1. Estimation of True (Amplitude-Dependent) Reflection Coefficients in 3-D Prestack Depth Migration of Seismic Data George A. McMechan, Center for Lithospheric Studies, University of Texas at Dallas
Getting reflection coefficients (RCs) from seismic data  distinguishes rock types and fluids. An RC is the dimensionless  ratio of the reflected to incident (R/I) wave amplitudes, but  this has a numerical problem of division by zero at all points  off the incident wavefront. The usual compromise is to cross-correlate (CC)  (multiply) the two wavefields, at the expense  of loss of physical relevance. We overcome these problems by numerically extrapolating the I wavefield and saving the  maximum amplitude at each point in the model grid. Then, the R/I image condition divides the propagating R wavefield by the maximum amplitude of the I wavefield at each point. This gives many improvements over the CC solution:
1) the image amplitude is now a physically correct, dimensionless, angle-dependent RC.
2) it avoids the zero divide and so is implicitly stable. 3) it doubles the resolution obtainable with CC (Figure 1).
4) it uses the highest signal-to-noise ratio part of the data 5) it reduces the low wavenumber artifact that is caused by amplitude accumulation
during CC (Figures 2a and b).  It acts locally rather than globally! 6) the disk space required is reduced by two orders of magnitude  from CC (only one
grid maximum amplitudes needs to be saved, compared to one per time step for CC).
This advantage  becomes greater in 3D, making 3D wave-based migration practical.
Figure 1. (a) is the compressional wave velocity model. (b) is  obtained by CC; (c) is by the R/I condition. The data for both  are synthesized by finite-difference calculations for 100 sources  each with 101 receivers, along the top of model (a). (c) has higher  quality and resolution than (b).
Figure 2. A more complicated example. The data are generated by finite-difference modeling for 180 sources, each with 801 receivers  along the top of the model. (a) is obtained by CC; (b) is by the  R/I image condition.