Non hyperbolic CRS
Non-hyperbolic Common Reflection Surface (non-hyperbolic CRS) is a CRS traveltime approximation developed by Sergey Fomel and Roman Kazinnik in 2013. This approximation is a stacking surface t(h,m) in half-offset h and Common Mid Point (CMP) m coordinates derived from the analytical solution for reflection traveltime from a hyperbolic reflector (Fomel and Kazinnik, 2013). The non-hyperbolic CRS is also a time function of zero-offset CRS parameters RN, RNIP and BETA and it can be used in VFSA global optimization by measuring the fitness between this traveltime surface and the reflection seimic data.
The Non-hyperbolic CRS traveltime approximation is shown bellow:
Where h is the half-offset and d=m-m0 is the difference between the central CMP m0 coordinate and a CMP m in the m0 neighborhood.
Function F is given by:
The c parameter is:
The a1 parameters is:
The a2 parameter is:
The b2 parameter is:
The KN and KNIP parameters are the inverses 1/RN and 1/RNIP, respectively.
For more information about the non-hyperbolic CRS, please refer to the paper:
- Non-hyperbolic common reflection surface, S. Fomel, R. Kazinnik, 2013 available in Madagascar reproducible documents: Non-hyperbolic common reflection surface