Regularization In Slope Tomography

Seismic imaging in depth is limited by the accuracy of velocity model estimation. Slope tomography uses the slowness components and traveltimes of picked reflection or diffraction events for velocity model building. The unavoidable data incompleteness requires additional information to assure stability to inversion. One natural constraint for ray based tomography is a smooth velocity model. We propose a new, reflection-angle-based kind of smoothness constraint as regularization in slope tomography and compare its effects to three other, more conventional constraints. The effect of these constraints are evaluated through comparison of the inverted velocity models as well as the corresponding migrated images. We find the smoothness constraints to have a distinct effect on the velocity model but a weaker effect on the migrated data. In numerical tests on synthetic data, the new constraint leads to geologically more consistent models.27133253329Billette, F., Lambare, G., Velocity macromodel estimation from seismic reflection data by stereotomography (1998) Geophysical Journal International, 135, pp. 671-690. , gji GJINEA 0956-540X Geophys. J. IntBillette, F., Le Begat, S., Podvin, P., Pratical aspects and applications of 2D stereotomography (2003) Geophysics, 68, pp. 1008-1021. , gpy GPYSA7 0016-8033 GeophysicsBishop, T.N., Bube, K.P., Cutler, R.T., Langan, R.T., Love, P.L., Resnick, J.R., Shuey, R.T., Wyld, H.W., Tomographic determination of velocity and depth in laterally varying media (1985) Geophysics, 50, pp. 903-923. , gpy GPYSA7 0016-8033 GeophysicsBube, K.P., Langan, R.T., Nemeth, T., Analysis of the spectral hole in velocity versus depth resolution for reflection traveltimes with limited aperture (2005) Geophysics, 70, pp. U37-U45. , gpy GPYSA7 0016-8033 GeophysicsBube, K.P., Langan, R.T., Resnick, J.R., Theoretical and numerical issues in the determination of reflector depths in seismic reflection tomography (1995) Journal of Geophysical Research, 100, pp. 12449-12458. , jgr JGREA2 0148-0227 J. Geophys. ResClapp, R.G., Biondi, B., Claerbout, J.F., Incorporating geologic information into reflection tomography (2004) Geophysics, 69, pp. 533-546. , gpy GPYSA7 0016-8033 GeophysicsDelprat-Jannaud, F., Lailly, P., What information on the earth model do reflection travel times provide? (1992) Journal of Geophysical Research, 97, pp. 19827-19844Delprat-Jannaud, F., Ill-posed and well-posed formulations of the reflection travel time tomography problem (1993) Journal of Geophysical Research, 98, pp. 6589-6605Farra, V., Madariaga, R., Nonlinear reflection tomography (1988) Geophysical Journal International, 95, pp. 135-147. , gji GJINEA 0956-540X Geophys. J. IntMenke, W., (1989) Geophysical Data Analysis, , Discrete inverse theory: Academic PressSinoquet, D., Modeling a priori information on the velocity field in reflection tomography (1993) 63rd Annual International Meeting, SEG, pp. 591-594. , Expanded Abstract