A new approximation to the reflection coefficient of the diffusive-viscous wave equation and its evaluation for frequency-dependent AVA inversion

Abstract

The frequency-dependent seismic anomalies related to the hydrocarbon reservoirs have lately attracted wide attentions, and the diffusive-viscous wave equation was built to explain these anomalies. Frequency-dependent amplitude versus angles of incidence (FAVA) inversion is a commonly used and effective reservoir prediction technique. The existing frequency-dependent reflection coefficient formula based on the diffusive-viscous wave equation is complex and highly nonlinear, containing eight model parameters, then it is difficult to apply for FAVA inversion. In this paper, we firstly apply the exact frequency-dependent reflection coefficient formula to FAVA inversion for two typical models. The inversion results indicate that the reflection coefficient formula can be reasonably simplified. Through a series of mathematical derivations, we obtain a new approximate frequency-dependent reflection coefficient formula. The new formula contains half of the model parameters of the exact formula, which greatly shrinks the search space of the global optimization algorithm and improves computational efficiency in FAVA inversion. Finally, the accuracy of the approximate formula is analyzed by the forward modeling and FAVA inversion. The inversion results show that our formula is applicable within incident angle of 35 degrees and the frequency band range of seismic exploration, which supplies a theoretical foundation for the practical application of the FAVA inversion based on the diffusive-viscous wave equation.