Optimized 6^th order NMO correction for long-offset seismic data

The conventional 2^nd order NMO assumes a small offset-to-depth ratio and straight raypaths.The accuracy for the travel-time calculations decreases significantly with increasing offset-to-depth ratio.The 2^nd order NMO may be improved by extending the hyperbolic approximation with higher order (4^th, 6^th) series.Conventional NMO is a small offset approximation, therefore, the explicit truncation of the higher order terms generates significant errors in the travel-time calculations at long offsets.Hence, the 2^nd order approximation is not suitable for velocity analysis, AVO study, and CMP stack using long offset seismic data.In this paper, we in troduce a more accurate travel-time approximation which we called the optimized 6^th order NMO equation.The accuracy of the new and proposed equation is better than Taner's 6^th order equation because the truncation error is smaller.Even though we truncate Taner's expansion to the 6^th order, we take all other higher orders terms into account as well.The tests using synthetic and real data show that our optimized 6^th order long offset NMO equation works well.The improvement at long offsets is more significant than Taner's 6^th order truncation.