REFERENCES

• Aki, K., and Richards, P. G., 1980, Quantitative seismology: W. H. Freeman and Company.

• Beydoun, W. B., and Mendes, M., 1989, Elastic ray-Born l-2 migration/inversion: Geophys. J., 97, 151-160.

• Beylkin, G., 1985, Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform: J. Math. Phys., 26, 99-108.

• Bleistein, N., 1987, On the imaging of reflectors in the earth: Geophysics, 52, 931-942.

• Cunha Filho, C., 1992, Elastic modeling and migration in earth models: Ph.D. thesis, Stanford University.

• de Bruin, C., 1992, Linear AVO inversion by prestack depth migration: Ph.D. thesis, Delft University, The Netherlands.

• Frazer, L. N., and Sen, M. K., 1985, Kirchhoff-Helmholtz reflection seismograms in a laterally inhomogeneous multi-layered elastic medium - I. Theory: Geophys. J. R. Astr. Soc., 80, 121-147.

• Gill, P. E., Murray, W., and Wright, M. H., 1981, Practical optimization: Academic Press, Inc.

• Goodman, J. W., 1968, Introduction to Fourier optics: McGraw-Hill.

• Le Bras, R., and Clayton, R. W., 1988, An iterative inversion of back-scattered acoustic waves: Geophysics, 53, 501-508.

• Lumley, D. E., and Beydoun, W. B., 1991, Elastic parameter estimation by Kirchhoff prestack depth migration/inversion: Stanford Exploration Project Report, 70, Stanford University, 165-192.

 

dips-shot
Figure 12 Synthetic shot gather for three reflectors having 0, 15, and 30 degrees dip respectively.

 

dips-mig
Figure 13 Standard prestack migration and stack. Reflection amplitudes are meaningless due to migration stack bias along hyperbolic prestack angle-dependent reflectivity variation.

 

dips-Rcrp
Figure 14 Migrated estimate of $\grave{P}\!\acute{P}({\bf x};{\bf x}_h)$ at a CRP or ``iso-x'' gather. Note correct AVO polarity reversal with offset.

 

dips-Tcrp
Figure 15 Migrated reflection angle estimates of $\Theta({\bf x};{\bf x}_h)$ for a CRP gather, contoured in 5 increments.

 

dips-RTcrp
Figure 16 Overlay of $\Theta({\bf x};{\bf x}_h)$ on $\grave{P}\!\acute{P}({\bf x};{\bf x}_h)$.

 

dips1-rth
Figure 17 $\grave{P}\!\acute{P}(\Theta)$ recovery on the horizontal reflector at 1.0 km depth.

 

dips2-rth
Figure 18 $\grave{P}\!\acute{P}(\Theta)$ recovery on the 15 dipping reflector at 2.0 km depth below the origin.

 

dips3-rth
Figure 19 $\grave{P}\!\acute{P}(\Theta)$ recovery on the 30 dipping reflector at 3.0 km depth below the origin.