Abstract
In this paper, we examine Gibbs's potential taken as a Cauchy function. This function depends on one parameter and can be useful in inserting a priori information in terms of chosen directions in Gibbs inversion. The results presented in this paper, show the possibility of using Gibbs's statistics for obtaining tomograms of superior quality compared with conventional methods using uncorrelated Gaussian least-squares optimization. Although Gibbs's statistics give images of higher quality when compared to conventional methods, the geophysical literature on Gibbs's algorithms is quite scanty. For example, Carrion et al. (personal communication) have determined the results of the 3-D Gibbs inversion in processing crosswell data. Carrion et al. (1993) have discussed a hybrid method based on the constrained traveltime inversion when "hard" bounds were driven by Gibbs's statistics. One major problem of crosswell geotomography is incomplete data coverage. A lack of information in the angular spectrum leads to smearing in directions of predominant wave vectors. For example, in crosswell tomography, smearing will occur predominantly in the horizontal direction.