp le of the ill-posed inverse prob lem. In order to obt ain a stable so lution and to rep lace an ill-posed problem by a well-posed one, a stabilizing functiona l (stabilizer) has to be introduced. The ro le of this functional is to select the desired stable so lution from a class of solutions with spec ific physical and/or geo metrica l properti es. One of these properties is the ex istence of sharp bound aries separa ting rocks with different pet rophysical parameters, e.g., oil and water -saturated reservoirs. In this paper, we develop a new tomographic meth od based on application of a minimum sup port stabilizer to the crosswell trave l-time inverse problem . Thi s stabilizer makes it possible to produ ce clear and focused images of geo logical targets with sharp boundaries . We demonstrate that the minimum support stabilizer allows a correc t recovery of not only the shape but also the velocity value of the target. We also point ou t that this stabilize r provides good resu lts even with a low ray density, when the traditional minimum norm stabilizer fails.