Non-hyperbolic common reflection surface

Conclusions

We have presented the non-hyperbolic common reflection surface, a new approximation for prestack reflection traveltimes. Non-hyperbolic CRS uses the same set of parameters as the hyperbolic CRS but in a different functional form, which can make the approximation significantly more accurate in a large range of offsets and midpoints. The proposed approximation is derived from the analytical expression of the reflection traveltime in the case of a hyperbolic reflector in a constant velocity medium.

Why use a hyperbolic reflector? A special property of this reflector is that it reduces to a plane reflector or a point diffractor with a special choice of parameters. ($z_0=0$ or $\alpha=\pi/2$ respectively). Thus, it encompasses two particularly important special cases.

Numerical experiments show that the new approximation can be significantly more accurate than the conventional hyperbolic CRS while using essentially the same set of parameters. The multifocusing approximation can be even more accurate but uses a different set of parameters, which makes it more difficult to extend it to 3-D.

Non-hyperbolic common reflection surface