(10) |
where h is the half-offset and x is the surface midpoint-location. By introducing the ratio, , and following Huub Den Rooijen's derivations, as well as work by (), I have the following standard form of elliptical equation:
(11) |
This equation introduces two more terms that were absent in equation 10, namely tn, the NMO-corrected time; and, D, this term represents the lateral shift responsible for the CMP to CCP/CRP correction. The main difference among the existing PS-DMO operators is in the computation and correction from CMP to CCP (D). Throughout this thesis I use the definition presented by ():
(12) |
The PS-DMO smile equation is presented as follows:
(13) |
where
(14) | ||
(15) |