Evaluating structural uncertainties associated with seismic imaging and target horizons can be of critical importance for decision making related to oil and gas exploration and production. An important breakthrough for industrial applications has been made with the development of industrial approaches to velocity model building. We have developed an extension of these approaches, sampling an equiprobable contour of the tomography posterior probability density function (PDF) rather than the full PDF, and using nonlinear slope tomography. Our approach allows for assessing the quality of uncertainty-related assumptions (linearity and Gaussian hypothesis within the Bayesian theory) and estimating volumetric migration positioning uncertainties (a generalization of horizon uncertainties), in addition to the advantages in terms of computational efficiency. We derive the theoretical concepts underlying this approach and unify our derivations with those of previous publications. Because the method works in the full model space rather than in a preconditioned one, we split the analysis into resolved and unresolved tomography spaces. We argue that resolved space uncertainties are to be used in further steps leading to decision making and can be related to the output of methods that work in a preconditioned model space. Unresolved space uncertainties represent a qualitative by-product specific to our method, strongly highlighting the most uncertain gross areas, thus useful for quality control. These concepts are developed on a synthetic data set. In addition, the industrial viability of the method is determined on two different 3D field data sets. The first one consists of a merge of different seismic surveys in the North Sea and indicates the corresponding structural uncertainties. The second one consists of a marine data set and indicates the impact of structural uncertainties on gross-rock volume computation.