This paper can be considered as a continuation of the work by Carrion and Carneiro (1989), where a generalized approach to linearized inversion of geophysical data was developed. Their method allows one to incorporate virtually any constraints in the inversion and reformulate the problem in the dual space of Langrangian multipliers (see also Carrion, 1989a). The constrained tomography makes traveltime inversion robust: it automatically rejects ''bad data'' which correspond to solutions beyond the chosen constraints and allows one to start inversion with an arbitrary chosen initial model.

In this paper, I will derive basic formulas for constrained tomographic imaging that can be used in such areas of geophysics as global mapping of the earth interior, exploration geophysics, etc. The method is fast: an example that will be shown in the paper took only 6 min. of VAX CPU time. Had the conventional least-square matrix inversion been used it would have taken more than 10 hours of the CPU time to solve the same problem. ¿ American Geophysical Union 1990