f Markov operator in constrained tomography

It is well accepted that seismic tomography does not perform well in the case of limited view angles. Therefore medical images are typically of much better quality than those of seismic origin. In exploration geophysics, a full angular coverage is not attainable and thus the limited view-angle problem emerges as a real issue . Carrion (Geophysics, 1991) has shown that unless an a priori information is incorporated in a traveltime inversion, one can not expect any fair and robust reconstruction. Moreover, it was shown that any smal) variation in the recorded apenure transforms into large variations in the computed results. The introduced a priori information in the form of "hard bounds" adds stability into inversion and largely rooles out the above mentioned detriment . Recently, Carrion and Vesnaver (BSSA,1991, submitted) have found that only those wave vectors can be recovered which present in the recorded data . This result simply means that a z-alongated object can not be recovered from a cross-well geometry since the vertical wavenumbers do not exist